=3.4 in

# Superconducting Spintronic Heat Engine

C. I. L. de Araujo<EMAIL_ADDRESS>NEST, Istituto Nanoscienze-CNR and Scuola
Normale Superiore, I-56127 Pisa, Italy  Departamento de Fìsica, Laboratório de
Spintrônica e Nanomagnetismo, Universidade Federal de Viçosa,
Viçosa,36570-900, Minas Gerais, Brazil  P. Virtanen<EMAIL_ADDRESS>Department of Physics and Nanoscience Center, University of Jyväskylä, P.O.
Box 35 (YFL), FI-40014 University of Jyväskylä, Finland  M. Spies NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy
Carmen González-Orellana Centro de Física de Materiales (CFM-MPC), Centro
Mixto CSIC-UPV/EHU, 20018 Donostia-San Sebastián, Spain  Samuel Kerschbaumer
Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, 20018
Donostia-San Sebastián, Spain  Maxim Ilyn Centro de Física de Materiales (CFM-
MPC), Centro Mixto CSIC-UPV/EHU, 20018 Donostia-San Sebastián, Spain  Celia
Rogero Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU,
20018 Donostia-San Sebastián, Spain  Donostia International Physics Center
(DIPC), 20018 Donostia-San Sebastián, Spain  T. T. Heikkilä Department of
Physics and Nanoscience Center, University of Jyväskylä, P.O. Box 35 (YFL),
FI-40014 University of Jyväskylä, Finland  F. Giazotto
<EMAIL_ADDRESS>NEST, Istituto Nanoscienze-CNR and Scuola Normale
Superiore, I-56127 Pisa, Italy  E. Strambini<EMAIL_ADDRESS>NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy

###### Abstract

Heat engines are key devices that convert thermal energy into usable energy.
Strong thermoelectricity, at the basis of electrical heat engines, is present
in superconducting spin tunnel barriers at cryogenic temperatures where
conventional semiconducting or metallic technologies cease to work. Here we
realize a superconducting spintronic heat engine consisting of a ferromagnetic
insulator/superconductor/insulator/ferromagnet tunnel junction
(EuS/Al/AlOx/Co). The efficiency of the engine is quantified for bath
temperatures ranging from 25 mK up to 800 mK, and at different load
resistances. Moreover, we show that the sign of the generated thermoelectric
voltage can be inverted according to the parallel or anti-parallel orientation
of the two ferromagnetic layers, EuS and Co. This realizes a thermoelectric
spin valve controlling the sign and strength of the Seebeck coefficient,
thereby implementing a thermoelectric memory cell. We propose a theoretical
model that allows describing the experimental data and predicts the engine
efficiency for different device parameters.

##  I Introduction

Thermoelectricity can be observed when an electron-hole-asymmetric conductor
is driven by a temperature difference. The resulting thermovoltages and
thermocurrents have been widely applied for thermometry and energy
harvesting[1, 2, 3]. In the current technology, semiconductors have been
extensively utilized due to the large Seebeck coefficient achievable in those
materials, allowing for amplitudes of up to hundreds of $\mathrm{\mu V/K}$ [4,
5, 6] and efficient energy harvesting [7]. However, semiconductor materials
are not ideal for thermoelectric-based applications in some important areas of
research such as aerospace and cryogenic electronics. At the extremely low
temperatures of space or in dilution cryostats, the carriers in semiconductors
freeze out[8] and the material becomes insulating. Approaches based on quantum
dot system have been proposed and realized [9, 6] showing sizable thermopower
down to $0.5$K but with limitations of scalability intrinsic to zero-
dimensional systems. Moreover semiconductor properties would be drastically
changed by the doping due to background cosmic particles [10].

Figure 1: Magneto-electric characterization of the superconducting tunnel
junction a, Optical microscope image of one the samples colored for clarity.
It consists of an EuS layer (blue, $13$ nm), an Al strip (gray, $16$ nm)
covered by AlOx ($\sim 4$ nm), and a cross bar of Co (red, $14$ nm). The
circuit shows the 4 probe measurement setup utilized in our study, and the
external magnetic field direction which is parallel to the Co strip. b,
Schematic of the sample side view (top) and simplified representation with
arbitrary scales of device density of states (bottom), with the spin-split Al
superconducting gap (left) and spin-polarized Co 3d bands (right). c, Contour
plot of the tunneling conductance ($G(V)=dI/dV$) measured vs the external
magnetic field ($B$) and the voltage drop across the junction ($V_{\rm
Co}-V_{\rm Al})$. The sweep direction of the magnetic field is indicated by
the arrow. d, Tunneling spectroscopy for parallel (P, green) and antiparallel
(AP, orange) configurations at representative magnetic field strengths. The
curves are extracted from (c) and indicated there with horizontal dashed lines
in the respective colors. Continuous lines are the fit to the experimental
data based on the tunneling model as described in the Methods section VII.2.
e, Tunneling magnetoresistance TMR=($R_{AP}$ \- $R_{P}$ )/$R_{P}$, where
$R_{AP}$ and $R_{P}$ are the junction resistances in the antiparallel and
parallel configurations, respectively, extracted from (d) vs voltage drop. The
red line is the theoretical expectation for the fits shown in panel (d). f
Tunneling conductance $G(V)$ vs external magnetic field. The vertical black
(purple) dashed line in (c) indicates the positive (negative) excitation used
to extract the magnetoconductance. Here, the magnetic field sweep directions
are indicated by the arrows and a hysteresis is discernible, presenting a
clear TMR behavior. All measurement were performed at a bath temperature
$T_{bath}=100$ mK.

A promising alternative based on superconductor materials can represent a step
forward in thermoelectric-based technology. Differing from semiconducting
materials, metals do not suffer charge freeze out, and semiconductor-like
properties are still present in the quasi-particle spectrum characterized by
the superconducting gap. Still, electron-hole asymmetry is difficult to
achieve in conventional superconductors due to charge neutrality constraints,
unless strong non-equilibrium conditions are present [11, 12]. Recently, a
superconducting spin-caloritronic scheme based on spin-selective tunnel
junctions was proposed, enabling breaking the electron-hole symmetry while
keeping charge neutrality and resulting in the generation of large
thermoelectric effects [13]. This prediction was confirmed by thermocurrents
measured in superconducting tunnel junctions, with spin-split superconductors
obtained via external fields [14], and by exchange interactions [15] present
in thin superconductor/ferromagnetic-insulator (S/FI) bilayers [16, 17, 18,
19]. So far, no thermovoltage or resulting thermopower has been demonstrated
despite its key role for energy harvesting at cryogenic temperatures and
resulting applications for radiation detection[20, 21]

Here, we implement a superconducting spin-selective tunnel junction based on a
multilayer of EuS/Al/AlOx/Co. A strong thermovoltage ($\sim 10$ $\mu$V) is
generated at sub-Kelvin temperatures ($<1$ K) with a magnitude close to its
upper bound dictated by the Al superconducting gap ($\Delta\simeq 200$
$\mu$eV). The resulting Seebeck coefficient is of the order of few hundred of
$\mu$V/K for different temperature and magnetic configurations. A sizable work
was extracted by the junction therefore demonstrating a superconducting
spintronic heat engine. Yet, the efficiency and functionality of the engine
are quantified for different magnetic configurations. Fianlly, the
implementation of a two-state thermoelectric memory cell based on the device
magnetic hysteresis is discussed.

##  II Sample design and non-reciprocity

The device consists of a superconducting thin film (aluminum-Al) proximitized
by a ferromagnetic insulator (europium sulfide-EuS) on one side and separated
from a ferromagnet (cobalt-Co) on the other side by an insulating barrier
(aluminum oxide-AlOx).

Figure 1a presents a micrograph of a typical device. A schematic of the four-
wire measurement used for the tunneling spectroscopy is likewise shown. In the
cartoon of Fig. 1b the side view of the sample is shown with a simplified
representation of its density of states (DOS) on the bottom. The tunneling
conductance of the device is strongly influenced by the exchange spin-
splitting of the superconductor DOS (on the left) facing the spin-split DOS of
the Co counter-electrode such that strong spin filtering is expected for
proper voltage bias. Such spin filtering is at the origin of the asymmetric
tunneling conductance $G(V)=dI/dV$ measured as a function of the bias voltage
and magnetic field, and presented in the color plot of Fig. 1c. The
characteristic asymmetry in $G(V)$ can be seen in Fig. 1d for the green line.
It is compatible with a parallel (P) alignment of the magnetizations of the
EuS and Co layers, visible for most of the magnetic fields explored. Only the
tunneling conductance at $B\simeq 10$ mT, obtained during the sequential
switching of the two ferromagnets, is characterized by an anti-parallel (AP)
alignment (Fig. 1c and d orange line). By fitting the experimental data with
the spin selective tunneling model [22] (see Methods section VII.2 for model
details and continuous lines in Fig. 1d for the fit) it is possible to extract
the spin polarization of the tunnel barrier $P\simeq 0.5$, the exchange
interaction induced in the Al layer $h\simeq 50$ $\mu$eV, the Al
superconducting gap $\Delta\simeq 195$ $\mu$eV, and the inelastic and spin-
flip scattering rates $\hbar\Gamma\simeq 32$ $\mu$eV and $\hbar\Gamma_{\rm
sf}\simeq 29$ $\mu$eV, for $B=-35$ mT, respectively. Notably, a large $\Gamma$
characterizes the superconducting tunnel barrier, as typically observed in
junctions with ferromagnetic counterelectrodes [23, 24]. Different devices
were tested showing similar results with slightly different $\Gamma$,
$\Gamma_{\rm sf}$, $h$ and $P$ (see the extended Figure 2). From the tunneling
spectroscopy it is also possible to extract the field evolution of the
tunneling magnetoresistance $TMR=\frac{R_{P}-R_{AP}}{R_{AP}}$, shown in Fig.
1e, and the magnetoconductance, shown in Fig. 1f. Values obtained are
compatible with previous $TMR$ measured in similar structures [23], showing a
maximum at voltage biases compatible with the superconducting gap
($eV_{MAX}\simeq\pm\Delta$).

Figure 2: Thermoelectric characterization. a, Scheme of the electric circuit
used to quantify the thermoelectric response of the device, with the
temperature difference obtained via a Joule heating current flowing through
the Co strip. b, Voltage measured vs heating current, with the positive
voltmeter electrode on Co and negative on Al at B=$10$mT . The thermovoltage
is obtained by subtracting the Ohmic contribution using the average $V_{\rm
th}=\frac{V(+I_{H})+V_{(}-I_{H})}{2}$. c, $V_{\rm th}$ measured at
$|I_{H}|=40$$\mu$A vs external magnetic field. d, $V_{\rm th}$ measured vs
$I_{H}$ for different bath temperatures up to $T=800$ mK (top panel) and
temperature difference $\delta T=T_{Co}-T_{Al}$ estimated from model fits to
the tunneling spectroscopy, performed at different bath temperatures and
heating currents (bottom panel). e, Thermovoltage (top) and Seebeck
coefficient ($S$, bottom) vs temperature difference at selected magnetic field
values measured at $T_{\rm bath}=100$mK. Dash-dotted lines represent the fits
to the data considering thermoelectricity with (blue) and without (red)
rectification effects. f, Seebeck coefficient $S$ extracted at different
$T_{\rm bath}$ and $I_{H}$

##  III Thermoelectric response

To quantify the thermoelectric response of the device, the thermovoltage
across the junction was measured in the presence of a thermal gradient imposed
across the junction. Such temperature difference is achieved via a Joule-
heating current $I_{H}$ which flows through the Co strip while the Al is
thermalized by the substrate at bath temperature ($T_{\rm bath}$), according
to the scheme presented in Figure 2a. The voltage measured across the junction
was then symmetrized with respect to $I_{H}$ ($V_{\rm
th}=\frac{V(+I_{H})+V(-I_{H})}{2}$) to remove the trivial ohmic contribution
originating from the shared electrical paths between the voltage probe and the
heating current, similarly to previous experiments on transversal
rectification in superconducting tunnel diodes [25]. Differing from tunnel
diodes, the larger impedance of the device makes thermoelectricity the main
contribution of the voltage drop summing to rectification components. A
representative example of symmetrization is presented in Figure 2b. In the top
panel the voltage measured as a function of $|I_{H}|$ presents the main linear
evolution, while only after symmetrization (bottom panel), small deviations
are visible and a clear monotonic increase of $V_{\rm th}(I_{H})$ up to
$\simeq 10\mu$V is observed at $I_{H}=50\mu$A. Above 50$\mu$A the large power
injected in the device is not fully dissipated by the substrate limiting the
thermalization of the cold Al lead and resulting in a saturation or decrease
of $V_{\rm th}$. The increase of the Al temperature at large $I_{H}$ was
confirmed by the damping of the critical current measured in the Al strip at
different $I_{H}$ as shown in the extended figure 3. The evolution of $V_{\rm
th}(B)$ in the external magnetic field at fixed $|I_{H}|$ is shown in Fig. 2c.
Consistently with the non-reciprocal tunneling spectroscopy measurements,
$V_{\rm th}$ strongly depends on $B$ and on the relative orientation of the
two ferromagnetic layers showing sign reversal in the AP phase. Hysteresis in
the magnetic field is visible, with a maximum signal at $|B|\simeq 20$ mT
vanishing above 120 mT due to the quenching of superconductivity, as observed
also in the tunneling spectroscopy measurements reported in fig. 1c. In the
inset, showing the central measurement range, it is possible to appreciate the
sizable signal ($>10~{}\mu$V) present even at zero field as a consequence of
the strong ferromagnetism of the device. Moreover, a clear negative
thermovoltage is visible between the coercive fields of the two ferromagnetic
layers ($7$ mT$\lesssim|B|\lesssim 10$ mT). Such inversion of $V_{\rm th}$
confirms the AP phase achieved between the Co and EuS ferromagnetic layers as
deduced from the tunneling spectroscopy in the same field range. The lower
amplitude of $V_{\rm th}$ in the AP phase with respect to the P case is
consistent with a weaker polarization and spin filtering of the device, and it
indicates a partially polarized magnetization of the EuS and Co layers in the
AP phase during the non simultaneous magnetization switching of the two
ferromagnets. At higher temperatures $V_{\rm th}$ tends to slowly decrease as
shown in the top panel of Fig. 2d with a sizable thermovoltage observed up to
800 mK. Such robustness in temperature is a consequence of the large exchange
splitting of the device $h\simeq k_{B}\times{}600$mK extending the operation
of the device to higher temperature, see Extended Data Fig. 1. To evaluate the
Seebeck coefficient from $V_{\rm th}$ the temperature gradient across the
junction $\delta T=T_{\mathrm{Co}}-T_{\mathrm{Al}}$ needs to be estimated. The
thermal model for the device (see Methods) indicates that at low heating power
$T_{\mathrm{Al}}\simeq T_{\mathrm{bath}}$, as confirmed also by monitoring the
critical current of the Al lead at different $I_{H}$ (see extended figure 3).
The temperature of the Co electrode is estimated from the broadening of the
tunneling spectroscopy as typically done in S/I/N thermometry [26] and was
measured at different $I_{H}$. In this case, the model needs to be extended to
account also for the additional lateral voltage drop due to the presence of
the heating current $I_{H}\neq 0$, (see Methods for details). The full model
provides the estimate $\delta
T(I_{H},T_{\mathrm{bath}})=(T_{\mathrm{bath}}^{5}+bI_{H}^{2})^{1/5}-T_{\mathrm{bath}}$
with $b\approx 5.6\cdot 10^{-5}\,\mathrm{K^{5}/\mu{}A^{2}}$, shown in the
bottom panel of Fig. 2d. Notably, a large temperature gradient up to $500$ mK
was achieved across the junction for low $T_{\mathrm{bath}}$. Using the
relation $\delta T(I_{H},T_{\mathrm{bath}})$ it is possible to remap the
thermovoltage in the temperature gradient $V_{\rm th}(\delta T)$ as shown in
Fig. 2e together with the resulting Seebeck coefficient $S=V_{\rm th}/\delta
T$. A Seebeck coefficient of up to $30\mu$V/K can be estimated both at 10 mT
and at zero magnetic field for a base temperature of $100$mK, which is on par
with state-of-the-art cryogenic thermoelectric elements [14, 11, 12, 9]. It is
worthwhile to mention that by increasing the bath temperature above $500$mK,
$S$ can obtain values as large as a few hundreds of $\mu$V/K. Moreover, a
smaller but sizable Seebeck coefficient of $-5~{}\mu$V/K is also visible in
the AP phase obtained at $B=-10$mT, thus implementing a thermoelectric spin
valve where the n-type and p-type Seebeck effect is controlled by the relative
orientation of the device magnetic moments.

Figure 3: Heat engine characterization. a Circuit utilized for the heat engine
measurement with the heating current ($I_{H}$) flowing through the cobalt
strip. The tunnel junction is shunted with a variable load resistor ($R_{L}$)
and two symmetric balancing resistances ($R_{B}\ll R_{L}$) to avoid spurious
leaks of $I_{H}$ in the load. b Voltage developed across the load ($V_{L}$)
measured at different $R_{L}$ for $|I_{H}|=40~{}\mu$A at $T_{\rm bath}=25$ mK
and three magnetic field values corresponding to different regimes, i.e., P
saturation at 10 mT, remanence at 0 mT, and AP configuration at -10 mT. c
Power load ($P_{L}=\frac{V_{L}^{2}}{R_{L}}$) extracted from panel (b) vs
$R_{L}$. The red curve is a fit to the 10 mT data considering the maximum
transferred power satisfying
$P_{L}=I^{2}R_{L}=\frac{R_{L}V_{S}^{2}}{(R_{L}+R_{S})^{2}}$ for a voltage
source of $V_{S}=V_{\rm th}\simeq 12.5~{}\mu$V, and an internal resistance
$R_{S}\simeq 60$ k$\Omega$. d Evolution of $P_{L}$ measured at $R_{L}=150$
k$\Omega$ and $T_{\rm bath}=25$ mK vs input power ($P_{\rm
in}=I_{H}^{2}/R_{\rm Co}$), with $R_{\rm Co}=11$ $\Omega$ corresponding to the
resistance of the Co strip on top of the tunnel junction. e Blow-up of the
$P_{L}$ behavior of panel (d) in a restricted range of $P_{\rm in}$. Dash-
dotted lines represent the fits to the data considering thermoelectricity with
(blue) and without (red) rectification effects. f Efficiency
$\eta=\frac{P_{L}}{P_{\rm in}}$, measured as a function of temperature $T$ at
$R_{L}=150$ k$\Omega$. Full lines are the theoretical prediction for $\eta$ in
the linear-response approximation (see Methods section VII.2 for details), and
evaluated for the junction parameters used in the fit of Fig. 1d.  Figure 4:
Thermoelectric memory cell. a Simplified scheme representing the hysteretic
behavior of the thermoelectric memory cell investigated with a low state
represented by the AP configuration between the spin-split superconductor and
the ferromagnetic cobalt layer, and a high state when the magnetization on the
device electrodes are P and a larger voltage is generated across the load
resistor. b Evolution of the differential voltage drop across the load
($\Delta V_{L}=V_{L}^{P}-V_{L}^{AP}$) measured in the memory cell vs magnetic
field $B$ with a load resistor $R_{L}=150$ k$\Omega$ at $T_{\rm bath}=300$ mK.
Note the sizable signal contrast $\sim 10\mu$V the memory cell can provide
even at zero magnetic field.

##  IV Heat Engine

Once $V_{\rm th}$ is applied on a load resistor $R_{L}$, work can be extracted
from the thermoelectric effect for the demonstration of a heat engine, and we
can quantify the thermal-to-electrical energy conversion. The circuit used for
this purpose is sketched in Fig. 3a. The junction is shunted to the ground
with $R_{L}$ and two additional balancing resistors ($R_{B}=10~{}k\Omega$)
have been included in the circuit in a symmetric configuration to prevent
spurious leaks from the heating-current source to the load. The voltage drop
($V_{L}$) across $R_{L}$ is probed for different measurement configurations
and the resulting dissipated power ($P_{L}=\frac{V^{2}_{L}}{R_{L}}$) is used
to estimate the power generated by the engine, then neglecting residual
thermoelectric power dissipated in the balancing resistors $R_{B}$. The
evolution of $V_{L}$ measured as a function of $R_{L}$, under constant heating
with $|I_{H}|=40~{}\mu$A is presented in Fig. 3b. Three different magnetic
configurations are compared, P saturation regime (green, $B=10$ mT), P
remanence (grey, $B=0$ mT) and AP (orange, $B=-10$ mT) characterized by a
negative $V_{L}$ as for the thermovoltage shown in Fig. 1c. In all presented
field regimes $V_{L}$ tends to increase with an increasing $R_{L}$, showing a
saturation towards the thermovoltage $V_{\rm th}$ when the load resistance is
above 500 k$\Omega$, i.e., much larger than the tunnel resistance ($R_{L}\gg
R_{T}\simeq 50$ k$\Omega$) as expected for an ideal voltage source
$V_{L}=V_{\rm th}\frac{R_{L}}{R_{L}+R_{T}}$, with $R_{T}$ as source
resistance. The resulting dissipated power shown in Fig. 3c has a different
non-monotonic behavior with a maximum observed for $R_{L}\sim R_{T}$. This
behavior is consistent with the maximum power transfer theorem (known as
Jacobi’s law) predicting
$P_{L}=I^{2}R_{L}=\frac{V_{L}^{2}R_{L}}{(R_{L}+R_{T})^{2}}$ as reported in the
red fit line in Fig. 3c.

The heat engine efficiency can be quantified from the ratio between the power
extracted by the engine ($P_{L}$) and the Joule power injected to generate the
thermal gradient $P_{\rm in}=R_{\rm Co}\times I_{H}^{2}$, where $R_{\rm
Co}=11$ $\Omega$ is the resistance of the cobalt strip at the junction.
Figures 3d and 3e show $P_{L}$ vs $P_{\rm in}$ for the three magnetic field
configurations. At low power $P_{L}$ is characterized by an almost linear
increase corresponding to an efficiency $\eta=P_{L}/P_{\rm in}\simeq 5\times
10^{-8}$ that tends to decrease at high power. We stress that this efficiency
is just a lower bound of the intrinsic efficiency of the effect, as most of
$P_{\rm in}$ may be lost in different heat channels including the heat
dispersed from the Co directly to the substrate. The temperature dependence of
$\eta$ displayed in Fig. 3f shows an almost constant efficiency below 400 mK,
and a quick damping at higher temperatures. The quick damping is consistent
with the expected behavior of $\eta(T)$ obtained from the theoretical model
shown in Fig. 3f based on the device parameters, as described in detail in the
methods section. The model shows that the main limiting factor for $\eta$ at
high temperatures is the electron-phonon coupling: most of the thermal energy
from the electrons is transferred to the lattice phonons, instead of being
converted into thermoelectric power. In fact, the thermal conductance between
electrons and lattice phonons scales as $\propto{}T^{4}$ [26, 27], leading to
a decreasing efficiency at increasing temperature. Yet, as observed from the
theoretical model, the heat engine efficiency could be strongly enhanced by
working below 100 mK.

##  V Heat-engine memory

It is worthwhile noting that combining the hysteretic behavior of the
thermoelectric effect as shown in Fig. 1f with the heat engine, it is possible
to envision a thermoelectric memory cell. Our device structure is an original
concept for a classical memory cell similar to a conventional magnetic random
access memory stack [28]. The latter, is composed by two ferromagnetic layers
with different coercivity, and separated by a tunnel junction. The first
ferromagnetic electrode provides the electronic spin polarization in two Mott
channels [29], while the second feromagnetic layer filters the spin polarized
currents after coherent tunneling, thereby allowing high conductance in P
configuration and lower conductance in the AP state. By contrast, in our
memory cell the logic states are codified by a thermoelectric voltage self
generated in the memory itself, and not requiring a local input current for
the state read-out. This advantage can strongly simplify the wiring of the
memory with net benefits for scalability. Additionally, it allows for a local
direct transduction of the electrical signal in to another physical
observable, for instance, a photon in the sketch of Fig. 4a. This may inspire
novel methods for read-out and packaging in dense arrays. In Fig. 4b, we
present an example of the heat-engine hysteretic cycle measured in the
proposed memory cell. The device is first polarized in the P state at -20 mT,
then $B$ is cycled between $-20$ mT to 10 mT. A clear hysteretic loop is
visible with a high contrast of 10 $\mu$V between the P and AP configuration
also at zero field, an important condition to operate the memory in the
absence of external magnetic fields.

##  VI Discussion and Conclusions

In summary, we have fabricated and characterized a superconductor-ferromagnet
tunnel junction structure based on aluminum proximitized by europium sulfide,
and separated from a cobalt electrode by an aluminum oxide tunnel barrier. Our
device shows a remarkable non-reciprocal charge transport due to electron-hole
symmetry breaking induced by the spin selectivity of the junction. As a
consequence, a sizable thermoelectric voltage is observed in the presence of a
thermal gradient, which is achieved via a Joule-heating current flowing
through the cobalt strip. The different coercivity of the two ferromagnetic
layers exploited in the junction joined to the large ferromagnetic remanence
of Co magnetization warrant two important features: (i) thermoelectricity is
observed even at zero magnetic field and (ii) a clear inversion of the
thermoelectric effect is achieved when the EuS and Co magnetizations are
antiparallel. The latter implements the first spin valve for thermoelectric
applications, by reversing the Seebeck coefficient from p-type to n-type. We
quantified the power generated by the structure over a series of external load
resistors thereby demonstrating the implementation of a superconducting
spintronic heat engine. From the thermal model of the device we identified the
heat losses through the electron-phonon coupling as the main factor limiting
the engine efficiency.

In light of future technological applications, several strategies could be
followed in order to increase the engine efficiency, such as decreasing the
junction size, and improving heat isolation via device suspension or by
lowering the operating temperature in order to limit the electron-phonon
coupling. Finally, we have also shown the operation of the device as a
thermoelectric superconducting memory cell. For that purpose, two main
advantages are envisioned: (i) junction durability, if operated in an open
circuit configuration with no detrimental currents flowing through the
junction; (ii) high scalability, due to a read-out signal self generated by
the thermoelectric power. We envision the application of such cryogenic
thermoelectric element in the implementation of sensitive self-biased
detectors of electromagnetic radiation with simplified approaches for
multiplexing [21, 30, 31]. Additionally, by scaling our heat engine to large
areas may find relevant applications for energy harvesting in the deep space
where the low temperature makes conventional approaches somewhat ineffective.

##  VII Methods

###  VII.1 Sample preparation and measurement

For the sample preparation we have first deposited $12.5$ nm EuS thin film by
molecular beam epitaxy on top of Si/SiOx substrates cooled at $150$K. The
pressure during growth was kept in the range of $10^{-9}$ mbar to avoid any
EuS oxidation and achieve a near stoichiometric EuS compound. Without breaking
the ultra high vacuum conditions, a $\sim 250-\mu$m-width Al lead was grown on
top by using a metallic shadow mask. The total thickness of the Al layer was
$20$ nm. To form the insulating AlOx barrier the sample was exposed $3\times
10^{-3}$ mbar of low-energy oxygen plasma created by inductevely coupled
plasma source for 5 hours, resulting in a $\sim 4$-nm-thick AlOx layer and
lowering the metallic Al thickness down to $16$ nm. The subsequent cross bar
geometry was realized with another shadow mask evaporation to grow a Co lead
of 14 nm thickness and $\sim 200~{}\mu$m width. Al and Co layers were grown
with e-beam metal evaporators. Finally, before extracting the sample from the
chamber, a $7$ nm calcium fluoride (CaF) layer was deposited covering the
whole system to avoid environmental oxidation. Samples were wire bonded with
aluminum wires and mounted in a dilution fridge, where the magneto-electrical
measurements were performed through low pass filters. All the signals were
amplified via low-noise voltage and current preamplifiers. For the application
of the heating currents and critical current measurements the filters were
bypassed in order to decrease the power load that would provide cryostat
excessive heating.

###  VII.2 Theoretical model

The current density through the Al/Co tunnel junction can be expressed as [13,
22],

$\displaystyle\mathcal{I}$
$\displaystyle=\sum_{\sigma=\uparrow,\downarrow}G_{\sigma}^{\square}\int_{-\infty}^{\infty}dE\,N_{\sigma}(E)[f(E,T_{S})-f(E+V,T_{N})]\,,$
(1)

and depends on the voltage $V$ over the junction and temperatures $T_{N}$,
$T_{S}$ on the normal (Co) and superconductor (Al) sides. Here $f(E,T)$ is a
Fermi function. The current is proportional to spin-dependent conductances per
square area $G^{\square}_{\uparrow/\downarrow}=\frac{1\pm P}{2}G_{\square}$,
which are due to Co spin polarization and interface properties. Here,
$-1\leq{}P\leq 1$ is the spin polarization and $G_{\square}$ the junction
conductance per square. The result also depends on the superconductor density
of states $N_{\sigma}(E)$. The superconducting gap $\Delta$ in it is spin-
split by an exchange field $h$ induced from EuS, but this is counteracted by
spin-flip scattering with rate $\Gamma_{\rm sf}$ and inelastic scattering with
rate $\Gamma$, which we account for using methods in Ref. [22]. We extract the
values of $\Delta$, $\Gamma_{\rm sf}$, $\Gamma$, $G$, $P$, and $h$ by fitting
Eq. (1) to experimental $I(V)$ characteristics at $T_{S}=T_{N}$.

As the Al/Co tunnel junction resistance is high compared to the total Co wire
resistance, the voltage profile along the Co wire is linear to a good
approximation, $V(x)=V_{0}+xI_{H}R_{x}/L_{x}$, where
$R_{x}=\rho_{\mathrm{Co}}L_{x}/(Wt_{\mathrm{Co}})$ is the lateral resistance
of the part of the Co film (cross-section $t_{\mathrm{Co}}\times{}W$, length
$L_{x}$, resistivity $\rho_{\mathrm{Co}}$) on top of the tunnel junction. Due
to superflow the voltage in the Al film is spatially constant. The total
tunneling current through the Al/Co junction then is

$\displaystyle
I_{T}=W\int_{-L_{x}/2}^{L_{x}/2}dx\,\mathcal{I}(V(x),T_{\mathrm{Co}},T_{\mathrm{Al}})$
(2)

where the Al/Co overlap has size $W\times{}L_{x}$ and $\mathcal{I}$ is the
local S/I/FM junction current density–voltage relation from Eq. (1), which
includes the S/FI thermoelectric effects. [13] Under these conditions, the
Joule heating via current $I_{H}$ in Co at low temperatures is mainly limited
by the electron-phonon coupling. The corresponding heat balance equation is,
[26]

$\displaystyle
L_{x}Wt_{\mathrm{Co}}\Sigma(T_{\mathrm{Co}}^{5}-T_{\mathrm{bath}}^{5})=R_{x}I_{H}^{2}\,,$
(3)

where $\Sigma$ the electron-phonon coupling parameter of Co. We have also
modeled the Al side with a similar equation, with tunneling current input
power on right-hand side and taking superconductivity into account. [26, 13,
20] We find that due to the high tunnel resistance, electronic heat transport
across the tunnel junction is suppressed, and we can neglect heating of the Al
side. Consequently $\delta
T=T_{\mathrm{Co}}-T_{\mathrm{Al}}=(T_{\mathrm{bath}}^{5}+bI_{H}^{2})^{1/5}-T_{\mathrm{bath}}$,
with $b=R_{x}/(Wt_{\mathrm{Co}}L_{x}\Sigma)$. To determine the effective
values of $\Sigma$ and $R_{x}$, a two-parameter fit of Eqs. (2),(3) is done on
the experimental $dI/dV$ curves of different $T_{\mathrm{bath}}$ and $I_{H}$.
In addition, fits at $I_{H}=0$ are used to determine the tunnel junction
parameters in Eq. (1).

The circuit model of Fig. 3a together with Eqs. (1),(2),(3) from the model of
the heat engine, from which efficiencies and relative contributions of the
rectification and thermoelectricity can be estimated. For small $I_{H}$, we
can expand $I_{T}\approx GV_{\mathrm{th}}+P\alpha\delta
T/T+\frac{G^{\prime}}{24}(R_{x}I_{H})^{2}$ where $G$ is the tunnel junction
conductance at zero bias, $\alpha$ the thermoelectric coefficient, [13] and
$G^{\prime}$ the zero-bias voltage derivative of the conductance,
characterizing the rectification. In the tunneling model,
$G^{\prime}\approx{}ce^{2}P\alpha/(2k_{B}^{2}T^{2})$ where $c\approx 1$ is a
weakly temperature-dependent numerical factor. From Eq. (3) one can then
deduce that for high-resistance tunnel junctions, the thermoelectric
contribution dominates when
$T_{\mathrm{bath}}\lesssim[9k_{B}^{2}/(e^{2}\rho_{\mathrm{Co}}\Sigma
L_{x}^{2})]^{1/3}\approx 300\,\mathrm{mK}$ and $I_{H}\lesssim
25[k_{B}^{5}/(e^{5}R_{x}^{4}Wt_{\mathrm{Co}}\Sigma L_{x})]^{1/3}\approx
20\,\mathrm{\mu{}A}$. The opposite limit of low-resistance junctions was
discussed in Ref. [25].

The thermoelectric coefficient $\alpha$ is related to the Seebeck coefficient
by $S=V_{\rm th}/\delta{}T=P\alpha/(GT)$, and its temperature and exchange
field dependence was discussed in Ref. [13]. The large value of $\Gamma$ in
the experiment modifies the temperature and exchange field dependence, as
illustrated in the theoretical prediction in Extended Data Figure 1.

## References

  * DiSalvo [1999] F. J. DiSalvo, Thermoelectric cooling and power generation, Science 285, 703 (1999).
  * Snyder and Toberer [2008] G. J. Snyder and E. S. Toberer, Complex thermoelectric materials, Nature materials 7, 105 (2008).
  * Pelegrini  _et al._ [2014] S. Pelegrini, A. Adami, C. Collini, P. Conci, C. I. de Araújo, V. Guarnieri, S. Güths, A. A. Pasa, and L. Lorenzelli, Development and characterization of a microthermoelectric generator with plated copper/constantan thermocouples, Microsystem technologies 20, 585 (2014).
  * Sootsman  _et al._ [2009] J. R. Sootsman, D. Y. Chung, and M. G. Kanatzidis, New and old concepts in thermoelectric materials, Angewandte Chemie International Edition 48, 8616 (2009).
  * Roddaro  _et al._ [2013] S. Roddaro, D. Ercolani, M. A. Safeen, S. Suomalainen, F. Rossella, F. Giazotto, L. Sorba, and F. Beltram, Giant thermovoltage in single inas nanowire field-effect transistors, Nano letters 13, 3638 (2013).
  * Prete  _et al._ [2019] D. Prete, P. A. Erdman, V. Demontis, V. Zannier, D. Ercolani, L. Sorba, F. Beltram, F. Rossella, F. Taddei, and S. Roddaro, Thermoelectric Conversion at 30 K in InAs/InP Nanowire Quantum Dots, Nano Letters 19, 3033 (2019).
  * Vullers  _et al._ [2009] R. Vullers, R. van Schaijk, I. Doms, C. Van Hoof, and R. Mertens, Micropower energy harvesting, Solid-State Electronics 53, 684 (2009).
  * Wachutka [1990] G. K. Wachutka, Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling, IEEE transactions on computer-aided design of integrated circuits and systems 9, 1141 (1990).
  * Josefsson  _et al._ [2018] M. Josefsson, A. Svilans, A. M. Burke, E. A. Hoffmann, S. Fahlvik, C. Thelander, M. Leijnse, and H. Linke, A quantum-dot heat engine operating close to the thermodynamic efficiency limits, Nature Nanotechnology 13, 920 (2018).
  * Keyes [2001] R. W. Keyes, Fundamental limits of silicon technology, Proceedings of the IEEE 89, 227 (2001).
  * Germanese  _et al._ [2022] G. Germanese, F. Paolucci, G. Marchegiani, A. Braggio, and F. Giazotto, Bipolar thermoelectric josephson engine, Nature Nanotechnology 17, 1084 (2022).
  * Germanese  _et al._ [2023] G. Germanese, F. Paolucci, G. Marchegiani, A. Braggio, and F. Giazotto, Phase control of bipolar thermoelectricity in josephson tunnel junctions, Physical Review Applied 19, 014074 (2023).
  * Ozaeta  _et al._ [2014] A. Ozaeta, P. Virtanen, F. Bergeret, and T. Heikkilä, Predicted very large thermoelectric effect in ferromagnet-superconductor junctions in the presence of a spin-splitting magnetic field, Physical review letters 112, 057001 (2014).
  * Kolenda  _et al._ [2016] S. Kolenda, M. J. Wolf, and D. Beckmann, Observation of thermoelectric currents in high-field superconductor-ferromagnet tunnel junctions, Physical review letters 116, 097001 (2016).
  * Kolenda  _et al._ [2017] S. Kolenda, C. Sürgers, G. Fischer, and D. Beckmann, Thermoelectric effects in superconductor-ferromagnet tunnel junctions on europium sulfide, Physical Review B 95, 224505 (2017).
  * Meservey and Tedrow [1994] R. Meservey and P. M. Tedrow, Spin-polarized electron tunneling, Physics Reports 238, 173 (1994).
  * Strambini  _et al._ [2017] E. Strambini, V. N. Golovach, G. De Simoni, J. S. Moodera, F. S. Bergeret, and F. Giazotto, Revealing the magnetic proximity effect in EuS/Al bilayers through superconducting tunneling spectroscopy, Physical Review Materials 1, 054402 (2017).
  * Hijano  _et al._ [2021] A. Hijano, S. Ilić, M. Rouco, C. González-Orellana, M. Ilyn, C. Rogero, P. Virtanen, T. T. Heikkilä, S. Khorshidian, M. Spies, N. Ligato, F. Giazotto, E. Strambini, and F. S. Bergeret, Coexistence of superconductivity and spin-splitting fields in superconductor/ferromagnetic insulator bilayers of arbitrary thickness, Physical Review Research 3, 023131 (2021).
  * De Simoni  _et al._ [2018] G. De Simoni, E. Strambini, J. S. Moodera, F. S. Bergeret, and F. Giazotto, Toward the Absolute Spin-Valve Effect in Superconducting Tunnel Junctions, Nano Letters 18, 6369 (2018).
  * Heikkilä  _et al._ [2018] T. Heikkilä, R. Ojajärvi, I. Maasilta, E. Strambini, F. Giazotto, and F. Bergeret, Thermoelectric radiation detector based on superconductor-ferromagnet systems, Physical Review Applied 10, 034053 (2018).
  * Geng  _et al._ [2023] Z. Geng, A. Hijano, S. Ilic, M. Ilin, I. J. Maasilta, A. Monfardini, M. Spies, E. Strambini, P. Virtanen, M. Calvo, C. González-Orellána, A. P. Helenius, S. Khorshidian, C. I. L. de Araujo, F. Levy-Bertrand, C. Rogero, F. Giazotto, F. S. Bergeret, and T. T. Heikkilä, Superconductor-ferromagnet hybrids for non-reciprocal electronics and detectors, Superconductor Science and Technology 10.1088/1361-6668/ad01e9 (2023).
  * Heikkilä  _et al._ [2019] T. T. Heikkilä, M. Silaev, P. Virtanen, and F. S. Bergeret, Thermal, electric and spin transport in superconductor/ferromagnetic-insulator structures, Progress in Surface Science 94, 100540 (2019).
  * Li  _et al._ [2013] B. Li, G.-X. Miao, and J. S. Moodera, Observation of tunnel magnetoresistance in a superconducting junction with zeeman-split energy bands, Physical Review B 88, 161105 (2013).
  * Münzenberg and Moodera [2004] M. Münzenberg and J. S. Moodera, Superconductor-ferromagnet tunneling measurements indicate $sp$-spin and $d$-spin currents, Physical Review B 70, 060402 (2004).
  * Strambini  _et al._ [2022] E. Strambini, M. Spies, N. Ligato, S. Ilić, M. Rouco, C. González-Orellana, M. Ilyn, C. Rogero, F. Bergeret, J. Moodera, _et al._ , Superconducting spintronic tunnel diode, Nature commun. 13, 1 (2022).
  * Giazotto  _et al._ [2006] F. Giazotto, T. T. Heikkilä, A. Luukanen, A. M. Savin, and J. P. Pekola, Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications, Reviews of Modern Physics 78, 217 (2006).
  * Fornieri and Giazotto [2017] A. Fornieri and F. Giazotto, Towards phase-coherent caloritronics in superconducting circuits, Nature nanotechnology 12, 944 (2017).
  * Bhatti  _et al._ [2017] S. Bhatti, R. Sbiaa, A. Hirohata, H. Ohno, S. Fukami, and S. Piramanayagam, Spintronics based random access memory: a review, Materials Today 20, 530 (2017).
  * Mott [1936] N. F. Mott, The electrical conductivity of transition metals, Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences 153, 699 (1936).
  * Heikkilä  _et al._ [2018] T. T. Heikkilä, R. Ojajärvi, I. J. Maasilta, E. Strambini, F. Giazotto, and F. S. Bergeret, Thermoelectric Radiation Detector Based on Superconductor-Ferromagnet Systems, Physical Review Applied 10, 034053 (2018).
  * Ilic  _et al._ [2023] S. Ilic, F. S. Bergeret, P. Virtanen, T. Heikkila, E. Strambini, F. Giazotto, and M. Spies, Apparatus and method for superconducting diode (2023).

## Data availability

The data that support the findings of this study are available from
corresponding author C.I.L.A., F.G and E.S. upon reasonable request.

## Code availability

The codes that support the findings of this study are available from
corresponding author P.V. upon reasonable request.

## Acknowledgments

C.I.L.A., P.V., T.H. and F.G. acknowledge funding from the EU’s Horizon 2020
Research and Innovation Program under Grant Agreement No. 800923 (SuperTED).
M.S. and E.S. acknowledge funding from the European Union’s Horizon 2020
research and innovation programme under the Marie Skłodowska Curie Action IF
Grant No. 101022473 (SuperCONtacts). F.G. and E.S. acknowledge the EU’s
Horizon 2020 Research and Innovation Framework Program under Grant Agreement
No. 964398 (SUPERGATE), No. 101057977 (SPECTRUM), and the PNRR MUR project
PE0000023-NQSTI for partial financial support. C.I.L.A. acknowledge Brazilian
agencies FINEP, FAPEMIG APQ-04548-22, CNPq and CAPES (Finance Code 001).

## Author contributions

C.I.L.A., M.S. and E.S. performed the experiment and analysed the data. P.V.
and T.T.H. provided theoretical support. C.G.O., S.K., M.I. and C.R.
fabricated the samples. E.S. conceived the experiment together with F.G. and
T.T.H.. C.I.L.A., M.S., P.V and E.S. wrote the manuscript with feedback from
all authors.

## Competing interests

The authors declare no competing interests.

## Extended figure

Extended Data Figure 1::  Predicted Seebeck coefficient. $S$ as a function of
the exchange field $h$ and temperature $T$. Left: for the same parameters as
in Fig. 2. Right: for $\Gamma_{\rm sf}=0$ and small $\hbar\Gamma=0.05\Delta$.
Dashed line indicates the superconducting transition.  Extended Data Figure
2::  Thermovoltage measurements on different samples. We present in i) open
circuit voltages in function of heating currents, performed at $T_{\rm
bath}=100$ mK, for different samples. The cobalt strip resistances and
junction resistances for the different devices are presented subsequently in
ii) and iii). Panels a), b) and c) are related to different junction developed
with aluminum thickness of 20nm, while in panel d) we present the results for
a sample with aluminum thickness of 12nm. CaF/Co(14nm)/AlOx (5hrs)/Al(20
nm)/EuS(21.5nm)/SiO2/Si  Extended Data Figure 3::  Thermal gradient limit.
Critical current in the superconducting aluminum in function of power injected
in the top cobalt strip, as depicted in the cartoon presented in a). b)
examples of critical currents measured for the sample without excitation (blue
dots) and under a power of $5\mu W$, input in the top cobalt strip (red dots),
the low negative voltage signal is due to a small offset in the voltage
amplifier used. In panel c) we present a summary of critical current evolution
in function of power, here it is possible to notice that the power generates a
temperature gradient on the junction, but it does not affect the aluminum
strip properties for the lower regime of power that we have used during the
thermal effects presented in the paper.


# Metaphor Generation with Conceptual Mappings

Kevin Stowe1, Tuhin Chakrabarty2, Nanyun Peng3
Smaranda Muresan2, Iryna Gurevych1
1Ubiquitous Knowledge Processing Lab, Technical University of Darmstadt
https://www.informatik.tu-darmstadt.de/ukp/
2Columbia University<EMAIL_ADDRESS>
3University of California Los Angeles<EMAIL_ADDRESS>
###### Abstract

Generating metaphors is a difficult task as it requires understanding nuanced
relationships between abstract concepts. In this paper, we aim to generate a
metaphoric sentence given a literal expression by replacing relevant verbs.
Guided by conceptual metaphor theory, we propose to control the generation
process by encoding conceptual mappings between cognitive domains to generate
meaningful metaphoric expressions. To achieve this, we develop two methods: 1)
using FrameNet-based embeddings to learn mappings between domains and applying
them at the lexical level (CM-Lex), and 2) deriving source/target pairs to
train a controlled seq-to-seq generation model (CM-BART). We assess our
methods through automatic and human evaluation for basic metaphoricity and
conceptual metaphor presence. We show that the unsupervised CM-Lex model is
competitive with recent deep learning metaphor generation systems, and CM-BART
outperforms all other models both in automatic and human evaluations.111All
code, models, and data are made available at:
https://github.com/UKPLab/acl2021-metaphor-generation-conceptual

##  1 Introduction

Recent neural models have led to important progress in natural language
generation (NLG) tasks. While pre-trained models have facilitated advances in
many areas of generation, the field of metaphor generation remains relatively
unexplored. Moreover, the few existing deep learning models for metaphor
generation Yu and Wan (2019); Stowe et al. (2020); Chakrabarty et al. (2020)
lack any conceptualization of the meaning of the metaphors.

Figure 1:  Metaphor generation guided by conceptual metaphors. Given a literal
input, we can generate metaphoric outputs based on different mappings between
conceptual domains.

This work proposes the first step towards metaphor generation informed by the
conceptual metaphor theory (CMT) Lakoff and Johnson (1980); Lakoff (1993);
Reddy (1979). CMT holds that we use conceptual mappings between domains
(conceptual structures that group related concepts) to generate linguistic
metaphors.222“Domains” are also often referred to as “image schema”, “frames”,
“scenes”, and more; see Kövecses (2020) Metaphoric mappings consist of a
source and a target conceptual domain. The source domain is the conceptual
domain from which we draw the metaphorical expressions, while the target
domain is the conceptual domain that we try to understand. A classical mapping
is argument is war, in which we conceptualize the target argumentation domain
as the more concrete source domain of war:

  * •

They fought against the contract.

  * •

They defended their new proposal.

We focus on verbs, as they are often the key component of metaphoric
expressions Steen et al. (2010); Martin (2006). When used metaphorically,
verbs typically evoke source domains (e.g. fought, defended in the above
examples): they are concrete, and are used to understand more abstract targets
(i.e., argumentation verbs such as argued, supported) via conceptual mappings
Sullivan (2013).

We propose a novel framework for metaphor generation informed by conceptual
metaphor theory. Given a literal input sentence that evokes a target domain we
generate metaphoric sentences that evoke desired corresponding source
domain(s).333We note that this source and target terminology used here is
opposite to that in machine translation. For example, given the literal
sentence The party ended as soon as she left evoking the target domain
cause_to_end, we can apply a variety of conceptual mappings to generate
different metaphoric outputs evoking different source domains (see Figure 1).
This allows us to generate metaphoric expressions that match known metaphoric
mappings, as well as generating from unseen mappings to explore novel
metaphors. Our contributions are:

  * •

Two metaphor generation models grounded in CMT: 1) An unsupervised lexical
model relying on frame embeddings learned from Framenet (CM-Lex, Section 3.1)
and 2) a BART Lewis et al. (2020) model encoding source/target domain
information through fine-tuning (CM-BART, Section 3.2).

  * •

Two metaphor generation tasks: 1) generate metaphoric expressions from known
concept mappings, for which we provide gold standard test data, and 2)
generate novel expressions from unknown metaphors using rare and unseen
mappings (Section 4).

  * •

A thorough evaluation using both automatic and human evaluations (Section 5).
We show that our CM-BART model improves over all others in terms of
metaphoricity (by $\geq 7\%$) and domain evocation (by $\geq 33\%$), and CM-
Lex is competitive with previous neural models on metaphoricity while
outperforming them on domain evocation (by $\geq 13\%$).

##  2 Task Definition

Traditional metaphor generation models focus only on whether the generated
output is in some way “metaphoric” or not. This ignores the semantic and
cognitive properties inherent in metaphoricity. These models can, to some
degree, generate metaphors given a literal input, but these outputs often do
not evoke the intended metaphor.

Controlled metaphor generation yields critical benefits over these
uncontrolled systems. For sentences in context, having metaphors that are
consistent with the text is essential for natural understanding. Also,
metaphors are not only used to express human knowledge, but can also help
shape our understanding of the world: having fine-grained control over the
generation process allows us to explore novel metaphoric mappings and perhaps
improve our understanding of the related domains.

To achieve controlled metaphor generation, we define our task as follows:
given a literal input sentence which evokes a target domain and an intended
conceptual mapping, generate a metaphoric sentence such that it evokes a
desired source domain. Thus, our generation models receive three inputs: 1) a
literal input sentence (They argued against the contract), 2) the target
domain evoked by the literal input (argument) and 3) the desired source domain
(war) for the metaphorical sentence. The output is a metaphorical sentence
which evokes the intended mapping (They fought against the contract)

##  3 Methods

We experiment with two general categories for generation. First, following
previous work in metaphor generation and interpretation Mao et al. (2018);
Stowe et al. (2020), we implement lexical methods for replacement, identifying
relevant verbs and replacing them with potential candidates for evoking
particular mappings. Second, we experiment with deep learning models,
employing controlled sequence-to-sequence generation.

###  3.1 CM-Lex

Metaphor generation can be conceptualized as finding key words and replacing
them with metaphoric counterparts. This can be done by employing vector
spaces, identifying the word most likely to fit in an appropriate context and
subjecting them to some constraints of metaphoricity. We build on this
paradigm by incorporating facets of conceptual metaphor theory.

Our procedure is as follows: we learn a joint embedded representations for
domains and lexical items. We then use the linear transformation between two
domains as a mapping, which can be applied to input words from the target
domain to generate a word from the source domain. As a proxy for domains, we
utilize FrameNet Baker et al. (1998), which contains semantic frames along
with the set of lexical units that evoke them. Frames can be defined as
related systems of concepts Fillmore (1982), which is exchangeable with the
term “domain” used in conceptual metaphor theory Cruse and Croft (2004). Thus,
we consider the transformation from one frame to another as a proxy for a
conceptual metaphoric mapping.

We first train FrameNet frame embeddings and employ evaluation metrics to
ensure their quality. We then apply transformations between domains to literal
verbs to generate metaphors grounded in conceptual metaphor theory.

####  3.1.1 Learning Frame Embeddings

In order to exploit FrameNet frames as conceptual domains, we will embed them
in vector space. While lexical and contextualized embeddings have proven
effective, the field of embedding concepts from lexical resources is less well
explored Sikos and Padó (2018); Alhoshan et al. (2019). These methods involve
tagging raw corpora using automatic FrameNet parsing and then inputting some
combination of the original text and the FrameNet information into standard
embedding algorithms.

To train and evaluate frame embeddings, we use 211k sentences of Gold
annotations used to train the Open-SESAME parser Swayamdipta et al. (2017),
along with a variety of other automatically tagged datasets: 250k individual
sentence from the Gutenberg Poetry Corpus Jacobs (2018), 17k from various
fiction section of the Brown Corpus Francis and Kucera (1979), and 80k
sentences randomly selected from Wikipedia. From this, we extract a 5-word
context window for each verb, creating 1.8M verb instances. We then replace
the focus verb with its FrameNet frame label (either provided in the Gold
data, or tagged via the parser), and train embedding models on the resulting
data. This yields joint embedding spaces that contain both common words and
FrameNet frame embeddings.

We define two intrinsic metrics to evaluate the quality of our produced
embeddings to enable fine-tuning and validation. First, following Sikos and
Padó (2018), we can evaluate quality based on the words that evoke that Frame.
FrameNet gives a set of lexical units (LUs) that evoke each frame $f$. We
calculate the lexical similarity by taking the distance from the mean
embedding of “local” words ($w\in f$) to the mean embedding of a random sample
$k$ of “distant” words ($w\not\in f$):

$lex(f)=\sum\limits_{w\in f}\frac{cos(E_{w},E_{f})}{|f|}-\sum\limits_{w\not\in
f}^{k}\frac{cos(E_{w},E_{f})}{k}$

This lexical metric ($lex$) is evaluates whether the frame embedding is
similar to words within its frame and dissimilar to those without.

FrameNet also contains linking relations between frames (eg. used-by, uses),
yielding a hierarchy of connected frames. Starting with the assumption that
frames connected in the structure should be more similar, we also calculate a
structural similarity metric $str$. We follow the same process as above,
taking the distance between the mean embedding of the local frames $n\in N$,
where $N$ is the immediate neighbors of $f$, to the mean embedding of a sample
$k$ of distant frames $n\notin N$.

$str(f)=\sum\limits_{n\in N}\frac{cos(E_{n},E_{f})}{|N|}-\sum\limits_{n\not\in
N}^{k}\frac{cos(E_{n},E_{f})}{k}$

We experiment with three lexical embeddings models: word2vec skip-gram Mikolov
et al. (2013), Glove Pennington et al. (2014), and FastText Bojanowski et al.
(2017). We experiment with 50, 100, and 300 dimensional representations; we
find the 50 dimensional word2vec embeddings perform best for both evaluation
metrics.444For full frame embedding evaluation, see Appendix 6.

####  3.1.2 Embedding Mappings

To apply these embeddings to generate metaphors based on conceptual mappings,
we learn mappings between frames and apply the mappings directly to lexical
items to facilitate lexical replacement.

We define a mapping $m$ as the pointwise distance between the target frame
embedding and the source frame embedding. Following the approach for learning
connections between concrete and poetic themes of Gagliano et al. (2016), we
sum the embedding of the target verb and the mapping $m$ for the selected
conceptual mapping, and select the most similar word to the resulting vector.
This word is then delemmatized using fitbert Havens and Stal (2019) and
inserted into the original sentence (Figure 2).

Figure 2:  Lexical generation process

Note that these resulting words are generated without context, as they rely
only on the input word and the conceptual mappings. This approach has
benefits: we require no labeled metaphor data, using only embeddings trained
on FrameNet-tagged corpora. However, ignoring context is likely detrimental.
In order to better use contextual information, we explore state-of-the-art
sequence-to-sequence modeling.

Literal (filled from LM) | Target Frame | Metaphoric (original) | Source Frame
---|---|---|---
That tyranny is destroyed | destruction | That tyranny is slain | killing
The house where love had ended | cause_to_end | The house where love had died | death
As the moments passed on | process_end | As the moments roll on | cause_motion
What I learned my senses fraught | coming_to_believe | What I bear my senses fraught | bringing
Table 1: Sample of extracted pairs from the data collection process.

###  3.2 CM-BART

For sequence-to-sequence learning, we fine-tune a pre-trained BART model Lewis
et al. (2020), adding source and target information to guide generation
towards the intended metaphors. We first outline a procedure for generating
semi-supervised paired data, then detail the training and generation process.

####  3.2.1 Method for Creating Parallel Data

In order to train sequence-to-sequence models for metaphor generation, we
require large scale parallel corpora. We follow the approach of Chakrabarty et
al. (2021) and build a corpus of literal/metaphoric paraphrases by starting
with the Gutenberg Poetry corpus Jacobs (2018), identifying and masking
metaphoric verbs, and replacing them with infilling from a language model. We
use a BERT-based metaphor classification model trained on the VUA metaphor
corpus Steen et al. (2010) to identify metaphoric verbs in a sentence (i.e
“died” in The house where love had died). Then we convert it to a literal
sentence (The house where love had ended) using infillings from pre-trained
BERT Devlin et al. (2019).

To ensure the literal sentence with replacements convey the same semantic
meaning as the metaphorical sentence they are then filtered using symbolic
meaning (SymbolOf relation) obtained from COMET Bosselut et al. (2019), a GPT
based language model fine-tuned on ConceptNet Speer et al. (2017). COMET
returns top 5 symbolic beams of (loss, loneliness, despair, sadness and
sorrow) for the sentence “The house where love had died” whereas it replaces
sorrow with life for the literal version. While Chakrabarty et al. (2021)
filter down to only those candidates with an exact match between the top 5
symbolic beams for the literal and metaphorical sentences returned by the
COMET model, we ease the restriction to cases where at least four of five
symbols are the same.

In order to learn more direct metaphoric information from this data, we
additionally tag each sentence with FrameNet frames using the Open-SESAME
parser Swayamdipta et al. (2017). We extract each pair in which both the focus
word in the literal, target-domain sentence and the metaphoric, source-domain
sentence are assigned a FrameNet frame. We then make the assumption that the
relation between the frames for the source and target domains reflects a
metaphoric mapping. This then yields a dataset of paired sentences for which
we have a metaphoric mapping between domains based on FrameNet for the focus
verbs.

Samples of the created data are shown in Table 1. In total this process yields
248k sentences spanning 8.5k unique mappings between FrameNet frames. Each
pair comprises a literal and metaphoric sentence, along with the literal
target frame and the metaphoric source frame. From these we can directly train
a sequence to sequence model for conceptual metaphor-based generation.

####  3.2.2 Models

We fine-tune BART Lewis et al. (2020), a pre-trained conditional language
model that combines bidirectional and auto-regressive transformers, on the
created parallel corpora described in Section 3.2.1. We incorporate
representations of the frame information to allow this model to control for
the metaphoric mappings evoked.

To transform a literal sentence from a given target domain to a metaphorical
sentence evoking a specific source domain, we incorporate both target and
source domains (as FrameNet frames) into the textual representation as a
control code, following the work of Schiller et al. (2020) who used this
procedure for Argument Generation. Following the example from Figure 1, the
input literal text fed to the BART encoder would be:

  * •

death $\langle EOT\rangle$ The party $\langle V\rangle$ ended : cause_to_end
$\langle V\rangle$ as soon as she left.

where $\langle EOT\rangle$ and $\langle V\rangle$ are delimiters, death is the
source frame, and cause_to_end the target frame. The decoding target is the
metaphoric text “The party died as soon as she left”, which evokes the
cause_to_end is death mapping.

Note that our training data differs only at the level of a single verb. We use
the generative BART seq2seq model to generate metaphoric paraphrases, but due
to the nature of the training data and the importance of verbs in metaphoric
expressions, this is often realized in the output as lexical replacement.

Post fine-tuning, we use top-k (k=5) sampling Fan et al. (2018) to generate
metaphors conditioned on the input literal sentence and source and target
domains for the required metaphoric mapping.555Full parameter tuning outlined
in Appendix C. We evaluate the lexical model (CM-Lex) and the sequence-to-
sequence model (CM-BART) under two experimental settings.

##  4 Experimental Setup

We evaluate our metaphor generation methods against two previous approaches to
metaphoric paraphrase generation: the mermaid system Chakrabarty et al. (2021)
and the metaphor masking model (MetMask) Stowe et al. (2020). We explore two
tasks: generating against gold standard metaphoric expressions, and using rare
and unseen metaphoric mappings. For the former, we build a gold test set of
metaphoric paraphrases that evoke a particular source/target mapping. For the
latter, we apply a variety of source/target mappings to literal inputs for
which we do not have gold outputs.

###  4.1 Building a Test Set

For a test set, we use the same procedure as our data collection approach from
Section 3.2.1. We apply this procedure to two datasets: a sample of the
Gutenberg Poetry Corpus and a sample of fiction from the Brown Corpus Francis
and Kucera (1979). This generates an initial set of literal/metaphoric pairs.
We also tagged the pairs from Mohammad et al. (2016) with FrameNet tags, as
these generally contain novel, well-formed metaphors. These three datasets
each have different properties with regard to metaphor. The Gutenberg Poetry
corpus has consistent, novel metaphors, but often unconventional syntactic
constructions, due to the poetic nature of the text. The Mohammad 2016 corpus
contains manually constructed metaphors which are novel, following relatively
basic syntactic patterns. The Brown Corpus is standard fiction texts, so the
metaphors within tend to be very conventional.

From these sources, we draw pairs randomly, checking that they reflect strong
literal/metaphoric paraphrases until we obtain 50 instances from each set.
Each pair is tagged with FrameNet frames for the focus verbs, which comprise
the metaphoric mapping.666In 22 cases, parsing errors in FrameNet frames were
manually corrected. For the Brown corpus, metaphoric expressions were
relatively rare, and thus valid pairings were sparse: to overcome this, we
manually modified 11 of the expressions to evoke the appropriate metaphoric
mappings.

In total this process yielded 150 literal/metaphoric pairs, along with the
source and target frames that they evoke. We use this dataset to evaluate
generating metaphors based on mappings with gold standard outputs, using both
automatic and human-based evaluations.

###  4.2 Expanding to Unknown Metaphors

To explore the flexibility of the system developed in this study, we also
evaluate them for generation of metaphoric expressions that are not directly
linked to gold literal/metaphoric pairs. For this, we begin with our 150 pairs
from above, but consider only the literal sentence and the evoked target
domain. For each sentence, we generate two source domains that could
potentially map to the target. These are selected in order to identify rare
and unseen mappings based on the observed mappings in our training data. For
rare mappings we select a source domain at random from the mappings with the
median frequency for a given target domain. For unseen mappings we select a
source domain at random from the FrameNet frames that are never used as a
source for the given target domain.

This set contains only the tuple (input sentence, target domain, source
domain) needed as input to our models; we do not have gold generated
metaphorical utterances. Thus, on this set we will only perform human-based
evaluation of the quality of the generated metaphors.

###  4.3 Automatic Evaluation Metrics

Word overlap metrics (eg. BLEU, ROUGE) are inherently weak for this task, as
these sentences inherently have high overlaps. So instead, we employ semantic
distance metrics. We generate sentence embeddings using SBERT777Specifically
using the roberta-large model, which shows the best performance for sentence
similarity tasks. Reimers and Gurevych (2019) for each of our components: the
literal input $L$, the original gold metaphoric expression $M$, and the
generated output $G$.

####  4.3.1 Distance from Gold Metaphor ($dis$)

The generated metaphoric expressions should match the semantics of the
original gold metaphor. We can evaluate this using the cosine distance, here
between $M$ and $G$. As SBERT embeddings have been shown to reflect semantic
similarity and entailment between paired sentences, this metric should be
capable of capturing whether the generated metaphoric expression matches the
gold.

####  4.3.2 Relational distance ($rel$)

Assuming that conceptual metaphoric mappings are responsible for the
connecting of meaning between our literal and metaphoric sentences, we would
also expect there to be a relation that holds between the original literal
input $L$ and metaphoric output $M$. This relation should also hold between
the $L$ and the generated metaphor $G$. As a simple metric we can employ
cosine distance: we aim for minimizing the distance between $cos(L,M)$ between
$cos(L,G)$.

Finally, we include the percentage of times the model produced the exact gold
output.

##  5 Results and Analysis

Results for automatic evaluation on the 150 gold metaphors are shown in Table
2. Note that we cannot automatically evaluate against rare or unseen
metaphoric mappings, as we lack gold metaphors.

Model | $dis$ | $rel$ | $mean$ | %=
---|---|---|---|---
MetMask | .191 | .094 | .143 | .087
mermaid | .147 | .087 | .117 | .133
CM-Lex | .151 | .086 | .122 | .107
CM-BART | .085 | .047 | .066 | .293
Table 2: Automatic evaluation for metaphor generation systems. %= indicates
the percentage that matched the gold metaphor exactly.

The CM-Lex model is competitive with the best neural baseline, which is
encouraging. This shows that simply incorporating basic understanding of
conceptual mappings can be a powerful tool for metaphor generation. The CM-
BART yields the best automatic performance over all metrics, significantly
outperforming all other models ($p<.01$, paired t-test.).

Automatic metrics allow us to quickly prototype metaphoric generation systems
based in conceptual metaphor theory. However, they rely on SBERT and inherit
the biases and weaknesses therein. We also perform human evaluations, against
both the gold test data and the set of rare and unseen mappings.

###  5.1 Human Evaluation

For human evaluation, we defined two objectives. First, we aim to capture the
metaphoricity of the output, as a core objective. The outputs should evoke
novel, interesting metaphors regardless of the domains involved. Second, we
want the generated metaphoric outputs to evoke the source domains (eg. “She
destroyed his argument” evokes the source domain of war).

We recruited three domain experts in metaphoricity. They were instructed to
rate each instance on a scale from 1 (not at all) to 4 (very) for
metaphoricity and for whether it evokes the source domain. If the sentence was
completely unintelligible, they were instructed to mark it as 0 for both
categories. For metaphoricity, annotators were given brief definitions of
metaphoricity which they incorporated into their expert knowledge to best rate
metaphors. For source domain evocation, they were additionally provided with
links to the respective FrameNet frames.

We evaluate three different models for the gold metaphors: the best performing
previous model, mermaid, as well as the lexical and CM-BART models. For all
models we evaluate generation using the mappings for our gold test set. For
the unknown metaphors without gold sentences, we only evaluate our two
controlled models, as the generic baselines give the same output regardless of
the intended source. This yields a total of 450 sentences (150 gold, 300
without) that are evaluated for metaphoricity and source domain.

All three experts annotated a random set of 100 training sentences, in order
to determine the feasibility and agreement for this task. Agreement rates were
.50 for metaphoricity and .37 for source domain (Krippendorff’s
$\alpha$).888Full annotation analysis can be found in Appendix B.

####  5.1.1 Gold Test Mappings

| Gold | Rare | Unseen
---|---|---|---
Model | Met | Src | Met | Src | Met | Src
MetMask | 2.27 | 1.60 | - | - | - | -
mermaid | 2.56 | 2.12 | - | - | - | -
CM-Lex | 2.34 | 2.43 | 2.28 | 2.10 | 1.58 | 1.14
CM-BART | 2.72 | 2.87 | 2.41 | 2.70 | 2.41 | 2.01
Table 3: Human evaluations for metaphoricity (Met) and source domain evocation (Src). |  Input/target/source | Model | Output | Met | Src
---|---|---|---|---|---
1 |  He resisted the panic of vertigo self_control is quarreling | Gold | He fought the panic of vertigo |  |
MetMask | He got the panic of vertigo | 3 | 1
mermaid | He felt the panic of vertigo | 1 | 2
CM-Lex | He confrontations the panic of vertigo | 0 | 0
CM-BART | He disputed the panic of vertigo | 3 | 4
2 |  A dim aurora rises in my east change_position_on_a_scale is residence | Gold | A dim aurora lives in my east |  |
MetMask | A dim aurora kicked in my east | 3 | 1
mermaid | A dim aurora hangs in my east | 4 | 2
CM-Lex | A dim aurora stands in my east | 3 | 3
CM-BART | A dim aurora lives in my east | 3 | 4
3 |  People were running out of the theater self_motion is fluidic_motion | Gold | People were streaming out of the theater |  |
MetMask | People were clogged out of the theater | 4 | 1
mermaid | People were running out of the theater | 1 | 4
CM-Lex | People were boiling out of the theater | 4 | 4
CM-BART | People were spilled out of the theater | 4 | 3
Table 4: Example outputs of each system along with the mean of their human evaluations. |  target/source | Model | Output | Met | Src
---|---|---|---|---|---
1 |  operate_vehicle is | Input | The car drove up alongside him |  |
Rare: self_motion | CM-Lex | The car drove up alongside him | 1 | 1
CM-BART | The car ran up alongside him | 4 | 4
Unseen: death | CM-Lex | The car fell up alongside him | 4 | 4
CM-BART | The car died up alongside him | 4 | 2
2 |  distributed_position is | Input | The meat was covered in a fatty gravy |  |
Rare: giving | CM-Lex | The meat was raised in a fatty gravy | 4 | 1
CM-BART | The meat was given in a fatty gravy | 2 | 4
Unseen: surrendering_possession | CM-Lex | The meat was cut in a fatty gravy | 1 | 1
CM-BART | The meat was yielded in a fatty gravy | 3 | 4
3 |  dispersal is | Input | At last the darkness began to dissolve |  |
Rare: attempt | CM-Lex | At last the darkness began to gorn | 0 | 0
CM-BART | At last the darkness began to try | 4 | 4
Unseen: warning | CM-Lex | At last the darkness began to Giffen | 0 | 0
CM-BART | At last the darkness began to bite | 4 | 1
Table 5: Examples of system outputs on rare and unknown metaphoric mappings.

Results for human evaluations of gold, rare, and unseen metaphoric mappings
are shown in Table 3. With regard to the gold mappings, the CM-BART model
performs best in metaphoricity and source domain evocation. CM-Lex has
middling performance for metaphoricity, but does well at generating correct
source domains. The mermaid system performs well in terms of metaphor
generation, but fails to capture the intended source domain.

Examples of each model’s generation are shown in Table 4. In 1, we see that
CM-Lex generates noise, making the results unintelligible. CM-BART is more
robust, generating fluent expressions, and shows evidence of conceptual
mapping control, generating a metaphoric expression matching the source
domain. In 2, the MetMask and mermaid models generate reasonable metaphors,
which do not evoke the intended domain. CM-Lex is better, generating “stand”
which can reflect residence, while the CM-BART performs best, generating the
gold metaphoric expression.

In 3, we see that the unconstrained models generate effective expressions:
”clog” is an evocative metaphor, and ”running”, while literal, can match the
intended domain via the idea of running water. However, our controlled methods
both generate novel metaphors that directly evoke the source domain, showing
the effectiveness of incorporating conceptual information in generation.

Overall, we see that the unconstrained models often generate good metaphors,
but lack consistency with the input, as they are naive with regard to the
conceptual backing of these metaphoric expressions. CM-Lex is effective to
some degree, even without metaphoric training data, and CM-BART performs best,
generating novel metaphors that frequently match the intended metaphoric
expression.

####  5.1.2 Unknown Metaphor Mappings

CM-BART outperforms CM-Lex for metaphoricity and source domain evocation for
rare and unseen source domains. Examples of the two proposed models’ generated
for rare and unseen metaphoric mappings are shown in Table 5.

Example 1 shows the ideal case. When given a source domain from a ”rare”
mapping, the resulting metaphor is fairly reasonable. CM-BART generates a
metaphor consistent with the original semantics; CM-Lex generates the literal
utterance. When presented with an unseen mapping in which operating a vehicle
is framed as death, we get diverse expressions, both adding meaning to the
original utterance. CM-Lex uses the verb ”fell” (albeit incorrectly
conjugated), which can be used to abstractly evoke the death domain, while CM-
BART directly uses the verb ”die”. The original expression can be ambiguous as
to whether the car stopped: the evoked metaphor enforces the stoppage of the
car, and also provides color to the expression.

Example 3 highlights a key issue: when the source and target domains are too
incongruent, the generated expressions can be inconsistent. CM-Lex here again
generates noise. However, CM-BART generates normal, expressive metaphors,
which are nonetheless incompatible with the original literal input, which
denotes the lessening of darkness. Rather, CM-BART generates a metaphor
expressing perhaps growing darkness with the verb try and a dangerous darkness
with the verb bite.

This is a critical point with regard to conceptual mappings. Not all pairs are
available: they require semantic consistency, and while generating from any
two pairs may yield insightful, interesting, and perhaps inspiring new
metaphoric expressions, generating metaphoric paraphrases requires additional
knowledge of which source/target pairings are compatible. This generally
supports notion of invariance and structure mapping, in which there is
inherent structure within domains that needs to be consistent in order to
evoke metaphoric mappings between them Gentner (1983); Lakoff (1993).

It must be noted that the systems proposed here have a distinct advantage in
this task: we add FrameNet frames, which, while neither perfect nor designed
to capture metaphoricity, provide a strong signal for which domains to
generate in. This highlights a possible benefit to the interaction between
deep, pre-trained models such as BART and available lexical resources: by
combining these, we are able to leverage the strength of each to build a
powerful metaphor generation system.

##  6 Related Work

We broadly cover two areas of related work: previous computational approaches
to CMT, and previous approaches to metaphor generation.

##### Computational Approaches to CMT.

There are a variety of approaches to identifying conceptual metaphors
themselves. The CorMet system Mason (2004) was built to extract conceptual
metaphors based on selectional preferences of verbs. Shaikh et al. (2014a)
builds ”conceptual spaces” for source domains, using rule-based extraction of
relations between lexical items. These conceptual spaces are then used to find
new conceptual metaphors. This process is extended to build a repository of
linguistic and conceptual metaphors Shaikh et al. (2014b). Mohler et al.
(2014) focus on identifying appropriate source domains for metaphoric
expressions, using vector-based approaches for metaphor interpretation.

The idea of using frames to represent metaphoric domains has been explored in
the MetaNet project Dodge et al. (2015). We however, restrict our work to
FrameNet due to the coverage and availability of reliable automatic parsing.

##### Metaphor Generation.

Early work in metaphor generation was based in heuristics, learning to
generate relatively simple ”A is like B” representations Abe et al. (2006);
Terai and Nakagawa (2010). In a similar vein, Veale (2016) uses template-like
structures to generate creative and metaphoric tweets.

Other works focus on identifying metaphoric mappings using WordNet clustering
and selectional preferences Mason (2004); Gandy et al. (2013), syntactic
relations to build proposition databases Ovchinnikova et al. (2014), and
embedding based approaches to identify poetic relationships Gagliano et al.
(2016). However, the goal of these works is to generate mappings, rather than
linguistic expressions that evoke them.

Amongst deep learning approaches Yu and Wan (2019) identify literal and
metaphoric words in corpora based on selectional restrictions, and using these
to train sequence-to-sequence models for metaphor generation, albeit without
reference to any input expression. Stowe et al. (2020) generates metaphors
using masked language modeling, masking metaphoric tokens in training in order
to encourage metaphoric generation. Other approaches use novel methods for
collecting literal/metaphor pairs, training sequence-to-sequence models for
simile generation and metaphoric paraphrasing Chakrabarty et al. (2020, 2021).
These approaches effectively generate figurative language, but the models have
no knowledge of the underlying metaphors, and thus simply generate ungrounded
expressions. This leads to outputs which are possibly metaphoric, but contain
no connection to the input, eschewing the critical connections that make novel
metaphors powerful. We instead propose methods for generating metaphoric
paraphrases grounded in CMT.

##  7 Conclusions and Future Work

In summary, we have shown two methods for incorporating knowledge of
conceptual metaphor theory in metaphor generation. We trained FrameNet frame
embeddings to represent conceptual domains, and applied shifts between them to
generate metaphors in an unsupervised fashion. Leveraging FrameNet further, we
build a dataset of semi-supervised pairs that evoke conceptual metaphors,
which can be used along with BART for controlled metaphor generation. This
model achieves state-of-the-art performance in metaphor generation by both
automatic and human evaluations.

Future work can expand these models to go beyond verbs, incorporating nominal
and other types of metaphors. The next necessary step is to go beyond
lexicalized metaphors: good, consistent conceptual metaphors often span long
stretches of text, and we need to design models that can learn and generate
metaphors over larger texts.

## Ethical Considerations

Although we use language models trained on data collected from the Web, which
have been shown to have issues with bias and abusive language Sheng et al.
(2019); Wallace et al. (2019), the inductive bias of our models should limit
inadvertent negative impacts. Unlike model variants such as GPT, BART is a
conditional language model, which provides more control of the generated
output. It should also be noted that our CM-BART model is fine-tuned on the
poetry corpus which is devoid of harmful and toxic text especially targeted at
marginalized communities

Advances in generative AI inherently come with concerns about models’ ability
to deceive, persuade, and misinform. Metaphorical language has been shown to
express and elicit stronger emotion than literal language Citron and Goldberg
(2014); Mohammad et al. (2016) and to provoke emotional responses in the
context of political discourse covered by mainstream newspapers Figar (2014).
We understand there may be concerns about building generative models for
metaphors aimed at persuasion. Social scientists distinguish persuasion from
manipulation based on two aspects: dissimulation and constraint Nettel and
Roque (2012). Dissimulation involves concealing intention, which requires
hiding information, whereas constraint involves removing options from the
audience and forcing them to accept the conclusion. Our work on metaphor
generation does not aim to hide information about a topic or present it as the
only choice, but aims to provide the same sentence using more expressive
language.

## References

  * Abe et al. (2006) Keiga Abe, Sakamoto Kayo, and Masanori Nakagawa. 2006.  A computational model of the metaphor generation process.  In _Proceedings of the 28th Annual Meeting of the Cognitive Science Society_ , pages 937–942, Vancouver, Canada. Psychology Press.
  * Alhoshan et al. (2019) Waad Alhoshan, Riza Batista-Navarro, and Liping Zhao. 2019.  Semantic frame embeddings for detecting relations between software requirements.  In _Proceedings of the 13th International Conference on Computational Semantics - Student Papers_ , pages 44–51, Gothenburg, Sweden. Association for Computational Linguistics.
  * Baker et al. (1998) Collin F. Baker, Charles J. Fillmore, and John B. Lowe. 1998.  The Berkeley FrameNet project.  In _36th Annual Meeting of the Association for Computational Linguistics and 17th International Conference on Computational Linguistics, Volume 1_ , pages 86–90, Montreal, Quebec, Canada. Association for Computational Linguistics.
  * Bojanowski et al. (2017) Piotr Bojanowski, Edouard Grave, Armand Joulin, and Tomas Mikolov. 2017.  Enriching word vectors with subword information.  _Transactions of the Association for Computational Linguistics_ , 5:135–146.
  * Bosselut et al. (2019) Antoine Bosselut, Hannah Rashkin, Maarten Sap, Chaitanya Malaviya, Asli Celikyilmaz, and Yejin Choi. 2019.  COMET: Commonsense transformers for automatic knowledge graph construction.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 4762–4779, Florence, Italy. Association for Computational Linguistics.
  * Chakrabarty et al. (2020) Tuhin Chakrabarty, Smaranda Muresan, and Nanyun Peng. 2020.  Generating similes effortlessly like a pro: A style transfer approach for simile generation.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 6455–6469, Online. Association for Computational Linguistics.
  * Chakrabarty et al. (2021) Tuhin Chakrabarty, Xurui Zhang, Smaranda Muresan, and Nanyun Peng. 2021.  MERMAID: Metaphor generation with symbolism and discriminative decoding.  In _Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 4250–4261, Online. Association for Computational Linguistics.
  * Citron and Goldberg (2014) Francesca MM Citron and Adele E Goldberg. 2014.  Metaphorical sentences are more emotionally engaging than their literal counterparts.  _Journal of cognitive neuroscience_ , 26(11):2585–2595.
  * Cruse and Croft (2004) D. Alan Cruse and William Croft. 2004.  _Cognitive Linguistics_.  Cambridge Textbooks in Linguistics. Cambridge University Press.
  * Devlin et al. (2019) Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019.  BERT: Pre-training of deep bidirectional transformers for language understanding.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)_ , pages 4171–4186, Minneapolis, Minnesota. Association for Computational Linguistics.
  * Do Dinh et al. (2018) Erik-Lân Do Dinh, Hannah Wieland, and Iryna Gurevych. 2018.  Weeding out conventionalized metaphors: A corpus of novel metaphor annotations.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 1412–1424, Brussels, Belgium. Association for Computational Linguistics.
  * Dodge et al. (2015) Ellen Dodge, Jisup Hong, and Elise Stickles. 2015.  MetaNet: Deep semantic automatic metaphor analysis.  In _Proceedings of the Third Workshop on Metaphor in NLP_ , pages 40–49, Denver, Colorado. Association for Computational Linguistics.
  * Fan et al. (2018) Angela Fan, Mike Lewis, and Yann Dauphin. 2018.  Hierarchical neural story generation.  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 889–898, Melbourne, Australia. Association for Computational Linguistics.
  * Figar (2014) Vladimir Figar. 2014.  Emotional appeal of conceptual metaphors of conflict in the political discourse of daily newspapers.  _Facta Universitatis, Linguistics and Literature_ , 12(1):43–61.
  * Fillmore (1982) Charles Fillmore. 1982.  Frame Semantics.  _Linguistics in the Morning Calm_ , 1:111–138.
  * Francis and Kucera (1979) W. N. Francis and H. Kucera. 1979.  Brown corpus manual.  Technical report, Department of Linguistics, Brown University, Providence, Rhode Island, US.
  * Gagliano et al. (2016) Andrea Gagliano, Emily Paul, Kyle Booten, and Marti A. Hearst. 2016.  Intersecting word vectors to take figurative language to new heights.  In _Proceedings of the Fifth Workshop on Computational Linguistics for Literature_ , pages 20–31, San Diego, California, USA. Association for Computational Linguistics.
  * Gandy et al. (2013) Lisa Gandy, Nadji Allan, Mark Atallah, Ophir Frieder, Newton Howard, Sergey Kanareykin, Moshe Koppel, Mark Last, Yair Neuman, and Shlomo Argamon. 2013.  Automatic identification of conceptual metaphors with limited knowledge.  In _Proceedings of the 27th AAAI Conference on Artificial Intelligence_ , pages 328–334, Bellevue, Washington. AAAI Press.
  * Gentner (1983) Dedre Gentner. 1983.  Structure-Mapping: A Theoretical Framework for Analogy.  _Cognitive Science_ , 7:1–5.
  * Havens and Stal (2019) Sam Havens and Aneta Stal. 2019.  Use bert to fill in the blanks.
  * Jacobs (2018) Arthur M Jacobs. 2018.  The Gutenberg English poetry corpus: exemplary quantitative narrative analyses.  _Frontiers in Digital Humanities_ , 5:5.
  * Kövecses (2020) Zoltán Kövecses. 2020.  _Extended Conceptual Metaphor Theory_.  Cambridge University Press.
  * Lakoff (1993) George Lakoff. 1993.  The Contemporary Theory of Metaphor.  In Andrew Ortony, editor, _Metaphor and Thought_ , pages 202–251. Cambridge University Press.
  * Lakoff and Johnson (1980) George Lakoff and Mark Johnson. 1980.  _Metaphors We Live By_.  University of Chicago Press, Chicago and London.
  * Lewis et al. (2020) Mike Lewis, Yinhan Liu, Naman Goyal, Marjan Ghazvininejad, Abdelrahman Mohamed, Omer Levy, Veselin Stoyanov, and Luke Zettlemoyer. 2020.  BART: Denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 7871–7880, Online. Association for Computational Linguistics.
  * Mao et al. (2018) Rui Mao, Chenghua Lin, and Frank Guerin. 2018.  Word embedding and WordNet based metaphor identification and interpretation.  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics_ , pages 1222–1231, Melbourne, Australia. Association for Computational Linguistics.
  * Martin (2006) James H Martin. 2006.  A corpus-based analysis of context effects on metaphor comprehension.  Technical report.
  * Mason (2004) Zachary J. Mason. 2004.  CorMet: A computational, corpus-based conventional metaphor extraction system.  _Computational Linguistics_ , 30(1):23–44.
  * Mikolov et al. (2013) Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey Dean. 2013.  Efficient estimation of word representations in vector space.  _CoRR_ , abs/1301.3781.
  * Mohammad et al. (2016) Saif Mohammad, Ekaterina Shutova, and Peter Turney. 2016.  Metaphor as a medium for emotion: An empirical study.  In _Proceedings of the Fifth Joint Conference on Lexical and Computational Semantics_ , pages 23–33, Berlin, Germany. Association for Computational Linguistics.
  * Mohler et al. (2014) Michael Mohler, Bryan Rink, David Bracewell, and Marc Tomlinson. 2014.  A novel distributional approach to multilingual conceptual metaphor recognition.  In _Proceedings of COLING 2014, the 25th International Conference on Computational Linguistics: Technical Papers_ , pages 1752–1763, Dublin, Ireland. Dublin City University and Association for Computational Linguistics.
  * Nettel and Roque (2012) Ana Laura Nettel and Georges Roque. 2012.  Persuasive argumentation versus manipulation.  _Argumentation_ , 26(1):55–69.
  * Ott et al. (2019) Myle Ott, Sergey Edunov, Alexei Baevski, Angela Fan, Sam Gross, Nathan Ng, David Grangier, and Michael Auli. 2019.  fairseq: A fast, extensible toolkit for sequence modeling.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics (Demonstrations)_ , pages 48–53, Minneapolis, Minnesota. Association for Computational Linguistics.
  * Ovchinnikova et al. (2014) Ekatarina Ovchinnikova, Vladimir Zaytsev, Suzanne Wertheim, and Ross Israel. 2014\.  Generating conceptual metaphors from proposition stores.  cs.CL/1409.7619.
  * Pennington et al. (2014) Jeffrey Pennington, Richard Socher, and Christopher Manning. 2014.  GloVe: Global vectors for word representation.  In _Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 1532–1543, Doha, Qatar. Association for Computational Linguistics.
  * Reddy (1979) Michael Reddy. 1979.  The Conduit Metaphor : A case of frame conflict in our language about language.  In Andrew Ortony, editor, _Metaphor and Thought_ , pages 284–324. Cambridge University Press, Cambridge.
  * Reimers and Gurevych (2019) Nils Reimers and Iryna Gurevych. 2019.  Sentence-BERT: Sentence embeddings using Siamese BERT-networks.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 3982–3992, Hong Kong, China. Association for Computational Linguistics.
  * Schiller et al. (2020) Benjamin Schiller, Johannes Daxenberger, and Iryna Gurevych. 2020.  Aspect-controlled neural argument generation.  _arXiv preprint arXiv:2005.00084_.
  * Shaikh et al. (2014a) Samira Shaikh, Tomek Strzalkowski, Kit Cho, Ting Liu, George Aaron Broadwell, Laurie Feldman, Sarah Taylor, Boris Yamrom, Ching-Sheng Lin, Ning Sa, Ignacio Cases, Yuliya Peshkova, and Kyle Elliot. 2014a.  Discovering conceptual metaphors using source domain spaces.  In _Proceedings of the 4th Workshop on Cognitive Aspects of the Lexicon (CogALex)_ , pages 210–220, Dublin, Ireland. Association for Computational Linguistics and Dublin City University.
  * Shaikh et al. (2014b) Samira Shaikh, Tomek Strzalkowski, Ting Liu, George Aaron Broadwell, Boris Yamrom, Sarah Taylor, Laurie Feldman, Kit Cho, Umit Boz, Ignacio Cases, Yuliya Peshkova, and Ching-Sheng Lin. 2014b.  A multi-cultural repository of automatically discovered linguistic and conceptual metaphors.  In _Proceedings of the Ninth International Conference on Language Resources and Evaluation (LREC’14)_ , pages 2495–2500, Reykjavik, Iceland. European Language Resources Association (ELRA).
  * Sheng et al. (2019) Emily Sheng, Kai-Wei Chang, Premkumar Natarajan, and Nanyun Peng. 2019.  The woman worked as a babysitter: On biases in language generation.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 3407–3412, Hong Kong, China. Association for Computational Linguistics.
  * Sikos and Padó (2018) Jennifer Sikos and Sebastian Padó. 2018.  Using embeddings to compare FrameNet frames across languages.  In _Proceedings of the First Workshop on Linguistic Resources for Natural Language Processing_ , pages 91–101, Santa Fe, New Mexico, USA. Association for Computational Linguistics.
  * Speer et al. (2017) Robyn Speer, Joshua Chin, and Catherine Havasi. 2017.  Conceptnet 5.5: An open multilingual graph of general knowledge. In _In Thirty-First AAAI Conference on Artificial Intelligence._ , pages 4444–4451, San Francisco, California.
  * Steen et al. (2010) Gerard J. Steen, Aletta G. Dorst, J. Berenike Herrmann, Anna Kaal, Tina Krennmayr, and Trijntje Pasma. 2010.  _A Method for Linguistic Metaphor Identification: From MIP to MIPVU_.  John Benjamins.
  * Stowe et al. (2020) Kevin Stowe, Leonardo Ribeiro, and Iryna Gurevych. 2020.  Metaphoric paraphrase generation.  _arXiv preprint arXiv:2002.12854_.
  * Sullivan (2013) Karen Sullivan. 2013.  _Frames and Constructions in Metaphoric Language_.  John Benjamins.
  * Swayamdipta et al. (2017) Swabha Swayamdipta, Sam Thomson, Chris Dyer, and Noah A. Smith. 2017.  Frame-Semantic Parsing with Softmax-Margin Segmental RNNs and a Syntactic Scaffold.  _arXiv preprint arXiv:1706.09528_.
  * Terai and Nakagawa (2010) Asuka Terai and Masanori Nakagawa. 2010.  A computational system of metaphor generation with evaluation mechanism.  In _International Conference on Artificial Neural Networks_ , pages 142–147, Thessaloniki, Greece. Springer.
  * Veale (2016) Tony Veale. 2016.  Round up the usual suspects: Knowledge-based metaphor generation.  In _Proceedings of the Fourth Workshop on Metaphor in NLP_ , pages 34–41, San Diego, California. Association for Computational Linguistics.
  * Wallace et al. (2019) Eric Wallace, Shi Feng, Nikhil Kandpal, Matt Gardner, and Sameer Singh. 2019.  Universal adversarial triggers for attacking and analyzing NLP.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 2153–2162, Hong Kong, China. Association for Computational Linguistics.
  * Yu and Wan (2019) Zhiwei Yu and Xiaojun Wan. 2019.  How to avoid sentences spelling boring? Towards a neural approach to unsupervised metaphor generation.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 861–871, Minneapolis, Minnesota. Association for Computational Linguistics.

##  Appendix A Appendix A

|  $lex$ sim |  $str$ sim | mean
---|---|---|---
Dimensions | 50 | 100 | 300 | 50 | 100 | 300 | 50 | 100 | 300
word2vec | .203 | .208 | .205 | .111 | .076 | .104 | .157 | .144 | .154
fasttext | .113 | .120 | .117 | .042 | .103 | .095 | .077 | .111 | .106
glove | .179 | .191 | .212 | -.106 | -.136 | -.108 | .037 | .028 | .052
Table 6:

Results for each frame embedding method using the distance metrics defined in
Section 3.1 are shown in Table 6.

Figure 3:  Frame embedding evaluation metrics as data is added. Paper | n | Method | Agreement
---|---|---|---
Do Dinh et al. (2018) | 15,180 | MTurk | .16-.38 $\alpha$
Yu and Wan (2019) | 80 | MTurk | -
Chakrabarty et al. (2020) | 900 | MTurk | .36-.49 $\alpha$
Stowe et al. (2020) | 513 | MTurk | -
Chakrabarty et al. (2021) | 900 | MTurk | -
This work | 450 | Experts | .505 $\alpha$
Table 7: Comparison of agreement rates for various metaphor evaluation tasks.
Note that Do Dinh et al. (2018) developed a real-valued scoring layer over an
existing corpus rather than evaluating generated outputs. “-” indicates
agreement is not reported.

Figure 3 tracks these evaluation metrics as more data is added to each
algorithm. The lexical evaluation relatively stable, peaking in most cases
between .1 and .2. The word2vec embeddings maintain their upward progression
even at maximal data: theoretically additional data could improve these
embeddings further. The structural evaluation shows something very different:
while word2vec and FastText embeddings improve as data is added, showing some
effects of model size, the Glove embeddings trend sharply negative at first
before proceeding beginning to improve.

##  Appendix B Appendix B

Agreement rates were measured using Krippendorff’s $\alpha$. For
metaphoricity, the mean score was .505, indicating moderate agreement.
However, given the difficulty of this task, we believe this to be relatively
stronger: see Table 7 for comparison to other work evaluating metaphor
generation.

For source domain annotation, annotators varied in the degree to which source
domains were evoked. Initial agreement was relatively poor (.249): we
performed a post-processing step, normalizing their results to a consistent
mean. This yields an agreement score of .387: which we deemed competitive for
the difficulty of the task. As we have no direct comparison for evaluation,
further work is required to refine this type of evaluation process.

##  Appendix C Appendix C

For retrieving commonsense symbolism of the sentences, we use the pre-trained
COMET model 999https://github.com/atcbosselut/comet-commonsense and retrieve
top 5 candidates for each input.

  1. 1.

No of Parameters: We use the BART large checkpoint (400M parameters) and use
the FAIRSEQ implementation Ott et al. (2019)
101010https://github.com/pytorch/fairseq/tree/master/examples/bart.

  2. 2.

No of Epochs: We fine-tune pre-trained BART for 25 epochs for CM-BART model
and save the best model based on validation perplexity.

  3. 3.

Training Time: Our training time is 60 minutes for CM-BART.

  4. 4.

Hardware Configuration: We use 4 RTX 2080 GPUs.

  5. 5.

Training Hyper parameters: We use the same parameters as the FAIRSEQ github
repository where BART was fine-tuned for the CNN-DM summarization task with
the exception of the size of each mini-batch, in terms of the number of
tokens, for which we used 1024.
111111https://github.com/pytorch/fairseq/blob/master/examples/roberta/README.glue.md

  6. 6.

Decoding Strategy & Hyper Parameters: For decoding we generate metaphors from
our models using a top-k random sampling scheme Fan et al. (2018). At each
timestep, the model generates the probability of each word in the vocabulary
being the likely next word. We randomly sample from the k = 5 most likely
candidates from this distribution.