# Laser-enhanced magnetism in SmFeO3

Mohsen Yarmohammadi<EMAIL_ADDRESS>Department of Physics,
The University of Texas at Dallas, Richardson, Texas 75080, USA  Marin Bukov
<EMAIL_ADDRESS>Max Planck Institute for the Physics of Complex Systems,
Nöthnitzer Str. 38, 01187 Dresden, Germany  Vadim Oganesyan
<EMAIL_ADDRESS>Physics program and Initiative for the
Theoretical Sciences, The Graduate Center, CUNY, New York, NY 10016, USA
Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue,
New York, NY 10010, USA  Department of Physics and Astronomy, College of
Staten Island, CUNY, Staten Island, NY 10314, USA  Michael H. Kolodrubetz
<EMAIL_ADDRESS>Department of Physics, The University of Texas at
Dallas, Richardson, Texas 75080, USA

###### Abstract

To coherently enhance inherent weak magnetic interactions in rare-earth
orthoferrite SmFeO3 as a functional material for spintronic applications, we
simulate the dissipative spin dynamics that are linearly and quadratically
coupled to laser-driven infrared-active phonons. When linear coupling
dominates, we discover a magnetophononic dynamical first-order phase
transition in the nonequilibrium steady state which can inhibit strong
enhancement of magnetic interactions. By contrast, when quadratic spin-phonon
coupling dominates, no phase transition exists at experimentally relevant
parameters. By utilizing a chirp protocol, the phase transition can be
engineered, enabling stronger magnetic interactions. We also discuss the route
for experimental observation of our results.

Introduction.—In recent years, the prospect of using spins as alternative
information carriers has led to the emerging field of spintronics, which
promises next-generation digital processing units that are fast, robust, and
energy efficient [1]. In solid materials exhibiting magnetic properties, the
electronic spins interact with lattice vibrations (phonons) opening up a
backaction channel, through electron orbital hybridization.

The famous magnetic material class whose role in spintronics is as significant
as silicon in electronics is the rare-earth orthoferrites (perovskite oxides)
RXO3, with magnetic rare-earth ion R and a magnetic ion X [2]. A primary
example is SmFeO3, where at low temperatures an unusual strong nonlinear spin-
phonon coupling (SPC) arises from the cross-talk between the two magnetic iron
and samarium ions [3], in contrast to most examples that deal only with one
magnetic lattice and linear SPC.

Even though the nonlinear SPC in SmFeO3 is strong, the magnetic exchange
interactions including Sm spins are weak [4]. Enhancing these interactions
will enhance the effects controlled by the unusual nonlinear SPC. This is
necessary to leverage their unusually large spin interactions for the design
of material properties from a scientific perspective, as they exhibit
intriguing features such as the measurable magnetoelectric effect [5, 6, 7, 8,
9], and for applications in industry, e.g., in solar cells and spintronics
[10, 11, 12].

A conventional way is to apply pressure [13] or magnetic field [14]. In
contrast to these static approaches, dynamic control techniques emerge as a
new frontier to induce and observe a broader array of novel phenomena that
only exist away from equilibrium [15, 16, 17]. Since spin motions in solids
typically have a timescale that coincides with the THz spectrum region,
detection and manipulation of spins by optical means is indispensable.

In this Letter, we propose a nonequilibrium magnetophononic mechanism to
manipulate inherent weak spin-spin interactions in SmFeO3 via laser-driven
infrared-active (IR-active) phonons that play the central role of a mediator
for dynamic control of spins. We first show that magnetic interactions are
enhanced in SmFeO3 for the on-resonance laser-phonon coupling regime. More
importantly, we discover a dynamical magnetophononic first-order phase
transition in SmFeO3 for the off-resonance laser-phonon coupling regime as a
more efficient way compared to the on-resonance one to further enhance
magnetism. We also discuss the origin of the transition from inherent non-
linearities in the mechanism as well as a feasible solution in the experiment
to observe these phenomena. Finally, we propose a linear chirp drive to
further enhance the magnetic response of the system.

Model.—We consider SmFeO3 at a very low temperature whose weak spin
interaction between Sm3+ and Fe2+ ions can be well-described by an anisotropic
antiferromagnetic (AFM) Heisenberg $S=5/2$ chain (XXZ model) [18, 3, 4, 19].
Vibrational modes are excited at an initial time by a THz continuous wave
laser that creates a coherent phonon field [20, 21, 22, 23] on every site
$\ell$, which couples both linearly and quadratically to the nearest isotropic
(in-plane) and anisotropic (easy-axis) spin interactions. Hence, the total
Hamiltonian that governs the dynamics comprises four terms

$\mathcal{H}=\mathcal{H}_{\rm s}+\mathcal{H}_{\rm ph}+\mathcal{H}_{\rm
sp}+\mathcal{H}_{\rm lp}\,,$ (1)

where $\mathcal{H}_{\rm
s}=\sum_{\langle\ell,j\rangle}\left(J\left[S^{x}_{\ell}S^{x}_{j}+S^{y}_{\ell}S^{y}_{j}\right]+J\Delta
S^{z}_{\ell}S^{z}_{j}\right)$ is the XXZ model with the spin operators
$S^{\alpha}$ for any flavor $\alpha=\\{x,y,z\\}$; $J\simeq 1.25$ meV describes
the in-plane isotropic exchange coupling, $\Delta>1$ describes the anisotropy
of the AFM interactions.

In the above Hamiltonian, $\mathcal{H}_{\rm
ph}=\omega_{0}\sum_{\ell}a^{\dagger}_{\ell}a_{\ell}$ characterizes a local
Einstein IR-active phonon mode with frequency $\omega_{0}$ described by the
boson creation operator $a^{\dagger}_{\ell}$. Unfortunately, no IR
experimental spectra are available for SmFeO3 to select a specific phonon
frequency. However, it has been found that most of the IR-active modes in
SmFeO3 are located far above the spin band [4]. Therefore, we choose
$\omega_{0}>2J\Delta$ in what follows: e.g., for $\Delta=1.2$ throughout the
paper, we set $\omega_{0}/J=2.5$.

Assuming the same symmetries as in the static spin Hamiltonian, there are two
possible contributions to the spin-phonon coupling part to locally couple
spins to the excited linear and quadratic lattice vibrations:
$\mathcal{H}_{\rm sp}^{\rm iso}=\sum_{\langle\ell,j\rangle}\big{[}g_{\rm
l}(a^{\dagger}_{\ell}+a_{\ell})+g_{\rm
q}(a^{\dagger}_{\ell}+a_{\ell})^{2}\big{]}\left[S^{x}_{\ell}S^{x}_{j}+S^{y}_{\ell}S^{y}_{j}\right]$
and $\mathcal{H}_{\rm sp}^{\rm aniso}=\sum_{\langle\ell,j\rangle}\big{[}g_{\rm
l}(a^{\dagger}_{\ell}+a_{\ell})+g_{\rm
q}(a^{\dagger}_{\ell}+a_{\ell})^{2}\big{]}\left[\Delta
S^{z}_{\ell}S^{z}_{j}\right]$; $g_{\rm l}$ ($g_{\rm q}$) is the linear
(quadratic) SPC strength. Since we have no microscopic values for the
different coupling strengths, we consider them separately to analyze their
individual effects. Both quadratic SPC and spin-spin interaction terms are
even under inversion symmetry. For a general geometry including a
perpendicular atomic motion to the bond, inversion symmetry also includes a
linear SPC to the spin-spin interaction.

Finally, the laser is linearly coupled to the phonon via $\mathcal{H}_{\rm
lp}=\sum_{\ell}\mathcal{E}(t)(a^{\dagger}_{\ell}+a_{\ell})$, where
$\mathcal{E}(t)=\mathcal{A}_{0}\cos(\omega\,t)$ describes the pump laser with
amplitude $\mathcal{A}_{0}$ and frequency $\omega$. Following the Lindemann
criterion [24] to avoid lattice melting, phonon occupation should not reach a
too large number. For this reason, we set $\mathcal{A}_{0}/J\ll 1$ in our
simulations.

To balance energy transfer and avoid heating effects related to driving and
coherence preservation, the entire system is coupled to a bath comprised of
other, undriven phonons. More details of the model, including the reciprocal-
space representation can be found in the Supplemental Material (SM) [25].

We employ the zeroth order expansion of the Holstein-Primakoff transformation
[26] within linear spin-wave theory to explore phononically driven magnons.
Since the population of excited magnons is low at low temperatures, we neglect
the magnon-magnon interaction. Due to the long wavelength of the pump field
compared to the lattice scale, we assume a local dispersionless phonon mode
($a^{\dagger}_{0}$) coupled to the laser. On the other hand, since the
expectation value of the phonon occupation is proportional to the number of
sites ($L=2501$ in our simulation), the relative quantum fluctuations,
proportional to $1/\sqrt{L}$, tend to zero in the thermodynamic limit
($L\to\infty$). We therefore employ a mean-field approximation [21] to
decouple the SPC term acting on the phonon and spin.

We simulate the time-evolution of physical observables of the model for both
the spin and phonon sectors, using the adjoint Lindblad quantum master
equation with phenomenological damping rates $\gamma_{\ell}=\gamma_{\rm
ph},\gamma_{\rm s}$ for an arbitrary observable $O(t)$:
$\langle\dot{O}\rangle(t)={}i\langle[\mathcal{H},O(t)]\rangle+\frac{1}{2}\sum_{\ell}\gamma_{\ell}\Big{<}\big{[}\mathcal{L}_{\ell}^{\dagger},O(t)\big{]}\mathcal{L}_{\ell}+\mathcal{L}_{\ell}^{\dagger}\big{[}O(t),\mathcal{L}_{\ell}\big{]}\Big{>}$,
where $\mathcal{L}_{\ell}=\\{a^{\dagger}_{0},a_{0}\\}$ and
$\\{\mathcal{B}^{\dagger}_{k},\mathcal{B}_{k}\\}$ are the phonon- and
Bogoliubov magnon-nonconserving time-independent Lindblad jump operators that
relax the system towards its ground state by employing
$\\{\mathcal{L}_{\ell}={}a^{\dagger}_{0}$ and
$a_{0}\mapsto\gamma_{\ell}=\gamma_{\rm ph}\,\mathcal{N}_{0}$ and $\gamma_{\rm
ph}[1+\mathcal{N}_{0}]$} and
$\\{\mathcal{L}_{\ell}={}\mathcal{B}^{\dagger}_{k}$ and
$\mathcal{B}_{k}\mapsto\gamma_{\ell}=\gamma_{\rm e}\,\mathcal{N}_{k}$ and
$\gamma_{\rm e}[1+\mathcal{N}_{k}]\\}$, where $\mathcal{N}_{0}$ and
$\mathcal{N}_{k}$ is the average number of phonon and magnon with energy
$\omega_{0}$ and $\varepsilon_{k}={}2J\sqrt{\Delta^{2}-\cos^{2}k}$,
respectively. Given the weakness of spin damping compared to direct phonon
decay, we set $\gamma_{\rm s}<\gamma_{\rm ph}$. Moreover, due to the weak
coupling of a single optical phonon to the ensemble of phonons (bath), we set
$0.01<\gamma_{\rm ph}/\omega_{0}<0.05$. Last, to treat the properties of
nonequilibrium steady states (NESS), we take the average of the late-time
signals over one period $T_{p}$ via
$\overline{O}=T_{p}^{-1}\int^{t+T_{p}}_{t}O(t)\mathrm{d}t$.

Figure 1: Laser manipulation of magnetism in SmFeO3 at low temperatures.
[(a),(b)] Laser amplitude dependency of the temporal isotropic ($J$) and
anisotropic ($\Delta$) magnetic interactions with dominant quadratic SPC
$g_{\rm q}/g_{\rm l}=5$. Time averaging in the NESS gives interactions as a
function of laser amplitude [(c), with $g_{\rm q}/g_{\rm l}=5$] and SPC [(d),
with $\mathcal{A}_{0}/\gamma_{\rm ph}=0.2$]. The inherent spin feedback effect
in the magnetophononic mechanism leads to a saturated spin response to the
laser field in the strong coupling regime, while a nonlinear (linear)
modulation of isotropic (anisotropic) response to the SPCs appears due to
different matrix elements of spin excitations, see Eq. (4). Here,
$\omega=\omega_{0}=2.5J$, $\Delta=1.2$, $\gamma_{\rm ph}/\omega_{0}=0.05$, and
$\gamma_{\rm s}/J=0.01$.  Figure 2: Dynamical magnetophononic first-order
phase transition. (a) Isotropic magnetic interaction as a function of drive
frequency for various linear SPCs at $g_{\rm q}/J=0.0$; at large $g_{\rm l}$,
the appearance of the cusp signals the first-order phase transition. (b)
Effective force in the NESS acting on the driven-dressed-damped phonon at
$g_{\rm l}/J=0.5$ and $g_{\rm q}/J=0.0$ expanding magnons around the dominant
$k=0$ mode, characterized by the first harmonic of phonon displacement
$q_{1}$, to confirm the first-order phase transition at $\omega_{\rm c}$. (c)
The same as (a) but vs. quadratic SPCs at $g_{\rm l}/J=0.0$ showing weak
shifts of the phonon resonance leading to the absence of a phase transition.
Here, $\omega_{0}=2.5J$, $\Delta=1.2$, $\mathcal{A}_{0}/\gamma_{\rm ph}=0.1$,
$\gamma_{\rm ph}/\omega_{0}=0.05$, and $\gamma_{\rm s}/J=0.01$.

Results.—Excitation of the IR-active phonons directly by the laser leads to a
modulation of both magnetic coupling constants $J$ and $\Delta$, given by

$\displaystyle\tilde{J}(t)/J={}$ $\displaystyle 1+g_{\rm l}q_{\rm ph,{\rm
iso}}(t)+g_{\rm q}q^{2}_{\rm ph,{\rm iso}}(t)\,,$ (2a)
$\displaystyle\tilde{\Delta}(t)/\Delta={}$ $\displaystyle 1+g_{\rm l}q_{\rm
ph,{\rm aniso}}(t)+g_{\rm q}q^{2}_{\rm ph,{\rm aniso}}(t)\,,$ (2b)

where $q_{\rm ph}(t)=\langle L^{-1/2}(a^{\dagger}_{0}+a_{0})\rangle(t)$
describes the coherent lattice displacement (oscillation) of the zero-momentum
phonon mode [25]. After solving the tightly coupled equations of motion
between subsectors, as a result, magnons acquire dynamics via laser-driven
phonons such that the properties of the spin band can be dynamically
engineered. In Eq. (2), the superscript “iso” (“aniso”) indicates that data is
taken with SPC given by $\mathcal{H}_{\rm sp}^{\rm iso}$ ($\mathcal{H}_{\rm
sp}^{\rm aniso}$). Note that, since isotropic SPC gives strong modification of
$J$ while anisotropic SPC gives strong modification of only $\Delta$, all data
for $\tilde{J}(t)$ ($\tilde{\Delta}(t)$) is taken using only $\mathcal{H}_{\rm
sp}^{\rm iso}$ ($\mathcal{H}_{\rm sp}^{\rm aniso}$) throughout this paper.

Figure 1 demonstrates the modulation of $J$ and $\Delta$ in the course of the
time evolution on short (left part of panels a and b) to long (right part of
panels a and b) timescales, as the system approaches its long-time steady
state at $t\simeq 100$ ps. We first consider the on-resonance laser-phonon
coupling (LPC) regime at $\omega=\omega_{0}$. Under the laser field, both
exchange interactions reach a NESS, associated with coherent oscillations of
about 5% above the bare interaction strengths, as shown in Figs. 1(a,b).
Coupling between spins and phonons already appears in the transient (early-
time) dynamics. The amplitude of oscillations increases with the laser
amplitude in both interactions; the phase of oscillations in isotropic and
anisotropic interactions slightly shifts to the right and left, respectively,
due to a negative sign difference in the matrix elements of the SPC part, see
Eq. (4). The change in the occupation of phonons and then magnons (following
the modulated interactions) with the SPC is a direct consequence of
hybridization effects.

Energy naturally flows from the laser to the spin system until a steady state
is reached, modifying the effective exchange interactions. Since the laser
fluence is proportional to $\mathcal{A}_{0}^{2}$, we would expect $J$ and
$\Delta$ to scale as $\mathcal{A}_{0}^{2}$ too. Such a response is satisfied
up to $\mathcal{A}_{0}/\gamma_{\rm ph}=0.1$ and $0.2$, respectively, for $J$
and $\Delta$, but is saturated at stronger laser fields, as shown in Fig.
1(c). This can be understood from an inherent spin feedback effect in the
strong coupling regime, where spin excitations shift the phonon resonance and
inhibit further excitations.

A key point visible in the data is that quadratic SPC is significantly more
effective at modifying magnetic interactions, both isotropic ($J$) and
anisotropic ($\Delta$) when the phonon is driven resonantly, as shown in Fig.
1(d). This is partially due to linear SPC having a stronger effect on the
phonon resonance frequency, as we will see, suggesting that perhaps we can
modify interactions more strongly by driving off-resonance.

It is common to pump the system at variable driving frequencies $\omega$ in
most ultrafast experiments. As we now show, that does not occur without
challenges, and in fact, can lead to a dynamical phase transition in the NESS.
We fix the phonon above the spin-band at $\omega_{0}/J=2.5$ and scan the laser
frequency to probe mutual dressing effects. For $g_{\rm q}=0$, the laser
electric field acting on the phonon rapidly becomes dressed with the feedback
from the spin,

$\widetilde{\mathcal{E}}(t)={}\mathcal{E}(t)+\frac{g_{\rm
l}}{L}\sum_{k}\big{[}\mathcal{R}_{k}n_{{\rm s},k}(t)+\mathcal{S}_{k}x_{{\rm
s},k}(t)\big{]}\,,$ (3)

where $n_{{\rm s},k}(t)$ is the magnon density, $x_{{\rm s},k}$ is the magnon
pair creation observable, and

$\displaystyle\mathcal{R}^{\rm iso}_{k}={}$
$\displaystyle-4J\cos^{2}k/\varepsilon_{k}\,\,,\,\,\mathcal{R}^{\rm
aniso}_{k}={}4J\Delta^{2}/\varepsilon_{k}\,,$ (4a)
$\displaystyle\mathcal{S}^{\rm iso}_{k}={}$ $\displaystyle 2J\Delta\cos
k/\varepsilon_{k}\,\,,\,\,\mathcal{S}^{\rm aniso}_{k}={}-2J\Delta\cos
k/\varepsilon_{k}\,,$ (4b)

are the matrix elements for the spin excitations. This implies that the
interplay between phonon and laser reflects the tendency of laser energy to
flow to the magnons; as a result, the resonance peak at $\omega=\omega_{0}$ is
shifted to lower frequencies due to the nonequilibrium magnon occupation, Fig.
2(a).

At strong linear SPCs, we observe a rapid jump of isotropic magnetic
interaction $J$ at a critical drive frequency $\omega_{\rm c}$ – doubling the
size of its strength compared to on-resonance modulation – accompanied by the
creation of 2% magnon density per site (see Sec. S3 of the SM). Such a jump
corresponds to a dynamical first-order phase transition, similar to one that
some of us found in previous work on a driven fermion chain coupled
quadratically to lattice vibrations [22]. In contrast to the dissipation-
induced nonlinearity found in the fermion chain, there is a direct
nonlinearity in the mean-field Hamiltonian, which leads to the phase
transition in a model with only linear SPC. Therefore, unlike for the fermion
chain, the mechanism that drives the phase transition reported here is
inherent to the spin system, and the drive only serves as a trigger. The peak
near $\omega/J\simeq 2.65$ is the fingerprint of the lower two-magnon band
edge.

Next, we strive to understand the mechanism behind the appearance of the phase
transition in the NESS, by evaluating the dominant harmonic of the driven-
dressed-damped phonon. We derive an effective theoretical picture for the
dynamics by approximating the magnons with their single, dominant, zero-
momentum ($k=0$) mode. To this end, we proceed with the Fourier decomposition
of phonon displacement in the NESS, $q_{\rm ph}(t)=\overline{q_{\rm
ph}}+\sum_{n\neq 0}q_{n}e^{in\omega t}$, where $q_{1}$ is the dominant first
harmonic. This leads to the following cubic equation

$\mathcal{F}=aq^{3}_{1}+bq^{2}_{1}+cq_{1}+d=0\,,$ (5)

where the hybridized driving, coupling and damping processes are described by:

$\displaystyle a$ $\displaystyle=$ $\displaystyle 4g^{2}_{\rm
l}\mathcal{S}^{2}_{k=0}[\gamma_{\rm
s}(\omega^{2}-\omega^{2}_{0}-{}^{\gamma^{2}_{\rm ph}}\\!/_{4})+\gamma_{\rm
ph}\omega^{2}],$ $\displaystyle b$ $\displaystyle=$
$\displaystyle-4\mathcal{A}_{0}\omega_{0}\gamma_{\rm s}g^{2}_{\rm
l}\mathcal{S}^{2}_{k=0},$ $\displaystyle c$ $\displaystyle=$
$\displaystyle\gamma_{\rm s}[\omega^{2}-\omega^{2}_{0}-{}^{\gamma^{2}_{\rm
ph}}\\!/_{4}][\omega^{2}-4\varepsilon^{2}_{k=0}-\gamma^{2}_{\rm s}]$
$\displaystyle+\gamma_{\rm ph}\gamma^{2}_{\rm s}\omega^{2}-4\gamma_{\rm
s}g^{2}_{\rm l}\mathcal{S}^{2}_{k=0}\omega_{0}\varepsilon_{k=0},$
$\displaystyle d$ $\displaystyle=$
$\displaystyle-\mathcal{A}_{0}\omega_{0}\gamma_{\rm
s}[\omega^{2}-4\varepsilon^{2}_{k=0}-\gamma^{2}_{\rm s}].$

Equation (5) behaves like an effective force acting on the phonon in the
driven-coupled-damped regime of the system. Thus, to sharply characterize the
phase transition, we track the solution of this equation preceding that
$\omega_{\rm c}$. Vanishing the effective force solutions at $\omega_{\rm c}$
is evidence for the phase transition, see Fig. 2(b). Not only does the
effective force theory produce the origin of the transition, but it also
provides an overall quantitative proxy for the exact $\omega_{\rm c}$.

It is important to note that near the first-order phase transition, we find a
fast initial growth of dynamics of observables for $t\lessapprox 1$ ns due to
enhanced magnon density and phonon occupation through linear SPC, see Sec. S3
of the SM. This remarkable behavior implies that an effective hybridized state
forms on transient timescales to anticipate the phase transition. The same
analysis, applied to the coupling of the phonon to the anisotropic magnetic
interaction, appears with a dynamical profile somewhat similar (albeit of
opposite sign for the presence of quadratic SPC) to the isotropic one.

Turning to the dynamical features of the system in the presence of quadratic
SPC, in Fig. 2(c) we scan the system’s response to the drive frequency at
$g_{\rm l}=0$. In contrast to the linear SPC, the drive pushes the system into
a simple NESS with $g_{\rm q}$. Importantly, no phase transition occurs in
this case, at least within the small to intermediate $g_{\rm q}$ regime. This
weak dynamical response of the nonlinearly coupled spin-phonon system implies
the existence of a quasi-decoupled phase in the system, which differs
significantly from the nonanalytic response of the quadratic electron-phonon
coupling in driven materials [22, 27, 28]. Thus, dominant quadratic SPC in
SmFeO3 should allow for the manipulation of the spin band in the on-resonance
LPC regime while avoiding the phase transition in the off-resonance LPC
regime. This, in turn, inhibits spin band engineering for cases where linear
SPC dominates. Still, the presence of both linear and quadratic SPCs does not
inhibit the appearance of the first-order phase transition.

Figure 3: Chirp protocol for tuning enhancement of magnetism and first-order
phase transition in SmFeO3. Linearly chirped isotropic magnetic interaction
with $\mathcal{E}(t)$ from Eq. (6) for {$\omega_{1}/J=2.3$, $\tau_{1}=500$ ps}
and {$\omega_{2}/J=2$, $\tau_{2}=5000$ ps}. Using this chirp allows one to
nearly double the size of $\tilde{J}$ compared to the unchirped case before a
second transition occurs at $\omega/J=2.1$. Here, $\omega_{0}=2.5J$,
$\Delta=1.2$, $\mathcal{A}_{0}/\gamma_{\rm ph}=0.1$, $g_{\rm q}/J=0$, $g_{\rm
l}/J=0.5$, $\gamma_{\rm ph}/\omega_{0}=0.05$, and $\gamma_{\rm s}/J=0.01$.

Having uncovered the phase transition physics in our model, we now ask whether
it can be used to engineer the size of the interaction strength. Inspired by
our recent work on electronic materials [22], we consider a linear chirp
protocol given by

$\mathcal{E}^{\rm
chirp}(t)=\mathcal{A}_{0}\cos(\omega_{1}\,t+\left[\frac{(\omega_{2}-\omega_{1})(t-\tau_{1})}{\tau_{2}-\tau_{1}}\right]t)\,,$
(6)

where $\omega_{1}/J=2.3$, $\tau_{1}=500$ ps, $\omega_{2}/J=2$, and
$\tau_{2}=5000$ ps. In this protocol, we slowly ramp the laser frequency down
from $\omega_{1}$ to $\omega_{2}$ by passing through the original phase
transition point; in doing so, stronger magnetic interactions (nearly twice
the enhancement compared to non-chirped interactions) can be generated through
a hysteresis loop of adiabatic NESSs, as shown in Fig. 3. Accordingly, it is
also accompanied by another first-order phase transition at $\omega/J=2.1$.

Experiment.—Continuous driving unavoidably leads to heating of the sample, and
remediation of thermal effects is necessary [21, 22]. To provide a measurable
quantity in the experiment, we roughly estimate the timescale for reaching the
NESS and phase transition. To this end, we focus on the dumped power, i.e.,
the part of input laser power that flows directly from the driven phonon to
the bath, given by $\mathcal{P}_{\rm du}(t)=wa\rho\,\omega_{0}\gamma_{\rm
ph}n_{\rm ph}(t)$. In doing so, we choose SmFeO3 sample with a thickness
$w=20$ nm, area $a=2$ mm2, and molar density $\rho\simeq 0.028$ mol.cm-3 [29].
We assume that the sample is in touch with a metal block (heat sink) to take
up the thermal energy; the sink should be at a low-temperature $T\simeq 2-5$ K
with a mass $m_{\rm b}\simeq 2-5$ g and specific heat $C(T)\simeq 1-3\,\times
10^{-4}\,T\,$JK-2g-1 such that overheating of the block at the phase
transition point with $\overline{n_{\rm ph}}^{\rm iso}\simeq 0.01$, occurs at:

$\,t^{\rm heat}=\frac{m_{\rm
b}\int_{0}^{T}C(T)\,d\,T}{\overline{\mathcal{P}_{\rm du}}^{\rm iso}}\simeq
50\,{\rm ns},$ (7)

for the isotropic scenario. This timescale to reach the NESS is much larger
than the obtained ps timescale in our simulation. Thus, the computed long-time
behavior is readily observable if we have such a heat sink to dampen thermal
effects. This, in turn, means that the uncovered phase transition can be
experimentally accessible under these conditions.

Conclusions.—In contrast to studies that have relied on equilibrium treatments
and static approaches to tune the magnetic responses of a system, we propose
the dynamical magnetophononic mechanism – modulation of magnetism through
phonon – beyond equilibrium. The rare-earth orthoferrite SmFeO3, as a
functional material in both science and industry, yields potentially unknown
features due to its multiple magnetic orderings associated with an unusual
nonlinear spin-phonon coupling, however, its inherent magnetic exchange
couplings are weak for spintronic applications. For the dynamic control of the
magnetic response of SmFeO3, we apply a continuous laser field. We consider
dissipation effects when pumping energy into the system to achieve
nonequilibrium steady states at long times. For the on-resonance drive of the
phonon, inherently weak Sm-Fe magnetic interactions are enhanced (manipulation
of the magnonic band), which is relevant for spintronic applications.

In connection to experimental setups; we scan the system’s responses to the
pump field when the laser and phonon are chosen to be in the off-resonance
regime, which unveils an intriguing phenomenon out of equilibrium, referred to
as dynamical magnetophononic first-order phase transition. In contrast to the
electron-phonon coupled chains [27, 28, 22] in which the quadratic model
reacts more strongly to a pump than the linear model, linear spin-phonon
coupling is sufficient to observe this phenomenon and is, indeed, more
effective than quadratic coupling in enabling phase transitions and
engineering magnetic interactions. We finally propose a chirp drive protocol
to engineer both the first-order phase transition and the enhancement rate of
magnetism.

## Acknowledgments

This work was performed with support from the National Science Foundation
(NSF) through award numbers MPS-2228725 and DMR-1945529 and the Welch
Foundation through award number AT-2036-20200401 (MK and MY). Part of this
work was performed at the Aspen Center for Physics, which is supported by NSF
grant No. PHY-1607611, and at the Kavli Institute for Theoretical Physics,
which is supported by NSF grant No. NSF PHY-1748958. This project was funded
by The University of Texas at Dallas Office of Research and Innovation through
the SPIRe program.

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# Mining Large-Scale Low-Resource Pronunciation Data From Wikipedia

Tania Chakraborty, Manasa Prasad, Theresa Breiner, Sandy Ritchie, Daan van
Esch
Google Research
{taniarini, pbmanasa, tbreiner, sandyritchie<EMAIL_ADDRESS>
(June 2020)

###### Abstract

Pronunciation modeling is a key task for building speech technology in new
languages, and while solid grapheme-to-phoneme (G2P) mapping systems exist,
language coverage can stand to be improved. The information needed to build
G2P models for many more languages can easily be found on Wikipedia, but
unfortunately, it is stored in disparate formats. We report on a system we
built to mine a pronunciation data set in 819 languages from loosely
structured tables within Wikipedia. The data includes phoneme inventories, and
for 63 low-resource languages, also includes the grapheme-to-phoneme (G2P)
mapping. 54 of these languages do not have easily findable G2P mappings online
otherwise. We turned the information from Wikipedia into a structured,
machine-readable TSV format, and make the resulting data set publicly
available so it can be improved further and used in a variety of applications
involving low-resource languages.

##  1 Introduction

There are thousands of languages spoken around the world, and many efforts to
learn about them and document them. However, information about low-resource
languages is not always easy to find, or leveraged to its full potential.
Wikipedia is a useful resource for language-specific information, with a
community of native speakers and linguistic experts who continue to improve
coverage and quality111See the LingWiki effort:
https://en.wikipedia.org/wiki/Wikipedia:GLAM/SOAS/Lingwiki. While Wikipedia is
often used to build monolingual or parallel text corpora [Prasad et al., 2018,
Rahma et al., 2018], its articles on specific languages contain useful
information that is not frequently extracted.

In this paper we describe how we extracted pronunciation information from
these Wikipedia pages for hundreds of languages, some of which are not
represented in other sources, which can be used in technologies for low-
resource languages. The data was mined from tables containing information such
as phonemes, associated graphemes, and sample words in each language. While
the tables are understandable to the human eye, it is nontrivial to
automatically parse and generate standardized TSV files from them. We publish
our mined data and encourage others to leverage and improve this source.

##  2 Uses for Pronunciation Data

While large-scale pronunciation data can be useful in many linguistic
pursuits, grapheme-to-phoneme (G2P) mappings are also a building block for
automatic language processing systems. Tools to generate pronunciations from
input words [Mortensen et al., 2018, Novak et al., 2016] typically support a
specific set of languages but can often be extended using G2P rules for new
languages. G2P data can also be used in cross-lingual transfer learning, e.g.
in named entity recognition [Bharadwaj et al., 2016].

G2P mappings are also required in typical automatic speech recognition (ASR)
and text-to-speech (TTS) systems. While these systems usually train on paired
audio and transcription data, several recent areas of research leverage G2P
mappings to overcome this requirement. If there is a G2P mapping and some text
available in a low-resource language, an ASR system can be built by
repurposing an acoustic model from a similar higher-resource language [Prasad
et al., 2019]. G2P mappings can even be bootstrapped for new languages using
only the language’s phoneme inventory combined with higher-resource language
text written in the same script [Bleyan et al., 2019], making even simple
phoneme data a more useful tool for scaling technologies to new languages.

##  3 Similar Resources

One similar resource in this space is PHOIBLE [Moran et al., 2014], a database
listing the phonemes of over 2,100 languages, their possible allophones, and
how common each phoneme is in the language, but not any G2P information.
Wikimedia’s Wiktionary and
Incubator222https://meta.wikimedia.org/wiki/Wiktionary#List_of_Wiktionaries
are open-content dictionaries written in about 500 languages, and can be used
to automatically extract phoneme and pronunciation information [Schlippe et
al., 2010, Lee et al., 2020]. Deri and Knight [Deri and Knight, 2016] as well
as Peters et al. [Peters et al., 2017] have been able to adapt this data even
to build G2P models for new languages that do not appear in the mined data.

Deri and Knight also published the G2P mappings that they mined from Wikipedia
IPA Help
tables333https://en.wikipedia.org/wiki/Category:International_Phonetic_Alphabet_help
for 98 languages. Our data set, which includes phoneme inventories for over
800 languages, offers G2P data in 63 low-resource languages, 54 of which are
not covered by Deri and Knight. There is also more potential G2P information
stored for an additional 224 languages, as we detail in section 4.3. We hope
that this additional data set will be a useful supplement to the existing
resources.

##  4 Mining Pronunciation Data from Wikipedia

The English Wikipedia contains hundreds of articles about specific
languages444https://en.wikipedia.org/wiki/Index_of_language_articles, often
including details on the phonology and writing systems, and covers languages
that are not represented in other data sources. We wanted to aggregate this
data into an easily comparable and processable data set to make it more widely
usable for the research that we described in section 2.

###  4.1 Extracting the Wikipedia Pages

Wikipedia’s category structure enabled us to target relevant pages inter-
linked from the category pages for Languages by
Country555http://en.wikipedia.org/wiki/Category:Languages_by_country and
Language
Phonologies666http://en.wikipedia.org/wiki/Category:Language_phonologies. We
also checked for other potential language pages by leveraging the Wikipedia
search query for ISO639 codes777https://iso639-3.sil.org/; for example, the
page on Amarasi (ISO 639 code ‘aaz’) can be found at
https://en.wikipedia.org/wiki/ISO_639:aaz. Using tooling similar to
wikitable2csv888https://github.com/gambolputty/wikitable2csv, we extracted the
table data embedded in each targeted page.

###  4.2 Parsing the Tables

From the tables on each language’s page, we wanted to parse: a) the phoneme
inventory of the language b) the pronunciation features of the phonemes,
including voicing, place/manner of articulation, and other phonetic features,
useful for clarity and in case of nonstandard transcriptions c) grapheme to
phoneme mappings d) words in the native script and e) the phonemic
transcriptions of the words.

While some or all of this data is present in most of the language pages,
different pages format their tables in different ways, which makes data
extraction and processing tricky. We aim to cover as many edge cases as
possible and successfully parse a majority of the table formats. Some
especially odd cases and ones that we left unaddressed can be found in section
4.3.

We mainly saw two different ways that data in a table are presented, which we
will call Type A and Type B. Type A has one set of headers, where the contents
are related to each other horizontally (or vertically if headers are on the
side). For example, Figure 1(a)999Screenshots of pages accessed on June 24,
2020: https://en.wikipedia.org/wiki/Amarasi_language and
https://en.wikipedia.org/wiki/Alekano_language is a Type A table where the
data in the column titled “Amarasi Alphabet” are graphemes, and the data in
the column titled IPA are the corresponding phonemes. Type B has two sets of
headers, in which case the data between columns is not related, but rather
classified in a similar way. For example, in Figure 1(b), the phonemes in the
columns are not related to each other; the data in each cell is classified by
two or more pronunciation features, namely place of articulation (column
headers) and manner of articulation/voicing (row headers).

(a) Amarasi (iso:aaz) grapheme-phoneme table

(b) Alekano (iso:gah) consonant phoneme table

Figure 1: Example Wikipedia tables with relatively simple formats.

Since there is no obvious indicator of a table’s type from its representation,
we have to automatically determine how to parse the data by observing the
structure of the table; i.e., how many headers the table has, if the table has
both column and row headers, etc. We determine that a given row or column is a
header if it has consecutive ‘header’ type cells, which are annotated with a
‘!’ symbol101010According to the Wikipedia Table Help page:
https://en.wikipedia.org/wiki/Help:Table. We treat tables with headers only on
the top or the side as Type A, while tables with both are Type B.

Category | Targeted Keywords
---|---
Grapheme | letter, grapheme, alphabet, written
Phoneme | IPA, pronunciation
Pronunciation Feature | description, vowel/consonant [found in table caption rather than header]
Example word | example, word
Transcription | transcription
Unclassified | [any unmatchable data]
Table 1: Keywords in table headers that helped us determine the category of
data in the table.

The data extracted from the tables is classified into one of the categories
listed in Table 1. The correct category for each data item is based on the
type of the table and the text in the header corresponding to the item’s
column. For Type A tables, a regular expression is used to determine the
category, based on keywords as you can see in Table 1. If the header text
contains any variation of the keywords we are searching for, we can classify
that data into the matching category.

For Type B tables, the data is classified as a pronunciation feature, with the
cell value representing the associated phoneme and the actual pronunciation
features extracted from the row and column headers.

###  4.3 Challenges

As we described in Section 4, the primary challenge in mining the data was the
variety of the table structures. We tried to account for the most common types
of tables, including the simpler Type A and Type B tables described above, as
well as tables with repeated headers, as seen in Figure 2111111Screenshot of
page accessed on June 24, 2020: https://en.wikipedia.org/wiki/Wakhi_language.
If repetition is not accounted for, the contents of an entire column would be
incorrectly associated with each other. Instead, we need to associate only two
adjacent rows with each other as we parse the table. The same principle
applies to tables that have a repetitions every N rows or every N columns for
any value of N. Some more table examples can be found in Appendix A.

Figure 2: Wakhi (iso:wbl) data table with repeated headers across rows

Another challenge is that the keywords in Table 1 may be insufficient to
classify data correctly for all cases. For example, if a table uses the name
of the language as the header for the graphemes in a G2P table instead of a
more generic keyword, we will not parse the data correctly. As we developed
the parser, we added in new keywords to cover more cases, but do not cover all
edge cases. When we find a table whose header is not a keyword, we store the
data item and its associated header together in the Unclassified category
rather than discarding it. Some examples can be found in Appendix A.

If a keyword is used in a way we do not expect, or if there is a very
intricate table format, there can be other problems. Some tables list multiple
data within a cell, and it is not clear what the relationship is in order to
split the data or classify it correctly. Some examples of these tables can be
found in Appendix B. Our dataset may include some of this noise, although we
hope that in most cases, tables that confused our system would store the data
in the Unclassified category to at least be human readable.

##  5 Our Data Set

We found phoneme data for 819 languages, and G2P mappings for 63 languages. 54
of these do not appear in Deri and Knight’s G2P data for 98 languages mined
from the Wikipedia IPA Help Tables
121212https://drive.google.com/drive/u/1/folders/0B7R_gATfZJ2aWkpSWHpXUklWUmM
[Deri and Knight, 2016]. An additional 224 languages had some data we could
only parse as Unclassified, but further analysis hints that 72 of them may
contain G2P information. Since the Wikipedia pages for higher-resource
languages do not often contain G2P tables (but tend to focus on grammar or
history), our data set does not include G2P for these languages, which are
more likely covered by Deri and Knight, and instead represents more low-
resource languages.

We publish our data 131313https://github.com/google/language-
resources/tree/master/mined-wiki-phoneme-tables in TSV format, where the
columns correspond to: grapheme, phoneme, pronunciation features, example
word, IPA transcription of the example word, and Unclassified data. Phonemes
can appear in more than one row if, for example, they are mapped to more than
one grapheme or example word. If a field is empty, it is filled in with
‘(n/a)’. See Figure 3 for an example excerpt, with more examples available in
the appendix. We also include a txt with all Wikipedia links that were used.

Figure 3: Excerpt of Amarasi (iso:aaz) TSV data file, containing g2p mappings

##  6 Conclusion

We mined a data set covering 819 languages’ phonemes, including 63 languages’
grapheme-to-phoneme mappings, 54 of which are low-resource languages that do
not have easily findable G2P mappings in other available sources. This
information is available on Wikipedia, but inconsistencies with how it is
formatted make it quite challenging to use in extending language technology.
While our extraction system might be improved to handle more edge cases in
future work, it may in fact be even more fruitful to collaborate with relevant
Wikipedia editors to standardize their contributions to make the data more
machine-readable. At any rate, we hope this work helps the research community
continue to scale research and technologies to more and more languages.

##  Appendix A Additional Examples of Table Formats We Handle

This appendix gives some further examples of table formats that are nontrivial
to parse in order to associate and classify the data correctly.

Figure 4: Ocaina (iso:oca) data table with repeated headers across columns

In Figure 4 141414Screenshot of page accessed on June 24, 2020:
https://en.wikipedia.org/wiki/Ocaina_language, we see that tables may have not
only repeated row headers (as seen in Figure 2) but may have repeated column
headers. We handle this case.

Figure 5: Albanian (iso:sq) data table with multiple layers of headers

In Figure 5 151515Screenshot of page accessed on June 24, 2020:
https://en.wikipedia.org/wiki/Albanian_language every element must be
connected with multiple columns and rows of headers to ensure that we do not
miss any information. We handle this case.

(a) Adyghe (iso:ady) data table with multiple orthographies

(b) Adyghe (iso:ady) extracted data example

Figure 6: Adyghe Language extraction example

Figure 6(a) 161616Screenshot of page accessed on June 24, 2020:
https://en.wikipedia.org/wiki/Adyghe_language combines the G2P mappings for
two scripts used by the language, with headers that are too specific compared
to our keywords for the correct category (grapheme). We handle this case by
storing the data and its associated header in the Unclassified category, which
is labeled as “Best Guess” in Figure 6(b), and allows the user to see some
more information for the language that wasn’t straightforward to parse
automatically.

##  Appendix B Additional Examples of Table Formats We Don’t Handle Well

(a) E (iso:eee) data table where keyword is
used unexpectedly

(b) Madurese (iso:mad) data table with multiple items per cell

In Figure 7(a) 171717Screenshot of page accessed on June 25, 2020:
https://en.wikipedia.org/wiki/E_language, a table has a header containing one
of the keywords, “letter”, but not in the way that we generally expect, which
would be in a table that shows G2P. We do not handle this case and this data
is parsed into the data set mistakenly.

In Figure 7(b) 181818Screenshot of page accessed on June 24, 2020:
https://en.wikipedia.org/wiki/Madurese_language, there are multiple data items
within each cell, and there is no clear way to understand automatically how to
split up or classify these items. We do not handle this case.

##  Appendix C Additional Example Excerpts from TSV Data Files

Figure 8 is an snippet from the oca.tsv file, and shows how G2P mappings could
be captured in the Unclassified column. Figure 9 is another example of the
type of data that could be captured by the Unclassified column. This language
did not have corresponding phonemes in the table, instead it had words from
the language and their English meaning.

Figure 8: Ocaina (iso:oca) tsv format Figure 9: Krio (iso:kri) tsv format

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