Origin of negative electrocaloric eect in Pnma -type antiferroelectric perovskites Ningbo Fan1 2Jorge I niguez3 4L. Bellaiche5and Bin Xu1 2 1Institute of Theoretical and Applied Physics Soochow University Suzhou 215006 China

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Origin of negative electrocaloric eﬀect in Pnma -type antiferroelectric perovskites

Ningbo Fan,1, 2 Jorge ´

I˜niguez,3, 4 L. Bellaiche,5and Bin Xu1, 2, ∗

1Institute of Theoretical and Applied Physics, Soochow University, Suzhou 215006, China

2School of Physical Science and Technology, Soochow University, Suzhou 215006, China

3Materials Research and Technology Department,

Luxembourg Institute of Science and Technology (LIST),

Avenue des Hauts-Fourneaux 5, L-4362 Esch/Alzette, Luxembourg

4Department of Physics and Materials Science, University of Luxembourg, Rue du Brill 41, L-4422 Belvaux, Luxembourg

5Physics Department and Institute for Nanoscience and Engineering,

University of Arkansas, Fayetteville, Arkansas 72701, USA

(Dated: October 11, 2022)

Anomalous electrocaloric eﬀect (ECE) with decreasing temperature upon application of an electric

ﬁeld is known to occur in antiferroelectrics (AFEs), and previous understanding refers to the ﬁeld-

induced canting of electric dipoles if there is no phase transitions. Here, we use a ﬁrst-principle-

based method to study the ECE in Nd-substituted BiFeO3(BNFO) perovskite solid solutions, which

has the Pnma-type AFE ground state. We demonstrate another scenario to achieve and explain

anomalous ECE, emphasizing that explicit consideration of octahedral tiltings is indispensable for

a correct understanding. This mechanism may be general for AFEs for which the antipolar mode is

not the primary order parameter. We also ﬁnd that the negative ECE can reach a large magnitude

in BNFO.

Electrocaloric eﬀect (ECE) can make temperature

change via adiabatic application (or removal) of an elec-

tric ﬁeld, providing an eﬃcient approach for cooling or

heating [1–3]. While ferroelectric (FE) or relaxor mate-

rials typically have “normal” positive sign of ECE, i.e.,

the temperature increases by applying a voltage, antifer-

roelectrics (AFEs) are known to have anomalous ECE

that can yield an opposite sign [4–6] . These two types

of ECE can be utilized in combination to improve the

performance of cooling/heating devices.

Such negative (or inverse) caloric eﬀect is also known

to occur in other occasions, e.g., magnetic Heusler alloys,

transitions between FE phases of diﬀerent polarization

directions, and application of an electric ﬁeld against the

polarization of a FE phase without switching [7–9]; how-

ever, its origin in AFEs is less well understood. AFEs

materials are characterized by anti-polar atomic distor-

tions that can be switched to a FE state under an electric

ﬁeld, and two mechanisms to explain their negative ECE

with no AFE-FE transition have been proposed: 1) the

“dipole-canting” model that dipolar entropy increases by

misaligning the anti-parallel dipoles upon application of

the ﬁeld [5]; 2) the perturbative theory based on the

Maxwell relation that only temperature and electric ﬁeld

dependencies of polarization need to be considered [10].

Interestingly, all these mechanisms only take the electric

degrees of freedom explicitly into account. In contrast,

most of the known AFEs are neither proper type (that

is, the AFE phase is rarely driven by an AFE soft mode

[11]), nor systems with the anti-polar mode being the

only signiﬁcant order parameter. In fact, quite often, the

AFE mode is secondary and coupled to other degrees of

freedom, such as the octahedral tiltings in perovskites.

For instance, PZO has a strong instability of anti-phase

octahedral tilting [12], while in Pnma-type perovskite,

such as rare earth orthoferrites and CsPbI3, the anti-

polar distortion arises from the condensation of both the

in-plane anti-phase (ωRx,y ) and out-of-plane in-phase tilt-

ings (ωMz) via trilinear coupling [13]. Although these

tilting modes are non-polar, they couple strongly with

the polar and anti-polar modes so that they can be in-

ﬂuenced by the electric ﬁeld as well, and in consequence

contribute to the ECE.

To get a deeper understanding of the (negative) ECE

in AFE, analysis based on Landau models involving the

most relevant degrees of freedom have been proved to be

very useful [14–17], and it may thus be necessary that all

the important order parameters are taken into consid-

eration. Furthermore, some previous phenomenological

models are often over simpliﬁed, since only one dimen-

sion is assumed [4]. In reality, the direction of the ap-

plied ﬁeld with respect to the crystallographic axis should

have diﬀerent eﬀects regarding ECE. In this Letter, we

take the antiferroelectric Nd substituted BiFeO3(BNFO)

solid solution as an example and demonstrate that the

octahedral tiltings can have very important eﬀect on the

sign and magnitude of the ECE. We also construct a

phenomenological model that allows us to rationalize the

contributions of each degree of freedom. In particular,

the dipoles alone are found to be insuﬃcient to explain

the negative ECE, while contributions from the in-phase

and anti-phase tilting modes are indispensible. More-

over, BNFO is predicted to yield rather large negative

ECE close to the AFE-to-FE transition.

BiFeO3(BFO) stabilizes in a R3c ground state, but

rare-earth doping with composition larger than 20−30%

is suﬃcient to alter it to the Pnma structure [18]. Here,

we adopt the eﬀective Hamiltonian scheme of Ref. [19]

to study the Bi0.6Nd0.4FeO3solid solution under elec-

tric ﬁeld at ﬁnite temperatures. With this composition,

arXiv:2210.04138v1 [cond-mat.mtrl-sci] 9 Oct 2022

BNFO is stabilized in the AFE Pnma phase at room

temperature and can transform to a FE state under an

electric ﬁeld [18–22]. The solid solutions are simulated

by a 12×12×12 supercell (containing 8,640 atoms) using

Monte-Carlo (MC) simulations, in which the Bi and Nd

atoms are randomly distributed (see Supplemental Ma-

terial (SM) Section S1 for details [23]).

FIG. 1. Eﬀect of Eﬁeld on the temperature dependence of

the order parameters. (a),(b) [001] ﬁeld of 0.87 MV/cm (solid

lines), in comparison with zero ﬁeld (dashed lines), (c),(d) ibid

for [1¯

10] ﬁeld of 0.87 MV/cm, (e),(f) ibid for [110] ﬁeld of 0.61

MV/cm. The four relevant order parameters are anti-phase

octahedral tilting ωR, in-phase tilting ωM, polarization P,

and antiferroelectric vector X. Note that Px=−Pyfor [1¯

10]

ﬁeld. The vertical dotted (or dashed) lines delimit diﬀerent

phases under ﬁnite (or zero) ﬁeld.

First, let us check how the order parameters are in-

ﬂuenced by the electric ﬁeld E[24], using the eﬀective

Hamiltomian scheme. Note that the initial Pnma struc-

ture has zero polarization, an in-plane anti-polar vec-

tor Xalong the [110] direction, and a−a−c+tilting in

Glazer’s notation (which corresponds to ﬁnite x- and y-

components of the antiphase tilting vector, ωR,x =ωR,y,

and ﬁnite z-component of the in-phase tilting vector,

ωM,z). Three representative ﬁeld directions are investi-

gated (Fig. 1), together with the zero-ﬁeld data (dashed

curves) for comparison (for other Emagnitudes, see SM

Section S2 [23]). With no applied ﬁeld, the Pnma phase

transforms to the paraelectric (PE) cubic phase at 1400

K (dashed lines in Fig. 1).

Under [001] ﬁeld, we consider a representative case

with E= 0.87 MV/cm, with which the AFE state trans-

forms to the ferroelectric P4mm phase at 880 K, char-

acterized by a large polarization Pzalong [001] and

no octahedral tiltings. In the AFE state, one can see

that the temperature dependence of ωM,z does not dif-

fer much from the zero-ﬁeld case, whereas Pand ωR,(x,y)

(ωR,x =ωR,y ) show apparent changes. The moderate

ﬁeld-induced change of Xcan be understood to a good

approximation via the change in ωR,(x,y)since X(x,y)

should be proportional to the product ωR,(x,y)ωM,z – as a

result of a trilinear coupling between X(x,y),ωR,(x,y)and

ωM,z [25]. Finite Pzis induced by the ﬁeld, whereas the

ﬁeld-induced suppression of ωR,(x,y)is due to the com-

petitive coupling with Pz.

Moreover, if the ﬁeld is applied along [1¯

10] (Figs. 1c

and 1d), Pis induced along the same direction, i.e., a

ﬁnite Px=−Pyﬁrst develops, and a transition to a FE

Cc phase occurs at 790 K, a structure characterized by a

polarization in huuvidirection (u > v) and a−a−c−oc-

tahedral tiltings (a > c). The third Edirection is along

[110], along which Pdevelops, while ωM,z is much sup-

pressed and ωR,(x,y)is more or less unchanged within the

AFE-based state [26]. Such AFE phase then transforms

also into a Cc phase at 780 K (Fig. 1e and 1f).

Let us now concentrate on the ECE coeﬃcient α=

∂T

∂E|Swith Tbeing temperature and Sbeing entropy,

which can be calculated from the cumulant formula using

outputs of the MC simulations[27–30].

αMC =−Z∗alattT(h|u|Etoti − h|u|i hEtoti

hE2

toti−hEtoti2+21(kBT)2

2N),(1)

where Z∗is the Born eﬀective charge associated with the

local mode, alatt represents the lattice constant of the

ﬁve-atom pseudo-cubic perovskite cell, Tis the simula-

tion temperature, |u|is the supercell average of the mag-

nitude of the local mode, Etot is the total energy given by

the eﬀective Hamiltonian, kBis the Boltzmann constant,

Nis the number of sites in the supercell, and h i denotes

average over the MC sweeps at a given temperature.

For ﬁelds applied along the [001] direction (Fig. 2a),

similar to the case in PZO-based AFE [5, 6], αis negative

in the AFE-based state, and its magnitude increases with

temperature, which maximizes at the transition point

where the AFE-based state disappears. Across the phase

transition, αjumps to be positive in the FE state, then

(slightly) increases with temperature, as such qualitative

temperature dependence is known for ferroelectrics [31].

In order to have insightful analysis of the ECE, Figs.

2b and 2c also report two other quantities related to

electro-caloric response, namely the total isothermal

change in entropy ∆S, and the adiabatic temperature

change ∆T, as well as their individual contributions.

Practically, in order to be able to compute the total en-

tropy change, we consider the following Landau model

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OriginofnegativeelectrocaloriceectinPnma-typeantiferroelectricperovskitesNingboFan,1,2JorgeI~niguez,3,4L.Bellaiche,5andBinXu1,2,1InstituteofTheoreticalandAppliedPhysics,SoochowUniversity,Suzhou215006,China2SchoolofPhysicalScienceandTechnology,SoochowUniversity,Suzhou215006,China3MaterialsResearch...

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Origin of negative electrocaloric eect in Pnma -type antiferroelectric perovskites Ningbo Fan1 2Jorge I niguez3 4L. Bellaiche5and Bin Xu1 2 1Institute of Theoretical and Applied Physics Soochow University Suzhou 215006 China.pdf

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Origin of negative electrocaloric eect in Pnma -type antiferroelectric perovskites Ningbo Fan1 2Jorge I niguez3 4L. Bellaiche5and Bin Xu1 2 1Institute of Theoretical and Applied Physics Soochow University Suzhou 215006 China

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