Polar phase transition in 180-domain wall of lead titanate I. Rychetsky Institute of Physics of the Czech Academy of Sciences

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Polar phase transition in 180◦-domain wall of lead titanate

I. Rychetsky∗

Institute of Physics of the Czech Academy of Sciences,

Na Slovance 2, 18221 Prague 8, Czech Republic.

W. Schranz and A. Tr¨oster

University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Wien, Austria.

(Dated: October 4, 2022)

A new mechanism leading to a switchable polarization in a ferroelectric domain wall (DW) is

proposed. A biquadratic coupling of the primary order parameter and its gradient triggers the

phase transition in the DW with softening of the local polar mode and anomalous increase of the

susceptibility at the phase transition temperature TDW . This mechanism describes the origin and

properties of the polar Bloch and antipolar N´eel components in the 180◦-DW of PbTiO3, which

were recently reported from ﬁrst-principles calculations.

Introduction.—The tensor properties of domain walls

(DWs) in ferroic materials become recently of increas-

ing interest driven by achievements in technological and

measurement methods allowing to fabricate and observe

submicron and nanoscale structures. Various methods

for modeling of DWs are widely used [1], i. e. ﬁrst-

principle calculations [2], machine-learned force ﬁelds [3],

phase-ﬁeld modeling [4], and phenomenological Landau-

Ginzburg theory [5], which are closely interconnected

with the DW symmetry analysis described by layer

groups [6–10]. Polarization inside DWs was predicted

in some perovskite structures [11, 12], where the crucial

role was assigned to ﬂexoelectricity [13], rotopolar cou-

pling [8, 14] or biquadratic coupling of the primary and

secondary order parameters [15].

The possible existence of polar 180◦-DW in PbTiO3

(PTO) was reported by several authors. However, the

situation is not so clear yet. Based on ab initio calcula-

tions an Ising structure of the DW proﬁle was reported

in Ref. [16]. Such a DW would not carry any polarization

within the wall. Other authors concluded that the DW

contains also a N´eel-like polarization (asymmetric polar-

ization proﬁle) originating from ﬂexoelectricity [17, 18]

and a switchable Bloch component indicating a ferroelec-

tric phase transition inside the DW [2, 19]. The latter

behavior was not found to be stable within the Landau-

Ginzburg approach [17, 18], where only the N´eel polar-

ization was obtained. In this contribution we show that

the symmetry of the DW (layer group) together with an

extended Landau-Ginzburg potential allow to properly

describe the polar properties of 180◦-DW in PTO.

Symmetry of 180◦DW — PTO exhibits a uniaxial fer-

roelectric phase transition from cubic to tetragonal struc-

ture without multiplication of the unit cell. The symme-

try decrease from P m¯

3mto P4mm implies 6 tetragonal

domain states (DSs) 11≡(−Ps,0,0), 21≡(0,−Ps,0),

31≡(0,0,−Ps) and 12,22,32with opposite sign of

polarization.

Here we consider the 180◦–DW (31|n,p|32) between

the DSs 31≡(0,0,−Ps) and 32≡(0,0, Ps), with the

normal nkxand the microscopic position within the

unit cell p[8, 9]. The macroscopic tensor properties of

DWs described by Landau theory are independent of the

microscopic position pand they are determined by the

layer group symmetry of the DW twin (31|n|32), which

contains 4 elements T12 =T{1, my,2y,¯

1},Tare trans-

lations parallel with the DW plane [9]. This symme-

try implies that the N´eel component is antisymmetric,

P1(x) = −P1(−x), and it can be nonzero in the whole

temperature range below Tc. The Bloch component is

forbidden by symmetry, since application of myyields

P2(x) = −P2(x) = 0. Therefore it could only occur as a

result of the phase transition lowering the symmetry to

12 =T{1,2y}. Then the Bloch component is nonzero

and symmetric: P2(x) = P2(−x)6= 0. The polarization

proﬁles and the phase transition in the DW are further

analyzed using the Landau-Ginzburg free energy descrip-

tion.

The free energy— The Gibbs free energy can be writ-

ten as:

G(P,σ) = G0+Ges +Gel +Gflex +Gbiq +Gg(1)

where the individual parts, pure polarization G0, elec-

trostriction Ges, elastic energy Gel, gradient term Gg,

ﬂexoelectric Gflex, biquadratic OP and its gradient Gbiq

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arXiv:2210.00793v1 [cond-mat.mtrl-sci] 3 Oct 2022

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Polarphasetransitionin180-domainwallofleadtitanateI.RychetskyInstituteofPhysicsoftheCzechAcademyofSciences,NaSlovance2,18221Prague8,CzechRepublic.W.SchranzandA.TrosterUniversityofVienna,FacultyofPhysics,Boltzmanngasse5,1090Wien,Austria.(Dated:October4,2022)Anewmechanismleadingtoaswitchablepolariz...

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Polar phase transition in 180-domain wall of lead titanate I. Rychetsky Institute of Physics of the Czech Academy of Sciences

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