A ferroelectric hysteresis depends on the orientation of the applied field with respect to the spontaneous polarization. The ferroelectric switching occurs through correlated domain movements forming avalanches. We tested whether avalanches in single crystals of the prototypic ferroelectric BaTiO3 and the relaxor ferroelectric 0.7Pb(Mg2/3Nb1/3)O3–0.3PbTiO3 show anisotropic field dependences. The anisotropy of the energy exponent of avalanches is very small in BaTiO3 with exponents between 1.53 and 1.6, which is remarkably close to the prediction of mean field theory 5/3. The anisotropy is much stronger in 0.7Pb(Mg2/3Nb1/3)O3–0.3PbTiO3 with one exponent slightly above the typical range of mean field values (4/3–5/3): 1.43 ± 0.02, 1.64 ± 0.03, and 1.79 ± 0.03 for fields along [100], [110], and [111], respectively. This anisotropy indicates a variation of the fractal dimensions of the transient domain patterns depending on the direction of the switching field.

1.
M. E.
Lines
and
A. M.
Glass
,
Principles and Applications of Ferroelectrics and Related Materials
(
Oxford University Press
,
2001
).
2.
K.
Uchino
,
Ferroelectric Devices
, 2nd ed. (
CRC Press
,
2009
).
3.
J. F.
Scott
,
Science
315
,
954
959
(
2007
).
4.
S.
Wada
,
H.
Kakemoto
, and
T.
Tsurumi
,
Mater. Trans.
45
,
178
(
2004
).
5.
B.
Noheda
,
J. A.
Gonzalo
,
L. E.
Cross
,
R.
Guo
,
S.-E.
Park
,
D. E.
Cox
, and
G.
Shirane
,
Phys. Rev. B
61
,
8687
(
2000
).
6.
R.
Guo
,
L. E.
Cross
,
S.-E.
Park
,
B.
Noheda
,
D. E.
Cox
, and
G.
Shirane
,
Phys. Rev. Lett.
84
,
5423
(
2000
).
7.
D. D.
Viehland
and
E. K. H.
Salje
,
Adv. Phys.
63
,
267
(
2014
).
8.
E. K. H.
Salje
,
Z. Kristallogr. Cryst. Mater.
134
(
1
),
107
115
(
1971
).
9.
Y.
Ishibashi
and
Y.
Takagi
,
J. Phys. Soc. Jpn.
31
,
506
(
1971
).
10.
S.
Hashimoto
,
H.
Orihara
, and
Y.
Ishibashi
,
J. Phys. Soc. Jpn.
63
,
1601
(
1994
).
11.
P.
Gao
,
C. T.
Nelson
,
J. R.
Jokisaari
,
S.-H.
Baek
,
C. W.
Bark
,
Y.
Zhang
,
E.
Wang
,
D. G.
Schlom
,
C.-B.
Eom
, and
X.
Pan
,
Nat. Commun.
2
,
591
(
2011
).
12.
A. R.
Akhmatkhanov
,
I. A.
Kipenko
,
A. A.
Esin
, and
V. Y.
Shur
,
Appl. Phys. Lett.
117
,
022903
(
2020
).
13.
C. T.
Nelson
,
P.
Gao
,
J. R.
Jokisaari
,
C.
Heikes
,
C.
Adamo
,
A.
Melville
,
S. H.
Baek
,
C. M.
Folkman
,
B.
Winchester
,
Y.
Gu
,
Y.
Liu
,
K.
Zhang
,
E.
Wang
,
J.
Li
,
L. Q.
Chen
,
C. B.
Eom
,
D. G.
Schlom
, and
X.
Pan
,
Science
334
,
968
(
2011
).
14.
M. P.
Cruz
,
Y. H.
Chu
,
J. X.
Zhang
,
P. L.
Yang
,
F.
Zavaliche
,
Q.
He
,
P.
Shafer
,
L. Q.
Chen
, and
R.
Ramesh
,
Phys. Rev. Lett.
99
,
217601
(
2007
).
15.
B.
Casals
,
G. F.
Nataf
,
D.
Pesquera
, and
E. K. H.
Salje
,
APL Mater.
8
,
011105
(
2020
).
16.
A.
Chanthbouala
,
V.
Garcia
,
R. O.
Cherifi
 et al,
Nat. Mater.
11
,
860
(
2012
).
17.
S.
Boyn
,
J.
Grollier
,
G.
Lecerf
 et al,
Nat. Commun.
8
,
14736
(
2017
).
18.
E. K. H.
Salje
,
D.
Xue
,
X.
Ding
,
K. A.
Dahmen
, and
J. F.
Scott
,
Phys. Rev. Mater.
3
,
014415
(
2019
).
19.
F. J.
Perez-Reche
,
E.
Vives
,
L.
Manosa
, and
A.
Planes
,
Phys. Rev. Lett.
87
,
195701
(
2001
).
20.
F. J.
Perez-Reche
,
B.
Tadic
,
L.
Manosa
,
A.
Planes
, and
E.
Vives
,
Phys. Rev. Lett.
93
,
195701
(
2004
).
21.
C. D.
Tan
,
C.
Flannigan
,
J.
Gardner
,
F. D.
Morrison
,
E. K. H.
Salje
, and
J. F.
Scott
,
Phys. Rev. Mater.
3
,
034402
(
2019
).
22.
E. K. H.
Salje
and
K. A.
Dahmen
,
Annu. Rev. Condens. Matter Phys.
5
,
233
(
2014
).
23.
M.
Porta
,
T.
Castan
,
A.
Saxena
, and
A.
Planes
,
Phys. Rev. E
100
,
062115
(
2019
).
24.
Y.
Zhang
,
D.
Xue
,
H.
Wu
,
X.
Ding
,
T.
Lookman
, and
X.
Ren
,
Acta Mater.
71
,
176
(
2014
).
25.
F.
Jona
and
G.
Shirane
,
Ferroelectric Crystals, Dover Books on Engineering
(
Dover Publications
,
1993
).
26.
B.
Noheda
,
D. E.
Cox
,
G.
Shirane
,
J.
Gao
, and
Z.-G.
Ye
,
Phys. Rev. B
66
,
054104
(
2002
).
27.
H.
Aburatani
,
J. P.
Witham
, and
K.
Uchino
,
Jpn. J. Appl. Phys., Part 1
37
,
602
(
1998
).
28.
S.
Zhang
,
N. P.
Sherlock
,
R. J.
Meyer
, and
T. R.
Shrout
,
Appl. Phys. Lett.
94
,
162906
(
2009
).
29.
Z.
Yu
,
R.
Guo
, and
A. S.
Bhalla
,
Mater. Lett.
57
,
349
(
2002
).
30.
M.
Zaiser
,
Adv. Phys.
55
,
185
245
(
2006
).
31.
X.
Xia
,
C.
Li
,
J.
Zeng
,
L.
Zheng
, and
G.
Li
,
J. Am. Ceram. Soc.
103
,
2694
(
2020
).
32.
G. F.
Nataf
,
P. O.
Castillo-Villa
,
J.
Baró
,
X.
Illa
,
E.
Vives
,
A.
Planes
, and
E. K. H.
Salje
,
Phys. Rev. E
90
,
022405
(
2014
).
33.
E. K. H.
Salje
,
P.
Soto
,
E.
Daniel
,
A.
Planes
,
E.
Vives
,
M.
Reinecker
, and
W.
Schranz
,
Philos. Mag. Lett.
91
,
554
(
2011
).
34.
E. K. H.
Salje
,
A.
Planes
, and
E.
Vives
,
Phys. Rev. E
96
,
042122
(
2017
).
35.
E.
Vives
,
J.
Baró
,
M. C.
Gallardo
,
J.-M.
Martín-Olalla
,
F. J.
Romero
,
S. L.
Driver
,
M. A.
Carpenter
, and
E. K. H.
Salje
,
Phys. Rev. B
94
,
024102
(
2016
).
36.
J. M.
Ball
,
P.
Cesana
, and
B.
Hambly
,
MATEC Web Conf.
33
,
02008
(
2015
).

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