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Dynamics of ferroelectric interphase boundaries in strong magnetic fields
Physca C 235-240 (1994) 1575-1576
PHYSICA
North-Holland
Dynamics of ferroelectric interphase boundaries in strong magnetic fields A. Gordon a, I.D. Vagner b and P. Wyder b aDepartment of Mathematics and Physics, Haifa University at Oranim, Tivon 36006, Israel bMax-Planck-lnstitut fir Festk~rperforschung, Hochfeld Magnetlabor, Grenoble Cedex 9, France.
Kinetics of ferroelectric phase transitions in strong magnetic fields are considered in high-temperature superconductive perovskites
As is known, a number of high - Tc superconductors belongs to ferroelectrics possessing the perovskite structure. A reason of coexistence of ferroelectricity and superconductivity is the considerable enhancement of the electron-phonon interaction in unstable lattices. The origin of the ferroelectricity is suggested to be related to anharmonicity of apex oxigen ions in all superconducting perovskites. On the other hand, it is known that the ferroelectricity in perovskites can be governed using strong magnetic fields [I]. Magnetic fields shift temperatures of first-order transitions. The growth and kinetics processes at symmetrybreaking first-order phase transitions are associated with the migration of interphase boundaries separating the coexisting paraelectric and ferroelectric phases. A magnetic field can effect on the propagation of ferroelectric interphase boundaries in perovskites due to the magnetoelectric effect. This effect is probably caused by the ~21~534~7.~
©1994-El~vmrScmnceB.V. A H n ~ t s ~ s e ~ e d
SSDI~21-4534~4)01354-3
coupling of the magnetic field with the orbitals of oxigen ions reponsible for polarizability. We consider here the kinetics of ferroelectric phase transitions in the presence of a magnetic field using an exact solution of the dynamic model of ferroeiectric interfaces. We start from the Landau functional of the total free energy taking into account an external magnetic field H 2 ~ P) F[P(x,t)] = [D(-~-~ + f(P)]dx (i) where P is the polarization f(P) is given [1,2]
and
f(P) = [1 ap2 _ ?I bp 4 + ~I cp6 _ p2 H2(g ~ hH 2)
(2)
2 The motion equation is given by [3] 2D
82p
2p
1
8P
8x 2
8t 2
F
8t
f --= P
0 (3)
where r is the kinetic coefficient, p = ~m2 , m and e are effective mass ne
1576
A Gordon et al,/Physica C 235-240 (1994) 1575-1576
charge of the ion, n is the number of ions in unit volume. The moving interface shape resulting from Eq. (3) is P0 (4) P= 1 x-vt and
[ z+
exp(T)
where Pn is the equilibrium value of p61arization, A is the interphase boundary width given by 1 l0 1 ( 3D )~ A= o: [ ._-qT-- (s) 21' bP0-a aVo
antiferroelectricity. Since the movement of the interphase boundary is related to the growth of ferroelectric and antiferroelectric crystals. The magnetic field effect can be used to govern growth processes and to lead to the magnetic field-induced motion of ferroelectric domain walls. 15
¸
1'
OS
(I+2--~-) o
3
Vo 4 V
A
=
A
2~ , v n
-
=
--
3
2 r J
0
(4a
-
bPo)
~5
(6)
0 0
and
v0
are given by the usual -i
Ginzburg-Landau theory [2]. In Fig. 1 the magnetic-field dependence of the interface velocity is calculated using experimental data in BaTiO 3 (well-studied perovskite material>. The velocity sign defines the direction in which the paraelectric phase grows at the expense of the ferroelectric one and vice versa. At the given temperature (397.9K) equilibrium between the two phases is possible only at H = 35T corresponding to the phase transition point (v = 0). The velocity slope depends on the inertial factor value. The sign of the magnetoelectric term in (2) i~ different from that in [3] because we use here the observed increase of the phase temperature when the magnetic field strength increases. The analogous consideration of phase transition kinetics can be carried out for the Kittel model of
5
,
-
10
•
15
It(T)
Figure I. The interphase boundary velocity as a function of magnetic field
a
at T - T 0 O = 6 .9K in units of -v"~ ~
rDb
0 is the temperature of the
TO
limit stability of the paraelectric phase at H = 0; a) - v 0' P for which - - = 20. 2D
b)"
-- V t
I. D. Wagner and D. Baierle0 Phys. Lett. A 83 (1981) 343. 2. A. Gordon and P. Wyder, Phys. Rev. B46 (1992) 5777. 3. A. Gordon, I.D. Vagner and P. Wyder, Physica B 191 (1993) 2]0.
PHYSICA
North-Holland
Dynamics of ferroelectric interphase boundaries in strong magnetic fields A. Gordon a, I.D. Vagner b and P. Wyder b aDepartment of Mathematics and Physics, Haifa University at Oranim, Tivon 36006, Israel bMax-Planck-lnstitut fir Festk~rperforschung, Hochfeld Magnetlabor, Grenoble Cedex 9, France.
Kinetics of ferroelectric phase transitions in strong magnetic fields are considered in high-temperature superconductive perovskites
As is known, a number of high - Tc superconductors belongs to ferroelectrics possessing the perovskite structure. A reason of coexistence of ferroelectricity and superconductivity is the considerable enhancement of the electron-phonon interaction in unstable lattices. The origin of the ferroelectricity is suggested to be related to anharmonicity of apex oxigen ions in all superconducting perovskites. On the other hand, it is known that the ferroelectricity in perovskites can be governed using strong magnetic fields [I]. Magnetic fields shift temperatures of first-order transitions. The growth and kinetics processes at symmetrybreaking first-order phase transitions are associated with the migration of interphase boundaries separating the coexisting paraelectric and ferroelectric phases. A magnetic field can effect on the propagation of ferroelectric interphase boundaries in perovskites due to the magnetoelectric effect. This effect is probably caused by the ~21~534~7.~
©1994-El~vmrScmnceB.V. A H n ~ t s ~ s e ~ e d
SSDI~21-4534~4)01354-3
coupling of the magnetic field with the orbitals of oxigen ions reponsible for polarizability. We consider here the kinetics of ferroelectric phase transitions in the presence of a magnetic field using an exact solution of the dynamic model of ferroeiectric interfaces. We start from the Landau functional of the total free energy taking into account an external magnetic field H 2 ~ P) F[P(x,t)] = [D(-~-~ + f(P)]dx (i) where P is the polarization f(P) is given [1,2]
and
f(P) = [1 ap2 _ ?I bp 4 + ~I cp6 _ p2 H2(g ~ hH 2)
(2)
2 The motion equation is given by [3] 2D
82p
2p
1
8P
8x 2
8t 2
F
8t
f --= P
0 (3)
where r is the kinetic coefficient, p = ~m2 , m and e are effective mass ne
1576
A Gordon et al,/Physica C 235-240 (1994) 1575-1576
charge of the ion, n is the number of ions in unit volume. The moving interface shape resulting from Eq. (3) is P0 (4) P= 1 x-vt and
[ z+
exp(T)
where Pn is the equilibrium value of p61arization, A is the interphase boundary width given by 1 l0 1 ( 3D )~ A= o: [ ._-qT-- (s) 21' bP0-a aVo
antiferroelectricity. Since the movement of the interphase boundary is related to the growth of ferroelectric and antiferroelectric crystals. The magnetic field effect can be used to govern growth processes and to lead to the magnetic field-induced motion of ferroelectric domain walls. 15
¸
1'
OS
(I+2--~-) o
3
Vo 4 V
A
=
A
2~ , v n
-
=
--
3
2 r J
0
(4a
-
bPo)
~5
(6)
0 0
and
v0
are given by the usual -i
Ginzburg-Landau theory [2]. In Fig. 1 the magnetic-field dependence of the interface velocity is calculated using experimental data in BaTiO 3 (well-studied perovskite material>. The velocity sign defines the direction in which the paraelectric phase grows at the expense of the ferroelectric one and vice versa. At the given temperature (397.9K) equilibrium between the two phases is possible only at H = 35T corresponding to the phase transition point (v = 0). The velocity slope depends on the inertial factor value. The sign of the magnetoelectric term in (2) i~ different from that in [3] because we use here the observed increase of the phase temperature when the magnetic field strength increases. The analogous consideration of phase transition kinetics can be carried out for the Kittel model of
5
,
-
10
•
15
It(T)
Figure I. The interphase boundary velocity as a function of magnetic field
a
at T - T 0 O = 6 .9K in units of -v"~ ~
rDb
0 is the temperature of the
TO
limit stability of the paraelectric phase at H = 0; a) - v 0' P for which - - = 20. 2D
b)"
-- V t
I. D. Wagner and D. Baierle0 Phys. Lett. A 83 (1981) 343. 2. A. Gordon and P. Wyder, Phys. Rev. B46 (1992) 5777. 3. A. Gordon, I.D. Vagner and P. Wyder, Physica B 191 (1993) 2]0.