- Email: [email protected]
Magnetic relaxation phenomena in the erbium orthoferrite ErFeO3
Journal of Magnetism and Magnetic Materials 140-144 (1995) 2165-2166
~i~ ~i 4~H
ELSEVIER
Journalof magnetism and magnetic materials
Magnetic relaxation phenomena in the erbium orthoferrite ErFeO3 J. Tejada a,,, X.X. Zhang a, F.J. Berry b, G. Dates b a Fac. Fisfca, Univ. Barcelona, Diagonal 647, 08028 Barcelona, Spain b Department. of Chemistry, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
Abstract We report here on low temperature magnetic relaxation in the erbium orthoferrite ErFeO 3. The variation of magnetic viscosity, S ==-OM/O In t, with temperature shows three different regimes below 40 K. The most remarkable is that at T < 3 K where S ( T ) remains constant suggesting the occurrence of macroscopic quantum tunneling of the magnetization.
The rare earth orthoferrites, RFeO3, crystallize in an orthorhombically distorted perovskite structure. This structure belongs to the space group D24-Pbnm with R in the (4c) and Fe in the (4b) positions [1,2]. Below the ordering N6el temperature, the Fe 3+ magnetic structure in ErFeO 3 is that of a 'canted antiferromagnet'. The magnetic structure of the iron moments can be envisaged as a two strongly antiferromagnetically coupled sublattice system slightly canted by perturbing interactions to produce net ferromagnetic moments perpendicular to the antiferromagnetic axis [3,4]. Magnetic relaxation in orthoferrite may be associated with the rotation of antiferromagnetic domain walls. The field exerts a force on the domain wall, which is opposed by the pinning force due to impurity defects. As the field reaches the coercive field, the pinning barrier for the wall motion disappears and the wall becomes mobile. However, some weak magnetic relaxation due to the diffusion of domain walls in the random pinning potential is observed well below the coercive field. This is due to the thermal overbarrier activation of domain walls. It is widely believe that this magnetic relaxation disappears as the temperature decreases. However it has recently been predicted [5-8] that in the limit of zero temperature the wall can depin itself via quantum tunneling under the barrier. This should manifest itself in the temperature independent relaxation rate below some temperature which marks the crossover from thermal to quantum regime. We have therefore determined the canted antiferromagnetic ErFeO 3 and report here on its thermal and non-thermal magnetic relaxation behaviors.
The dependence of the magnetization on temperature in the presence of a field of 50 Oe is shown in Fig. 1. The data are in full agreement with the results of several authors [1,2]. The canted antiferromagnetic Fe3+-Fe 3+ structure is antiparalled to the net polarization of the Er 3+ spin system which results in a compensation point at T = 80 K. The total magnetization of the sample increases with decreasing the temperature until T = 4.5 K. Below this temperature the magnetization drops sharply with decreasing temperature. The sharp peak at T ~- 4.5 K has, on the basis of neutron diffraction [3] and M6ssbauer spectroscopy [4], been associated with a reorientation of the Fe 3+ antiferromagnetic axis from the c axis toward the b axis. In our experiments the sample was first cooled in the absence of an applied magnetic field ( H ~--0.1 Oe) to a target temperature. A field H = 50 Oe was then applied and the evolution of magnetization with time in intervals of 20 s measured.
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T (K) * Corresponding author. Email: [email protected]; fax: + 34 3 402 1149.
Fig. 1. M(T) dependence from ZFC-FC measurement with applied field of 50 Oe.
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 0 5 1 4 - 1
J. Tejada et al./Journal of Magnetism and MagneticMaterials 140-144 (1995)2165-2166
2166 0.605
........
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,,,
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--1.8K:
Inf(s) Fig. 2. Time dependence of magnetization with applied field of 50 Oe. After 200 s the relaxation of the zero field cooled magnetization follows quite well the log(t) law (Fig. 2):
M ( t ) = const + S(T) I n ( t )
(1)
where S(T) is the so called magnetic viscosity (S(T)= dM/dln(t)), which characterizes the relaxation behavior of the sample. The magnetic viscosity obtained from fitting of the M(t) evolution using Eq. (1) is displayed in Fig. 3. These viscosity data show the following important features. (1) S(T) shows a maximum at a temperature T = 4.5 K and decreases as the temperature increases above 5 K. (2) S(T) is linear in T at temperatures 3 < T < 5 K, and independent of temperature below 3 K as well as its extrapolation to T = 0 intercepts the S axis at a positive value. The first point means that the maximum of the magnetic viscosity corresponds to the temperature at which the reorientation of the Fe 3+ antiferromagnetic axis occurs. 1.6
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(K)
Fig. 3. Magnetic viscosity versus temperature.
The linear dependence of S(T) on T observed between 3 and 5 K may be interpreted in terms of independently relaxing domain walls. This temperature behavior extrapolates to zero at T = 0 in agreement with the disappearance of the thermal overbarrier activation of domain walls as the temperature decreases. By further decreasing the temperature, thermal effects become less important and a plateau for the S(T) values is observed which is associated with macroscopic quantum tunneling. More precisely, the plateau in the S(T) curves can be explained by quantum domain wall motion. Though our orthoferrite does not have ferromagnetic domain walls, we can estimate the value for the crossover temperature Tc using the predictions for ferromagnetic domain wall [5-8] [Eq. (2)], because the oxide is a canted antiferromagnet having a net magnetic moment,
where H c is the coercive field corresponding to the maximum pinning barrier, M is the magnetization of the domain wall and E = 1 - H / H c where H is the applied field. In our experiments H c --700 Oe, M s ( T = 3 K ) = 315 e m u / c m 3 and H = 50 Oe, we have got Tc = 1 K in agreement with the experimental Tc value of 3 K. Acknowledgement: JT and XXZ thank CIRIT of Catalunya for financial support. References [1] G. Gorodetiky, R.M Homreich, I. Yaeger, H. Pinto, G. Shacher and H. Shaked, Phys. Rev. B 8 (1972) 3398. [2] R.L. White, J. Appl. Phys. 40 (1969) 1061. [3] R.M. Bozorth, H.J. Williams and D.E. Walsh, Phys. Rev. 103 (1956) 572. [4] L.A. Prelorendjo, C.E. Johnson, M.F. Thomas and B.M. Wanklyn, J. Phys. C 15 (1982) 3199. [5] P.C.E. Stamp, Phys. Rev. Lett. 66 (1991) 2802. [6] P.C.E. Stamp, E.M. Chudnovsky and B. Barbara, Int. J. Mod. Phys. B 6 (1992) 1355. [7] E.M. Chudnovsky, O. Iglesias and P.C.E. Stamp, Phys. Rev. B 46 (1992) 5392. [8] X.X. Zhang, R. Zquiak, B. Barbara and J. Tejada, J. Phys. C 4 (1992) 10347.
~i~ ~i 4~H
ELSEVIER
Journalof magnetism and magnetic materials
Magnetic relaxation phenomena in the erbium orthoferrite ErFeO3 J. Tejada a,,, X.X. Zhang a, F.J. Berry b, G. Dates b a Fac. Fisfca, Univ. Barcelona, Diagonal 647, 08028 Barcelona, Spain b Department. of Chemistry, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
Abstract We report here on low temperature magnetic relaxation in the erbium orthoferrite ErFeO 3. The variation of magnetic viscosity, S ==-OM/O In t, with temperature shows three different regimes below 40 K. The most remarkable is that at T < 3 K where S ( T ) remains constant suggesting the occurrence of macroscopic quantum tunneling of the magnetization.
The rare earth orthoferrites, RFeO3, crystallize in an orthorhombically distorted perovskite structure. This structure belongs to the space group D24-Pbnm with R in the (4c) and Fe in the (4b) positions [1,2]. Below the ordering N6el temperature, the Fe 3+ magnetic structure in ErFeO 3 is that of a 'canted antiferromagnet'. The magnetic structure of the iron moments can be envisaged as a two strongly antiferromagnetically coupled sublattice system slightly canted by perturbing interactions to produce net ferromagnetic moments perpendicular to the antiferromagnetic axis [3,4]. Magnetic relaxation in orthoferrite may be associated with the rotation of antiferromagnetic domain walls. The field exerts a force on the domain wall, which is opposed by the pinning force due to impurity defects. As the field reaches the coercive field, the pinning barrier for the wall motion disappears and the wall becomes mobile. However, some weak magnetic relaxation due to the diffusion of domain walls in the random pinning potential is observed well below the coercive field. This is due to the thermal overbarrier activation of domain walls. It is widely believe that this magnetic relaxation disappears as the temperature decreases. However it has recently been predicted [5-8] that in the limit of zero temperature the wall can depin itself via quantum tunneling under the barrier. This should manifest itself in the temperature independent relaxation rate below some temperature which marks the crossover from thermal to quantum regime. We have therefore determined the canted antiferromagnetic ErFeO 3 and report here on its thermal and non-thermal magnetic relaxation behaviors.
The dependence of the magnetization on temperature in the presence of a field of 50 Oe is shown in Fig. 1. The data are in full agreement with the results of several authors [1,2]. The canted antiferromagnetic Fe3+-Fe 3+ structure is antiparalled to the net polarization of the Er 3+ spin system which results in a compensation point at T = 80 K. The total magnetization of the sample increases with decreasing the temperature until T = 4.5 K. Below this temperature the magnetization drops sharply with decreasing temperature. The sharp peak at T ~- 4.5 K has, on the basis of neutron diffraction [3] and M6ssbauer spectroscopy [4], been associated with a reorientation of the Fe 3+ antiferromagnetic axis from the c axis toward the b axis. In our experiments the sample was first cooled in the absence of an applied magnetic field ( H ~--0.1 Oe) to a target temperature. A field H = 50 Oe was then applied and the evolution of magnetization with time in intervals of 20 s measured.
0.015
•'•0.010 ; ..............
~u.u1u
°oooooaooooo
0.000
0
o o ° ° ° ° ° °
100
200
T (K) * Corresponding author. Email: [email protected]; fax: + 34 3 402 1149.
Fig. 1. M(T) dependence from ZFC-FC measurement with applied field of 50 Oe.
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 0 5 1 4 - 1
J. Tejada et al./Journal of Magnetism and MagneticMaterials 140-144 (1995)2165-2166
2166 0.605
........
%" 0.585
i
0.565
%
0.545
..........
~
0.525
-
0.505 3.2 4.2 5.2 6.2 7.2 8.2 9.2
L •
,
•
,,,
......
--1.8K:
Inf(s) Fig. 2. Time dependence of magnetization with applied field of 50 Oe. After 200 s the relaxation of the zero field cooled magnetization follows quite well the log(t) law (Fig. 2):
M ( t ) = const + S(T) I n ( t )
(1)
where S(T) is the so called magnetic viscosity (S(T)= dM/dln(t)), which characterizes the relaxation behavior of the sample. The magnetic viscosity obtained from fitting of the M(t) evolution using Eq. (1) is displayed in Fig. 3. These viscosity data show the following important features. (1) S(T) shows a maximum at a temperature T = 4.5 K and decreases as the temperature increases above 5 K. (2) S(T) is linear in T at temperatures 3 < T < 5 K, and independent of temperature below 3 K as well as its extrapolation to T = 0 intercepts the S axis at a positive value. The first point means that the maximum of the magnetic viscosity corresponds to the temperature at which the reorientation of the Fe 3+ antiferromagnetic axis occurs. 1.6
o o
1.2
.6 k13
°
0.8
t~ o
03 0 . 4
o
a o
0.0
i
0
i
4
8
r
12
1
16
(K)
Fig. 3. Magnetic viscosity versus temperature.
The linear dependence of S(T) on T observed between 3 and 5 K may be interpreted in terms of independently relaxing domain walls. This temperature behavior extrapolates to zero at T = 0 in agreement with the disappearance of the thermal overbarrier activation of domain walls as the temperature decreases. By further decreasing the temperature, thermal effects become less important and a plateau for the S(T) values is observed which is associated with macroscopic quantum tunneling. More precisely, the plateau in the S(T) curves can be explained by quantum domain wall motion. Though our orthoferrite does not have ferromagnetic domain walls, we can estimate the value for the crossover temperature Tc using the predictions for ferromagnetic domain wall [5-8] [Eq. (2)], because the oxide is a canted antiferromagnet having a net magnetic moment,
where H c is the coercive field corresponding to the maximum pinning barrier, M is the magnetization of the domain wall and E = 1 - H / H c where H is the applied field. In our experiments H c --700 Oe, M s ( T = 3 K ) = 315 e m u / c m 3 and H = 50 Oe, we have got Tc = 1 K in agreement with the experimental Tc value of 3 K. Acknowledgement: JT and XXZ thank CIRIT of Catalunya for financial support. References [1] G. Gorodetiky, R.M Homreich, I. Yaeger, H. Pinto, G. Shacher and H. Shaked, Phys. Rev. B 8 (1972) 3398. [2] R.L. White, J. Appl. Phys. 40 (1969) 1061. [3] R.M. Bozorth, H.J. Williams and D.E. Walsh, Phys. Rev. 103 (1956) 572. [4] L.A. Prelorendjo, C.E. Johnson, M.F. Thomas and B.M. Wanklyn, J. Phys. C 15 (1982) 3199. [5] P.C.E. Stamp, Phys. Rev. Lett. 66 (1991) 2802. [6] P.C.E. Stamp, E.M. Chudnovsky and B. Barbara, Int. J. Mod. Phys. B 6 (1992) 1355. [7] E.M. Chudnovsky, O. Iglesias and P.C.E. Stamp, Phys. Rev. B 46 (1992) 5392. [8] X.X. Zhang, R. Zquiak, B. Barbara and J. Tejada, J. Phys. C 4 (1992) 10347.