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Shape effects and magnetic properties of TbFeO3
Volume 40A, number 2
PHYSICS LETTERS
3 July 1972
SHAPE EFFECTS AND MAGNETIC PROPERTIES OF ThFeO3 R. BIDAUX, J. E. BOUREE and J. HAMMANN Service de Physique du Solide et de Resonance Mánetique, Centre d’Etudes Nucleaires de Saclay, 91 Gif-sur-Yvette, France
Received 21 April 1972
Absence of significant exchange coupling between Fe and Tb moments in TbFeO3 leaves dipolar interactions as preponderant in determining low temperature structures. Therefore, the nature of the stable structure at given temperature depends upon (and is approximately predicted as a “function” of) the shape of the sample.
With respect to the types of interactions which are responsible for their low temperature magnetic ordering, rare earth orthoferrites can be divided in two classes. In the first one, a significant exchange coupling exists between the rare earth (RE) and the Fe magnetic moments, and rules the choice of the total magnetic structure; this is the circumstance met in HoFeO3 becomes [11 In the second one,tothe coupling small enough letRE-Fe dipolarexchange interactions take the lead of the terms to be included in the energy balance in addition to Fe-Fe interactions; this is the situation met in TbFeO 3 [2] From this point of view, it is not surprising to record, as pointed out by [3] the conflicting conclusions [4, 5] on the low temperature behavior of TbFeO3 These relate to various reordering processes found at low temperatures and to the nature and temperature range of stability of the corresponding magnetic structures. In the following we propose to show to which extent shape effects can be held responsible for such a situation. Close inspection of dipolar energies shows that, at o K, competition takes place between structures A
and B, characterized as shown in table I. These structures are supposed to remain the only competitive ones at non zero temperatures, as long as the RE system does not become disordered. Their respective free energies have been calculated, within the frame of the following assumptions [1,2]: 1) Iron moments saturated to their 5~Band doare not contribute to themaximum entropy. valueFe-system 1~~I = The takes a canted antiferromagnetic structure, the final direction of antiferromagnetism depending on the dominating source of anisotropy.
.
2) Terbium induced moments are well described using a two-singlet picture. When ordered, either according to structure A or according to structure B, the magnitude of the Tb moments is approximated by:
-
,
-
m
=
-
tanh(~’/2fl,
and the entropy per ion by S’
=
k[p~ log p’1
+
p~logp~]
where 3 K is the two-singlet gap, p~/p’1 8-6MB is the saturated Tb=moment exp(—~’/fl, m0 at 0 K. ~‘
Table 1 Coupling between Fe and Tb systems
Sensitivity to shape effects
Fe system
Tb system
A
F~G~
F~C 3,
yes
yes
B
F~G~
A~G~ > 0
no
negligible
167
Volume 40A, number 2
PHYSICS LFTTERS
ledge of the x axis demagnetizing factor N. (For con-
-
T
3 July 1972
nection between dipolar sums and their volume of summation, cf. ref. [71) The phase diagram presented in the figure illustrates the results of the calculations. (For simplicity, exchange coupling between Fe and Tb moments has
R
P
been put equal to zero). One can see that, as the tem-
1
T~
-
5
______________
TN
perature decreases: a) For O
(AF, which refers to Tb antiferromagnetism) at TR2. One can notice that, as N increase, TR 2 increase and TR! decreases.
c) For 2.24 7r~N~41r,the system passes directly at T = TN from the paramagnetic state to the type B
(AF) structure. U
3
3
x_axis demagnetizing factor hg. 1.
When disordered, Tb moments have zero magnitude, but there is an entropic contribution of the two-singlet system: S
These results are well representative of the experi-
mental situation. For example, the fact pointed out by [6] that the reorientation taking place at TR2, observed on powder samples, does not occur on single crystals, would be due to shape effects instead of Pb salts inclusions. Experimental verification of this point, altogether with systematic study of the shape dependence, is in progress.
k[p1logp1 +p2logp2} per ion, References
where p2/p1 — exp( .~/T),~ 2K is the gap between the Tb ground levels in absence of induced magnetism. 3) When the terbium magnetic system is not ordered, the Fe moments behave as they do in structure B (weak ferromagnetism directed along the Z axis). The three free energies FA, FB and Fp~a (“paramagnetic” applies to the Tb system only), have been calculated using the molecular field approxima-
tion; the shape effects break in naturally when writing the expression of FA which requires the know-
1 68
[I] R. Bidaux, J. F. Bouree and J. Hammann, to be published. [21 R. Bidaux, J. E. Bouree and J. Hammann, to be published. [3j R. L. White, J. Appi. Phys. 40(1969)1061. [4] K. P. Belov, A. M. Kadomtseva, L. M. Ledneva, T. L. Orchinnikova, Ya. G. Panomarev and V. A. Timofeeva, Soy. Phys. Solid State 9 (1968) 2190. 15] L. I - Bertaut, J. Chappert, J. Mareschal, J. P. Rebouillat and J. Sivardiere, Solid State Comm. 5 (1967) 293. [6] M. Belakhovsky, J. Chappert, T. Rouskov and J. Sivardiere, J. de Phys. Colloque Cl, 32 (1971) 492. [7] R. Bidau~,P. Carrara and B. Vivet, Compt. Rend. 263 (1966) 176.
PHYSICS LETTERS
3 July 1972
SHAPE EFFECTS AND MAGNETIC PROPERTIES OF ThFeO3 R. BIDAUX, J. E. BOUREE and J. HAMMANN Service de Physique du Solide et de Resonance Mánetique, Centre d’Etudes Nucleaires de Saclay, 91 Gif-sur-Yvette, France
Received 21 April 1972
Absence of significant exchange coupling between Fe and Tb moments in TbFeO3 leaves dipolar interactions as preponderant in determining low temperature structures. Therefore, the nature of the stable structure at given temperature depends upon (and is approximately predicted as a “function” of) the shape of the sample.
With respect to the types of interactions which are responsible for their low temperature magnetic ordering, rare earth orthoferrites can be divided in two classes. In the first one, a significant exchange coupling exists between the rare earth (RE) and the Fe magnetic moments, and rules the choice of the total magnetic structure; this is the circumstance met in HoFeO3 becomes [11 In the second one,tothe coupling small enough letRE-Fe dipolarexchange interactions take the lead of the terms to be included in the energy balance in addition to Fe-Fe interactions; this is the situation met in TbFeO 3 [2] From this point of view, it is not surprising to record, as pointed out by [3] the conflicting conclusions [4, 5] on the low temperature behavior of TbFeO3 These relate to various reordering processes found at low temperatures and to the nature and temperature range of stability of the corresponding magnetic structures. In the following we propose to show to which extent shape effects can be held responsible for such a situation. Close inspection of dipolar energies shows that, at o K, competition takes place between structures A
and B, characterized as shown in table I. These structures are supposed to remain the only competitive ones at non zero temperatures, as long as the RE system does not become disordered. Their respective free energies have been calculated, within the frame of the following assumptions [1,2]: 1) Iron moments saturated to their 5~Band doare not contribute to themaximum entropy. valueFe-system 1~~I = The takes a canted antiferromagnetic structure, the final direction of antiferromagnetism depending on the dominating source of anisotropy.
.
2) Terbium induced moments are well described using a two-singlet picture. When ordered, either according to structure A or according to structure B, the magnitude of the Tb moments is approximated by:
-
,
-
m
=
-
tanh(~’/2fl,
and the entropy per ion by S’
=
k[p~ log p’1
+
p~logp~]
where 3 K is the two-singlet gap, p~/p’1 8-6MB is the saturated Tb=moment exp(—~’/fl, m0 at 0 K. ~‘
Table 1 Coupling between Fe and Tb systems
Sensitivity to shape effects
Fe system
Tb system
A
F~G~
F~C 3,
yes
yes
B
F~G~
A~G~ > 0
no
negligible
167
Volume 40A, number 2
PHYSICS LFTTERS
ledge of the x axis demagnetizing factor N. (For con-
-
T
3 July 1972
nection between dipolar sums and their volume of summation, cf. ref. [71) The phase diagram presented in the figure illustrates the results of the calculations. (For simplicity, exchange coupling between Fe and Tb moments has
R
P
been put equal to zero). One can see that, as the tem-
1
T~
-
5
______________
TN
perature decreases: a) For O
(AF, which refers to Tb antiferromagnetism) at TR2. One can notice that, as N increase, TR 2 increase and TR! decreases.
c) For 2.24 7r~N~41r,the system passes directly at T = TN from the paramagnetic state to the type B
(AF) structure. U
3
3
x_axis demagnetizing factor hg. 1.
When disordered, Tb moments have zero magnitude, but there is an entropic contribution of the two-singlet system: S
These results are well representative of the experi-
mental situation. For example, the fact pointed out by [6] that the reorientation taking place at TR2, observed on powder samples, does not occur on single crystals, would be due to shape effects instead of Pb salts inclusions. Experimental verification of this point, altogether with systematic study of the shape dependence, is in progress.
k[p1logp1 +p2logp2} per ion, References
where p2/p1 — exp( .~/T),~ 2K is the gap between the Tb ground levels in absence of induced magnetism. 3) When the terbium magnetic system is not ordered, the Fe moments behave as they do in structure B (weak ferromagnetism directed along the Z axis). The three free energies FA, FB and Fp~a (“paramagnetic” applies to the Tb system only), have been calculated using the molecular field approxima-
tion; the shape effects break in naturally when writing the expression of FA which requires the know-
1 68
[I] R. Bidaux, J. F. Bouree and J. Hammann, to be published. [21 R. Bidaux, J. E. Bouree and J. Hammann, to be published. [3j R. L. White, J. Appi. Phys. 40(1969)1061. [4] K. P. Belov, A. M. Kadomtseva, L. M. Ledneva, T. L. Orchinnikova, Ya. G. Panomarev and V. A. Timofeeva, Soy. Phys. Solid State 9 (1968) 2190. 15] L. I - Bertaut, J. Chappert, J. Mareschal, J. P. Rebouillat and J. Sivardiere, Solid State Comm. 5 (1967) 293. [6] M. Belakhovsky, J. Chappert, T. Rouskov and J. Sivardiere, J. de Phys. Colloque Cl, 32 (1971) 492. [7] R. Bidau~,P. Carrara and B. Vivet, Compt. Rend. 263 (1966) 176.