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Magnetic resonance in the weak ferromagnet Fe3BO6
1261
MAGNETIC RESONANCE IN THE WEAK FERROMAGNET FeaBO6 E.U. MOLLERWIEBUS and K.A. H E M P E L Werkstoffe der Elektrotechnik der R W T H Aachen, 5100 Aachen, W. Germany
Six different magnetic resonances have been observed in the weak ferromagnet Fe,BO, in the frequency range 68-89 Gcps at temperatures between 360 K and TN = 508 K. The anisotropy fields, determined from the experiments using a new four sublattice model, show that the sublattices have different mutual orientation below and above TsR = 415 K.
C=(JF--3JFc)/(3Jc--JFc).
1. Introduction The weak ferromagnet Fe3BO6 exhibits a spin reorientation at Tsg = 415 K. For T < WSR the spins are parallel to [001] with canting along [100], for T > WSR the spins are aligned parallel to [100] and the spontaneous moment is in the [ 0 0 1 ] direction [1-4]. Magnetization measurements in connection with symmetry arguments [3,4] give information about the dominant antiferromagnetic spin arrangement in Fe3BO6. In order to explain the anisotropy of the susceptibility, the direction dependence of the weak ferromagnetic moment and the microwave spectrum we calculated a new four sublattice model for the space group P~a. 2. Theory
The subscripts denote the coupling between two of the four magnetic basic vectors [3]. J describes an isotropic exchange. The contribution to energy is given by Dvo" [F x G], AvG(F~Gz + FzOx), JFF, D13" ( M I × M3), a . s . o .
3. Experimental Ferromagnetic and antiferromagnetic modes could be excited. The used crystals were platelets with dimensions of 0 . 3 m m × 0 . 5 m m x 1.0 mm grown from a melt of Bi203, B203 and Fe203. Frequency and resonance field are measured with an accuracy of 0.1%. The temperature is accurate within 0.2 K.
4. Results
Fe3BO6 has twelve magnetic sublattices. The Fe3+-ions in the chemical unit cell are on the 8dand 4c-sites. Our model is composed of a two sublattice model for the 8d sites, a two sublattice model for the 4c sites and mutual coupling of all four sublattices. The free energy is compatible with the symmetry of the space group 16 D2h-Pma. Two of the four resonance frequencies for B]I[100] are given by:
Fig. 1 shows the temperature dependence of the resonance field B for three antiferromagBU[001]X t
BT30 - A 82,6Gcps
Z5 v _A ~rDGCp$
(a,/3,) 2 = B 2 + B(5Aloo - D1oo) + B2A1,
(1)
( . , / v ) 2 = B(A,oo - Dioo) + B 2.
(2)
The other resonances are in the infrared region. B~I and B22 a r e field independent and contain all kinds of crystal fields. D and A represent the Dzialoshinski-exchange and single-ion anisotropy, respectively. The measured D and A is an abbreviation for D,0o = 16Mo(3 + C ) - t ( D F G -t- DCG" C ) , Ai00 = 16Mo(3 + C)-I(AFo + AcG" C), Physica 86-88B 0977) 1261-1262 (~) North-Holland
(3)
BilBo ZO
1.0 0,5
%
370
/20
~70 K 520
Fig. 1. Resonance fields versus temperature for antiferromagnetic modes.
1262 netic modes. Almost the same temperature dependence of the resonance field is obtained for the ferromagnetic modes except for the range 370-400 K there is no resonance found above 75 Gcps. From a comparison of these experiments with the above mentioned equations we obtained the temperature dependence of D0m, D~0o, A0m and A 100given in fig. 2 and fig. 3. It can be shown that the resonances in the temperature range 370-400 K with B parallel to [001] are due to misorientation of the sublattices and must not be analysed. The single ion anisotropy is small compared with the Dzialoshinski exchange and nearly independent from temperature and crystal direction whereas the Dzialoshinski fields show a great change with temperature and crystal direction. A O II
[T]o["
4oo ~2o ~4o
~5o 48o t[K]
-7
A D! [t]e ~ X
TIK]
Fig. 3. Anisotropy fields versus temperature.
that exchange fields remain constant (the susceptibility is steady) and the anisotropic exchange changes its sign and value. The change of lattice constants at 415 K is unknown but such an unsteady behaviour is not probable. 2) Only a six sublattice model describes the magnetic behaviour and the measured effective fields are wrongly interpreted. 3) During the reorientation the sublattices of the 8d-places turn cw and the sublattices of the 4c places turn ccw in the (010) plane by 90 degree. This gives a change in coupling and the difference D100- D001 is proportional to D13 - Di4. With neutron scattering experiments it is possible to test this explanation.
-13 15
References [1] J.G. White, A. Miller and R.E. Nielsen, Acta cryst. 19
Fig. 2. Anisotropy fields versus temperature.
There exist three possible explanations: 1) In the course of the reorientation the dimensions of the unit cell are changed in such a way,
(1965) I060. [21 R. Wolfe, R.D. Pierce, M. Eibschfitz and J.W. Nielsen, Sol. State Comm. 7 0969) 949. [3] M. Hirano, T. Okuda and T. Tsushima, Sol. State Comm. 15 (1974) 1129. [4] C. Voigt and D. Bonnenberg, Physica 80B (1975) 439.
MAGNETIC RESONANCE IN THE WEAK FERROMAGNET FeaBO6 E.U. MOLLERWIEBUS and K.A. H E M P E L Werkstoffe der Elektrotechnik der R W T H Aachen, 5100 Aachen, W. Germany
Six different magnetic resonances have been observed in the weak ferromagnet Fe,BO, in the frequency range 68-89 Gcps at temperatures between 360 K and TN = 508 K. The anisotropy fields, determined from the experiments using a new four sublattice model, show that the sublattices have different mutual orientation below and above TsR = 415 K.
C=(JF--3JFc)/(3Jc--JFc).
1. Introduction The weak ferromagnet Fe3BO6 exhibits a spin reorientation at Tsg = 415 K. For T < WSR the spins are parallel to [001] with canting along [100], for T > WSR the spins are aligned parallel to [100] and the spontaneous moment is in the [ 0 0 1 ] direction [1-4]. Magnetization measurements in connection with symmetry arguments [3,4] give information about the dominant antiferromagnetic spin arrangement in Fe3BO6. In order to explain the anisotropy of the susceptibility, the direction dependence of the weak ferromagnetic moment and the microwave spectrum we calculated a new four sublattice model for the space group P~a. 2. Theory
The subscripts denote the coupling between two of the four magnetic basic vectors [3]. J describes an isotropic exchange. The contribution to energy is given by Dvo" [F x G], AvG(F~Gz + FzOx), JFF, D13" ( M I × M3), a . s . o .
3. Experimental Ferromagnetic and antiferromagnetic modes could be excited. The used crystals were platelets with dimensions of 0 . 3 m m × 0 . 5 m m x 1.0 mm grown from a melt of Bi203, B203 and Fe203. Frequency and resonance field are measured with an accuracy of 0.1%. The temperature is accurate within 0.2 K.
4. Results
Fe3BO6 has twelve magnetic sublattices. The Fe3+-ions in the chemical unit cell are on the 8dand 4c-sites. Our model is composed of a two sublattice model for the 8d sites, a two sublattice model for the 4c sites and mutual coupling of all four sublattices. The free energy is compatible with the symmetry of the space group 16 D2h-Pma. Two of the four resonance frequencies for B]I[100] are given by:
Fig. 1 shows the temperature dependence of the resonance field B for three antiferromagBU[001]X t
BT30 - A 82,6Gcps
Z5 v _A ~rDGCp$
(a,/3,) 2 = B 2 + B(5Aloo - D1oo) + B2A1,
(1)
( . , / v ) 2 = B(A,oo - Dioo) + B 2.
(2)
The other resonances are in the infrared region. B~I and B22 a r e field independent and contain all kinds of crystal fields. D and A represent the Dzialoshinski-exchange and single-ion anisotropy, respectively. The measured D and A is an abbreviation for D,0o = 16Mo(3 + C ) - t ( D F G -t- DCG" C ) , Ai00 = 16Mo(3 + C)-I(AFo + AcG" C), Physica 86-88B 0977) 1261-1262 (~) North-Holland
(3)
BilBo ZO
1.0 0,5
%
370
/20
~70 K 520
Fig. 1. Resonance fields versus temperature for antiferromagnetic modes.
1262 netic modes. Almost the same temperature dependence of the resonance field is obtained for the ferromagnetic modes except for the range 370-400 K there is no resonance found above 75 Gcps. From a comparison of these experiments with the above mentioned equations we obtained the temperature dependence of D0m, D~0o, A0m and A 100given in fig. 2 and fig. 3. It can be shown that the resonances in the temperature range 370-400 K with B parallel to [001] are due to misorientation of the sublattices and must not be analysed. The single ion anisotropy is small compared with the Dzialoshinski exchange and nearly independent from temperature and crystal direction whereas the Dzialoshinski fields show a great change with temperature and crystal direction. A O II
[T]o["
4oo ~2o ~4o
~5o 48o t[K]
-7
A D! [t]e ~ X
TIK]
Fig. 3. Anisotropy fields versus temperature.
that exchange fields remain constant (the susceptibility is steady) and the anisotropic exchange changes its sign and value. The change of lattice constants at 415 K is unknown but such an unsteady behaviour is not probable. 2) Only a six sublattice model describes the magnetic behaviour and the measured effective fields are wrongly interpreted. 3) During the reorientation the sublattices of the 8d-places turn cw and the sublattices of the 4c places turn ccw in the (010) plane by 90 degree. This gives a change in coupling and the difference D100- D001 is proportional to D13 - Di4. With neutron scattering experiments it is possible to test this explanation.
-13 15
References [1] J.G. White, A. Miller and R.E. Nielsen, Acta cryst. 19
Fig. 2. Anisotropy fields versus temperature.
There exist three possible explanations: 1) In the course of the reorientation the dimensions of the unit cell are changed in such a way,
(1965) I060. [21 R. Wolfe, R.D. Pierce, M. Eibschfitz and J.W. Nielsen, Sol. State Comm. 7 0969) 949. [3] M. Hirano, T. Okuda and T. Tsushima, Sol. State Comm. 15 (1974) 1129. [4] C. Voigt and D. Bonnenberg, Physica 80B (1975) 439.