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Thermomagnetic study of ErFe10.5Mo1.5
ELSEVIER
Journal of Magnetism and Magnetic Materials 196-197 (1999) 307-308
Journalof magnetism and magnetic ~ H materials
Thermomagnetic study of ErFelo.sMoa.5 J.J. Melero a'*, R. Burriel a, E. T o m e y a, D. Fruchart b aInstituto de Ciencia de Materiales de Arag6n, CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain bLaboratoire de Cristallographie, CNRS, B.P. 166, 38042 Grenoble Cedex 9, France
Abstract
The heat capacity of the compound ErFeao.sMo~.5 has been measured from 5 to 330 K with adiabatic calorimetry. An anomaly due to a spin reorientation is observed around 50 K. The magnetic contribution to the heat capacity has been obtained and described with a theoretical model taking into account crystalline-electric-field and exchange contributions. The crystal-field and exchange parameters, taken from previous fits to magnetization measurements on a single crystal, give a good agreement with the experimental results of the heat capacity. © 1999 Elsevier Science B.V. All rights reserved. Keywords." Permanent magnets; Heat capacity; Spin reorientation; Crystal field
In the search for new permanent magnets the series of rare-earth intermetallics 1-12 invoke a special interest because of the potential applications of some of their interstitial derivatives. The pure binary RFe12 (R = rare earth) cannot be obtained, but the structure can be stabilized by replacing a small amount of some elements such as Ti, V, Cr, Mn, Mo, W, Re, A1, or Si by some of the Fe content [1]. For the molybdenum family, compounds RF%2 xMox for 0.5 ~
*Corresponding author. Tel.: + 34-976761929; fax: + 34976761229; e-mail: [email protected].
a theoretical model that takes into account crystal-electric-field (CEF) and exchange interactions. The parameters derived from other techniques will be used to compare our experimental values with the theoretical model. This will permit to establish the reliability of these parameters in view of their thermodynamic consequences. Two samples, ErFexo.sMol.5 and LuFelo.sMol.5, were prepared by melting the pure constituents in an induction furnace. The resulting ingots were characterized by X-ray diffraction, scanning electron microscopy and X-ray microanalysis. Only small traces of ~-Fe and rare-earth oxide were observed. The heat-capacity measurements were performed in an adiabatic calorimeter from 5 to 330 K and the experimental results are shown in Fig. 1. The magnetic contribution to the heat capacity of the compound ErFel0.sMo~.5 was obtained by direct subtraction of the heat capacity of LuFelo.sMo~.5. Both compounds have the same structure and very similar lattice constants and atomic weights. So, the heat-capacity contribution of the lattice vibrational modes will be quite similar for both compounds. The magnetic contribution shows an anomaly at around 50 K (inset in Fig. 1), due to the spin reorientation present in the Er compound, where the easy magnetization direction changes from being parallel to
0304-8853/99/$ - see front matter (c) 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 7 2 6 - 4
308
ZJ. Melero el al. /Journal o/Magnetism and Magnetic Malerial.v 196-197 (1999) 307- 30~'
describe the magnetic behavior of the Fe sublattice at each temperature tanisotropy constant and spontaneous magnetization) are the same used to fit magnetization experiments on a ErEelo.sMol.5 single crystal [2]. The total free energy can bc written as
50
40
o/
3D
g
,,,e
,
f-
c lRi
.
.
F,,,t - - k B T In ZR + K I sin 2 0~.
. '
2o
(r:,,//
10
"
: .?. ~l
5.
The calculations are performed as follows: for a given set of C E F and exchange parameters, and for each temperature, the magnetic state of the system is determined by the equilibrium direction of the Fe sublattice magnetization, 0~, obtained by minimizing the total free energy given in Eq. (3). The magnetic heat capacity is then calculated from the second derivative of the total fiee energy evaluated with that angle
.y~- ~;~:. ca
5
',,
_~51~
FK, (I
5(I
100
150
200
25(1
3t10
351)
T (K) Fig. 1. Heat capacities of the compounds ErFelo sMo~.~ {open circles) and LuFe~o.sMol.s (full line). The magnetic anomaly of ErFc~o ~Mo~.s is shown m the inset (dots) and compared with the theoretical calculations (full line).
the crystallographic c axis to form a non-zero angle with this axis [2]. In order to describe the magnetic heat capacity, we have used a theoretical model with two interacting sublattices, the rare-earth sublattice and the Fe sublattice [3]. The former can be described by a Hamiltonian acting on the ground state multiplet of the Er 3 ~ ion as follows: '~t/ R -- "~CEF IF 2(,q.I -- 1}l.tB JH~:x,
( 1)
where J/g"CEF
0 0 0 0 : B 20 0 20 + B404. + B 44 0 44 4- BOO(, 4- B 64 0 46,
13)
(2)
is the C E F contribution in tetragonal symmetry• The BI" terms are the C E F parameters and the O}" are the Stevens equivalent operators. The second term in Eq. (1) corresponds to the exchange energy between both sublattices, being HEx the exchange field, that is taken to be proportional and antiparallel to the magnetization of the Fe sublattice. The exchange energy between rare-earth ions is much smaller and has not been considered. At a given temperature, the free energy of the rare-earth sublattice is calculated as FR = -- k B T In ZR, where kB is the Boltzmann constant and ZR the partition function. The free energy of the Fe sublattice is described with an anisotropy term, F F e = K 1 sin 20L,~, K1 being the anisotropy constant and Ow the angle that forms the Fe magnetic moments with the c axis. The isotropic part of the Fe sublattice energy has not been taken into account. This energy is important in defining the ferrimagnetic ordering temperature, but it is above the temperatures of our study, it has no effect in the spin reorientation, and its heat-capacity contribution also exists in the isostructural compound used to subtract the non-anomalous contributions. The phenomenological parameters taken to
Co,
T[deFTo,(T, O{~}/dT'-].
14t
The resuhs of the calculations are shown in the inset of Fig. 1 (full line) compared with the experimental magnetic heat capacity. The parameters used were B° = 0 . 2 4 5 x 1 0 2K, B4° = 0 . 2 1 8 x 1 0 3K. B ~ = -0.365x10 ZK, B [ l = 0 . 4 8 1 x 1 0 ('K. B ~ - 0 . 1 9 2 x 10 "~K, and 2gRHEx(0K) = 222 K. This set of parameters fit the magnetization curves at different temperatures and the spin reorientation angle for a single crystal [2]. It can be seen that the theoretical calculations reproduce quite well our experimental Cm results for this set of parameters. Calculations using parameters derived from ErFe~ 1Ti [4] give much bigger differences with the experimental results of heat capacity, magnetization, and direction of the magnetic moments. Usually, tk)r a particular rare-earth ion, the anisotropy is determined by the sign of B °. In this case, B 2 is not the leading parameter in determining the anisotropy, and the fourthorder terms have the main influence in the temperature variation of the magnetization direction. It can be concluded that the C E F and exchange parameters given in Ref. [2] provide a good description of the magnetic and heat capacity results of ErFe~o.sMo~ >
This work has been supported by the Spanish CICYT. Project number MAT97-0987 and the L E A - M A N E S Program
References [l] H. Li, J.M.D. Coey, in: K.H.J. Buschow (Ed.i, Handbook of Magnetic Materials, Vol. 6, Elsevier, Amsterdam. 1993. [2] B. Garcia-Landa, D. Gignoux, R. Vert, D. Fruchart, R. Skolozdra, J. Phys.: Condens. Matter 10 (1998) 1403. [3] C. Pique, R. Burriel. J. Bartolom~:, J. Magn. Magn. Mater. 154 (19961 71. [4] X.C. Kou, T.S. Zhao, R. Gr6ssmger, H.R. Kirchmayr. X. El. F.R. de Boer, Phys. Rev. B 47 11993) 3231.
Journal of Magnetism and Magnetic Materials 196-197 (1999) 307-308
Journalof magnetism and magnetic ~ H materials
Thermomagnetic study of ErFelo.sMoa.5 J.J. Melero a'*, R. Burriel a, E. T o m e y a, D. Fruchart b aInstituto de Ciencia de Materiales de Arag6n, CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain bLaboratoire de Cristallographie, CNRS, B.P. 166, 38042 Grenoble Cedex 9, France
Abstract
The heat capacity of the compound ErFeao.sMo~.5 has been measured from 5 to 330 K with adiabatic calorimetry. An anomaly due to a spin reorientation is observed around 50 K. The magnetic contribution to the heat capacity has been obtained and described with a theoretical model taking into account crystalline-electric-field and exchange contributions. The crystal-field and exchange parameters, taken from previous fits to magnetization measurements on a single crystal, give a good agreement with the experimental results of the heat capacity. © 1999 Elsevier Science B.V. All rights reserved. Keywords." Permanent magnets; Heat capacity; Spin reorientation; Crystal field
In the search for new permanent magnets the series of rare-earth intermetallics 1-12 invoke a special interest because of the potential applications of some of their interstitial derivatives. The pure binary RFe12 (R = rare earth) cannot be obtained, but the structure can be stabilized by replacing a small amount of some elements such as Ti, V, Cr, Mn, Mo, W, Re, A1, or Si by some of the Fe content [1]. For the molybdenum family, compounds RF%2 xMox for 0.5 ~
*Corresponding author. Tel.: + 34-976761929; fax: + 34976761229; e-mail: [email protected].
a theoretical model that takes into account crystal-electric-field (CEF) and exchange interactions. The parameters derived from other techniques will be used to compare our experimental values with the theoretical model. This will permit to establish the reliability of these parameters in view of their thermodynamic consequences. Two samples, ErFexo.sMol.5 and LuFelo.sMol.5, were prepared by melting the pure constituents in an induction furnace. The resulting ingots were characterized by X-ray diffraction, scanning electron microscopy and X-ray microanalysis. Only small traces of ~-Fe and rare-earth oxide were observed. The heat-capacity measurements were performed in an adiabatic calorimeter from 5 to 330 K and the experimental results are shown in Fig. 1. The magnetic contribution to the heat capacity of the compound ErFel0.sMo~.5 was obtained by direct subtraction of the heat capacity of LuFelo.sMo~.5. Both compounds have the same structure and very similar lattice constants and atomic weights. So, the heat-capacity contribution of the lattice vibrational modes will be quite similar for both compounds. The magnetic contribution shows an anomaly at around 50 K (inset in Fig. 1), due to the spin reorientation present in the Er compound, where the easy magnetization direction changes from being parallel to
0304-8853/99/$ - see front matter (c) 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 7 2 6 - 4
308
ZJ. Melero el al. /Journal o/Magnetism and Magnetic Malerial.v 196-197 (1999) 307- 30~'
describe the magnetic behavior of the Fe sublattice at each temperature tanisotropy constant and spontaneous magnetization) are the same used to fit magnetization experiments on a ErEelo.sMol.5 single crystal [2]. The total free energy can bc written as
50
40
o/
3D
g
,,,e
,
f-
c lRi
.
.
F,,,t - - k B T In ZR + K I sin 2 0~.
. '
2o
(r:,,//
10
"
: .?. ~l
5.
The calculations are performed as follows: for a given set of C E F and exchange parameters, and for each temperature, the magnetic state of the system is determined by the equilibrium direction of the Fe sublattice magnetization, 0~, obtained by minimizing the total free energy given in Eq. (3). The magnetic heat capacity is then calculated from the second derivative of the total fiee energy evaluated with that angle
.y~- ~;~:. ca
5
',,
_~51~
FK, (I
5(I
100
150
200
25(1
3t10
351)
T (K) Fig. 1. Heat capacities of the compounds ErFelo sMo~.~ {open circles) and LuFe~o.sMol.s (full line). The magnetic anomaly of ErFc~o ~Mo~.s is shown m the inset (dots) and compared with the theoretical calculations (full line).
the crystallographic c axis to form a non-zero angle with this axis [2]. In order to describe the magnetic heat capacity, we have used a theoretical model with two interacting sublattices, the rare-earth sublattice and the Fe sublattice [3]. The former can be described by a Hamiltonian acting on the ground state multiplet of the Er 3 ~ ion as follows: '~t/ R -- "~CEF IF 2(,q.I -- 1}l.tB JH~:x,
( 1)
where J/g"CEF
0 0 0 0 : B 20 0 20 + B404. + B 44 0 44 4- BOO(, 4- B 64 0 46,
13)
(2)
is the C E F contribution in tetragonal symmetry• The BI" terms are the C E F parameters and the O}" are the Stevens equivalent operators. The second term in Eq. (1) corresponds to the exchange energy between both sublattices, being HEx the exchange field, that is taken to be proportional and antiparallel to the magnetization of the Fe sublattice. The exchange energy between rare-earth ions is much smaller and has not been considered. At a given temperature, the free energy of the rare-earth sublattice is calculated as FR = -- k B T In ZR, where kB is the Boltzmann constant and ZR the partition function. The free energy of the Fe sublattice is described with an anisotropy term, F F e = K 1 sin 20L,~, K1 being the anisotropy constant and Ow the angle that forms the Fe magnetic moments with the c axis. The isotropic part of the Fe sublattice energy has not been taken into account. This energy is important in defining the ferrimagnetic ordering temperature, but it is above the temperatures of our study, it has no effect in the spin reorientation, and its heat-capacity contribution also exists in the isostructural compound used to subtract the non-anomalous contributions. The phenomenological parameters taken to
Co,
T[deFTo,(T, O{~}/dT'-].
14t
The resuhs of the calculations are shown in the inset of Fig. 1 (full line) compared with the experimental magnetic heat capacity. The parameters used were B° = 0 . 2 4 5 x 1 0 2K, B4° = 0 . 2 1 8 x 1 0 3K. B ~ = -0.365x10 ZK, B [ l = 0 . 4 8 1 x 1 0 ('K. B ~ - 0 . 1 9 2 x 10 "~K, and 2gRHEx(0K) = 222 K. This set of parameters fit the magnetization curves at different temperatures and the spin reorientation angle for a single crystal [2]. It can be seen that the theoretical calculations reproduce quite well our experimental Cm results for this set of parameters. Calculations using parameters derived from ErFe~ 1Ti [4] give much bigger differences with the experimental results of heat capacity, magnetization, and direction of the magnetic moments. Usually, tk)r a particular rare-earth ion, the anisotropy is determined by the sign of B °. In this case, B 2 is not the leading parameter in determining the anisotropy, and the fourthorder terms have the main influence in the temperature variation of the magnetization direction. It can be concluded that the C E F and exchange parameters given in Ref. [2] provide a good description of the magnetic and heat capacity results of ErFe~o.sMo~ >
This work has been supported by the Spanish CICYT. Project number MAT97-0987 and the L E A - M A N E S Program
References [l] H. Li, J.M.D. Coey, in: K.H.J. Buschow (Ed.i, Handbook of Magnetic Materials, Vol. 6, Elsevier, Amsterdam. 1993. [2] B. Garcia-Landa, D. Gignoux, R. Vert, D. Fruchart, R. Skolozdra, J. Phys.: Condens. Matter 10 (1998) 1403. [3] C. Pique, R. Burriel. J. Bartolom~:, J. Magn. Magn. Mater. 154 (19961 71. [4] X.C. Kou, T.S. Zhao, R. Gr6ssmger, H.R. Kirchmayr. X. El. F.R. de Boer, Phys. Rev. B 47 11993) 3231.