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Crystal field investigation of Pd2REIn (RE = rare earth)
ELSEVIER
Physica B 213&214 (1995) 300-302
Crystal field investigation of Pd2REIn (RE = rare earth) M. Babateen a, J. Crangle h, F. Fauth c, A. Furreff, K.-U. N e u m a n n a'*, K.R.A. Z i e b e c k a aDepartment of Physics, Loughborough University, Loughborough, LEll 3TU, UK bDepartment of Physics, University of Sheffield, Sheffield, $3 7RH, UK Labor fiir Neutronenstreuung, ETH Ziirich, CH-5232 Villingen. PSI, Switzerland
Abstract
Inelastic neutron scattering experiments have been carried out on rare earth based Heusler alloys. Results are reported for Pd2Holn and Pd2Ybln. The crystal field (CF) level scheme is determined and the results are compared to bulk measurements of the magnetisation in the temperature range 2 K to room temperature and in applied magnetic fields of up to 5 T. A comparison is carried out for the CF schemes between the In and Sn based series.
The investigation of the magnetic properties of rare earth alloys, for which the rare earth atom exhibits localised magnetism without the onset of a correlated state at low temperatures, necessitates the characterisation of single-ion properties as determined by the crystal-field (CF) splitting. This information is most directly obtained in an inelastic neutron scattering experiment for which the transitions between crystal-field eigenstates are immediately accessible. For cubic compounds Lea et al. [1] have developed a parameterization scheme which allows the description of the crystal-field splitting for sites with cubic symmetry using two parameters, W and X. The parameter W measures the overall splitting of the CF scheme whereas X, which takes on values in the range 1 ~< X ~< 1, is a measure of the strength of the fourthto the sixth-order terms in the original Hamiitonian. The intensities Of the inelastic transitions have been calculated and tabulated by Birgeneau I-2]. The inelastic neutron scattering spectra of Pd2Holn have been investigated in the temperature range 10 to 80 K. Two strong crystal field transitions have been identified. A fit of the neutron spectra using the CF parameters W = 0.02673 and X = 0.3543 resulted in good *Corresponding author.
overall agreement between calculated and observed intensities. Using the above crystal field level scheme of Pd2Holn the CF parameters of other rare earth compounds in the series may be extrapolated. Here only the results of the Yb compound are presented. For PdzYbln values of W = -0.5194 and X--- -0.7485 are obtained. These values are close to the ones obtained by a model fit to the inelastic neutron spectrum at 10 K as shown in Fig. 1. For this temperature only one excitation out of the ground state is observable. In order to test the above assignment of CF parameters and to characterise the properties of these compounds more fully the magnetisation has been determined in the temperature range between 2 K and room temperature and in fields of up to 5T. The magnetisation measurements were carried out using a SQUID magnetometer (Quantum Design) on the same powder samples as used in the neutron scattering experiments. A crystal field model and CF parameters as determined by the neutron scattering experiments were used for the calculation of the experimental magnetisation data. A mean field description was employed in order to take into account interactions between magnetic
0921-4526/95/$09.50 (t~, 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 1 3 6 - 0
M. Babateen et al./ Physica B 213&214 (1995) 300-302
J'
301
Pd2Ybln T = 10K Q = 2,0 ,~-1
/
~ T-2K
T " 4 K
6O
T-6K 5O
:g
/
I
40
,
T-10K
I
'! 10'
/'/
.20K
°L o energy
transfer
io [mev]
Fig. 1. Inelastic neutron scattering spectrum of Pd2Ybln. The solid line is a fit using a crystal field model.
moments. The magnetic moment was self-consistently iterated for each value of the external magnetic field and each orientation of the magnetic field with respect to the crystallographic axis. Thereafter a powder average was carried out for each value of the external magnetic field, using the assumption that the induced ferromagnetic moment is always parallel to the external magnetic field direction. At low temperatures the increased importance of the single ion anisotropy renders the approximation MllBext.... i doubtful. Not including an optimisation of the tilt angle between the magnetic moment M and the external magnetic field S e x t. . . . I for each orientation of the magnetic field with respect to the lattice leads to an underestimate of the magnitude of the magnetisation. In order to include this effect in the model calculations approximately, an asymmetry contribution was incorporated into the fitting procedure, the magnitude of which was taken to be proportional to the thermal average of the single ion anisotropy. The magnetisation fit shown here in Fig. 2 includes this correction term. For Pd2Holn reasonable agreement is obtained between the calculated and measured magnetisations. In order to allow a comparison of the CF parameters of Pd2REIn alloys with those of the isostructural Pd2RESn series, the crystal field splitting of PdzYbSn has been determined. One spectrum and the resultant fit are shown in Fig. 3. A comparison of Fig. 1 and Fig. 3 reveals that the first inelastic transition is lower in energy in the Sn compound as compared to the In compound. This finding is reflected in the CF parameters which
Fig. 2. Experimental magnetisation data (crosses) of Pd2Ybln. The lines are fits to the data.
/20 0i --
l
T=10K Q = 3 . 5 ,~.-1
00
°t Fig. 3. Inelastic neutron scattering spectrum of PdzYbSn. A crystal field model with W = - 0.21, X = - 0.79 (solid line) is shown as a fit to the data.
indicated a reduction in the W parameter while X remains essentially unchanged. A comparison of the CF parameters of the Yb compounds or, more directly, their neutron spectra, reveals that the overall pattern is not changed by the substitution
302
M. Babateen et al./Physica B 213&214 (1995) 300 302
of Sn for In. While the level scheme remains essentially the same the overall energy is scaled up for the In compound compared to the Sn compound. When the CF scheme of Pd2HoIn is compared to that of Pd2HoSn as determined by Li et al. [5] the CF parameters for the Sn compound are found to be very similar to those of the In compound. However, on changing the third element essentially no change of the overall energy scale is observed for the Ho compounds. In order to understand the apparent insensitivity of the CF level scheme to the nature of the third element it is necessary to consider the crystallographic structure. The rare earth atom has eight Pd atoms as nearest neighbours and it is located at the centre of a palladium cube. The six In or Sn atoms are next nearest neighbours. It is reasonable to assume that the main influence for the crystal field splitting is exerted on the rare earth atom by its nearest neighbours, with the conduction electrons effectively shielding the influences of the more distant neighbours. It is thus possible to study in these compounds the (presumably small) effect of more distant atoms on the CF scheme and the strength of the CF interactions as measured by the overall CF splitting. However, the replacement of the In by Sn will increase the number of conduction electrons by one. For free atoms Sn has two 5p electrons compared to one for In. Taking into account the large extent of the 5p wave function and locating the Sn atom within a metallic alloy it is to be expected that the additional electron is delocalized. While having to screen the additional nuclear charge on the Sn lattice site, the large spread of the 5p-elelctronic wave function will alter the effective charge located on the palladium atoms,
thereby reducing its value for the Sn compound compared to In. If, as for example is assumed within a simple point-charge model for the crystal field splitting, the matrix elements of the crystal field hamiltonian are determined mainly by the effective charge located on the Pd atoms, a reduction of this charge will occur on replacing In by Sn. However, for a metallic compound the origin of the CF splitting is also due to hybridisation of the 4f wave function with conduction electrons, rendering this simple argument as given above inappropriate. Nevertheless, the above consideration may serve as a guide for understanding the systematics of crystal-field schemes in the alloys of interest here. In conclusion, the magnetic characteristics of some rare earth compounds in the series Pd2REIn have been determined by inelastic neutron scattering. The results are used to compare the predictions with the results of magnetisation measurements. Satisfactory agreement between observation and calculation is obtained for the magnetisation.
References [1] K.R. Lea, M.J.M, Leask and W.P. Wolf, J. Phys. Chem. Solids 23 (1962) 1381. [2] R.J. Birgeneau, J. Phys. Chem. Solids 33 (1972) 59. [3] P.J. Webster and R.S. Tebble, Phil. Mag. 16 (1967) 347. [4] D.J. Doherty, J. Crangle, K.-U. Neumann, J.G. Smith, N.K. Zayer and K.R.A. Ziebeck, J. Magn. Magn. Mater. 140 144 (1995) 189. [5] W.-H. Li, J.W. Lynn, H.B. Stanley, T.J. Udovic, R.N. Shelton and P. Klavins, Phys. Rev. B 39 (1989)4119.
Physica B 213&214 (1995) 300-302
Crystal field investigation of Pd2REIn (RE = rare earth) M. Babateen a, J. Crangle h, F. Fauth c, A. Furreff, K.-U. N e u m a n n a'*, K.R.A. Z i e b e c k a aDepartment of Physics, Loughborough University, Loughborough, LEll 3TU, UK bDepartment of Physics, University of Sheffield, Sheffield, $3 7RH, UK Labor fiir Neutronenstreuung, ETH Ziirich, CH-5232 Villingen. PSI, Switzerland
Abstract
Inelastic neutron scattering experiments have been carried out on rare earth based Heusler alloys. Results are reported for Pd2Holn and Pd2Ybln. The crystal field (CF) level scheme is determined and the results are compared to bulk measurements of the magnetisation in the temperature range 2 K to room temperature and in applied magnetic fields of up to 5 T. A comparison is carried out for the CF schemes between the In and Sn based series.
The investigation of the magnetic properties of rare earth alloys, for which the rare earth atom exhibits localised magnetism without the onset of a correlated state at low temperatures, necessitates the characterisation of single-ion properties as determined by the crystal-field (CF) splitting. This information is most directly obtained in an inelastic neutron scattering experiment for which the transitions between crystal-field eigenstates are immediately accessible. For cubic compounds Lea et al. [1] have developed a parameterization scheme which allows the description of the crystal-field splitting for sites with cubic symmetry using two parameters, W and X. The parameter W measures the overall splitting of the CF scheme whereas X, which takes on values in the range 1 ~< X ~< 1, is a measure of the strength of the fourthto the sixth-order terms in the original Hamiitonian. The intensities Of the inelastic transitions have been calculated and tabulated by Birgeneau I-2]. The inelastic neutron scattering spectra of Pd2Holn have been investigated in the temperature range 10 to 80 K. Two strong crystal field transitions have been identified. A fit of the neutron spectra using the CF parameters W = 0.02673 and X = 0.3543 resulted in good *Corresponding author.
overall agreement between calculated and observed intensities. Using the above crystal field level scheme of Pd2Holn the CF parameters of other rare earth compounds in the series may be extrapolated. Here only the results of the Yb compound are presented. For PdzYbln values of W = -0.5194 and X--- -0.7485 are obtained. These values are close to the ones obtained by a model fit to the inelastic neutron spectrum at 10 K as shown in Fig. 1. For this temperature only one excitation out of the ground state is observable. In order to test the above assignment of CF parameters and to characterise the properties of these compounds more fully the magnetisation has been determined in the temperature range between 2 K and room temperature and in fields of up to 5T. The magnetisation measurements were carried out using a SQUID magnetometer (Quantum Design) on the same powder samples as used in the neutron scattering experiments. A crystal field model and CF parameters as determined by the neutron scattering experiments were used for the calculation of the experimental magnetisation data. A mean field description was employed in order to take into account interactions between magnetic
0921-4526/95/$09.50 (t~, 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 1 3 6 - 0
M. Babateen et al./ Physica B 213&214 (1995) 300-302
J'
301
Pd2Ybln T = 10K Q = 2,0 ,~-1
/
~ T-2K
T " 4 K
6O
T-6K 5O
:g
/
I
40
,
T-10K
I
'! 10'
/'/
.20K
°L o energy
transfer
io [mev]
Fig. 1. Inelastic neutron scattering spectrum of Pd2Ybln. The solid line is a fit using a crystal field model.
moments. The magnetic moment was self-consistently iterated for each value of the external magnetic field and each orientation of the magnetic field with respect to the crystallographic axis. Thereafter a powder average was carried out for each value of the external magnetic field, using the assumption that the induced ferromagnetic moment is always parallel to the external magnetic field direction. At low temperatures the increased importance of the single ion anisotropy renders the approximation MllBext.... i doubtful. Not including an optimisation of the tilt angle between the magnetic moment M and the external magnetic field S e x t. . . . I for each orientation of the magnetic field with respect to the lattice leads to an underestimate of the magnitude of the magnetisation. In order to include this effect in the model calculations approximately, an asymmetry contribution was incorporated into the fitting procedure, the magnitude of which was taken to be proportional to the thermal average of the single ion anisotropy. The magnetisation fit shown here in Fig. 2 includes this correction term. For Pd2Holn reasonable agreement is obtained between the calculated and measured magnetisations. In order to allow a comparison of the CF parameters of Pd2REIn alloys with those of the isostructural Pd2RESn series, the crystal field splitting of PdzYbSn has been determined. One spectrum and the resultant fit are shown in Fig. 3. A comparison of Fig. 1 and Fig. 3 reveals that the first inelastic transition is lower in energy in the Sn compound as compared to the In compound. This finding is reflected in the CF parameters which
Fig. 2. Experimental magnetisation data (crosses) of Pd2Ybln. The lines are fits to the data.
/20 0i --
l
T=10K Q = 3 . 5 ,~.-1
00
°t Fig. 3. Inelastic neutron scattering spectrum of PdzYbSn. A crystal field model with W = - 0.21, X = - 0.79 (solid line) is shown as a fit to the data.
indicated a reduction in the W parameter while X remains essentially unchanged. A comparison of the CF parameters of the Yb compounds or, more directly, their neutron spectra, reveals that the overall pattern is not changed by the substitution
302
M. Babateen et al./Physica B 213&214 (1995) 300 302
of Sn for In. While the level scheme remains essentially the same the overall energy is scaled up for the In compound compared to the Sn compound. When the CF scheme of Pd2HoIn is compared to that of Pd2HoSn as determined by Li et al. [5] the CF parameters for the Sn compound are found to be very similar to those of the In compound. However, on changing the third element essentially no change of the overall energy scale is observed for the Ho compounds. In order to understand the apparent insensitivity of the CF level scheme to the nature of the third element it is necessary to consider the crystallographic structure. The rare earth atom has eight Pd atoms as nearest neighbours and it is located at the centre of a palladium cube. The six In or Sn atoms are next nearest neighbours. It is reasonable to assume that the main influence for the crystal field splitting is exerted on the rare earth atom by its nearest neighbours, with the conduction electrons effectively shielding the influences of the more distant neighbours. It is thus possible to study in these compounds the (presumably small) effect of more distant atoms on the CF scheme and the strength of the CF interactions as measured by the overall CF splitting. However, the replacement of the In by Sn will increase the number of conduction electrons by one. For free atoms Sn has two 5p electrons compared to one for In. Taking into account the large extent of the 5p wave function and locating the Sn atom within a metallic alloy it is to be expected that the additional electron is delocalized. While having to screen the additional nuclear charge on the Sn lattice site, the large spread of the 5p-elelctronic wave function will alter the effective charge located on the palladium atoms,
thereby reducing its value for the Sn compound compared to In. If, as for example is assumed within a simple point-charge model for the crystal field splitting, the matrix elements of the crystal field hamiltonian are determined mainly by the effective charge located on the Pd atoms, a reduction of this charge will occur on replacing In by Sn. However, for a metallic compound the origin of the CF splitting is also due to hybridisation of the 4f wave function with conduction electrons, rendering this simple argument as given above inappropriate. Nevertheless, the above consideration may serve as a guide for understanding the systematics of crystal-field schemes in the alloys of interest here. In conclusion, the magnetic characteristics of some rare earth compounds in the series Pd2REIn have been determined by inelastic neutron scattering. The results are used to compare the predictions with the results of magnetisation measurements. Satisfactory agreement between observation and calculation is obtained for the magnetisation.
References [1] K.R. Lea, M.J.M, Leask and W.P. Wolf, J. Phys. Chem. Solids 23 (1962) 1381. [2] R.J. Birgeneau, J. Phys. Chem. Solids 33 (1972) 59. [3] P.J. Webster and R.S. Tebble, Phil. Mag. 16 (1967) 347. [4] D.J. Doherty, J. Crangle, K.-U. Neumann, J.G. Smith, N.K. Zayer and K.R.A. Ziebeck, J. Magn. Magn. Mater. 140 144 (1995) 189. [5] W.-H. Li, J.W. Lynn, H.B. Stanley, T.J. Udovic, R.N. Shelton and P. Klavins, Phys. Rev. B 39 (1989)4119.