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Specific heat and crystalline electric field parameters in TmxY1−xAl2
Volume 47A, number 1
PHYSICS LETTERS
25 February 1974
SPECIFIC HEAT AND CRYSTALLINE ELECTRIC FIELD PARAMETERS IN Tm, Y, _xAl2 F. HEINIGER.
H.-G. PURWINS and E. WALKER
Depnrternent de Physique de la Matibe Condensee Universitk de Genbe, CH-I 211 Genkve 4, Switserland Received 10 January 1974 Specific heat measurements on Tm,Yt-,Ala have been performed to determine the crystalline electric field parameters in TmxYi_x Ala. We find for the ground state the Ps(‘)triplet and for the Lea, Leask and Wolf parameters X = (0.47 f 0.03) and IV= (0.034 t 0.013) meV.
TmXY1,A12 crystallizes in the cubic MgCu2 structure [ 11, and the Tm3+ ions experience a cubic crystalline electric field (CEF) which is described in terms of two parameters X and IV [2]. Measurements by inelastic neutron scattering and susceptibihty give values of (0.50 f. 0.05) and (0.040 f 0.005) meV for X and W res ctively [3,4]. According to these parameters the . FS(F triplet is the ground state. However, very recent EPR measurements propose negative values for IV, and Fl , r2 or F3 as the ground state [5]. To clarify this point we have done specific heat measurements on TmXY1,A12 (X = 0.15,0.25) in the temperature range from 1.2 K to 18 K. Indeed we find that the specific heat measurements allow a unique determination of the CEF parameters, and these parameters are the same as those obtained from the neutron and susceptibility measurements. The Tm,Yl, Al2 samples have been prepared from 99.9% pure Tm and Y and from 99.999% pure Al by melting together the metals by induction heating in a water cooled silver crucible. The specific heats have been measured by a heat pulse method between 1.2Kand 18K. The results for the total specific heat Ctot for Tm, Yl _XAl2 are shown in fig. 1. To obtain the experimental Schottky specific heat per g-at Tm we write GE{ = (3/x) (Ctot- CEL-Cd where CEL and CL are the electronic specific heat and the lattice specific heat per g-at Tm,Yl _XA12 respectively. CEL is obtained from the experimental specific heat of YA12 [6] assuming that the electronic part of the specific heat is not affected by the substitution of Y by Tm. In order to obtain CL we corrected the lattice specific heat of YA12
-Tm
0
10
5
Y 15 35
Al
2
1
15
TIK)
Fig. 1. Total specific heat (upper part) and Schottky specific heat (lower part) of Tm,Y i-x Ala. The lower part also shows the level scheme giving the best fit (heavy continuous line).
[6] for the mass difference in assuming the Debye tern. perature to be proportional to M-‘12 (M = mean atomic mass). The magnetic specific heat per g-at Tm, as obtained for the two samples with x = 0.15 and 0.25, are in good agreement (lower part of fig. 1). In fact the corrections for CEL and CL are not critical because these contributions to the total specific heats are 53
Volume
47A, number
1
PHYSICS
small compared to the magnetic specific heats for T < 10 K and become comparable to the latter only at about 17 K. To determine the CEF parameters we write the theoretical Schottky specific heat as Csch = (1 /Z2kT2)
with Z = cg,,
exp (-A,/kT)
where A,, is the energy of the n-th level and g, the degeneracy of this level. The A,, are given by X and W according to ref. [2]. N is the Avogadro number. The best fit of this equation to the experimental Schottky specific heat is obtained for X = (0.47 + 0.03) and W = (0.034 + 0.013) meV and is shown as a continuous curve in the lower part of fig. 1, together with the corresponding level scheme. We also include the theoretical curves for X = 0.50 and X = 0.44 showing that the magnitude and the temperature dependence of the magnetic specific heat are very sensitive to the value of X. In our analysis we tried all values -1 G X < +l for positive and negative W and come to the conclusion that X = (0.47 f 0.03) is the only possibility to explain the experimental specific heat. The value of W = (0.034 t 0.013) meV was determined from the position of the maximum around (5.5 f 2)K. Since the Curie point in (RE-Y)A12 compound decreases roughly linearly with the Y-concentration [7] we estimate the Curie point of our Tm,Y, _xA12 samples to be 2 K or lower. Thus we expect a considerable
54
LETTERS
25 February
1974
contribution to the specific heat in this temperature range and explain the deviation of the experimental specific heat below about 3 K from the Schottky specific heat curve by magnetic ordering effects. Although we are not able to analyse the specific heat at these temperatures we realize that the set of X and W as given above is the only possible one within the experimental uncertainty, and that the agreement with the values obtained by neutron and susceptibility measurements is excellent [3,4]. In contrast there is no evidence from our measurements to support the recently reported EPR results. We conclude that in the particular case of Tm,YI,Al, specific heat measurements are suitable to determine without supplementary measurements the CEF parameters.
References [ll J.H. Wernick and S. Geller, Trans. AIME 218 (1960) 806. 121 K.R. Lea, M.J.M. Leask and W.P. Wolf, J. Phys. Chem. Solids 23 (1962)
1381.
[31 H.-G. Purwins et al., Solid State Commun. 12 (1973) 117. [41 A. Furrer, W. Buhrer, H. Heer, H.-G. Purwins and E. Walker, Int. J. Magnetism 4 (1973) 63. R.A.B. Devine, W. Zings, J.-M. Moret ,and D. Shaltiel, Solid State Commun. 12 (1973) 515. K.A. Gschneidner Jr, J. Phys. Chem. 161 R.E. Hunsbergand, Solids 33 (1972) 401. [71 K.H.J. Buschow, J.F. Fast, A.M. Van Diepen and H.W. De Wijn, Phys. Stat, Sol. 24 (1967) 715.
iSI
PHYSICS LETTERS
25 February 1974
SPECIFIC HEAT AND CRYSTALLINE ELECTRIC FIELD PARAMETERS IN Tm, Y, _xAl2 F. HEINIGER.
H.-G. PURWINS and E. WALKER
Depnrternent de Physique de la Matibe Condensee Universitk de Genbe, CH-I 211 Genkve 4, Switserland Received 10 January 1974 Specific heat measurements on Tm,Yt-,Ala have been performed to determine the crystalline electric field parameters in TmxYi_x Ala. We find for the ground state the Ps(‘)triplet and for the Lea, Leask and Wolf parameters X = (0.47 f 0.03) and IV= (0.034 t 0.013) meV.
TmXY1,A12 crystallizes in the cubic MgCu2 structure [ 11, and the Tm3+ ions experience a cubic crystalline electric field (CEF) which is described in terms of two parameters X and IV [2]. Measurements by inelastic neutron scattering and susceptibihty give values of (0.50 f. 0.05) and (0.040 f 0.005) meV for X and W res ctively [3,4]. According to these parameters the . FS(F triplet is the ground state. However, very recent EPR measurements propose negative values for IV, and Fl , r2 or F3 as the ground state [5]. To clarify this point we have done specific heat measurements on TmXY1,A12 (X = 0.15,0.25) in the temperature range from 1.2 K to 18 K. Indeed we find that the specific heat measurements allow a unique determination of the CEF parameters, and these parameters are the same as those obtained from the neutron and susceptibility measurements. The Tm,Yl, Al2 samples have been prepared from 99.9% pure Tm and Y and from 99.999% pure Al by melting together the metals by induction heating in a water cooled silver crucible. The specific heats have been measured by a heat pulse method between 1.2Kand 18K. The results for the total specific heat Ctot for Tm, Yl _XAl2 are shown in fig. 1. To obtain the experimental Schottky specific heat per g-at Tm we write GE{ = (3/x) (Ctot- CEL-Cd where CEL and CL are the electronic specific heat and the lattice specific heat per g-at Tm,Yl _XA12 respectively. CEL is obtained from the experimental specific heat of YA12 [6] assuming that the electronic part of the specific heat is not affected by the substitution of Y by Tm. In order to obtain CL we corrected the lattice specific heat of YA12
-Tm
0
10
5
Y 15 35
Al
2
1
15
TIK)
Fig. 1. Total specific heat (upper part) and Schottky specific heat (lower part) of Tm,Y i-x Ala. The lower part also shows the level scheme giving the best fit (heavy continuous line).
[6] for the mass difference in assuming the Debye tern. perature to be proportional to M-‘12 (M = mean atomic mass). The magnetic specific heat per g-at Tm, as obtained for the two samples with x = 0.15 and 0.25, are in good agreement (lower part of fig. 1). In fact the corrections for CEL and CL are not critical because these contributions to the total specific heats are 53
Volume
47A, number
1
PHYSICS
small compared to the magnetic specific heats for T < 10 K and become comparable to the latter only at about 17 K. To determine the CEF parameters we write the theoretical Schottky specific heat as Csch = (1 /Z2kT2)
with Z = cg,,
exp (-A,/kT)
where A,, is the energy of the n-th level and g, the degeneracy of this level. The A,, are given by X and W according to ref. [2]. N is the Avogadro number. The best fit of this equation to the experimental Schottky specific heat is obtained for X = (0.47 + 0.03) and W = (0.034 + 0.013) meV and is shown as a continuous curve in the lower part of fig. 1, together with the corresponding level scheme. We also include the theoretical curves for X = 0.50 and X = 0.44 showing that the magnitude and the temperature dependence of the magnetic specific heat are very sensitive to the value of X. In our analysis we tried all values -1 G X < +l for positive and negative W and come to the conclusion that X = (0.47 f 0.03) is the only possibility to explain the experimental specific heat. The value of W = (0.034 t 0.013) meV was determined from the position of the maximum around (5.5 f 2)K. Since the Curie point in (RE-Y)A12 compound decreases roughly linearly with the Y-concentration [7] we estimate the Curie point of our Tm,Y, _xA12 samples to be 2 K or lower. Thus we expect a considerable
54
LETTERS
25 February
1974
contribution to the specific heat in this temperature range and explain the deviation of the experimental specific heat below about 3 K from the Schottky specific heat curve by magnetic ordering effects. Although we are not able to analyse the specific heat at these temperatures we realize that the set of X and W as given above is the only possible one within the experimental uncertainty, and that the agreement with the values obtained by neutron and susceptibility measurements is excellent [3,4]. In contrast there is no evidence from our measurements to support the recently reported EPR results. We conclude that in the particular case of Tm,YI,Al, specific heat measurements are suitable to determine without supplementary measurements the CEF parameters.
References [ll J.H. Wernick and S. Geller, Trans. AIME 218 (1960) 806. 121 K.R. Lea, M.J.M. Leask and W.P. Wolf, J. Phys. Chem. Solids 23 (1962)
1381.
[31 H.-G. Purwins et al., Solid State Commun. 12 (1973) 117. [41 A. Furrer, W. Buhrer, H. Heer, H.-G. Purwins and E. Walker, Int. J. Magnetism 4 (1973) 63. R.A.B. Devine, W. Zings, J.-M. Moret ,and D. Shaltiel, Solid State Commun. 12 (1973) 515. K.A. Gschneidner Jr, J. Phys. Chem. 161 R.E. Hunsbergand, Solids 33 (1972) 401. [71 K.H.J. Buschow, J.F. Fast, A.M. Van Diepen and H.W. De Wijn, Phys. Stat, Sol. 24 (1967) 715.
iSI