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The crystal field levels in cerium-yttrium
Physica B 156 & 157 (1989) North-Holland, Amsterdam
THE CRYSTAL
E.P. GIBBONS’,
777-779
FIELD LEVELS
E.M. FORGAN’,
‘Institut Law-Langevin, ‘Department of Physics, ‘Department of Physics, 41nstitut Laue-Langevin,
IN CERIUM-YTTRIUM
K.A. McEWEN3 and A.P. MURAN14
156X, 38042 Grenoble Cedex, France Birmingham University, P.O. Box 363, Birmingham B15 ZTT, UK Birkbeck College, London University, Malet Street, London WC1 E 7HE, 156X, 38042 Grenoble Cedex, France
UK
Inelastic neutron scattering measurements have been performed on the system Ce, 7sY0 25 to determine the crystal field level scheme of the cerium ions in the double hexagonal close packed structure. The level scheme obtained is discussed in relation to the magnetic ordering observed below 7 K.
Magnetic susceptibility measurements on /3cerium by Burgardt et al. [l] indicate that the cerium 4f electron is localized and its magnetic moment has the value expected for a Ce3’ ion. This makes /3-cerium quite different from the low temperature a-phase of cerium in which the 4f electron is thought to be hybridized with the conduction electrons. It is therefore of interest to study the excitations of the 4f electron in pcerium to verify its localized character and determine the crystal field level scheme. The preparation of p-cerium and its use in neutron experiments is hampered, however, by the transformation to the a-phase on cooling between 40 K and 15 K. It has been shown by Panousis [2] that the P-phase can, however, be stabilized by additions of yttrium. Gibbons et al. [3] have recently studied Ce,,,,Y,,,, by powder neutron difraction and propose that its magnetic structure is very similar to that of p-cerium which was first investigated with neutrons by Wilkinson et al. [4]; this claim has been strengthened by recent results from /3-cerium by McEwen et al. [5]. The present study is therefore of the crystal field excitations in Ce0,75Y0.25in the expectation that they are similar to those in p-cerium. Although Burgardt et al. [l] refer to inelastic neutron scattering results these have never been published to our knowledge. The experiment was performed on the instrument IN4 at Institut Laue-Langevin, Grenoble, using incident energies of 12.5 meV and 50 meV.
The contribution to the scattering due to phonons was determined by similar measurements on a sample of La,.,,Y,,,,. The results at 20 K taken at small scattering angles are shown in fig. 1. The results at high angles for 50 meV incident energy are similar for both samples indicating that the phonons are, as expected, similar in the two cases. Comparison of the results therefore shows that the intensity at low angles from Ce,,,,Y,,,, is almost all magnetic in origin. The results in fig. 1 show a large quasi-elastic contribution to the scattering as well as a broad inelastic peak at about 16.5 meV and a smaller inelastic component at about 8 meV To obtain more exact parameters for these components the results were fitted, after subtraction of a suitable amount of the La,,,,Y,,,,, to three such components, each having a Lorentzian shape convoluted with the resolution function of IN4. The parameters of the peaks were varied to give the best fit to both the 12.5 meV and the 50meV data sets together; excluding the elastic region in each. The fit is shown by the solid line in the figures. The integral of S(Q, o) for each component is given in table I. Also given in the table is the value of these integrals expected from different possible ground states. In the evaluation of these we assume that at 20 K only the ground state is populated, justification for this being the observed separations to the higher states of 8 meV and 16.5 meV We also assume the crystal
0921-4526 / 89 / $03.50 0 Elsevier Science Publishers B .V. (North-Holland Physics Publishing Division)
E. P. Gibbons
778
I
’
a
I 02
.
0
-5
5
10
et al. 1 Excitations
b
-50
in Cr 07? Y 02’
i\
-25
Energy/meV
0
25
50
-40
-20
0
20
40
Energy/m&
Energy/m&
1. Measured S(Q, w) in units of b sr~ ’ meV ’ per cerium ion. (a) 12.5 meV Ce,, ,TY,, hi, 20 K, 28 = 13.5”. (b) 50meV (c) 50 meV La,, 7iY,, zr. 5 K, 20 = 6.8”. Ce,, 7iYo 21, 20 K. 20 = 6.8” with 0.69 of (c) subtracted. Fig.
field Hamiltonian to be either hexagonal or cubic depending on which site of the dhcp structure is considered. This results in three doublets on the hexagonal site (*l/2), ]+3/2) and (*5/2); and two states on the cubic sites, the r, doublet and the r, quartet. We used the cerium occupations for the different sites as given by Gibbons et al. [3]. From general arguments the sum of the integrals of S(Q, w) per cerium ion, using the values j = 5 I2 and g, = 6 17, has a value of 0.313. The sum of column 1 in table I is however higher than that at a value of 0.393. This discrepancy of 23% is not yet understood. In column 2 of table I the values in column I are divided by 1.25 to normalize them. From the figures in table I it is seen that the results are best explained by a r, doublet ground state on the cubic site and a I*1 12) doublet ground state on the hexagonal site. It is found that the susceptibility of a system of such ground states is anisotropic giving a tendency for the moments in the ordered state to lie in the basal
plane, as observed by Gibbons et al. [3]. Doublet ground states also would explain the entropy change associated with the magnetic ordering observed by Panousis [2]. This level scheme is also expected from the Stevens’ factors for cerium and the crystal field parameters of its neighbor praseodymium as given by Houmann et al. [6]. However, it should be noted that direct comparison of these values leads to a ) l/2) to l-+3/2) separation of 19 K, and a r, to & separation of 159 K which are different from the values of 97 K and 197 K observed for the respective transitions. Concluding
remarks
The inelastic scattering at cerium ions in Ce,,,,5Y,,,2, can by transitions between crystal allowing determination of the scheme. Although the level explains why the moments in
20 K from the be well described field split states crystal field level scheme obtained the ordered state
Table I Column 1: Integrals over energy of S(Q w) for the component peaks observed at 20 K. The units are b sr ’ per cerium atom. Inell corresponds to the 8.4 meV peak and Ine12 corresponds to the 17 meV peak. Column 2: Integrals of column 1 divided by 1.25(see text). Columns 3-8: Expected equivalents of entries in column 2 for the six possible combinations of groundstates. The first entry is the quasi-elastic component and then the inelastic components are given.
Quasi: Inell: Inel2:
1
2
l112), r,
ll/2),
0.151 0.070 0.171
0.120 0.056 0.136
0.115 0.061 0.137
0.183 0.061 0.068
r,
13/2), 0.077 0.061 0.038 0.137
I;
(312). r,
1512). r,
/5/2),
0.145 0.061 0.038 0.068
0.138 0.038 0.137
0.206 0.038 0.068
r,
-
E. P. Gibbons et al.
lie in the basal plane, it predicts however saturated moments of 1.29c~g on the hexagonal sites and 0.72c~g on the cubic sites. These values are larger than the 0.91c~g and 0.38c~g observed by Gibbons et al. [3] for the saturated moments on the respective sites; a discrepancy which is not understood. On cooling below the NCel temperature of 7 K the widths of the excitations at 8meV and 16.5 meV remain at values of 3.4 meV and 3.8 meV respectively. The quasielastic response which has a width 1.3 meV at 20 K, however, changes to an inelastic response of width 1.0 meV centered at 1 meV Measurements of this excitation using a single crystal would give valu-
179
Excitations in Ce, 75YO25
able information the material.
on the exchange interactions
in
References
PI P. Burgardt et al , Phys. Rev. B 14 (1976) 2995.
PI
N.T. Panousis and K.A. Gschneidner Jr., Phys. Rev. B 5 (1972) 4767. 131E.P. Gibbons, E.M. Forgan and K.A. McEwen, J. Phys. F: Met. Phys. 17 (1987) LlOl-L104. [41M.K. Wilkinson, H.R. Child, C.J. McHargue, W.C. Koehler and E.O. Wollan, Phys. Rev. 122 (1961) 1409. [51K.A. McEwen, E.P. Gibbons and E.M. Forgan, ICM, Paris (1988). WI J.G. Houmann, B.D. Rainford, J. Jensen and A.R. Mackintosh, Phys. Rev. B 20 (1979) 1105.
THE CRYSTAL
E.P. GIBBONS’,
777-779
FIELD LEVELS
E.M. FORGAN’,
‘Institut Law-Langevin, ‘Department of Physics, ‘Department of Physics, 41nstitut Laue-Langevin,
IN CERIUM-YTTRIUM
K.A. McEWEN3 and A.P. MURAN14
156X, 38042 Grenoble Cedex, France Birmingham University, P.O. Box 363, Birmingham B15 ZTT, UK Birkbeck College, London University, Malet Street, London WC1 E 7HE, 156X, 38042 Grenoble Cedex, France
UK
Inelastic neutron scattering measurements have been performed on the system Ce, 7sY0 25 to determine the crystal field level scheme of the cerium ions in the double hexagonal close packed structure. The level scheme obtained is discussed in relation to the magnetic ordering observed below 7 K.
Magnetic susceptibility measurements on /3cerium by Burgardt et al. [l] indicate that the cerium 4f electron is localized and its magnetic moment has the value expected for a Ce3’ ion. This makes /3-cerium quite different from the low temperature a-phase of cerium in which the 4f electron is thought to be hybridized with the conduction electrons. It is therefore of interest to study the excitations of the 4f electron in pcerium to verify its localized character and determine the crystal field level scheme. The preparation of p-cerium and its use in neutron experiments is hampered, however, by the transformation to the a-phase on cooling between 40 K and 15 K. It has been shown by Panousis [2] that the P-phase can, however, be stabilized by additions of yttrium. Gibbons et al. [3] have recently studied Ce,,,,Y,,,, by powder neutron difraction and propose that its magnetic structure is very similar to that of p-cerium which was first investigated with neutrons by Wilkinson et al. [4]; this claim has been strengthened by recent results from /3-cerium by McEwen et al. [5]. The present study is therefore of the crystal field excitations in Ce0,75Y0.25in the expectation that they are similar to those in p-cerium. Although Burgardt et al. [l] refer to inelastic neutron scattering results these have never been published to our knowledge. The experiment was performed on the instrument IN4 at Institut Laue-Langevin, Grenoble, using incident energies of 12.5 meV and 50 meV.
The contribution to the scattering due to phonons was determined by similar measurements on a sample of La,.,,Y,,,,. The results at 20 K taken at small scattering angles are shown in fig. 1. The results at high angles for 50 meV incident energy are similar for both samples indicating that the phonons are, as expected, similar in the two cases. Comparison of the results therefore shows that the intensity at low angles from Ce,,,,Y,,,, is almost all magnetic in origin. The results in fig. 1 show a large quasi-elastic contribution to the scattering as well as a broad inelastic peak at about 16.5 meV and a smaller inelastic component at about 8 meV To obtain more exact parameters for these components the results were fitted, after subtraction of a suitable amount of the La,,,,Y,,,,, to three such components, each having a Lorentzian shape convoluted with the resolution function of IN4. The parameters of the peaks were varied to give the best fit to both the 12.5 meV and the 50meV data sets together; excluding the elastic region in each. The fit is shown by the solid line in the figures. The integral of S(Q, o) for each component is given in table I. Also given in the table is the value of these integrals expected from different possible ground states. In the evaluation of these we assume that at 20 K only the ground state is populated, justification for this being the observed separations to the higher states of 8 meV and 16.5 meV We also assume the crystal
0921-4526 / 89 / $03.50 0 Elsevier Science Publishers B .V. (North-Holland Physics Publishing Division)
E. P. Gibbons
778
I
’
a
I 02
.
0
-5
5
10
et al. 1 Excitations
b
-50
in Cr 07? Y 02’
i\
-25
Energy/meV
0
25
50
-40
-20
0
20
40
Energy/m&
Energy/m&
1. Measured S(Q, w) in units of b sr~ ’ meV ’ per cerium ion. (a) 12.5 meV Ce,, ,TY,, hi, 20 K, 28 = 13.5”. (b) 50meV (c) 50 meV La,, 7iY,, zr. 5 K, 20 = 6.8”. Ce,, 7iYo 21, 20 K. 20 = 6.8” with 0.69 of (c) subtracted. Fig.
field Hamiltonian to be either hexagonal or cubic depending on which site of the dhcp structure is considered. This results in three doublets on the hexagonal site (*l/2), ]+3/2) and (*5/2); and two states on the cubic sites, the r, doublet and the r, quartet. We used the cerium occupations for the different sites as given by Gibbons et al. [3]. From general arguments the sum of the integrals of S(Q, w) per cerium ion, using the values j = 5 I2 and g, = 6 17, has a value of 0.313. The sum of column 1 in table I is however higher than that at a value of 0.393. This discrepancy of 23% is not yet understood. In column 2 of table I the values in column I are divided by 1.25 to normalize them. From the figures in table I it is seen that the results are best explained by a r, doublet ground state on the cubic site and a I*1 12) doublet ground state on the hexagonal site. It is found that the susceptibility of a system of such ground states is anisotropic giving a tendency for the moments in the ordered state to lie in the basal
plane, as observed by Gibbons et al. [3]. Doublet ground states also would explain the entropy change associated with the magnetic ordering observed by Panousis [2]. This level scheme is also expected from the Stevens’ factors for cerium and the crystal field parameters of its neighbor praseodymium as given by Houmann et al. [6]. However, it should be noted that direct comparison of these values leads to a ) l/2) to l-+3/2) separation of 19 K, and a r, to & separation of 159 K which are different from the values of 97 K and 197 K observed for the respective transitions. Concluding
remarks
The inelastic scattering at cerium ions in Ce,,,,5Y,,,2, can by transitions between crystal allowing determination of the scheme. Although the level explains why the moments in
20 K from the be well described field split states crystal field level scheme obtained the ordered state
Table I Column 1: Integrals over energy of S(Q w) for the component peaks observed at 20 K. The units are b sr ’ per cerium atom. Inell corresponds to the 8.4 meV peak and Ine12 corresponds to the 17 meV peak. Column 2: Integrals of column 1 divided by 1.25(see text). Columns 3-8: Expected equivalents of entries in column 2 for the six possible combinations of groundstates. The first entry is the quasi-elastic component and then the inelastic components are given.
Quasi: Inell: Inel2:
1
2
l112), r,
ll/2),
0.151 0.070 0.171
0.120 0.056 0.136
0.115 0.061 0.137
0.183 0.061 0.068
r,
13/2), 0.077 0.061 0.038 0.137
I;
(312). r,
1512). r,
/5/2),
0.145 0.061 0.038 0.068
0.138 0.038 0.137
0.206 0.038 0.068
r,
-
E. P. Gibbons et al.
lie in the basal plane, it predicts however saturated moments of 1.29c~g on the hexagonal sites and 0.72c~g on the cubic sites. These values are larger than the 0.91c~g and 0.38c~g observed by Gibbons et al. [3] for the saturated moments on the respective sites; a discrepancy which is not understood. On cooling below the NCel temperature of 7 K the widths of the excitations at 8meV and 16.5 meV remain at values of 3.4 meV and 3.8 meV respectively. The quasielastic response which has a width 1.3 meV at 20 K, however, changes to an inelastic response of width 1.0 meV centered at 1 meV Measurements of this excitation using a single crystal would give valu-
179
Excitations in Ce, 75YO25
able information the material.
on the exchange interactions
in
References
PI P. Burgardt et al , Phys. Rev. B 14 (1976) 2995.
PI
N.T. Panousis and K.A. Gschneidner Jr., Phys. Rev. B 5 (1972) 4767. 131E.P. Gibbons, E.M. Forgan and K.A. McEwen, J. Phys. F: Met. Phys. 17 (1987) LlOl-L104. [41M.K. Wilkinson, H.R. Child, C.J. McHargue, W.C. Koehler and E.O. Wollan, Phys. Rev. 122 (1961) 1409. [51K.A. McEwen, E.P. Gibbons and E.M. Forgan, ICM, Paris (1988). WI J.G. Houmann, B.D. Rainford, J. Jensen and A.R. Mackintosh, Phys. Rev. B 20 (1979) 1105.