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Abstract
The zero temperature direction of spontaneous magnetisation of lanthanide ions at a site of cubic symmetry is investigated as a function of the electrostatic and magnetic interactions. For all the values of J between J = 3 and J = 8, two-dimensional diagrams giving the orientation of spontaneous magnetisation are obtained as a function of the parameters R representing the relative strength of the magnetic to electrostatic interaction and the parameter x representing the relative strength of the fourth to the sixth order terms in the crystal field. The boundaries between regions of the parameter space with different directions of spontaneous magnetisation are investigated. It is found that at some boundaries there is a gradual rotation of the direction of spontaneous magnetisation and that at other boundaries there is a sudden change of orientation of spontaneous magnetisation at a critical value of the (R,x) parameters. Two types of behaviour are observed when there is a critical value of (R,x). There are boundaries where there is at the critical value a degenerate plane in which all the orientations can be direction of spontaneous magnetisation and some boundaries where two different principal crystallographic axes can be direction of spontaneous magnetisation at the critical value. In the latter case there is a region near the boundary where an unstable equilibrium orientation for the magnetisation can be found.
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References
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References
AUBERT, G., GIGNOUX, D., GIVORD, F., LEMAIRE, R. and MICHELUTTI, B. 1978. Magnetization Reorientation in HoCo2 . Solid State Com., 25: 85.
BUNBURY, D.ST.P., CARBONI, C., McCAUSLAND, M.A.H., CONE, R., MROCZKOWSKY, S. and ROSS, J.W. 1995. The hyperfine splitting of the ground state and first excited state of holmium in yttrium hydroxide. J Phys. Condens. Matte, 7, 6125-36.
BUNBURY, D.ST.P., CARBONI, C., MCCAUSLAND, M.A.H. and PRAKASH, O.1986. Spin reorientation in HoCo2, an NMR study, Proc. XXIII Congress Ampere on Magnetic Resonance (Istituto Superiore di Sanita, Roma) p. 296.
CARBONI, C. 1984. Diploma Report, Design of a microwave resonator to measure the NMR of 3+Ho in metallic single crystals. University of Manchester, unpublished.
CARBONI, C., GIGNOUX, D. and ROSS, J.W. 1996. The field dependence of the hyperfine splitting of terbium in TbNi5, J. Phys Condens. Matter, 8: 1763-74.
CARBONI, C., McCAUSLAND, M.A.H., BUNBURY, D.S.P., REID, B.L., LATAIFEH, M. and ABELL, J.S. 1992. Crystal-field anisotropy of Tb3+, Ho3+, and Tm3+ in gadolinium. J. Magn. Magn. Matter. 104-107: 1513.
CASTET, A., GIGNOUX, D. and HENNION, B. 1982. New aspects of the magnetic excitations in HoCo2. Phys. Rev. B25: 337.
GERMANO, D.J. and BUTERA, R.A. 1981. Heat capacity of, and crystal-field effects in, the RFe2 intermetallic compounds (R=Gd, Tb, Dy, Ho, Er, Tm, and Lu) Phys. Rev. B, 24(1): 3912.
GIGNOUX, D., GIVORD, F., LEMAIRE, R. 1975. Magnetic properties of single crystals of GdCo2, HoNi2, and HoCo2; Phys. Rev. B12: 3878.
LEA, K.R., LEASK, J.M. and WOLF, W.P. 1962. The raising of angular momentum degeneracy of f-electrons by cubic crystal field, Journal of the Physics and Chemistry of Solids, 23: 1381-1405.
McCAUSLAND, M.A.H, and MAKENZIE, I.S. 1980. Nuclear Magnetic Resonance in Rare earth Metals, Taylor and Francis Ltd., London.
MORRISSON, C.A. and LEAVITT, R.P. 1982. Handbook of Physics and Chemistry of Rare Earths, Vol 5, Gschneider, K.A and Eyring, L eds. North Holland Publishing Company.
PRAKASH, O., BUNBURY, D.ST.P., McCAUSLAND, M.A.H. 1984. On the ground state of Ho3+ in ferromagnetic HoAl2, Z Phys B58, 39.
STEVENS, K.W.H. 1952. Matrix elements and operator equivalents connected with the magnetic properties of rare-earth ions, Proceedings of the Physical Scociety, A, 65: 209-215.