he Direction of Spontaneous Magnetisation of Lanthanide Ions at a Site of Cubic Symmetry

Abstract

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.C. CARBONI, E. AL-ABRY and S. ARAFIN 54

Investigation of the Direction of Spontaneous Magnetisation at 0 K in HoCo2 and TmFe2

“…The magnitude of the vector parameter represents the relative strength of the magnetic to the electrostatic interactions; the balance between the relative strengths of |R| and x determines the direction of spontaneous magnetization [4,5].…”

“…Given the values of x and |R| and the orientation (of R, the direction of spontaneous magnetization which is the direction of the angular momentum J can be in principle computed by diagonalising the Hamiltonian 7. However, for arbitrary values of (the computed direction of J will not in general be parallel to the input direction of R. To be the direction of spontaneous magnetization, the value of () must satisfy the two conditions that the computed direction of J is parallel to R, and that the energy of the state is at a minimum with respect to () [4,5].…”

“…The published parameters for the two compounds given in table 1 are also shown in the figures. In the notation of Al-Abry et al (4,5), the boundary in the case of J = 6 is of the type Da where the transition is discontinuous across the boundary. At a critical value of the parameters the two orientations (110) and (111) have the same energy but all the orientations in the plane containing these two directions have a higher energy.…”

“…For ions at a site of cubic symmetry the Hamiltonian can be expressed in the dimensionless form given in equation 7 below which it depends on two parameters only. Al-Abry et al [4,5] have done a systematic investigation of the direction of spontaneous magnetization at zero temperature in the two-parameter space for all the values of J found in the ground state of lanthanide ions. In the present paper we discuss the direction of spontaneous magnetization in two compounds, HoCo 2 and TmFe 2 .…”