Theory of the low-temperature susceptibility of spin systems with magnetic anisotropy
Abstract
The energy spectrum and the magnetization and susceptibility in the ground state of a spin system describing a paramagnetic ion placed in a nonmagnetic crystal with an "easy axis" anisotropy, when the magnetic field is perpendicular to this axis, are studied. The calculations are performed exactly for some values of the spin S∼1. It is shown that for any S, the eigenvalues of the Hamiltonian of the spin system coincide with the first 2S+1 energy levels of some effective one-dimensional Schrödinger equation, whose potential is constructed from the hyperbolic functions. For S≫1, the effective potential corresponds to a considerably anharmonic oscillator, which transforms into a quartic oscillator at some magnetic field. The application of different variants of perturbation theory and quasiclassical and numerical methods permitted obtaining results for all values of the magnetic field and spin. It is established that for S ≥ 3/2, the susceptibility in the ground state has a maximum as a function of the field, which is a purely quantum mechanical effect due to the reconstruction of the energy spectrum.