One-magnon systems in an isotropic non-Heisenberg ferromagnetic impurity model

Abstract

We consider a one-magnon system in an isotropic non-Heisenberg impurity model with an arbitrary spin and investigate the spectrum and the localized impurity states of the system on the ν-dimensional integer lattice Z ν . We show that there are at most three types of localized impurity states (not counting the degeneracy multiplicities of their energy levels) in this system. We find the domains of these states and calculate the degeneracy multiplicities of their energy levels.The use of films in various areas of physics and technology arouses great interest in studying a localized impurity state (LIS) of a magnet. The LISs in a Heisenberg ferromagnet with ferromagnetic and antiferromagnetic impurities were investigated in many papers (see, e.g., [1]), where the situations with linear and cubic lattices were considered in detail. It was shown that there are two LIS types in the linear case and three types in the cubic case.In [2], the case of a ν-dimensional lattice was considered, and it was proved that there are at most three types of LISs (not counting the degeneracy multiplicities of their energy levels) in the ν-dimensional case. It was shown that the number of types of LISs in the system changes with varying parameters of the Hamiltonian, and the LIS domains were found. In this case, it turns out that the three types of LISs in the system are respectively nondegenerate, ν-fold degenerate, and (ν−1)-fold degenerate.In theoretical investigations of magnetically ordered systems and in the interpretation of experimental data, the starting point was usually the Heisenberg exchange Hamiltonian (for an arbitrary spin s),where J is the parameter of the bilinear exchange interaction between the nearest-neighbor atoms, S m is the atomic spin operator for the spin s at the mth lattice site in the ν-dimensional lattice Z ν , and the summation over τ ranges the nearest neighbors.For an arbitrary spin s, the isotropic spin exchange Hamiltonian in fact has the form [3]where J n are the parameters of the multipole exchange interactions between the nearest-neighbor atoms. Hamiltonian (2) coincides with (1) only for s = 1/2, whereas if s > 1/2, then some terms containing higher degrees of (S m S m+τ ) appear, which must be taken into consideration in studying magnets with spins s > 1/2. Expression (2) is called a non-Heisenberg Hamiltonian.