The cause of compensation temperature appearance of a spin-1 and spin-3/2 ferrimagnetic system

Abstract

In this paper, we use the double-time Green’s function method to study the properties of the mixed spin-1 and spin-3/2 Heisenberg ferrimagnets with exchange anisotropy and single-ion anisotropy on a three-dimensional lattice. We derive the equation of motion of the Green’s function by a standard procedure. In the course of this, the higher order Green functions have to be decoupled. For the terms concerning exchange interaction in the Hamiltonian, a Tyablikov or random phase approximation decoupling are used to decoupling the higher order Green functions. For the terms concerning the single-ion anisotropy, we adopt the Anderson-Callen decoupling to decoupling. Based on the above procedure, the effects of the exchange anisotropy and the single-ion anisotropy on the critical and compensation temperature are investigated. The cause of compensation temperature appearance of a spin-1 and spin-3/2 ferrimagnetic system is discussed in detailed. Our results show that, when the large spin S b single-ion anisotropy is equal to zero, i.e., D b =0, the drop of the sublattice magnetization | m a | with the increase of temperature is slower than the sublattice | m b |magnetization of large spin as the single-ion anisotropy D a of small spin increases. Under general condition, S b is larger than S a so that | m a | is always smaller than | m b |. It means that the difference between | m a | and | m b | decreases with the increasing of D a below the critical temperature. Therefore, as D a increases a certain value D a min, we obtain m a = - m b ≠0 below the critical temperature. It shows that the compensation point appears. And the compensation temperature decreases with increasing D a . The value of D a min will alter with changing of other parameters in the Hamiltonian. It means that the value of D a min depends on the other parameters in the Hamiltonian. Nevertheless, for D a =0, the drop of the sublattice magnetization | m b | with the increase of temperature is slower than the sublattice | m a | magnetization of large spin when D a increases. It shows that, below the critical temperature, the condition of m a = - m b ≠0 cannot be satisfied. This means that as D a =0, no matter what value of other parameters in the Hamiltonian, the compensation temperature cannot appear. Therefore, for our model, the prerequisite of the compensation point to occur is that the single-ion anisotropy of small spin quantum number is included. And there is a minimum value for D a , i.e., D a min. When D a is beyond D a min, the compensation temperature appears. Otherwise, the compensation point disappears. Meanwhile, it shall be noted that our Hamiltonian will be recover an ordinary three-dimensional Heisenberg antiferromagnetic model with the nearest-neighbor interactions at S a = S b . Our results agree with the high temperature series, the linked-cluster series approach and ratio method results.