Origin of Anisotropy in Gadolinium Crystal Using a New Spin Hamiltonian*

Abstract

Single crystal rare-earth magnets, such as hexagonal-close-packed gadolinium, usually have a large second order anisotropy K 2 and a negative first order anisotropy K 1 at low temperatures, which are difficult to explain using microscopic theories. An atomic scale effective spin Hamiltonian ℱ[{ S i }] is proposed, which, apart from the usual isotropic nearest neighbor coupling J, consists of two new terms that are different for in-plane and out-of-plane neighbors and which are characterized by two new couplings C 1 and C 2, respectively. The hybrid Monte–Carlo method is utilized to sample this system to the desired Boltzmann-like distribution exp(−ℱ/k B T). It is found that K 2 and K 1 are compatible with the experimental values and arise naturally from the exchange anisotropy C 1 and C 2, which are less than 0.01 in magnitude of the isotropic exchange energy J. This new model spin Hamiltonian can also be applied to study other magnetic properties.