| 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_BT).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. |
