Origin of Anisotropy in Gadolinium Crystal Using a New Spin Hamiltonian
Dan Wei1,2**, Zhibin Chen3, Hui Yang3, Yongjun Cao3, Chuan Liu4,5
1College of Physics and Electronic Information, Inner Mongolia Normal University, Hohhot 010022 2School of Materials Science and Engineering, Tsinghua University, Beijing 100084 3College of Physics and Electronic Information, Inner Mongolia Normal University, Hohhot 010022 4School of Physics and Center for High Energy Physics, Peking University, Beijing 100871 5Collaborative Innovation Center of Quantum Matter, Beijing 100871
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 ${\mathcal F}[\{{\boldsymbol S}_i\}]$ 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 $\exp(-{\mathcal F}/k_{_{\rm B}}T)$. 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.
2020, Vol. 37 
