Ground-state properties of uniaxial magnetic model for antiferromagnetic 1/1 periodic approximants to icosahedral quasicrystals

Abstract

The ground-state properties of the uniaxial magnetic model in the 1/1 periodic approximant to the icosahedral quasicrystal with antiferromagnetic interactions for the nearest-neighbor bond $J_1$ and the next-nearest-neighbor bond $J_2$ are analyzed theoretically. By performing numerically-exact calculation, we have determined the ground-state phase diagram for the interaction strength $J_2/J_1$ and the magnetic anisotropy defined within the mirror plane reflecting the effect of the crystalline electric field. We have discovered non-collinear magnetic structures, whose magnetic space groups are identified as the antiferromagnetic orders $I_{\rm P}m'\bar{3}'$ and $R_{\rm R}\bar{3}$ with the magnetic propagation vector $(111)$ as well as the antiferromagnetic orders $Im'm'm'$ and $R\bar{3}'$ with the magnetic propagation vector $(000)$ and the ferrimagnetic orders $Im'm'2$, $I2'2'2$, $P2'/m'$, and $P\bar{1}$. By analyzing each ground state with degeneracy, we have revealed the magnetic as well as topological properties, which are useful to analyze experimental observations of rare-earth-based 1/1 approximants considering the effect of magnetic domains.