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

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 P m ' 3' and R R 3 with the magnetic propagation vector (111) as well as the antiferromagnetic orders I222 and R 3' with the magnetic propagation vector (000) and the ferrimagnetic orders Im ' m ' 2, I2 ' 2 ' 2, P 2 ' /m ' , and P 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.