Phenomenological Magnetic Model in Tsai-Type Approximants

Recent neutron diffraction study has reported a curious ferromagnetism in Tsai-type approximants Au-Si-RE (RE=Tb,Dy,Ho), which have the same local structure as quasi-crystals with a translational symmetry simultaneously. In these materials, magnetic moments of rare-earth atoms have a single-ion anisotropy determined locally via spin-orbit coupling around crystal fields satisfying a distorted icosahedral crystal structure. We phenomenologically propose a possible magnetic model reproducing the magnetic structure and the thermodynamical quantities. The corresponding energies of the single-ion anisotropy and RKKY exchange couplings are also estimated by comparing magnetization curves and susceptibility of our model and experiments. Moreover, simulated annealing calculations with the energies in our model coincide with the strange ferromagnetism. In conclusion, a distortion of icosahedral cluster in body-centered cubic structure plays a key role to emerge the peculiar magnetic structure. Our magnetic model does not only explain magnetic behaviors in quasi-crystal approximants, but also can approach to a coexistence of a long-ranged order and a quasi-periodicity.