Effect of magnetic field on whirling-anti-whirling order in icosahedral-quasicrystal approximant

Abstract Recent neutron measurement in the icosahedral quasicrystal approximant Au-SM-Tb (SM=Al, Ga) has revealed unique noncollinear magnetic order “whirling-anti-whirling states”. Here, we report theoretical analysis on the magnetic-field-direction dependence on the whirling-anti-whirling order in the 1/1 approximant crystal. By performing exact-diagonalization calculation for the effective model taking into account the uniaxial magnetic anisotropy arising from the crystalline electric field, we show the metamagnetic transition takes place simultaneously with the topological transition under the magnetic field along the (111) direction. After the metamagnetic transition, the emergent fictious magnetic field induced by the chirality of noncoplanar magnetic moments appears, the analysis of which concludes that the topological Hall effect is expected to be observed in the electrical conductivity σ xy and σ yz for the applied field direction from (111) to (001).