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).

Figures (3)

• Figure 1: (a) Whirling-moment state on the IC for $\theta=90^{\circ}$. The vector passing through the rare-earth site from the center of the IC is the pseudo 5-fold axis drawn with the dashed line with an arrow indicates the pseudo 5-fold axis, which is in the mirror plane colored by yellow surface. The same is applied to each rare-earth site where the mirror planes are colored by pink and purple surfaces. (b) Whirling moment state on the IC seen from the (111) direction. (c) Whirling-moment state at the center IC and the anti-whirling-moment state at the corner IC in the 1/1 AC viewed from the (111) direction. The frame box is the bcc unit cell.
• Figure 2: (a) Magnetic field dependence of the magnetization $m$ and the magnitude of the topological charge $|n|$ and the total chirality $|{\bm \chi}^{\rm T}|$. The magnetic field is applied along the (111) direction to the effective model (\ref{['eq:H']}) with $J_1=1.0$ and $J_2=8.0$. (b), (c), (d) Magnetic states for $h>h_{\rm M}$ viewed from the (111) direction, which are energetically degenerate.
• Figure 3: (a) The ground state at $J_1=1.0$, $J_2=8.0$, and ${\bm h}=(0.0,0.0,0.5)$. (b) Another ground state with the same energy as that of (a). (c) The ground state for $0^{\circ}<\theta_{\rm h}<54.7^{\circ}$. The angle $\theta_h$ is defined between the magnetic field ${\bm h}$ and the $z$ axis. (d) The field-direction dependence on the total chirality $\chi^{\rm T}_{x}$ (green square), $\chi^{\rm T}_{y}$ (light blue circle), and $\chi^{\rm T}_{z}$ (orange diamond) for $J_1=-1.0$, $J_2=-8.0$, and $|{\bm h}|=0.5$. The field direction is changed from the (001) direction to the (111) direction. (e), (f), (g) The ground states for ${\bm h}=(0.5,0.5,0.5)/\sqrt{3}$, which are energetically degenerate.