Non-Collinear and Non-Coplanar Magnetic Orders in 1/1 Periodic Approximant to the Icosahedral Quasicrystal

Abstract

Ground-state properties of rare-earth based 1/1 periodic approximants of icosahedral quasicrystal are clarified theoretically on the basis of an effective model for magnetism taking into account uniaxial anisotropy arising from crystalline electric field. By performing numerically-exact calculation on the 1/1 approximant crystal with a lattice constant $a$=14.725 Å, we have determined the ground-state phase diagram for ferromagnetic interactions. The result shows that eight kinds of noncollinear and noncoplanar magnetic structures are stabilized, whose magnetic space groups are identified as $I_{\rm P}m'\bar{3}'$, $C2'/m'$ and $R\bar{3}$. We have clarified the degeneracy of each ground state, which is expected to be reflected in the numbers of the domains. By analyzing each state, the magnetic as well as topological properties are revealed. Our results are shown to explain the measured magnetic structures in the 1/1 approximants and the effective model is discussed to be useful for understanding the magnetic structures and their topological properties in broad range of rare-earth based 1/1 approximants.

Figures (19)

• Figure 1: (Color online) Tsai-type cluster of the Au-SM-Tb consists of (a) cluster center, (b) dodecahedron, (c) icosahedron, (d) icosidodecahedron, and (e) defect rhombic triacontahedron with Au (yellow), Au/SM (green), and Tb (gray). The frame box is the unit cell of the (expanded) unit cell of the 1/1 AC Au-SM-Tb. (f) The local configuration of atoms surrounding the Tb atom in the Tsai-type cluster. The angle $\theta$ is defined between the magnetic easy axis ${\bm J}$ for the CEF ground state and the pseudo 5-fold axis ($z$ axis).
• Figure 2: (Color online) The nearest-neighbor (N.N.) interactions $J_1$ (solid line) and next-nearest-neighbor (N.N.N.) interactions $J_2$ (dashed line) for (a) the intra icosahedron and (b) the inter icosahedron are illustrated. In (b), the frame box represents the unit cell of the bcc lattice of the 1/1 AC with the lattice constant $a$.
• Figure 3: (Color online) (a) The ground-state phase diagram in the 1/1 AC (a) for $J_1=0$ (top) and in the plane of $J_2/J_1$ and the magnetic anisotropy angle $\theta~(^{\circ})$ (lower panel). The open symbol denotes the ferrimagnetic order where the magnetic states on the icosahedrons located at the center and the corner of the bcc unit cell are distributed uniformly. The filled symbol denotes the antiferromagnetic order where the magnetic states on the icosahedrons located at the center and the corner of the bcc unit cell are distributed in the antiferromagnetic alignment. The vertical dashed lines at $\theta=0^{\circ}$, $90^{\circ}$, and $180^{\circ}$ are guides for the eyes. (b) The enlargement for $0\le J_2/J_1 \le 1$. In (a) and (b), the pink regions denote the ordered states with the topological charge $|n|=1$ on the icosahedron. In (a), the blue region denotes the ordered state with the topological charge $|n|=3$ on the icosahedron.
• Figure 4: (Color online) The antiferromagnetic orders on the icosahedrons located at the center and the corner of the bcc unit cell in the 1/1 AC. (a) The anti-hedgehog state at the center icosahedron and the hedgehog state at the corner icosahedron with the anisotropy angle $\theta=0^{\circ}$. (b) The anti-whirling state at the center icosahedron and the whirling state at the corner icosahedron with the anisotropy angle $\theta=90^{\circ}$.
• Figure 5: (Color online) The ferrimagnetic orders on the icosahedrons located at the center and the corner of the bcc unit cell in the 1/1 AC. The alignment of the magnetic moments on the central icosahedron is viewed from the (111) direction.