Magnetism and topology in Tb-based icosahedral quasicrystal

Abstract

Quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in conventional crystals. The electric property is far from complete understanding and it has been a long-standing issue whether the magnetic long-range order is realized in the QC. The main difficulty was lack of microscopic theory to analyze the effect of the crystalline electric field (CEF) at the rare-earth atom in QCs. Here we show the full microscopic analysis of the CEF in Tb-based QCs. We find that magnetic anisotropy arising from the CEF plays a key role in realizing unique magnetic textures on the icosahedron whose vertices Tb atoms are located at. Our analysis of the minimal model based on the magnetic anisotropy suggests that the long-range order of the hedgehog characterized by the topological charge of one is stabilized in the Tb-based QC. We also find that the whirling-moment state is characterized by unusually large topological charge of three. The magnetic textures as well as the topological states are shown to be switched by controlling compositions of the non-rare-earth elements in the ternary compounds. Our model is useful to understand the magnetism as well as the topological property in the rare-earth-based QCs and approximant crystals.

Magnetism and topological property in icosahedral quasicrystal

“…We have shown that various magnetic states appear in the ground state of the IC [37,38]. Among them, we have found topological magnetic textures which are characterized by the non-trivial topological invariant, i.e., the topological charge.…”

“…Next, to get insight into the CEF in the QC Au-Ga-Tb, we have analyzed the CEF at the Tb site in the Tsai-type cluster [37,38]. The Tb 3+ ion with 4f 8 configuration is regarded to have the charge q = 6|e| in the hole picture since 4f 14 configuration is the closed shell of the 4f electrons.…”

“…To clarify the principal axis of the magnetic moment in the CEF ground state, we have calculated 3 × 3 matrix M ξ,ζ ≡ ψ 0 | Ĵξ Ĵζ |ψ 0 for ξ, ζ = x, y, and z [37,38]. By diagonalizing M , we have obtained the normalized eigenvector J for the largest eigenvalue, which gives the largest-moment direction.…”

“…It should be noted that the model (3) was introduced by T. J. Sato to analyze the 1/1 AC Au 72 Al 14 Tb 14 [10] where the model (3) applied to the icosahedron (IC) was succeeded in explaining main features of the measured temperature dependence of the magnetic susceptibility as well as the magnetic-field dependence of the magnetization. We have applied the model (3) to the IC, 1/1 AC, and the QC both with the FM interaction [38] and AFM interaction [37]. We have shown that various magnetic states appear in the ground-state phase diagram in the plane of J 2 /J 1 and the magnetic anisotropy θ.…”

Magnetic dynamics of ferromagnetic long range order in icosahedral quasicrystal

“…This has succeeded in formulating the full CEF Hamiltonian of any rare-earth ion in terms of the total angular momentum, which enables us to analyze the CEF accurately. By applying this formulation to the QC Au–SM–Tb and the AC, the CEF has been analyzed theoretically 31 , 32 . Then, it has been revealed that the magnetic anisotropy arising from the CEF plays a key role in realizing unique magnetic states on the icosahedron (IC) at whose vertices the Tb atoms are located.…”