Ab initio exploration of short-pitch skyrmion materials: Role of orbital frustration

Abstract

In recent years, the skyrmion lattice phase with a short lattice constant has attracted attention due to its high skyrmion density, making it a promising option for achieving high-density storage memory and for observing novel phenomena like the quantized topological Hall effect. Unlike conventional non-centrosymmetric systems where the Dzyaloshinsky–Moriya interaction plays a crucial role, the short pitch skyrmion phase requires a quadratic magnetic interaction [Formula: see text] with a peak at finite-[Formula: see text], and weak easy-axis magnetic anisotropy is also critical. Thus, conducting first-principles evaluations is essential for understanding the formation mechanism as well as for promoting the discovery of new skyrmion materials. In this Perspective, we focus on recent developments of the first-principles evaluations of these properties and apply them to the prototype systems Gd[Formula: see text] and Eu[Formula: see text], where [Formula: see text] denotes a transition metal and [Formula: see text] represents Si or Ge. In particular, based on the spin density functional theory with the Hubbard correction combined with the Liechtenstein method in the Wannier tight-binding model formalism, we first show that the Hubbard [Formula: see text] and Hund’s coupling is essential to stabilize a skyrmion lattice state by enhancing the easy-axis anisotropy. We then discuss mechanisms of finite-[Formula: see text] instability and show that competition among Gd-5[Formula: see text] orbitals determines whether ferromagnetism or a finite-[Formula: see text] structure is favored in Gd[Formula: see text]Si[Formula: see text] with [Formula: see text] Fe and Ru. Our systematic calculations reveal that GdRu[Formula: see text], GdOs[Formula: see text], and GdRe[Formula: see text] are promising, while GdAg[Formula: see text], GdAu[Formula: see text], and EuAg[Formula: see text] are possible candidates as the skyrmion host materials. Analysis based on a spin spiral calculation for the candidate materials is also presented.

Effect of In-Plane Magnetic Field on Skyrmions in a Centrosymmetric Triangular-Lattice System with Symmetric Anisotropic Exchange Interaction

“…For example, the emergence of a magnetic skyrmion crystal (SkX) and vortex crystal with topologically nontrivial spin textures have been theoretically clarified as a consequence of multiple-Q states in the Kondo lattice model [29][30][31][32][33][34][35][36], even without the Dzyaloshinskii-Moriya (DM) interaction [37,38] and antisymmetric spin-orbit interaction (spin-dependent hopping). Simultaneously, such multiple-Q states have been observed in a variety of itinerant magnetic materials under centrosymmetric lattice structures, such as Gd 2 PdSi 3 [16,[39][40][41][42][43][44][45][46][47], Gd 3 Ru 4 Al 12 [48][49][50][51], GdRu 2 Si 2 [52][53][54][55][56], and Y 3 Co 8 Sn 4 [57,58], as well as noncentrosymmetric lattice structures, such as MnSi [9,[59][60][61][62][63][64][65][66][67][68][69][70][71]…”