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

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 J(q) with a peak at finite-Q, 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 GdT2X2 and EuT2X2, where T denotes a transition metal and X 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 U and Hund’s coupling is essential to stabilize a skyrmion lattice state by enhancing the easy-axis anisotropy. We then discuss mechanisms of finite-Q instability and show that competition among Gd-5d orbitals determines whether ferromagnetism or a finite-Q structure is favored in GdT2Si2 with T= Fe and Ru. Our systematic calculations reveal that GdRu2X2, GdOs2X2, and GdRe2X2 are promising, while GdAg2X2, GdAu2X2, and EuAg2X2 are possible candidates as the skyrmion host materials. Analysis based on a spin spiral calculation for the candidate materials is also presented.