GdRu2X2: Skyrmion Magnetism in Intermetallics
- GdRu2X2 are rare-earth intermetallic compounds crystallizing in the ThCr2Si2-type structure with square-planar Gd layers and intervening RuX4 tetrahedra that set the stage for unique skyrmion physics.
- The electronic structure features metallicity dominated by Ru 4d and X p orbitals, while localized Gd 4f electrons drive magnetic behavior through RKKY-type exchange interactions.
- Three-dimensional magnetic order arises from competing isotropic exchange interactions—with a dominant body-diagonal (J2) coupling—illustrating the complex interplay of structural geometry and bonding.
Searching arXiv for papers on GdRu2X2 and related compounds to ground the article in published work. GdRuX denotes a family of rare-earth intermetallics with Si, Ge, or Sn that crystallize in the ThCrSi-type structure and have emerged as a model platform for centrosymmetric skyrmion physics. Within this family, GdRuSi is established as a magnet with a short-period skyrmion square lattice in the absence of Dzyaloshinskii-Moriya interaction, while subsequent work on GdRuGe and comparative analyses across Si, Ge, and Sn connect skyrmion formation to RKKY-type exchange frustration, interlayer magnetic modulation, –0 hybridization, Fermi-surface nesting, and chemical-bonding-driven electronic instability (Sarkar et al., 2024, Rathnaweera et al., 28 Feb 2025, Rathnaweera et al., 25 Jul 2025).
1. Crystal structure and family definition
GdRu1X2 (3 Si, Ge, Sn) crystallizes in the well-known ThCr4Si5-type structure, space group 6 (No. 139) (Rathnaweera et al., 28 Feb 2025). In GdRu7Si8, the Gd atoms form a body-centered tetragonal sublattice with lattice constants
9
and occupy fractional coordinates
0
(Sarkar et al., 2024). For GdRu1Ge2, the experimentally determined lattice parameters are
3
with Wyckoff positions
4
and 5 (Rathnaweera et al., 28 Feb 2025).
Structurally, the family consists of square nets of Gd6 ions separated by edge-sharing RuX7 tetrahedra (Rathnaweera et al., 28 Feb 2025). In GdRu8Si9, the Ru–Si tetrahedral network separates the Gd planes by roughly half a unit cell along 0, yet the Gd–Gd spacing along the body diagonal is only slightly larger than the in-plane nearest-neighbor distance (Sarkar et al., 2024). This crystallographic detail is central to the current understanding of the family: although the square-planar Gd layers suggest a quasi-two-dimensional magnet, the actual Gd sublattice geometry favors substantial three-dimensional magnetic coupling (Sarkar et al., 2024).
A plausible implication is that the formal layered appearance of GdRu1X2 can obscure the dominant magnetic pathways unless the body-centered geometry is treated explicitly.
2. Electronic structure, orbital character, and chemical bonding
Spin-polarized DFT (3, 4 eV) shows that both GdRu5Si6 and GdRu7Ge8 are metallic, with multiple bands crossing the Fermi level 9 (Rathnaweera et al., 28 Feb 2025). The Gd 0 states are split by Hund’s rule, appearing as a sharp majority-spin peak at 1 eV and a minority peak at 2 eV, effectively localized, whereas near 3 the density of states is dominated by Ru 4 and 5 orbitals (Rathnaweera et al., 28 Feb 2025). The total DOS at 6 is 7 states eV8 f.u.9, which gives the bare Sommerfeld coefficient
0
(Rathnaweera et al., 28 Feb 2025).
A key trend across the series is the increasing spatial extent of the 1-site 2 orbitals from Si-3 to Ge-4 to Sn-5 (Rathnaweera et al., 25 Jul 2025). In GdRu6Ge7, the 8 bandwidth is broader than in the Si compound, and the qualitative hybridization parameter
9
is inferred to be larger for 0Ge than for 1Si (Rathnaweera et al., 28 Feb 2025). The later comparative study formalizes this trend using crystal-orbital Hamilton population (COHP) and integrated COHP (ICOHP),
2
where negative ICOHP values indicate net bonding character (Rathnaweera et al., 25 Jul 2025).
The reported ICOHP values show that Gd–Ru bonding strengthens substantially from Si to Ge to Sn, while Ru–X and Gd–X bonding remain sizable throughout the series (Rathnaweera et al., 25 Jul 2025). The main values are summarized below.
| Bond | ICOHP trend across 3 |
|---|---|
| Gd–Ru | 4 eV in Si, 5 eV in Ge, 6 eV in Sn |
| Ru–X | 7 eV in Si, 8 eV in Ge, 9 eV in Sn |
| Gd–X | 0 eV in Si, 1 eV in Ge, 2 eV in Sn |
These data support a family-level picture in which the [Ru3X4] conduction layer increasingly mediates the Gd moments as 5 becomes chemically heavier (Rathnaweera et al., 25 Jul 2025). This suggests that chemical bonding is not merely a structural background variable but a direct control parameter for the magnetic instability landscape.
3. Exchange hierarchy and three-dimensional magnetic order
The low-energy magnetism of the Gd sublattice is governed by competing RKKY-type exchange interactions (Sarkar et al., 2024, Rathnaweera et al., 28 Feb 2025). In GdRu6Si7, first-principles calculations of isotropic exchange constants up to the fifth shell yield the following hierarchy in meV: 8 with 9 corresponding to 0, i.e. the [111] body-diagonal directions (Sarkar et al., 2024). The dominant coupling is therefore along the body diagonal, and 1 meV is almost five times larger than the in-plane nearest-neighbor 2 (Sarkar et al., 2024).
This exchange hierarchy leads to a magnetic-ordering description that cannot be reduced to a purely two-dimensional model. The principal helical modulation vectors in reciprocal-lattice units are
3
with
4
in GdRu5Si6 (Sarkar et al., 2024). The associated real-space pitches are 7 and 8 (Sarkar et al., 2024). Sarkar et al. therefore describe the