Mechanical control of magnetic exchange and response in GdRu$_2$Si$_2$: A computational study

TL;DR

This work addresses how uniaxial strain along the $c$-axis tunes magnetic exchange and anisotropy in the centrosymmetric magnet GdRu$_2$Si$_2$, which hosts a field-induced skyrmion lattice. The authors integrate first-principles density functional theory (DFT) calculations to extract exchange parameters $J_{ij}$ and magnetocrystalline anisotropy energy $K_U$, with atomistic spin-dynamics simulations to map the magnetic phase diagram under strain. They find that compressive strain of about $2\%$ expands the stability region of the $\vec Q_{100}$-driven topologically nontrivial phases, while tensile strain promotes a different ground state associated with $\vec Q_{110}$, leading to distinct phase behavior. The results demonstrate that strain engineering is a viable and quantitative route to control and optimize topological magnetic phases in centrosymmetric magnets, providing actionable guidance for experimental strain tuning and device applications.

Abstract

We present a systematic computational study of the effect of uniaxial strain on the magnetic properties of GdRu$_2$Si$_2$, a centrosymmetric material known to host a field-induced skyrmion lattice (SkL). Using first-principles density functional theory, we first demonstrate the pronounced sensitivity of the exchange and anisotropy to specific structural distortions. These DFT-derived interactions are then integrated into a classical spin model to construct comprehensive magnetic phase diagrams under both compressive and tensile strain. Our key finding is that compressive strain ($\sim 2\%$) acts as an effective tuning parameter, substantially expanding the stability region of the $\vec Q_{100}$-driven topologically nontrivial phases. This results from the shifts in the critical magnetic fields and enhancement of the energy scale of the favored magnetic wave vector. In contrast, tensile strain induces a different magnetic ground-state by promoting a different magnetic ordering vector, $\vec Q_{110}$, leading to entirely distinct phase behavior. This work not only provides a quantitative understanding of the structural-magnetic coupling in GdRu$_2$Si$_2$ but also establishes strain engineering as a powerful approach to control and optimize topologically non-trivial magnetic phases in centrosymmetric magnets.

Figures (9)

• Figure 1: (a) A schematic showing the effect of compressive uniaxial strain along $c$ axis ($+\epsilon_c$ indicated by the green arrows). The Gd-Gd interlayer distance decreases, whereas the intralayer Gd-Gd distances increase. The Gd atoms in the unstrained/strained state are shown with light grey/black spheres, respectively. (b) Variation of unit cell lattice parameters (Top and Middle panels), and unit cell volume (Bottom panel) under uniaxial strain along $c$ axis ($\epsilon_c$). '+'/'-' values indicate compressive and tensile strains, respectively. The zero strain values are from our unstrained GGA-PBE optimized structure reported in Table \ref{['tab:str_table']}.
• Figure 2: (a) Calculated total DOS for different strained systems with FM spin order of the Gd moments. (b) ELF for an isosurface level of $\eta$ = 0.80 (in cyan colour), showing the location and qualitative amount of localized electrons in the unit cell for different strained systems. The dark grey spheres represent a Gd atom, while the smaller red and yellow spheres indicate the positions of Ru and Si atoms, respectively, in the unit cell. An ELF with $\eta$ = 0.80 - 1.00 generally shows the localized electrons like lone-pairs, core-shell electrons, and covalent bond electrons. See text for details.
• Figure 3: A one-to-one comparison between the magnetic properties of the experimental structure and the QE optimized unstrained structure. (a) Calculated interatomic magnetic exchange interactions as a function of distance scaled by the lattice constant $a$. (b) Fourier transform of the same along $\Gamma - X - \Gamma$ (left) and $\Gamma - M$ (right) directions, respectively.
• Figure 4: (a) Variation in the calculated interatomic magnetic exchange interactions from tensile (-) to compressive values (+) of the uniaxial strain ($\epsilon_c$). The corresponding variations in the Fourier transform $J(q)$ are also shown along (b) $\Gamma - X - \Gamma$ and (c) $\Gamma - M$ directions, respectively. The peaks corresponding to the spiral modulation vectors $\vec{Q}_{100}$ and $\vec{Q}_{110}$ in (b) and (c) are depicted by solid/black and dashed/red vertical lines, respectively.
• Figure 5: (a) Variation in the magnitude of the spiral modulation vectors $\vec{Q}_{100}$ and $\vec{Q}_{110}$ from tensile (-) to compressive values (+) of the uniaxial strain ($\epsilon_c$). Values of $\vec{Q}_{100}$ and $\vec{Q}_{110}$ are expressed in the unit of the reciprocal lattice vectors $\vec{G}_{100} (2\pi/\vec{a})$ and $\vec{G}_{110} (2\pi/\vec{R}_{110})$ respectively. (b) The corresponding variation in the stabilization energy (per Gd moment) of the spiral phases governed by $\vec{Q}_{100}$ and $\vec{Q}_{110}$ with respect to a uniform FM state.