Field-orientation-dependent magnetic phases in GdRu$_2$Si$_2$ probed with muon-spin spectroscopy

TL;DR

This study uses muon-spin spectroscopy to investigate how magnetic phases in GdRu$_2$Si$_2$ depend on the orientation of an applied magnetic field, revealing complex multi-Q states including skyrmion-lattice phases.

Contribution

It provides the first muon-spin spectroscopy analysis of GdRu$_2$Si$_2$, identifying field-orientation-dependent magnetic phases and confirming the presence of skyrmion and meron-lattice states.

Findings

Distinct muon responses for different field directions.

Evidence for skyrmion and meron-lattice phases.

A magnetic phase transition at 39 K.

Abstract

Centrosymmetric GdRu$_2$Si$_2$ exhibits a variety of multi-Q magnetic states as a function of temperature and applied magnetic field, including a square skyrmion-lattice phase. The material's behavior is strongly dependent on the direction of the applied field, with different phase diagrams resulting for fields applied parallel or perpendicular to the crystallographic $c$ axis. Here, we present the results of muon-spin relaxation ($\mu^+$SR) measurements on single crystals of GdRu$_2$Si$_2$. Our analysis is based on the computation of muon stopping sites and consideration of zero-point motion effects, allowing direct comparison with the underlying spin textures in the material. The muon site is confirmed experimentally, using angle-dependent measurements of the muon Knight shift. Using transverse-field $\mu^+$SR with fields applied along either the [001] or [100] crystallographic directions, we distinguish between the magnetic phases in this system via their distinct muon response, providing additional evidence for the skyrmion and meron-lattice phases, while also suggesting the existence of RKKY-driven muon hyperfine coupling. Zero-field $\mu^+$SR provides clear evidence for a transition between two distinct magnetically-ordered phases at 39 K.