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Abstract:

Centrosymmetric GdRu2⁢Si2 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 (𝜇+⁢SR) measurements on single crystals of GdRu2⁢Si2. Our analysis is based on the computation of muon stopping sites and consideration of quantum zero-point motion effects of muons, 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 𝜇+⁢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 𝜇+⁢SR provides clear evidence for a transition between two distinct magnetically ordered phases at 39 K.

Abstract:

General relativity is a field theory that describes gravity. It engages profoundly with the nature of space and time and is based on simple ideas from the physics of fields. It can be summarised by the Einstein equation which relates a geometrical quantity, the curvature of space and time that follows from the metric field., to a physical quantity that reflects a field that describes the matter content of the Universe. We begin in Part I with an introduction to the geometry of flat spacetime, reviewing special relativity and setting up the mathematics of the metric. Part II introduces the mathematics of curvature and sets up the physics of general relativity and finishes with the Einstein field equation. Part III applies these ideas to the Universe and studies various models used in cosmology. Part IV turns to smaller structures inside the Universe: stars, black holes and their orbits. Part V contains a more formal treatment of geometry which may be of more interest to those with more mathematical inclinations. Part VI considers general relativity as a type of field theory and examines how one might link the ideas in our best theory of gravitation to our most successful theories of quantum fields.