Muons and magnets

Abstract:

<jats:p>Skyrmions are particlelike vortices of magnetization with nontrivial topology, which are usually stabilized by Dzyaloshinskii-Moriya interactions (DMI) in noncentrosymmetric bulk materials. Exceptions are centrosymmetric Gd- and Eu-based skyrmion-lattice (SL) hosts with zero DMI, where both the SL stabilization mechanisms and magnetic ground states remain controversial. We address these here by investigating both the static and dynamical spin properties of the centrosymmetric SL host <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>Gd</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msub><a:msub><a:mrow><a:mi>PdSi</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msub></a:mrow></a:math> using muon spectroscopy. We find that spin fluctuations in the noncoplanar SL phase are highly anisotropic, implying that spin anisotropy plays a prominent role in stabilizing this phase. We also observe strongly anisotropic spin dynamics in the ground-state (IC-1) incommensurate magnetic phase of the material, indicating that it hosts a meronlike multi-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>q</c:mi></c:math> structure. In contrast, the higher-field, coplanar IC-2 phase is found to be single <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>q</e:mi></e:math> with nearly isotropic spin dynamics.</jats:p> <jats:sec> <jats:title/> <jats:supplementary-material> <jats:permissions> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material> </jats:sec>

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.