Muons and magnets

Abstract:

Abstract Muon spectroscopy has become a leading tool for the investigation of local magnetic fields in condensed matter physics, finding applications in the study of superconductivity, magnetism, ionic diffussion in battery materials, and numerous other fields. Though the muon yields quantitative information about the material, this can only be fully interpreted if the nature of the muon site and its stability is fully understood. Electronic structure calculations are of paramount importance for providing this understanding, particularly through a group of techniques that has become known as DFT+µ, density functional theory including the presence of the implanted muon. We describe how these electronic structure calculations can be used to underpin muon spectroscopy, and some examples of the science that follows from this, as well as some of the available software tools that are currently being developed.

Abstract:

An emerging concept for identification of different types of spin liquids [C. Broholm et al., Science 367, eaay0668 (2020)] is through the use of spontaneous spin noise [S. Chatterjee, J. F. Rodriguez-Nieva, E. Demler, Phys. Rev. B 99, 104425 (2019)]. Here, we develop spin noise spectroscopy for spin liquid studies by considering Ca₁₀Cr₇O₂₈, a material hypothesized to be either a quantum or a spiral spin liquid (SSL). By enhancing techniques introduced for magnetic monopole noise studies [R. Dusad et al., Nature 571, 234-239 (2019)], we measure the time and temperature dependence of spontaneous flux [Formula: see text] and thus magnetization [Formula: see text] of Ca₁₀Cr₇O₂₈ samples. The resulting power spectral density of magnetization noise [Formula: see text] reveals intense spin fluctuations with [Formula: see text] and [Formula: see text]. Both the variance [Formula: see text] and the correlation function [Formula: see text] of this spin noise undergo crossovers at a temperature [Formula: see text]. While predictions for quantum spin liquids are inconsistent with this phenomenology, those from Monte-Carlo simulations of a two-dimensional (2D) SSL state in Ca₁₀Cr₇O₂₈ yield overall quantitative correspondence with the measured frequency and temperature dependences of [Formula: see text], and [Formula: see text], thus indicating that Ca₁₀Cr₇O₂₈ is an SSL.

Abstract:

<jats:p>Centrosymmetric <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>GdRu</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi>Si</a:mi><a:mn>2</a:mn></a:msub></a:mrow></a:math> exhibits a variety of multi-<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>Q</b:mi></b:mrow></b:math> 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:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>c</c:mi></c:math> axis. Here, we present the results of muon-spin relaxation (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msup><d:mi>μ</d:mi><d:mo>+</d:mo></d:msup><d:mi>SR</d:mi></d:mrow></d:math>) measurements on single crystals of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>GdRu</e:mi><e:mn>2</e:mn></e:msub><e:msub><e:mi>Si</e:mi><e:mn>2</e:mn></e:msub></e:mrow></e:math>. 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msup><f:mi>μ</f:mi><f:mo>+</f:mo></f:msup><f:mi>SR</f:mi></f:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:msup><g:mi>μ</g:mi><g:mo>+</g:mo></g:msup><g:mi>SR</g:mi></g:mrow></g:math> provides clear evidence for a transition between two distinct magnetically ordered phases at 39 K.</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:

<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>