Muons and magnets

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>