μSR evidence for the spin-liquid–to–spin-glass transition inβ−Mn1−xAlx

Abstract

Positive muon spin relaxation (\ensuremath{\mu}SR) has been used to investigate the evolution of spin dynamics in \ensuremath{\beta}-phase ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}$ alloys over the concentration range $0<~x<~0.2.$ A comparison of measured and calculated nuclear dipolar linewidths indicates that the muon is localized at the $(\frac{3}{8},$$\frac{3}{8},$$\frac{3}{8})$ interstitial lattice site in the center of a distorted octahedron of ``magnetic'' site II Mn atoms. For Al concentrations at and below $x=0.09$ the contribution to the muon relaxation from the dynamic atomic dipolar fields takes the form of a simple exponential ${e}^{\ensuremath{-}\ensuremath{\lambda}t}.$ For pure \ensuremath{\beta}-Mn the associated muon relaxation rate \ensuremath{\lambda} is very small (0.02 \ensuremath{\mu}${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$) and temperature independent, while for Al concentrations in the range $0.03<~x<~0.09$ the muon senses a critical slowing down of Mn spin fluctuations and \ensuremath{\lambda} diverges as temperature decreases towards an apparent critical temperature in the range 3--5 K. For concentrations beyond $x=0.09,$ the \ensuremath{\mu}SR spectra are of a stretched exponential form, i.e., ${e}^{\ensuremath{-}(\ensuremath{\lambda}{t)}^{\ensuremath{\beta}}},$ characteristic of those obtained from concentrated spin-glass systems, with \ensuremath{\beta} decreasing from unity to approximately $\frac{1}{3}$ as the magnetic transition is approached. At these higher concentrations \ensuremath{\lambda} maintains the same critical form observed for $x<~0.09,$ although the associated magnetic transition temperatures are now substantially higher, reaching 38 K at $x=0.2.$ It is suggested that these features are evidence of a quantum spin-liquid--to--spin-glass crossover in the $\ensuremath{\beta}\ensuremath{-}{\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}$ system in which Al substitution leads, on the one hand, to a slowing down of spin fluctuations and partial localization of the Mn moments as the \ensuremath{\beta}-Mn lattice expands, and on the other hand to a lifting of the spin configurational degeneracy associated with topological frustration in the triangular symmetry of the site II Mn sublattice.