Muon-spin relaxation inAuFe andCuMn spin glasses

Abstract
Zero- and longitudinal-field muon-spin relaxation (ZF μSR and LF μSR) measurements have been applied to dilute-alloy spin glasses AuFe(1.0 and 1.4 at %) and CuMn(1.1, 3, and 5 at. %). A stochastic theory of muon-spin relaxation has been formulated, and an analytic form of zero-field (ZF) muon-spin-relaxation function has been derived to describe the depolarization of muon spins in static, dynamic, and coexisting static and dynamic random local fields from magnetic impurities. The observed experimental results for the muon-spin-relaxation function Gz(t) in all the specimens have been well explained by the model functions based on the present theory. Depolarization of muon spins due to the rapidly fluctuating dynamic local field has been indicated by the ‘‘root-exponential’’ shape of Gz(t) observed above the susceptibility-cusp temperature Tg. The spin correlation time τc of Mn (or Fe) moment, deduced from the dynamic depolarization rate of muon spins, shows a rapid change from τc1012 sec at T≳2Tg towards τc109 sec at T∼Tg in all the specimens. Coexistence of static and dynamic random fields at each muon site has been found by ZF and LF μSR below Tg. The average amplitude scras of static random fields, determined precisely by ZF μSR, attains finite values only below Tg, and increases towards the full amplitude scra0 at T=0. scras/scra0 is proportional to the static polarization of Mn (or Fe) moment, and its temperature dependence has been found to be consistent with a Mössbauer-effect study in AuFe. The squared quantity (scras/scrao )2 of ZF μSR shows good agreement with the static order parameter Q(T) determined by ac-susceptibility (χac) and by neutron-spin-echo (NSE) measurements for cut-off pieces of the same specimen. In view of the fundamental difference of the hyperfine-fieldtype from the susceptibility-type measurements, this comparison reveals that spin freezing is characterized by a rather homogeneous amplitude of static spin polarization among different spins in spin glasses, i.e., ‘‘homogeneous freezing.’’ The combined results of ZF μSR, χac and NSE measurements in AuFe and CuMn spin glasses have demonstrated rapid slowing down of impurity spin fluctuations above Tg, and the appearance of long-time, persisting static spin polarization below Tg.

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