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Below Tc = 29.5K, MnSi orders magnetically into a rather exotic structure: the magnitude of the local magnetization is constant but its direction is a function of position: there is a constant axial component and a transverse component that spirals about that axis with a long (compared to the lattice spacing) wavelength. Fortunately, µSR can measure the magnitude of the local field regardless of its direction. |
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Although one expects a crystallographically unique site for the µ+ in MnSi, there are evidently two magnetically distinct versions. The earlier experiment revealed only the lower-field site's Bhf(T). |
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The muon Knight shift is proportional to the local spin density
and therefore varies linearly with the susceptibility in a
``Jaccarino plot'' just as does the 55Mn Knight shift,
for the same reasons. By comparing the slopes of these plots
one can determine the hyperfine couplings of the muon and
the Mn nucleus with the polarized conduction electrons.
Temperature is an implicit parameter in the plots. |
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Since MnSi is so emphatically magnetic, it might seem the least likely material in which to observe static nuclear dipolar relaxation; nevertheless, it was the first substance in which the now-familiar ``static gaussian Kubo-Toyabe relaxation function'' (predicted by Kubo & Toyabe many years earlier) was ever observed. This is because the paramagnetic spin density fluctuates so fast at room temperature that it is effectively decoupled from the muon and the 55Mn nuclei, leaving the latter to generate random static dipolar fields that produce a gaussian distribution at the muon in zero external field (ZF). |
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At 61.2K one is able to detect a very slow fluctuation of the 55Mn nuclear spins via its effect on the muon's ZF Kubo-Toyabe relaxation function Gzz(t): the ``1/3 tail'' (due to the component of the muon polarization that is parallel to the local field in a completely random disribution) slowly relaxes as the local field fluctuates so that it is no longer parallel to that polarization component. This gets more interesting later. . . . |
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At lower T the muon is strongly relaxed by the large fluctuating fields of the paramagnetic conduction electron spin density. Where 55Mn NMR had failed to get within 100K of the critical temperature, µSR was able to follow the critical slowing down of spin density fluctuations down to within half a degree of Tc and confirm Moriya's self-consistent renormalization (SCR) theory. |
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This picture shows the same results along with a little more detail about the SCR predictions. |
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Recall this picture from above. Now consider what happens when the paramagnetic spin density fluctuates more slowly and causes the 55Mn nuclear moments to fluctuate (relax) faster, while at the same time beginning to have a direct effect on the muon spins. . . . |
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The unmistakeable characteristic signature of ``double relaxation'' of this type is when the muon polarization function falls below the (high temperature) static gaussian ZF Gzz(t) at early times but rises above same at late times. This clearly cannot be due to a simple multiplication of Gzz(t) by an additional exponential relaxation function representing the direct effect of the paramagnetic moments. |
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Excellent fits are possible over the entire temperature range in ZF, using a constant value for the static dipolar width (due to Mn nuclear moments) and allowing the 55Mn and µ+ relaxation rates to vary independently. |
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Knowing that the muon relaxation at high T is dominated by nearly-static 55Mn nuclear dipoles whereas that at low T is dominated by fluctuating paramagnetic moments, and in between both must be taken into account, a much better determination of the critical divergence of T1-1(µ) was possible. At the same time, by equating the fluctuation rate of the nuclear dipolar fields in GKT(t) with the relaxation rate of the 55Mn nuclei, it was possible to obtain the critical divergence of T1-1(Mn) more than an order of magnitude closer to Tc than was possible using NMR. |
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Avoided Level Crossings in MnSi at several temperatures. |
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Temperature dependence of the resonant fields. |