Random anisotropy causes wide distributions of relaxation rates in Tb-Mg-Zn quasicrystals and amorphous DyAg

Power-exponential zero-field (ZF) muon spin relaxation (muSR), where the power varies with temperature, as observed in icosahedral Tb8Mg42Zn50 and in amorphous (am-)DyAg, is shown to be consistent with a wide distribution of relaxation rates by construction of a closed-form relaxation function representing such a distribution that fits the muSR data. This relaxation function is obtained by Laplace transform of a "double-square" distribution of relaxation rates, an example of a distribution that is asymmetric about its mean so that its width can be larger than that mean, a property that is necessary to fit the more extremely nonexponential cases. Combination with the results of Dy-161 Mossbauer effect measurements in DyAg indicates that this behavior is due to random axial crystalline electric-field (CEF) anisotropy. In addition to creating the random distribution of moment pointing directions in the asperomagnetic ordered state of am-DyAg, this creates a wide distribution of splittings between the J(z)=J ground doublet and the first excited state, thus causing a wide distribution of rare-earth paramagnetic fluctuation rates, leading to the wide distribution of muon spin relaxation rates deduced above. The contrast of simple-exponential ZF-muSR in i-Gd8Mg42Zn50 with double-square-distribution relaxation in the Tb quasicrystal clearly indicates that a CEF mechanism, probably the same one, is causing the nonexponential relaxation in the Tb quasicrystal, as well.