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We study the critical dynamics of three-dimensional ferromagnets with uniaxial anisotropy by taking into account exchange and dipole-dipole interaction. The dynamic spin correlation functions and the transport coefficients are calculated within a mode coupling theory. It is found that the crossover scenario is determined by the subtle interplay between three length scales: the correlation length, the dipolar and uniaxial wave vector. We compare our theoretical findings with hyperfine interaction experiments on Gd and find quantitative agreement. This analysis allows us to identify the universality class for Gd. It also turns out that the $\mu$SR relaxation rate can be best fitted if it is assumed that muons occupy octahedral interstitials sites within the Gd lattice.Comment: 21 pages, 23 figure

We resolve a longstanding puzzle for the static and dynamic critical behavior of Gadolinium by a combined theoretical and experimental investigation. It is shown that the spin dynamics of a three dimensional ferromagnet with hcp lattice structure and a spin-spin interaction given by both exchange and dipole-dipole interaction belongs to a new dynamic universality class, model J * . Comparing results from mode coupling theory with results from three different hyperfine interaction probes we find quantitative agreement. The crossover scenario for the wavevector dependence of the hyperfine relaxation rate is determined by a subtle interplay between three length scales: the correlation length, the dipolar and the uniaxial wave vector.PACS numbers: 75.40. Gb, 75.40.Cx, 76.75.+i, 76.80.+y The spin dynamics of simple ferromagnets in the vicinity of their Curie point T c are archetypical examples of dynamic critical phenomena near second-order phase transitions. Much experimental and theoretical effort has been put into identifying the dynamic universality classes and assigning them to magnetic substances. Nevertheless, experimental observations on gadolinium [1][2][3][4][5][6][7] remained a puzzle up to now. Because of its large localized magnetic moment, and the fact that it is an Sstate ion, Gd should have a very small magnetocrystalline anisotropy and therefore be much better a model system for an isotropic Heisenberg magnet than either Fe, Ni or EuO. As a consequence it should belong to the model J dynamic universality class in the classification scheme of Ref. [8]. The measured static and especially dynamic critical exponents are, however, not at all compatible with model J. The objective of this paper is to resolve this longstanding seemingly contradictory situation by a combined theoretical and experimental study.Early experimental observations [9] clearly demonstrate that Gd has an easy axis which coincides with the hexagonal axis of its hcp lattice. The origin of such an easy axis cannot be understood from the magnetocrystalline anisotropy. But, based on a mean field theory [10] it has been argued that a combined effect of the lattice structure and dipolar interaction favors the c-axis as the easy direction. This view is supported by measurements [7] of the c-axis and basal-plane susceptibility on a single crystal of Gd. It is found that the basal-plane susceptibility crosses over from a singular behavior to a constant at a characteristic temperature scale which can be accounted for by dipolar effects. The analysis of the static critical behavior [7] is, however, complicated by the fact that all experiments are done in the non-asymptotic regime where superposed crossover lead to complex temperature dependences. This may not be easily interpreted in terms of one or the other universality class. This is even more so, as the static critical exponents for the various universality classes are of comparable magnitude.A surprising and yet unexplained observation was made by a measurement of the critical dynamics u...

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