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Henneberger, S.; Schreier, E.; Kratzer, A.; Asch, L.; Kalvius, G. M.; Frey, Erwin; Schwabl, Franz; Hartmann, O.; Ekström, Mikael; Wäppling, R.; Litterst, F. J.; Klauss, H.-H.

doi:10.1023/a:1012664802023

Cited by 4 publications

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“…the eigenvectors e i (q) are given in a forthcoming publication [13]. It is interesting to note that due to the combined effect of the dipolar interaction and the uniaxial anisotropy of the lattice the eigenvalues of the susceptibility matrix remain finite in the limit q → 0 and upon approaching the critical temperature.…”

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confidence: 99%

“…It is found that the mode coupling equations obey a generalized dynamic scaling law where the linewidth depend on three scaling variables, x 1 = 1/qξ, x 2 = q D /q and x 3 = q A /q, and the angle ϑ between the direction of the wave vector and the z-axis. The explicit functional form is too complicated to be presented in this letter and we refer the reader to a forthcoming publication [13]. But, note that it is implicitly contained in the damping rates for the hyperfine interaction probes discussed below.…”

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confidence: 99%

“…Now we compare the above theoretical results with experimental data obtained from hyperfine interaction experiments. We have performed zero field µSR experiments on Gd [16]. Spin polarized muons were implanted in order to measure the distribution and the dynamics of the internal magnetic field at the muon site via the temporal loss of the initial spin polarization.…”

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confidence: 99%

“…We could describe the temporal loss of the initial muon spin polarization by an exponential decay function P (t) = exp (−λ z t). Taking into account anisotropic dipolar fields as well as the isotropic Fermi contact field to the local field at the muon site the muon damping rate can be written as [17,18,13] …”

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confidence: 99%

“…Since the most dominant contribution to the damping rate comes from wave vectors close to the Brillouin zone center, the form of the coupling tensor Gxβ q at small values of q will be important. In the limit q → 0 [18,13] one finds G…”

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Determination of the Universality Class of Gadolinium

et al. 1997

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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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confidence: 99%

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confidence: 99%

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