Determination of the Universality Class of Gadolinium

Abstract

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...

Critical dynamics of a uniaxial and dipolar ferromagnet

“…In this paper we extend this analysis to anisotropic magnetic systems. A short account of part of these results with emphasis on the interpretation of experiments on Gd has been given recently [6]. Anisotropy acts to suppress critical fluctuations perpendicular to the easy axis of magnetization and breaks certain local conservation laws.…”

Dynamic critical behavior in models of ferromagnetic gadolinium

“…It is obvious that some of our results are impossible to explain within the framework of the scheme proposed in [3], and so are some results obtained in experimental studies of critical dynamics of gadolinium [4,[15][16][17][18][19][20]. As noted in the Introduction, the classification of universal critical behavior proposed in [3] ignores certain additional factors, such as dipole-dipole interaction.…”

“…We believe that many special characteristics exposed here, as well as the anomalous dynamic critical behavior of real gadolinium, can be explained by the combined effects of all factors. Note that a new dynamic universality class, model J*, has been proposed for gadolinium in [19].…”

“…3. The complex dynamic critical behavior of gadolinium has been analyzed in a number of theoretical studies [19,20]. 4.…”

Critical behavior in the inhomogeneous ferromagnetSrFe0.80Co0.20O3.Lago1, Rosseinsky2, Blundell3 et al. 2011Phys. Rev. B11060View full textAdd to dashboardCite

“…The obtained value, w = 1.37(3) is slightly higher than the theoretical prediction for 3DH ferromagnet (1.023), 43 and agrees well with that reported for Gd [1.39(3)], 45 with a well-established Heisenberg-to-dipolar crossover. 46 Following Suter's approach, 47 we have further checked the validity of this interpretation calculating the effective generalized dynamical exponent z from the derived value of w. w is related to other critical exponents by the expression 48…”