Possibility of observation of the critical paramagnetic longitudinal spin fluctuations in gadolinium by muon spin rotation spectroscopy

Abstract

The theory described here showers that the muon spin depolarization rates measured on gadolinium in the critical paramagnetic region give direct information on the longitudinal (along the wave vector q) spin fluctuations. In the Ising regime it is possible to distinguish the parallel (along the c axis) from the perpendicular fluctuations.PACS numbers: 76.75.+i, 75.40.Gb, 75.30.Gw Gadolinium is a rare earth metal which crystallizes in the hexagonal close packed structure (hcp) and exhibits simple ferromagnetic ordering along the c axis at temperatures near the Curie temperature, Tr: = 293 K. Its ferromagnetism is due to the Ruderman-Kittel-Kasuya-Yosida interaction between the Gds+ ions which are in the Sq/q state. This ionic electronic structure suggests that the magnetocrystalline anisotropy is very small. Therefore a simple Heisenberg behavior was expected for the magnetic properties of gadolinium near Tr. . Contrary to these expectations, measurements have shown that these properties are quite complicated. It is only recently that a consistent experimental picture of the static properties has emerged [1,2]. It seems that all the complications are due to the magnetic dipole-dipole interactions. These long range interactions cause a crossover as the temperature is reduced in the paramagnetic region from an isotropic Heisenberg regime to a dipolar Heisenberg regime with a crossover temperature of approximately 4 K above Tr. . As the temperature is reduced further, there is a second crossover temperature to Ising behavior approximately 0.5 -1 K above Tr. [3].The dynamics properties of gadolinium have been studied mainly by two hyperfine techniques: the perturbed angular correlation method [4] and the positive muon spin relaxation and rotation spectroscopy (ttSR) [5,6]. There is little information from neutron experiments [7]. lsSR measurements performed on a single crystal seem to show that the magnetic fluctuations have a pronounced anisotropy when the temperature is approached to within -0.5 K from Tr. [5]. The lsSR data recorded on a polycrystalline sample indicate that the magnetic fluctuations are almost temperature independent for 1 K + T -Tr: + 10 K [6]. Because pSR measurements can be carried out in a wide temperature range which can extend from Tc, up to very high temperature, they should allow us to study in detail the different crossovers. Up to now no quantitative information has been extracted from these measurements mainly because the relation between the data and the correlation functions which characterize the fluctuations of the Gd + total moments has not been available. Recently it has been shown that it is possible to understand quantitatively pSR data recorded in cubic paramagnets [8]. The purpose of this Letter is to provide a theoretical framework for the interpretation of the available ltSR data on gadolinium and to initiate further and more accurate experiments. For an anisotropic crystal structure, the dipolar part of the Hamiltonian is the sum, near the Brillouin zone center, of two te...

Muon-spin-relaxation study of the critical longitudinal spin dynamics in a dipolar Heisenberg ferromagnet

“…This may explain the 15% anisotropy. The saturation effect observed in this temperature range has a simple explanation: 15 Z probes mainly the longitudinal ͑along the wave vector q) magnetic fluctuations. It has been shown for nickel, iron and gadolinium that Z can be written as a weighted sum of the contributions from the longitudinal and transverse fluctuation modes:…”

“…This increase of the damping rate could be due to the Ising crossover that has been for instance observed beyond the dipolar Heisenberg regime in metallic Gd. 20,15 We have just established that GdNi 5 is an axial dipolar magnet. We have determined its anisotropy magnetic field, its dipolar wave vector and the fact that SR essentially measures the longitudinal fluctuations in the critical paramagnetic region.…”

“…4,15,19 We have ϭ arctan(q D 0 ϩ t Ϫ ) where 0 ϩ is the correlation length at Tϭ2T C , t ϵ ͉TϪT C ͉/T C , and the correlation length critical exponent ( Ӎ 0.69͒. The superscripts L and T refer to the longitudinal and transverse ͑relative to q… fluctuations, respectively.…”

“…It has been explained as an effect of the dipolar interaction. 4,15 Therefore we are led to attribute the behavior of Z (T) for TϾT C to that interaction.…”

“…We express Z in terms of correlation functions. 4,15 An energy conservation argument tells us that only the parallel ͑to the easy axis which we denote z; the Z and z axes are parallel͒ fluctuations contribute to Z , 16 i.e., Z depends on the zz component of the spin correlation tensor of the magnet ⌳ zz (q, ) taken at zero energy transfer. Modeling the effect of the dipolar interaction between the Gd 3ϩ ions by B a , we compute ⌳ zz (q, ϭ0) and then derive the following expression: …”