Muon spin relaxation in uniaxial ferromagnets

Journal of Magnetism and Magnetic Materials 140-144 (1995) 1949-1950

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Journalof magnetism and magnetic materials

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Muon spin relaxation in uniaxial ferromagnets A. Yaouanc a,*, p. Dalmas de R6otier a, P.C.M. Gubbens b F. Kayzel c P. Bonville d, J.J.M. Franse c, A.M. Mulders b a C E A / D R F M C , F-38054 Grenoble cedex 9, France b Interfaculty Reactor Institute, 2629 JB Delft, The Netherlands c University of Amsterdam, 1018 XE Amsterdam, The Netherlands d C E A / D R E C A M , F-91191 Gif-sur-Yvette, France

Abstract We present ~SR data recorded on two ferromagnets: GdNi 5 and ErNi 5. Depending on the anisotropy of the magnet, the muon spin lattice relaxation rate, A, is controlled at low temperature either by a magnon process or a phonon process.

Recently it has been shown that muon spin relaxation (~SR) measurements give direct information on the anisotropy in real and q-space of the critical paramagnetic fluctuation modes in simple ferromagnets [1]. Up to now the study by IxSR measurements of the spin dynamics below the Curie temperature has not attracted much interest, probably because of a lack of theoretical framework to analyse the data. Here we present experimental results on the orientation and temperature dependence of the spin lattice relaxation rate measured in zero field on two hexagonal uniaxial ferromagnets: GdNi 5 and ErNi 5. We give a first analysis of the data recorded below the Curie temperature. Detailed reports of these works are in preparation. Note that a simple model based analysis of the ErNi 5 paramagnetic data has been given in Ref. [2]. The single crystal samples have been prepared at the University of Amsterdam. For each compound we use two samples which differ by the orientation of the initial muon beam polarisation, P~, relative to the c axis [2,3], i.e. PI, is either parallel or perpendicular to the c axis. Most of the measurements have been performed at the ISIS surface muon beam facility of the Rutherford Appleton Laboratory (UK). Complementary measurements have been done at the Paul Scherrer Institute (Switzerland). We first present our GdNi 5 data. This compound has a weak magnetic anisotropy which is probably only due to the dipolar interaction between the Gd 3+ magnetic moments. The orientation dependence of the IxSR signal shows deafly that the easy axis is the c axis, contrary to a previous report [4]. The pxSR spectra can all be described

by an exponential function. In Fig. 1 we present the temperature dependence of the IxSR damping rate, A, which is a measure of the muon spin lattice relaxation rate. In the critical paramagnetic region, for ( T - T c ) / T c < 0.004, A(T) is different for the two samples because of the Ising anisotropy induced by the dipolar interaction [1]. At low temperature the muon spin relaxation is induced by a Raman magnon process which leads at low temperature to a quadratic temperature dependence of the damping [5]. A detailed theoretical analysis confirms that A is inversely proportional to D3(T) where D ( T ) is the magnon stiffness constant. In Fig. 2 we present D ( T ) deduced from the IxSR relaxation data. Note that the deduced stiffness constant is independent of the muon site. Its low temperature value is within the expected range and its temperature dependence is probably due to the renormalisation induced by the magnon-magnon interaction. For (Tc - T ) / T c < 0.05 we observe the critical behaviour of A which follows a power law with an exponent of ~ 0.8 down to ( T c T ) / T c ~ 0.01. Closer to Tc A saturates to a temperature

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maximum at 12 K (see Fig. 3) indicates that the spin dynamics is quasi-static below that temperature (there is in addition the possibility that there is more than one muon localisation site). Then A is inversely proportional to the correlation time of the Er 3+ spin dynamics. The full line in Fig. 3 is a fit to the following formula

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Fig. 2. Temperature dependence of the magnon stiffness constant deduced from the spin lattice relaxation rate extracted from the ~SR data. independent value. This behaviour is probably due to the dipolar interaction. Secondly we show the ErNi 5 data. This compound has a very strong magnetic anisotropy induced by the crystal field acting on the Er 3÷ ions. When P~ is perpendicular to the c axis the spectra are well described by exponential functions down to = 55 K. A(T) is presented in Fig. 3. Below that temperature we do not observe any signal. When P~ is parallel to the c axis a single exponential function describes the spectra down to ~ 7 K. Below that temperature the signal is a sum of two components: an exponential and a time independent function. Below 12 K (therefore above Tc = 9.2 K) we observe a drop of the total initial asymmetry. The complicated temperature dependence of the initial asymmetry and the fact that A has a

where a = 0.15 MHz, A / k B > 5 K and b = 1.1 Hz K -7. This strong temperature dependence (T 7) is a clear signature that the relaxation of the Er 3÷ magnetic moments is induced by the phonons [6]. This type of model has been used quite often in the past to explain Electron Paramagnetic Resonance results. In our case we understand that the same type of model can describe the txSR data if we remember that in the molecular field approximation the fact that T < Tc is simply taken into account by an effective magnetic field acting on the Er 3÷ ions. We note that the bound found on the energy splitting d is consistent with the known energy level diagram [7]. One could have tried to describe the ErNi 5 data with a magnon model as done for GdNi 5. This would not be satisfactory because in systems with huge crystal field anisotropy the excitations are the magnetic excitons (crystal field excitations) [8]. Whereas we have reached a satisfactory understanding of the meaning of the spin lattice rate measured in a weakly anisotropic Heisenberg ferromagnet such as GdNi 5 (Ref. [1] for T close to Tc and this work at low temperature), our understanding of the t~SR signal for strongly anisotropic ferromagnet such as ErNi 5 is still poor. References

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[1] P. Dalmas de R6otier and A. Yaouanc, Phys. Rev. Lett. 72 (1994) 290 and references therein. [2] P.C.M. Gubbens et al., J. Magn. Magn. Mater. 104-107 (1992) 1269. [3] P.C.M. Gubbens et al., Hyperfine Interactions (1994), in press. [4] D. Gignoux et al, Solid State Commun. 19 (1976) 891. [5] A. Yaouanc and P. Dalmas de R6otier, J. Phys.: Condens. Matter 3 (1991) 6195. [6] R. Orbach and H.J. Stapleton, in: Electron Paramagnetic Resonance, ed. S. Geschwind (Plenum, New York, 1972). [7] F.A. Goremychkin et al., Phys. Status Solidi B 121 (1984) 623. [8] J. Jensen and A.R. Mackintosh, Rare Earth Magnetism (Clarendon, Oxford, 1991).