IDENTIFICATION OF FLUCTUATING SUSCEPTIBILITY COMPONENTS IN Rb2CrCl4 : A QUASI-2-DIMENSIONAL EASY PLANE FERROMAGNET

-Inelastic neutron scattering with polarisation analysis has been used to investigate the critical long wavelength spin fluctuations in Rb2CrClr. As well as spin wave and central peak components expected from fluctuations within the easy plane, weak central peak components are observed which may result from the diffusion of spin vortices. The ionic ferromagnet RbzCrCl4 adopts a slightly distorted K2NiF4 type structure in which the cr2+ ions (S = 2) lie in square planar arrays in well separated layers [I]. Since the cr2+ sublattice is pseudo tetragonal i t -& convenient to refer to cell constants in the I4/mmm space group, in which case a0 = 5.086 A and co = 15.715 A at 4.5 K. The exchange coupling is predominantly near neighbour Heisenberg (J/be % 7.6 K), with relatively much weaker interplaner coupling J' (J'/ J = [2]. When a small canting is neglected, the spin wave behaviour is well described by an approximate Hamiltonian with dominant planar anisotropy (-1 K) which confines the spins to the (001) plane, and weaker four fold anisotropy (N 0.1 K) which defines (110) as the easy axes of magnetisation. The magnetic dipolar interaction is generally negligible at a microscopic level. Rb2CrClr orders three dimensionally at Tc = 52.2 K as a result of the weak interplanar coupling. 2d, possibly XY-like, behaviour sets in above Tc + 3 K, whence the critical neutron scattering takes the form of rods of intensity parallel to [OOl] in reciprocal space [3]. The dynamic critical scattering in zero external field at (q, q, 2.9) was previously studied using unpolarised neutrons [4]. The data as q -r 0 and T -r Tc were successfully analysed in terms of sharp (resolution limited) spin waves and a broad Lorentzian central peak, although the polarisation of the fluctuations giving rise to these components could not be identified. The q = 0 spin wave mode was found to be a soft mode, renormalising rapidly and anomalously within 1 K of Tc. In the present experiment a crystal of 0.27 cm3 was mounted in a helium filled aluminium can attached to the cold fmger of an Oxford Instruments vertical field cryomagnet, with temperature measured by a P t resistance thermometer. The IN12 triple axis spectrometer on the cold neutron guide, ILL, Grenoble, was used in the UW" configuration with neutron wavelength X = 5.02 A, and nominal collimation angles 60'30'30'-60'. The monochromator was pyrolitic graphite (002 plane) and a cooled Be filter minimised X/2 contamination. Between this and the sarnple, a polarising mirror defined a vertical neutron spin polarisation. Polarisation analysis [5] was achieved by the combination of a polarisation sensitive Heusler alloy (111) analyser crystal plane, and a "flipper" solenoid mounted between this and the sample. Spin flip (SF) and non spin flip (NSF) cross sections were measured with constant incident energy and scattering vector Q, counting for typically 21 minutes per point. The resolution function was carefully determined, and the flipping ratio (N 40) was regularly checked. In the scattering geometry used [I101 was vertical and [I101 and [001] lay in the scattering plane. These axes are labelled y, x, and z respectively, for consistency with Mertens et al. 161, who have predicted the dynamic critical behaviour of 2d XY magnetic systems. Most scans were taken near to (O,0, 2.9) in a vertical field of 2 KG, a value strong enough to prevent neutron depolarisation by the sample, but not so strong as to suppress the critical scattering. In this configuration the field H, the neutron polarisation P and the magnetisation M were all vertical, and perpendicular to Q. Therefore easy plane magnetic fluctuations longitudinal (Syy, NSF) and transverse (Sxx, SF) to the spin direction were measured, along with background and incoherent scattering from various sources [5]. The measured intensity was analysed using the Harwell routine FITSQW. This convolves the calculated dynamic structure factor S (Q, w ) with the experimentally determined instrumental resolution function and enables parameters in the former to be fitted to the data. In all fits proper account was taken of the background and incoherent scattering. Typical results are shown in figure 1. The NSF (longitudinal) cross section fitted well to a central peak of Lorentzian form. The peak height was observed to reach a maximum at TC in zero field, and at progressively higher temperatures the larger the applied field. The energy width was approximately constant above Tc. The longitudinal polarisation of this central peak suggests that its origin is diffusive [7]. The SF (transverse) cross section was successfully analysed in terms of spin wave excitations which were sharp at all temperatures (50-60 K) Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888658 C8 1436 JOURNAL DE PHYSIQUE ~ b * CrCI, clear evidence of a Lorentdan or Gaussian central peak of approximate FWHM 0.024 THz (0.1 meV), and of 300 intensity too great to arise from any source other than out-of-plane fluctuations. In summary, the principal sources of dynamic critical scattering in Rb2CrC14 are (i) sharp in-plane spin waves, as previously observed [4]; (ii) a strong inplane longitudinal central peak, presumably due to spin diffusion; (iii) a weak central peak corresponding to in-plane transverse fluctuatiol~s; and (iv) a weak $ 0 6 -0 OL 0 0 2 o 0 0 2 O O L 0 0 6 central peak corresponding to out-of-plane transverse Energy Transfer I T H Z I fluctuations. All these features were observed in the Fig. 1. SF ( 0 ) and NSF (e) scattering observed at Q = temperature range where 2d XY-like behaviour is ex(0,0, -2.9) from Rb2CrC14 at 50 K with H = 2 KGThe pected, and where according to Kosterlitz-Thouless solid lines are the best fits of contributions described in the theory [8, 9], vortices are the relevlmt spin text . tions. Vortex diffusion has been predicted to give rise and wavevectors (q = 0-0.01 lattice units), and at energies consistent with previous results [4]. Additionally there was evidence of a broad central peak which decreased in intensity below 60 K. Both Lorentzian and squared Lorentzian forms gave equally good fits to its energy profile. Scans were also taken near to (1, 1,c) at 60 K and in zero external field. Finite values of C were used in order to avoid contamination by the (1, 1, 0) nuclear Bragg peak. In this configuration Q( // x) was perpendicular to P( // y), but not at a fixed angle with respect to the local magnetisation which could be directed anywhere in the x-y plane. The NSF cross section therefore measured both longitudinal and transto both inand out-of-plane transverse central peaks, with squared Lorentzian and Gaussian peak shapes respectively [6]. Although our data are insficient to determine peak shapes unambiguously, central peaks of both polarisations are observed. The in-plane central peak was measured in a magnetic field, making direct comparison with the theory tlifficult. However, the out-of-plane transverse central peak width, calculated using expression (4) of reference 171, the parameters appropriate to Rb2CrC14, and taking b = 1.5 [9], is found to be 0.028 THz (FWHM). This compares favourably with the observed width of N 0.024 THz. We may conclude that there is promising evidence of vortex diffusion in Rb2CrC4. verse SYY fluctuations, and the SF cross section meaAcknowledgments sured out of plane Szz transverse fluctuations. The latter cross section at (0.975, 0.975, 0.54) and (0.98, This work was supported in part by the Underlying 0.98, 0.54) and T = 60 K was analysed as described Research Programme of the UKAElA, and the U.K. above. A typical fit to the data is shown in figure 2. SERC. We wish to thank Miss G. Pilling for assistance Weak sharp spin wave intensity was observed at the with the data analysis. S.T.B. thanks Lincoln College, expected finite energy, probably as a result of Q not Oxford, for an E.P.A. Cephalosporii~ Junior Research lying exactly in the a;y plane. Additionally there was Fellowship. Energy Tronsfer I T H z I Fig. 2. SF scattering observed at Q = (0,98,0.98,0.54), from RbzCrC14 at 60 K in zero field. the solid line is the best fit of contributions from spin waves (short dash) and a broadened Lorentdan (dot-dash) scattering, together with nuclear incoherent (long dash) and linear background (not shown) components determined seperately. [I] Janke, E., Hutchings, M. T., Da~y, P. and Walker, P., J. Phys. C. 16 (1983) 5959. [2] Hutchings, M. T., Als-Nielsen, J., Lindgard, P. A. and Walker, P. A., J. Phys. C 1.4 (1981) 5327. [3] Hutchings, M. T. and Als-Neilst?n, J., in preparation. [4] Hutchings, M. T., Day, P., Janke, E. and Pynn, R., J. Magn. Magn. Mater. 54-57 (1986) 673. [5] Moon, R. M., Riste, T. and Koehler, W. C., Phys. Rev. 181 (1969) 920. [6] Mertens, F. G., Bishop, A. R., Wysin, G. M. and Kawabata, C., Phys. Rev. Lett. 59 (1987) 117. [7] Marshall, W. and Lowde, R. ID., Rept. Progr. Phys. 31 (1968) 705. [8] Kosterlitz, J. M. and Thouless, D. J., J. Phys. C 6 (1973) 1181. [9] Kosterlitz, J. M., J. Phys. C 7 (1974) 1046.