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IDENTIFICATION OF FLUCTUATING
SUSCEPTIBILITY COMPONENTS IN Rb2CrCl4 : A
QUASI-2-DIMENSIONAL EASY PLANE
FERROMAGNET
S. Bramwell, M. Hutchings, J. Norman, R. Pynn, P. Day
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Supplement au no 12, Tome 49, dkembre 1988
IDENTIFICATION OF FLUCTUATING SUSCEPTIBILITY COMPONENTS IN
Rb2CrC14:
A
QUASI-2-DIMENSIONAL EASY PLANE FERROMAGNET
S. T. Bramwell ( I ) , M. T. Hutchings (2), J. Norman (2), R. Pynn (3) and P. Day (I)
( I ) Inorganic Chemistry Laboratory, South Parks Road, Ozford, G. B.
(2) Materials Physics and Metallurgy Division, Hanuell Laboratory, Didcot, OX11 ORA, G.B. ( 3 ) Institut Laue Langevin, BP156, 38042 Grenoble, France
Abstract. -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 sepa- rated 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 = 15.715A
at 4.5 K. The exchange coupling is predominantly near neighbour Heisenberg (J/be % 7.6 K), with relatively much weaker inter-planer coupling J'
(J'/
J=
[2]. When a small canting is neglected, the spin wave behaviour is well de- scribed 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 mag- netisation. The magnetic dipolar interaction is gener- ally negligible at a microscopic level.Rb2CrClr orders three dimensionally at Tc
=
52.2 K as a result of the weak interplanar coupling. 2d, possi- bly 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 weresuccessfully analysed in terms of sharp (resolution lim- ited) 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, renor- malising 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 at- tached to the cold fmger of an Oxford Instruments vertical field cryomagnet, with temperature measured by a P t resistance thermometer. The IN12 triple axisspectrometer on the cold neutron guide, ILL, Greno- ble, was used in the UW" configuration with neutron wavelength X = 5.02
A,
and nominal collimation angles 60'30'30'-60'. The monochromator was py- rolitic graphite (002 plane) and a cooled Be filter min- imised X/2 contamination. Between this and the sarn-ple, 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 t o (O,0, 2.9) in a vertical field of 2 KG, a value strong enough to prevent neu- tron depolarisation by the sample, but not so strong as to suppress the critical scattering. In this config- uration the field H, the neutron polarisation P and the magnetisation M were all vertical, and perpendic- ular to Q. Therefore easy plane magnetic fluctuations longitudinal (Syy, NSF) and transverse (Sxx, SF) to the spin direction were measured, along with back- ground and incoherent scattering from various sources [5]. The measured intensity was analysed using the Harwell routine FITSQW. This convolves the calcu- lated dynamic structure factor S (Q, w ) with the ex- perimentally determined instrumental resolution func- tion 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 temper-atures the larger the applied field. The energy width was approximately constant above Tc. The longitudi-
nal 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 excita- tions which were sharp a t all temperatures (50-60 K)
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 criti- cal scattering in Rb2CrC14 are (i) sharp in-plane spin waves, as previously observed [4]; (ii) a strong in- plane longitudinal central peak, presumably due to spin diffusion; (iii) a weak central peak correspond- ing to in-plane transverse fluctuatiol~s; and (iv) a weak
$ 0 6 - 0 O L - 0 0 2 o 0 0 2 O O L 0 0 6 central peak corresponding to out-of-plane transverse
E n e r g y T r a n s f e r 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 K G - The pected, and where according t o 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 ener-
gies consistent with previous results [4]. Additionally there was evidence of a broad central peak which de- creased 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 t o avoid contamination by the (1, 1, 0) nuclear Bragg peak. In this configuration Q(//
x) was per- pendicular toP(
//
y), but not a t a fixed angle with respect t o the local magnetisation which could be di- rected anywhere in the x-y plane. The NSF cross sec- tion therefore measured both longitudinal and trans--
to both in- and out-of-plane transverse central peaks, with squared Lorentzian and Gaussian peak shapes re- spectively [6]. Although our data are insficient to determine peak shapes unambiguously, central peaks of both polarisations are observed. The in-plane cen- tral peak was measured in a magnetic field, making direct comparison with the theory tlifficult. However, the out-of-plane transverse central peak width, calcu- lated using expression (4) of reference 171, the parame- ters appropriate t o 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 mea-Acknowledgments
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 T r o n s f e r 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 prepara-tion.
[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.
