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Investigation of critical fluctuations near Tc in ferromagnetic UTe
H. Bjerrum Møller, G. Lander, O. Vogt
To cite this version:
H. Bjerrum Møller, G. Lander, O. Vogt. Investigation of critical fluctuations near Tc in ferromagnetic UTe. Journal de Physique Colloques, 1979, 40 (C4), pp.C4-28-C4-30. �10.1051/jphyscol:1979409�.
�jpa-00218805�
JOURNAL DE PHYSIQUE Colloque C4, supplhnent au no 4 , Tome 40, avril 1979, page C4-28
Investigation of critical fluctuations near T , in ferromagnetic UTe (*)
H. Bjerrum Mailer, G. H. Lander ( 7 ) and 0. Vogt ( t t ) Riser National Laboratory, Roskilde, Denmark '
( t ) Ris0 Nat. Lab., and Argonne National Laboratory (*), Argonne, IL 60439, U.S.A.
( t t ) Laboratorium fiir Festkorperphysik, ETH, Ziirich, Switzerland
RBsum6.
-
Par diffusion de neutrons nous avons mesurk dans UTe la corrklation spatiale des fluctuations magnktiques B longue distance aux environs de T c . La diffusion critique au-dessus de Tc a kt6 ajustCe B une fonction de Lorentz B symktrie sph6rique ( d a / d O ) a s/(K'+ q S .
L'inverse du domaine de corrClation, K, varie de 0,006 B 0,150 h;-'. Pour une temperature rCduite variant d'un ordre de grandeur on trouve K cc t " avec v = 0,84 +- 0,05, cette valeur est supkrieure B celle que prkvoit une thkorie simple (0,64).En dkpit du soin apport6 B nos mesures, aucune dkpendance d'6nergie des fluctuations ni aucune anisotropic entre les composantes transversales et longitudinales n'ont pu 6tre observtes.
Abstract.
-
The spatial correlations in the long-range magnetic fluctuations near Tc have been measured in UTe by means of neutron scattering.The critical scattering above Tc was fit to a spherically symmetric Lorentzian function ( d a / d O ) s/(K'+
q3.
The inverse correlation range, K, varies from 0.006 to 0.150A-'.
Over a decade of reduced temperature K cc t " with v = 0.84 2 0.05, which is greater than expected from simple theory (0.64).Careful scans failed to detect any energy dependence in the fluctuations or anisotropy between the transverse and longitudinal components.
1 . Introduction.
-
Measurements of the long- dependence of the susceptibility about the ( 1 1 1 ) range magnetic fluctuations in the actinide antiferro- ordering point, q = 0 . The final analytical form is magnets USb and UN have shown that the interac-tions are highly anisotropic [ I ] . In an attempt to S examine these properties in ferromagnetic systems
( )
~ ' + ( q - qJ2 we have measured the spatial and temporal depen-dence of the fluctuations in UTe, an actinide ferro- with variables S, K and q, the exact geometric centre magnet with the NaCl crystal structure, of the scattering.
a = 6.155
A,
and T ,-
103 K [ 2 ] . 3. Experimental and results.-
The experiments The experiment consists of measuring weak critical were performed near the ( 1 1 1 ) reflection from a scattering around the ordering point ( 1 1 1 ) above T,. single crystal of UTe oriented with a[lie]
axis vertical at the DR-3 Reactor, R i m A triple axis 2. Theory.-
Ornstein-Zernicke written
Following the conventional form [3] the susceptibility may be
where S is a scale factor and is only weakly depen- dent on temperature, and K ( T ) is the inverse correlation range of the fluctuation. This form for the susceptibility gives rise to a neutron cross- section which is Lorentzian in shape with a half- width of K . In fact, apart from geometric terms and the magnetic form factor, which are constant over the region of our measurements, the cross-section gives directly ( d u / d f l ) a T . ~ ( q , T ) where we are now interested in looking at the reduced wave vector
(*) Work supported by U.S. Department of Energy.
spectrometer with graphite monochromator and ana- lyser, together with a Be filter to eliminate second order, were used with incident neutrons of 5 meV (4.1 A). The horizontal and vertical collimation was lo.
The results of an experimental scan at T ,
+
0.55 are shown in figure 1. Note first the log scale of intensity. The nuclear Bragg peak is represented by the broken curve and was determined by measure- ments outside the critical regime. A Gaussian func- tion gives an excellent fit over 3 orders of magni- tude between 0.01<
1 q 1 < 0.04A-'.
Clearly, for I q I 6 0.02 A-', the identification of critical scatter- ing relies on the subtraction of two large numbers, a process leading to large error bars at small q, which can be seen in the resultant critical scattering plotted in figure 2. Both longitudinal and transverse scans were performed, but no measurable differences we- re found at any temperature.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979409
INVESTIGATION OF CRITICAL FLUCTUATIONS NEAR T, IN FERROMAGNETIC UTe C4-29
1 1 1 1 1 1 1 1 1 1 1
-0.08 -0.04 0 0.04 0 0 8 REDUCED WAVEVECT0R.q 1A-I)
Fig. 1. - Longitudinal scan through the (1 11) point at Tc
+
0.55 K. The broken curve represents the Gaussian (+background) fit to the nuclear Bragg peak. The solid line includes the Lorentzian of critical scattering.REDUCED WAVEVECTOR,q ( i - ' )
Fig. 2. - Least-squares fit (solid curve) to the Lorentzian func- tion at T ,
+
0.55 K. The observed points have had the Gaussian and background subtracted.The 3-axis spectrometer can also examine the temporal fluctuations of the spin components by anaIysing any energy differences between the inci- dent and scattered neutrons. Measurements at q = 0 showed a constant (resolution limited) width of 0.1 meV at all temperatures. We conclude from this that the fluctuations are long-lived with lifetimes greater than lo-" s.
To process the data we convolute a 3-dimensional resolution function, which is determined experimen- ' tally about the (111) point, with the analytical ex-
pression for the critical scattering, and least-squares fit to the data. For temperatures near
Tc
the least- squares analysis gives a clear minimum, but this is not the case for higher temperatures, where the critical scattering is weak, and the subtraction pro- cess correspondingly more important. To reduce the number of parameters we have kept S fixed= 3.96, which is the average value (
+
0.25) obtained for t = ( T - Tc)/ Tc =s 0.02. Such a restricted form for the susceptibility implies that all the temperature dependence occurs in the function K (T). The results for K are shown in figure 3.Fig. 3. -Inverse correlation range us. reduced temperature for.
UTe. In the experiment we determine Tc = 99.80 2 0.15 K.
4. Discussion.
-
The value of v = 0.84 & 0.05 is considerably higher than the values of 0.643 and= 0.7 expected for 3-dimensional Ising and Heisen- berg systems, respectively. However, the non- Lorentzian form of the scattering at higher tempera- tures implies that this value of v may not be too meaningful. A similar situation was found in USb and UN [I].
The presence of a large rhombohedra1 distortion and the large anisotropy in the magnetization [4]
imply strong single-ion anisotropic interactions exist in the ordered state of UTe. The aim of the present experiment was to search for possible anisotropy in the critical scattering above
Tc
that would indicate anisotropic two-ion coupling between spins. Unfor- tunately, the very nature of the ferromagnetic order- ing means that the scattering from all 4 domains appears at the (11 1) point. This geometric fact makes it very difficult to determine whether there are anisotropic critical fluctuations, unless they are very large.H. BJERRUM MDLLER, G . H. LANDER AND 0. VOGT
References
[I] LANDER, G . H., SINHA,
s.
K., SPARLIN, D. M. and VOGT, O . , [3] SCHULHOF, M. P., HELLER, P., NATHANS, R. and LINZ, A., Phys. Rev. Lett. 40 (1978) 523 ; BUYERS, W. J. L. et al. in Phys. Rev. B 1 (1970) 2304.R o c . of Intl. Conf. on Inelastic Neutron Scattering, [4] BusCH, G . , VOGT, O . , DELAPALME, A. and LANDER, G. H., J.
Vienna, October 1977. Phys. C.
121 WEDGWOOD, F. A. and KUZNIETZ, M. K., J. Phys. C 5 (1972) 3012.
