Magnetic scattering of neutrons in chromium

Solid State Communications Vol.2, pp. 109-114, 1984. Pergamon Press, Inc. Printed in the United States

MAGNETIC SCATTERING OF NEUTRONS IN CHROMIUM H. Bjerrum M$ller, K. Blinowski*, A. R. Mackintosh and T. Brun~ Danish Atomic Energy Commission,Research Establishment Risö Technical University, Copenhagen, Denmark (Received 18 March 1964 by H. H. Jensen) The results of a study of the magnetic scattering of neutrons in chromium near the Nêel temperature are presented. It is deduced from these results that short range ordering persists in chromium unusually high above the Néel temperature, and that the magnetic structure below the N4e1 temperature can exhibit lower than cubic symmetry. THE magnetic scattering of neutrons from chromium metal has been studied both above and below the Néel temperature. From the angular and temperature dependence of the critical magnetic scattering, information about the periodicity and polarization of the shortrange magnetic order above the Néeltemperature can be deduced, together with the temperature dependence of the range of order. Studies of the magnetic Bragg reflections have revealed that, under some circumstances, the magnetic order can have lower than cubic symmetry, and this provides an explanation for recent Montalvo and Marcus1 and the Watts2 on results the bulk ofmagnetization,

of the reciprocal lattice points. By appropriate independent rotations of the crystal and the counter arm, we were able to scan the regions of reciprocal space near (100) and (010) in the manner shown in Fig. 1. The results of measurements on the magnetic Bragg reflection at 23°Care also shown in Fig. 1. These curves show that the amplitudes of the transverse magnetization waves along [100] are much greater than those along [010]. By suitable masking, the four quarters of the crystal were studied independently and this same phenomei~onwas found in each. Montalvo and Marcus’ and Watts2 have recently shown that the magnetic properties and Fermi surface of chromium can exhibit lower, than cubic symmetry, when It is cooled through the Nêel temperature in a high magnetic field. Our data strongly suggest that these results are to be interpreted in terms of the anisotropy of the magnetization wave amplitudes and the associated energy gaps4 in the conduction electron dispersion relation. Although the results of Fig. 1 were not obtained in a magnetic field, our crystal, which was grown by strainannealing, probably retained a small amount of residual strain which, by virtue of the anisotropic modification of the exchange inter-

A crystal spectrometer situated at the DR 3 reactor was used for these experiments, An intense beam of 0.855 ~R neutrons, filtered through erbium to remove second-order contamination, was scattered from a single crystal of chromium, in the approximate form of a cylinder 4 cm long and 1 cm in diameter, placed in a constant temperature oven whose temperature could be varied. The magnetic order in chromium consists of 6 sinusoidal magnetization waves along the cubic axes, whose period is Incommensurate with that of the lattice3, and which give rise to satellites

Present address: Institute of Nuclear Research, Swierk k. Otwocka, Poland. § On leave from Iowa State University, Ames, Iowa, U. S. A.

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action, is equivalent to an anisotropic internal field. An attempt was made to modify the magnetic properties of our crystal by cooling it through the N~eltemperature in a field of ternperature in a field of approximately 1 kilogauss near the [100] direction. The intensity of the reflections corresponding to the [100] magnetization wave was reduced by about 8% relative to those associated with the [010] wave, and the intensities returned to their original values when the crystal was again heated and cooled through the Néel 5 were temperature unable to indetect no field. any change Shiraneinand the Takei intensities in a chromium crystal relative cooled through the Néel temperature in a field of 10 kilogauss. Our positive result can again probably be attributed to the strain in the crystal and this makes it difficult to interpret

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where the summations are over six (100) propagation vectors Q of the magnetization waves and the reciprocal lattice vectors ‘r. The A~depend upon the amplitude and polari-’ zation of the waves, and F is the magnetic form factor. K1 and A describe the decay in space and time of the pair correlation. The “rigid-spin” model gives a similar, but slightly modified, expression. In the vicinity of the N~eltemperature the scattering is largely elastic, so we can approximately put Atransfers = o. Wenear thenafind reciprocal that, forlattice momentum vector, the cross section has the approximate form do —

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where = ‘F + Q and the sum is restrict~J to the six ‘Fm around the reciprocal lattice vector. The critical scattering near a point of the reciprocal lattice therefore has the form of six superposed Lorentzian peaks, centered around theand magnetic reflections, with heights widths Bragg determined by K 1, the inverse of the correlation range.

Near the Néel temperature, neutrons are strongly scattered by spontaneous fluctuations in the magnetization. This phenomenon 6. isThe known critical magnetic scattering cross generalasexpression for the differential section for the scattering of neutrons oer unit solid angle6 and per unit energy of the scattered neutron Is d2o

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around (100) and (010) both above and below TN. For temperatures close to TN, where k0 and k are the incident and scattered the “shoulders” on the curves at the positions neutrofl”wave vectors, *w is the energy change of the magnetic Bragg reflections can clearly on scattering, g is the neutron’s magnetic be seen, but as Ki increases these gradually moment, and! is a unit vector in the direction disappear. Since changes of the propagation of the scattering vector K. The pair-correvector Q are thought to be due to the modifilation function y~’~ is defined by cation of the Fermi surface 4,by we the should magnetic ~ 1 N energy Qgaps expect to be constant above y (r, t) = N •.fdr1S~(o) 6 (r + r~(o)-r1) S. (t) 6 (r r. (t)~,)(2) the Néel temperature. Our. ____________________________ results appear to be consistent with this assumption, but the sum being over all pair.s i, j of N magnetic more detailed analysis is required to check electron spins. The magnetic structure of it in detail. Li Fig. 3 the temperature chromium is believed4 to be intermediate bedependence of the scattered intensity at di!tween two ext~,e~me models. In the “flexibleferent angles is compared with similar spin”model, y above the Néel temperature results for iron8. The Intensity decreases has the asymptotic form rapidly with temperature below the N~èl temperature, but above it there is a much slower y°’0(r,t)= ~ +~). 4-Kir1r e~t (3) decrease. This — — that, although theimplies correlation

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ranges for iron and chromium are similar (about 60A) just above the transition temperaturea, the long-range correlations in chromium persist far above the Néel temperature. This phenomenon is presumably associated with the small energy difference between the paramagnetic and antiferromagnetic phases9, and the long range of the exchange forces responsible for the magnetic ordering,

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we shall attempt to determine the exact ternperature depencence of Kj, and also te deduce the polarization of the magnetization fluctuations. At present, we can conclude only that they must have a transverse component. In addition, plan to study the inelastic neutron scatteringwe and hence to determine a value for the parameter A. These results together with a more detailed account of the present work, will be published in due course.

From a detailed analysis of our results,

References 1.

MONTALVO R.A. and MARCUS J.A., Phys. Letters 8, 151 (1964).

2.

WATTS B., Private communication.

3.

CORLISS L. M., HASTINGS J. M. and WEISS R. J., Phys. Rev. Letters 3, 211 (1959); BYKOV V. N., GOLOVKIN V. S., AGEEV N. F. and LEVDIK V.A., Dokl. Akad. Nauk SSSR 128, 1153 (1959); BACON G.E., Acta Cryst. 14, 823 (1961).

4.

OVERHAUSER A.W., Phys. Rev. 128, 1437 (1962).

5.

SH~ANEG. and TAKEI W.J., J. Phys. Soc. Japan 17, Suppi. B III, 35 (1962).

6.

VAN HOVE L., Phys. Rev. 93, 1374 (1954).

7.

ELLIOTT R.J. and MARSHALL W, Rev. Mod. Phys. 30, 75 (1958).

8.

PASSELL L., BLINOWSKI K., BRUN T. and NIELSEN P., Phys. Rev, to be published.

9.

BEAUMONT R. H., CHIHARA H. and MORRISON J. A., Phil. Mag. 5, 188 (1960). Die Ergebnisse von Untersuchungen Uber magnetische Streuung von Neutronen an Chrom in der N~hedes N~elpunkteswerden vorgelagt. Es wird geschlossen, das eine Nahordnung in Chrom ungew~hnlich weit über der N~eltemperaturbestehen bleibt, und ferner, dass die magnetlsche Struktur unterhalb des Néelpunktes niedrigere als kubische Symmetric besitzen kann.