HIGH ENERGY MAGNETIC EXCITATIONS IN CHROMIUM

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HIGH ENERGY MAGNETIC EXCITATIONS IN

CHROMIUM

J. Booth, S. Hayden, P. Mitchell, D. Mck. Paul, W. Stirling

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, SupplGment au no 12, Tome 49, ddcembre 1988

HIGH ENERGY MAGNETIC EXCITATIONS IN CHROMIUM

J. G. Booth (I), S. M. Hayden (2), P. W. Mitchell (3), D. McK. Paul (4) and W. G. Stirling ( 5 )

(l) Dept. of Pure t.3 Applied Physics, University of Salford, G.B.

(2) Institut Laue-Langevin, Grenoble, France

(3) Dept. of Physics, University of Manchester, G.B.

(4) Dept. of Physics, University of Wanuick, G.B

(') Dept. of Physics, University of Keele, G.B.

Abstract.

-

Magnetic excitations in the range 1 2 THz-30 THz have been measured in chromium at 5 K near the (100) magnetic zone centre. The intensity does not vary appreciably over that range, after corrections for background and resolution effects. The scattering is highly localised in wavevector.

Pure chromium metal orders magnetically below

TN = 311 K, as a modulated antiferromagnet, with a basic type I AF structure, and an incommensurate modulation vector (Q) parallel to (100)

.

Above the spin flip temperature

(T,

= 122 K) the spin di- rection is orthogonal to Q (transverse spin density wave, TSDW) and below it is parallel (longitudinal spin density wave, LSDW). The low temperature ordered moment is 0.59 ,LAB, and the magnitude of Q is

about 0.953 x 27~

/

a, varying a little with temperature

[I]. The mechanism driving the ordering is thought to be a nesting of two sheets of the Fermi surface, whose geometry determines the ordering wavevector [2]. Thus chromium is an itinerant antiferromagnet whose structure is well known. Strong coupling (Nambu-Eliashberg) theory of the SDW gives a good account of both TN and the magnitude of the ordered moment [3].

The excitations are.not yet well-characterised in their entirety, although some aspects have been thor- oughly explored.

he

low energy (v

<

4 THz) region contains a wealth of well-defined excitation branches which have been measured by neutron inelastic scattering [4, 51. Optical absorption spectroscopy at low temperatures has been used to examine the energy range 25 THz

<

v

<

250 THz [6]. There is very little pub- lished work relating to the intermediate energy range except near room temperature [7] and it is hard t o build up a coherent picture. The low energy measurements show modes going more or less straight up in energy from the (commensurate) magnetic zone centre, which die away in intensity beyond 6.5 THz a t 295 K. The optical absorption at low temperatures shows strong peaks at about 30 THz and 100 THz, which Fenton and Leavens [3] interpret as transitions across the two gaps which arise in place of the one (BCS-type) gap in the incommensurate phase. Each of the four bands is not a simple up or down spin band, but a mixture. It would seem reasonable to expect features in the magnetic excitation spectrum at the same

We have performed neutron inelastic scatterig experiments on the hot-source triple-axis spectrometer, IN1, at the Institute Laue-Langevin, Grenoble, in an attempt t o bridge the gap between the known excitation spectrum at low energies, and the optical absorption data. The sample was a cylindrical crystal, oriented with [OlO] along the length of the cylinder, 50 mm long and 12 mm diameter. It was prepared in a single-Q state with Q along its length by cool- ing through TN in a field of 15 T. It was mounted in a helium flow cryostat with the [010] axis and the Q- vector vertical (orthogonal to the scattering plane) and cooled t o 5 K. The monochromator was Cu (220), and the analyser was Cu (002). The spectrometer was op- erated in various configurations, chosen to avoid background problems.

Preliminary experiments had indicated that the magnetic zone-centre scattering at low temperature di- minished in intensity at higher energies just as the results of Ziebeck and Booth

[q

at room temperature, and that there were additional modes at about 20 THz near the magnetic zone boundary. However, on closer inspection, both of these conclusions were shown to be incorrect. The zone boundary modes were found to be spurious, generated by the long tail of the resolution function meeting with high frequency (- 10 THz) phonon modes at a significantly different wavevector.

More careful measurement of the zone centre mode intensity revealed that, far from diminishing at higher energies, it remains constant t o within the experimental error from 12 THz up to 30 THz, (Fig. 1). The earlier results had failed to treat both the background and the resolution sufficiently carefully. Two factors contribute to the background, namely the incoherent phonon scattering and the background arising at small scattering angles at the sample

(4).

To arrive at the present result,s, we used the follow- ing procedures. At each energy transfer, a set of scans was performed in the vicinity of the (100) magnetic zone centre. At each energy, a single peak was ob- energies. served in the scattering at the (100) position. In the

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C8

-

222 JOURNAL DE PHYSIQUE

E n e r g y T r a n s f e r / THz

Fig. 1. - Measured intensity of magnetic response in

chromium at (100) magnetic zone centre, reIative to 12 THz

intensity.

most extreme case (30 THz, the highest frequency), two thirds of the intensity in the peak in a transverse scan was contributed by the small-4 background (4 being at its smallest at (100) in a (10q) transverse scan), and the corrections for this were made by curvi- linear scans in wavevector which kept

4

constant. Over the range of energies for which this background prob- lem was not acute, full contours of the magnetic scattering in wavevector were measured, and the widths compared with the expected resolution-limited widths for scattering of no extent in wavevector, and of equal weight a t all energies within the resolution function. Agreement was found to within 20 %

,

which repre- sents the limit of reliability of the resolution calcula- tions. Using these measured widths and shapes of the scattering, as well as the height of the observed peak, the intensity of the mode was estimated. At higher energies, where the background problems became se- vere, it was not possible to measure the widths in the same way. In this case, widths calculated from the resolution function were used instead.

Values of the scattered wavevector of 7.42 and 8.41 A-l (erbium filter), 11.3

A-1

(hafnium filter), 12.5

A-1

and 13.5 A-l (no filter necessary, no 2 k ~ de- tected) were used a t different energy transfers. Each time the configuration was changed, the scans were re- peated at an energy transfer already measured, and the results used to cross-calibrate the intensities measured under different conditions.

The experimental conditions rapidly become tougher a t higher energy transfers, and we estimate 30 THz to be the realistic ceiling for measurements at the (100) position. Measurements at (201) were not productive because of the much smaller intensity due to the form factor. (111) might be possible, but our ex-

perimental geometry did not permit us to access that wavevector transfer.

Ziebeck and Booth took the falling intensity above 6.5 THz at 295

K

as evidence that the SDW gap is about 6.5 THZ. If we are expecting a gap of 30 THz a t low temperature, consistent with the optical absorp tion results, then our data, though woefully incom- plete, are compatible with this value, if this criterion is valid.

It would seem more natural to expect a peak in the scattering intensity at the energy of the gapat-the- gap-edge, as in the optical absorption. On the other hand, if the phonon de-pairing effects are strong ([3] argue that this is what gives rise to 2 A.

/

kg

TN

=

10 in the commensurate itinerant antiferrornagnet Cro.99Mno.01, by reducing TN more rapidly than Ao) then it may be wrong to take the one-electron band picture too seriously, since the electron-phonon coupling must be very important. Against this, however, relatively sharp features survive in the optical data, and the model of [3] gives a very good estimate of the ordered moment.

Much remains to be done in chromium. On the experimental side, what is the form of the magnetic excitation spectrum at and above 30 THz, where the collective modes meet a region of single-particle excitations? At what energies does the magnetic response away from the magnetic zone centre arise? What is the temperature dependence of the response, and does it change on going from below to above

T,

? On the theoretical side, what is the predicted effect on the collective modes of the single-particule modes? We hope to pursue these questions in the near future.

Acknowledgments

This work was supported by SERC. The chromium crystal was grown by Metal Crystals and Oxides Ltd, and poled at the SNCI, CNRS, Grenoble.

[I] Bacon, G. E., Neutron Diffraction, 3rd ed. (Ox- ford) 1975 and reference cited therein.

[2] Lomer, W. M., Proc. Phys. Soc. 80 (1962) 489. [3] Fenton, E. W. and Leavens, C. R., J. Phys. F 10

(1980) 1853.

[4] Burke, S. K., Stirling, W. G . , Ziebeck, K. R. A.

and Booth, J. G., Phys. Rev. Lett. 51 (1983) 494. [5] Grier, B. H., Shirane, G. and Werner, S. A., Phys.

Rev. B 31 (1985) 2892.

[6] Lind, M. A. and Stanford, J. L., Phys. Lett. A 39

(1972) 5.

[7] Ziebeck, K. R. A. and Booth, J. G., J. Phys. F 9