NEUTRON SCATTERING EXPERIMENTS ON GADOLINIUM

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NEUTRON SCATTERING EXPERIMENTS ON GADOLINIUM

W. Koehler, R. Moon, J. Cable, H. Child

To cite this version:

W. Koehler, R. Moon, J. Cable, H. Child. NEUTRON SCATTERING EXPERIMENTS ON GADOLINIUM. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-296-C1-298.

�10.1051/jphyscol:19711100�. �jpa-00213914�

TERRES RARES ET ALLIAGES

NEUTRON SCATTERING EXPERIMENTS ON GADOLINIUM

W. C. KOEHLER, R. M. MOON, J. W. CABLE and H. R. CHILD Solid State Division Oak Ridge National Laboratory operated

by Union Carbide Corporation for the U. S. Atomic Energy Commission, Oak Ridge, Tennessee

Rksum6. - Nous avons fait des expkriences de la diffusion et de la diffraction de neutrons avec des monocristaux de Gd enrichis en l6oGd. Nous avons mesur6 les courbes de dispersion pour les ondes de spin selon les trois directions principales a la temperature de 7 8 ^OKaussi bien que les relations correspondantes pour quelques temp6ratures plus 61e- v k s selon la direction c. Le facteur de forme magn6tique a kt6 mesur6 avec des neutrons polarises pour toutes les raies (hkO) jusqu'a sin 8/12 = 1,275 et (hOl) jusqu'k sin B / A = 1,04. Les rksultats sY6cartent sensiblement du calcul Hartree-Fock de Blume, Freeman et Watson. Nous avons conclu que les fonctions d'onde 4-f dans le metal sont rkllement diffirentes que dans l'ion fibre.

Abstract. - Neutron scattering experiments on gadolinium have been carried out on single crystal specimens highly enriched in 160Gd. The spin wave dispersion relations have been determined in the three principal a-, b-, and c-directions at 78 ^OKand at several elevated temperatures along the c-direction. The form factor has been measured for all (hkO) reflec- tions out to sin 8/12 = 1.275 and for (h01) reflections out to (1.04). The data deviate markedly from the Hartree-Fock calculation of BIume, Freeman and Watson. It is indicated that the metallic 4-f wave functions must be substantially different in the metal than in the free ion.

Introduction. - In many respects gadolinium is one of the simplest magnetic materials known and as such it is in principle an ideal candidate for a number of neutron scattering experiments. It is a simple ferro- magnet below its Curie point of 292.7 OK. The metal behaves-as if it contained tripositive ions in 'S,,, states ; accordingly, the influence of crystalline anisotropy, and of magnetoelastic effects on the magnon-dispersion curves can be expected to be small. Moreover the dispersion curves in the c-direction will measure directly the exchange energy. The saturation magneti- zation of Gd exceeds by 0.55 ^p, the value of 7.0 ^p, expected from the Hund's Rule ground state. The excess is usually attributed t o conduction electron polarization. By measuring the form factor of gadoli- nium, one may hope to gain direct information about the 4-f radial wave functions in the metal and about the nature of the conduction electron contribution.

This paper summarizes briefly progress which has been made at the Oak Ridge National Laboratory on the two experiments mentioned. Other types of investiga- tions, namely critical magnetic scattering and parama- gnetic scattering, may be expected to yield important information about the rare earths and will be under- taken in due course. The results summarized here will be published in more complete and detailed form elsewhere.

The specimens. - Natural gadolinium has a capture cross section for neutrons of energy 0.07 eV of 2 x lo4 barns. (The major absorbers are 15'Gd(2.2 x lo4 b) and '57Gd(105 b). Although specialized diffraction expe- riments carried out with natural Gd have yielded important results [1,2] it is clear that for measurements of spin wave dispersion curves, where relatively large single crystals are required, a low capturing isotope of G d is necessary. Such an isotope, 160Gd is known to exist [3] ; however, since 1 % 15'Gd is worth 1,000 b

(*) Research sponsored by the U. S. Atomic Energy Com- mission under contract with the Union Carbide Corporation.

it is evident that a very good isotopic separation is required. Recently, some fifty grams of 99.993 %

160Gd as Gd2O3 were produced by the Stable Isotopes Division of the Oak Ridge National Laboratory. Some of this was studied as the oxide. The balance was reduced to the metal and a single crystal grown by a modification of the strain-anneal technique reported by Nigh [4]. The button after annealing consisted of one large grain, approximately half the button, and four smaller grains of various sizes. The large grain as finally isolated weighed 23 grams ; this specimen was used in the inelastic scattering measurements.

From one of the smaller grains three pillar shaped crystals, two with the long axis parallel to a c-direction, one to a n a-direction were cut and these were used to determine the form factor. In these experiments both polarized and unpolarized neutron techniques were used. At 0.07 eV the total neutron cross section of 160Gd is 20.3 blatom. In a separate experiment the coherent amplitude b was measured as

Results : the spin-wave dispersion relations.

The spin-wave dispersion relations [5] have been mea- sured for the three high symmetry a-, b-, and c-direc- tions a t 78 OK, and at a number of elevated tempera- tures in the c-direction. The measurements were carried out by means of the triple-axis spectrometer located at the High Flux Isotope Reactor. Both cons- tant-q and constant-E modes of operation were used.

The neutron groups observed were well defined and quite strong with peak intensities ranging from fifty t o a thousand counts per minute. Phonon scattering was separated from that of the magnons by appropriately discriminatory scans at 78 OK and by separate room temperature phonon measurements.

The measured dispersion curves are shown in figure 1. These have a rather similar shape to those reported for terbium [6]. Notably different are (1) the tendency of Ro to 0 at q = 0 (2) the much greater

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711100

NEUTRON SCATTERING EXPERIMENTS ON GADQLiINIUM C1-297

0 0.2 0 . 4 0 . 5 0.4 0.3 0.2 0.1 0 0.2 0.4 0.6 0.8 1.0

r M K r A r

4r/0* 4 r / 0 ZS/C

WAVE VECTOR

Magnon Dispersion Curves I6O6d 78-K .

FIG. 1. - Magnon dispersion curves for 160Gd at 78 OK.

maximum energies. Since the anisotropy is at least an order of magnitude smaller in Gd than in Tb these data have been analyzed in terms of the simple Hamil- tonian

= -

,Fm

and the Fourier transformed exchange parameters J ' ' ~ ( ~ ) = J(rz) exp i q

.

rl

(2) where the superscripts signify that the sum is to be taken over atoms on the same (s) or different (d) sublattices.

In the c-direction the dispersion relation has the particularly simple form

-= ca

"(q) _S J(O) - ~ ( q ) = 2 _{m = l}

c

where q, = q/(2 n/c) and J,O is the interplanar constant corresponding to m'th nearest neighbor planes normal to c. Thus the measured dispersion curve is directly proportional to J(0) - JC(q) for the c-direction. The solid line in the figure is a five parameter fit with Aw = 0 at q = 0. With slightly more complicated expressions interplanar exchange parameters in the other directions have been obtained and these are listed in table I.

Interlayer Exchange Parameters for Gadolinium at 78 OK. All constants are expressed in meV except those for Jd in the b direction which are (meV)2.

The exchange interaction in Gd is thus long range

and oscillatory. The curve J(0)

-

Data have been obtained for c-axis magnons at 195 OK and 232OK and these are shown in figure 2.

ORNL-DWG 69-8124

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 4.0 q/q,,, , WAVE VECTOR

'60~d Experimental Dispersion Curves c - A x i s Magnons.

FIG. 2. - Temperature variation of c-axis magnon energies.

Again, since crystal anisotropy is negligible, these dispersion curves, proportional to J(0)

-

The magnetic form factor. - Polarized beam data have been obtained at 96 OK for all Bragg peaks (hkO) out to sin 9 / 1 = 1.275 and for all (hOl) reflections out to sin 9 / 1 = 1.04. Unpolarized beam data have been collected for high flipping ratio reflections. The data are summarized in figure 3 together with some partial interpretation of the results.

As we have mentioned above, we expect to find a contribution (0.55 pB at 4.2 O K ) from the conduction electrons. Since these are expected to be d-like [7]

their contribution t o the form factor will occur at small scattering angles. Thus we have fitted the data beginning at sin 9/;l = 0.55 to the BIume-Freeman- Watson [8] free ion form factor. For the high sin 912 values the fit is excellent. On extrapolation to sin

C 1 -298 W. C . KOEHLER, R. M. MOON, J. W. CABLE AND H. R. CHILD

FIG. 3. -The magnetic form factor of 16oGd. In the insert is shown ( P / b ) o b s - ( p / b ) c a l e for a Blume-Freeman-Watson fit to

the high-angle data.

O/A = 0 one obtains a value for the 4-f moment of 5.63 p, as compared to that expected for ,u4f at 96 OK of 6.48 pB. In the insert to the figure are shown values for the difference (plbj,,, - (plbj,,,,. If this is to be attributed to conduction electron scattering, one is required to have 1.36 pB from this source (since magne- tization at 96 OK yields 6.99 p,). Thus in order to account for our data on the basis of the Freeman- Watson radial wave functions it is necessary to postu- late a 4-f moment which is much too small to be reasonable and a 5-d moment which is much too large to be reasonable. Moreover the 5-d form factor goes through zero at sin O / A = 0.275 so that there is much too great a difference (obs-calc) than can be accounted for. We are forced to the conclusion that the 4-f

Refer WILL (G.), NATHANS (R.) and ALPERIN (H. A.), J.

Appl. Phys., 1964, 35, 1045.

CABLE (J. W.) and WOLLAN (E. O.), Phys. Rev., 1968, 165, 733.

Neutron Cross Sections. BNL-325. Second Edition.

Supplement No 2, ~ o l . IIC, 1966.

NIGH (H. E.). J. ADD[. Phys.. 1963. 34, 3323.

A short report of-some7 of this 'work appears in KOEHLER (W. C.), CHILD (H. R.), NICKLOW (R. M.), SMITH (H. G.), MOON (R. M.) and CABLE (J. W.), Phys. Rev. Letters, 1970, 24, 16.

wave functions in the metal are significantly different than the free ion calculation.

We have made measurements on the metal in the paramagnetic region where experimental corrections to the low angle data are less severe, and these are in excellent agreement with the low temperature data.

This gives us confidence in our treatment of the expe- rimental corrections and indicates that there is little temperature dependence of the form factor.

ORNL-DWG 70-1838

I I

"

0 0.4 0.2 0.3 0.4 0.5

sine/,

Gd203 Pararnognetic Form Factor.

FIG. 4. - The form factor obtained from paramagnetic scatte- ring by Gd+3 at room temperature in Gd7.03.

We have measured the paramagnetic scattering cross section of I6OGd in the sesquioxide [9] by the polari- zation analysis technique which permits a clean separation of magnetic from nuclear scattering. The cross sections were placed on an absolute scale by comparison with silicon powder and normalized to the effective moment for a spin 712 ion. The results are shown in figure 4. The full line is the theoretical Blume-Freeman-Watson form factor for Gd+3. It may be seen that the fit to the data is excellent except at very small scattering angles.

[6] BJERRUM-M L?I LLER (H.) and HOUMANN (J. C . G.), Phys. Rev. Letters, 1966, 16, 737.

[7] FREEMAN (A. J.), DIMMOCK (J. B.) and WATSON (R. E.), Phys. Rev. Letters, 1966,16,94 ; WATSON (R. E.), FREEMAN (A. J.) and DIMMOCK (J. P.), P h y ~ . Rev., 1968, 167, 497.

[8] BLUME (M.), FREEMAN (A. J.) and WATSON (R. E.), J. Chem. Phys., 1962, 37, 1245 ; 1964,41,1874.

[9] An earlier measurement was made by CHILD (H. R.), MOON (R. M.), RAUBENHEIMER (L. J.) and KOEHLER (W. C.), J. Appl. Phys., 1967,38,1381.