3d magnetism in LuFe2

3d M A G N E T I S M IN LuFe 2 D. GIVORD*, A. R. G R E G O R Y * * and J. SCHWEIZER* Institut Laue-Langevin, 156 X, 38042 Grenoble Cedex, France

The magnetization density in LuFe2, measured by polarized neutrons, is located around the Fe sites. Spin and orbital contributions are deduced. The form factor anisotropy shows that the unpaired d-electrons tend to avoid orbitals pointing towards the neighbouring Fe atoms, which is consistent with the bonding character of these orbitals.

1. Introduction The RFe 2 alloys crystallize in the cubic Laves phase structure of MgCu 2 type, the Fe atoms being distributed on the corners of tetrahedra. YFe 2 and LuFe 2 are ferromagnets which order above 500 K [1], thus showing Fe to be magnetic. We have undertaken a polarized neutron study of LuFe 2 in order to determine the 3d magnetic density. Especially, comparisons of results with those obtained in Fe metal [2] should be interesting since the packing of the Fe atoms is very different from that of the metal structure.

2. Experimental and results A single crystal of LuFe 2 was grown by the Czochralski method. A sample was cut into a parallelepiped of 7 x 7 x 0.7 mm 3 the first dimension being parallel to [170]. The magnetization at 4.2 K in 1.65 T was measured to be 2.85 (5) /~B/LuFe2 along Ill0]. The neutron measurements were performed on the diffractometer D5 placed at the hot source of the ILL. The sample was placed in a vertical magnetic field of 1.65 T parallel to [110]. A complete set of 66 independent reflections was collected at 4.2 K out to sin O/X = 1.2 ,~-i. The 18 first reflections were measured at 3 different wavelengths, namely X = 0.84, 0.50 and 0.42 .~, in order to perform the extinction corrections. Polarized neutron measurements yields the flipping ratio R

=(F

M + F N ) 2 / ( F M - FN) 2,

where F M and F N are the magnetic and the nuclear structure factors respectively. The magnetic ampli*Lab. Louis N~el, CNRS, 166X, 38042 Grenoble Cedex. **And: Institut fiir Kristallographie Universifiit Frankfurt, Germany. ?DRF-CENG, 85X, 38041 Grenoble Cedex.

tudes were corrected for extinction and instrumental imperfections. Some reflections appeared to be strongly altered by extinction. Consequently, a small crystal of 4 x 2 x 0.24 mm 3 was cut out of the first sample. The 26 strongest reflections were remeasured. For the 7 strongest of these, agreement was not satisfactory between measurements on both samples. Using the small crystal measurements for these reflections, a projection of the magnetization density along [170] (fig. 1) was calculated. Magnetism is located on the Fe site only, no magnetic density appears on the Lu site. Fig. 2 shows the magnetic amplitudes as a function of sin O/X normalized to one Fe atom. The overall feature of a 3d form factor is observed. However, the experimental points are scattered around a smooth curve, showing that the magnetization density is not spherical around the nuclei.

3. Analysis The analysis of the experimental magnetic amplitudes is based on a model of 3-d magnetic

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Journal of Magnetism and Magnetic Materials 15-18 (1980) 293-294 ©North Holland

293

D. Givord et al./3d Magnetism in LuFe2

294

TABLE I Magnetic moment, population factors and cos t value in LuFe2. a, fl, y for a spherical distribution would be 0.20, 0.40, 0.40. Spin

Moments Orbitals

ms(P'B)

mL(P'B)

1.67(6)

0.07(3)

Population factors

a

0.25(1)

moments. The amplitude diffused b y one Fe m o ment can be written as m L f L + m s f s where m E and m s are the orbital and spin m o m e n t s respectively. The form factor fL and fs are obtained with radial distribution values; those calculated by W a t s o n and F r e e m a n for the Fe E+ free ion [3]. The usual dipole approximation is applied to the form factor fL as the orbital contribution is m u c h weaker than the spin o n e (rE ---- ( J 0 ) + ( J 2 ) ) " For the spin form factor one considers the effect of the crystal field on the 3-d wave functions. In the simple case of a uniaxial symmetry crystal field the 5-fold degeneracy of the 3-d level is r e m o v e d into one singlet, A~g, corresponding to an orbital mostly localized along the axis and two doublets, E2g in the plane perpendicular to the axis and Elg intermediate between the axis and the plane. I n L u F e 2, where the Fe atoms form tetrahedra, the local s y m m e t r y (3m) is not simply axial. The singlet Alg(F]) is not affected, whereas two new doublets (['3, F~) are formed by mixing the Elg and E2g orbitals through a parameter cos t which is not determined by the 2.00

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Wave function parameter

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0.29(1)

0.46(1)

0.47(5)

symmetry. The angular wave functions are =

r o

~bl(F3) , ~b2(I'3) - cos I Y 2 2 + sin t Y ~ I tpl(r3' ), ~b2(F3') = sin t Y 2 z ¥ c o s t Y ~ I. m L, m s, cos t, the populations a,/3, y of the three levels F 1, 1-"3 and F~ can be determined by refinement using the data. This has been achieved without the 7 Bragg reflections whose measurements on the two crystals do n o t correspond. Table 1 shows the results. The calculated magnetic amplitudes appear in fig. 2. 4. D i s c u s s i o n

The ratio between the spin and the orbital contributions to the 3-d m o m e n t in L u F e 2 is close to that f o u n d for the Fe metal [2]. The value of the total m o m e n t (1.74#B/Fe) c o m p a r e d with the bulk magnetization (1.43#B/Fe) gives an additional electron polarization of 0.31/t a, which is larger than that (0.21/~B) f o u n d in metallic iron [2]. The value f o u n d for the wave function parameter (cos t = 0.47) implies that F 3 tends to be directed towards the 6 neighbouring Fe atoms while F~ avoids them. The level populations show that 1"3 is less populated than in a spherical case, which indicates the b o n d i n g nature of the orbital as the magnetic electrons in iron are k n o w n to have an antibonding character. Indeed covalent effects which occur in R - M alloy [4] should favour such orbitals. T h e y would give rise to an additional electron polarization as observed.

u_

References .0

[1] D. Givord, F. Givord and R. Lemaire, J. de Phys. 32 (1971) - "S.O0

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CI-668. [2] C. (3. Shull and Y. Yamacla, J. Phys. Soc. Jap., 17 (1962) Blll-l. [3] R. E. Watson and A. J. Freeman, Acta Cryst. 14 (1961) 27,

[4] E. Parthe and R. Lemaire, Acta Cryst. B31 (1975) 1879.