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Polarized neutron study of the intermetallic conpound GdAl2
Journal of Magnetism and Magnetic Materials 31-34 (1983) 247-248 POLARIZED
NEUTRON
247
STUDY OF THE INTERMETALLIC
J.S. A B E L L *, J.X. B O U C H E R L E
t, R. O S B O R N
COMPOUND
*, B.D. R A I N F O R D
GdAI z
§ a n d J. S C H W E I Z E R
t*
* Centre for Material Science, POB 363, Birmingham B15 2TT, UK t DRF/DN, CENG, 85X, 38041 Grenoble Cedex, France * ILL, 156X, 38042 Grenoble Cedex, France § Dept, of Physics, University Southampton, S09 5NH, UK
We report the Gd magnetic form factor in GdAI 2. In order to avoid the strong absorption of neutrons by natural gadolium very short wavelenghts were used. The 4f part of the form factor agrees with the relativistic radial integral ~Jo) calculated for a free ion, with a moment of only 6.6#B instead of the 7.0#n expected. The value of the conduction electron polarization is consistent with values measured in other R A I 2 compounds. The rare earth properties have been much investigated in the intermetallic compounds RAI 2. Unlike pure rare earth metals, most of these c o m p o u n d s are ferromagnets at low temperature. It is therefore easier to compare their magnetic characteristics (such as the bulk magnetization or magnetization distribution [1]), from rare earth to rare earth. Such distributions are characterized by two contributions: one distribution well localized around the rare earth nucleus and due to 4f electrons and one more extended distribution due to the polarization of the conduction electrons and whose spatial extension is similar to that of 5d electrons [2]. The 4f electron magnetization is generally affected by the crystal field: the magnetization distribution loses spherical symmetry around the rare earth nuclei and the total magnetic moment is reduced with respect to the free R 3+ ion. It is therefore of importance to investigate the magnetic distribution of the particular compound G d A I 2. In this c o m p o u n d the G d 3+ ion is in an S state and no crystal field effect is expected. The magnitude of the conduction electron polarization varies throughout the series in a complex way: from the bulk magnetization it is only 0.25#B/atom in GdA12, whereas it is much larger in other compounds like H o A I 2 [3]. Orbital interactions have been proposed to explain these variations [4]. In GdA12 only spin interactions are present, and it is important to determine accurately the non 4f magnetization density. An important difficulty arises with gadolinium. For usual neutron wavelenghts, due to the proximity of several absorption peaks for two gadolinium isotopes ~55Gd and 157Gd, the G d absorption cross section is too high (o = 3000 barn at )~ = 1.3 A) for experiments to be possible. Only experiments made on J6°Gd isotope have been performed [5]. This problem has been overcome by the use of short wavelengths. In fact, the G d absorption cross section decreases very abruptly with wavelength falling to 760 barn at X = 0.50 ,~ and 280 barn at ~, = 0.42 ,g,. The
0304-8853/83/0000-0000/$03.00
experiment was performed on the polarized neutron diffractomater D5 located on a hot source beam of the ILL. Two GdA12 crystals, m a d e from natural gadolinium, were used with thicknesses 0.3 and 1.1 ram. The crystals were cooled to 4.2 K with their axis [110] vertical and parallel to a 16.5 kOe applied field. Two types of experiments were performed: (1) integrated intensities were recorded with the thin crystal and unpolarized neutrons at ~, = 0.453 ,~, and (2) flipping ratios were measured on both crystals at wavelengths 0.602, 0.502 and 0.442/k. Finally, the bulk magnetization was determined by the extraction method, with the same crystals and in the same conditions of field and temperature as for the neutron experiments. It was found to be 7.25(4)#B/mole, in good agreement with previous measurements [6,7]. As in the other RAI 2 investigations [8], the integrated intensities, together with the values of the ratios ~, = F M / F N obtained from the polarized neutron experiments, allowed us to determine the nuclear structure parameters. In the present case, due to the proximity of the absorption peaks, the scattering amplitude bed is not constant: bed = b 0 + b ' + i b " , with b' and b" varying with neutron wavelength according to the Breit-Wigner formulae [9]. We refined the scattering amplitude at ~, = 0.453 ,~ from the nuclear structure factors. Using the Breit-Wigner formulae we found the values given in table 1. These values agree with that determined previously, 1.08(5) 10-12 cm at X = 0.50 A
Tablle 1 Natural gadolinium scattering lengths ~(.~)
bo + b'(10 -12 cm)
b"(10 -12 cm)
0.422 0.453 0.502 0.602
0.999 1.026 (7) 1.072 1.180
-
© 1983 N o r t h - H o l l a n d
d
0.021 0.029 0.044 0.095
248
J.S. Abell et al. / Polarized neutron study of GdAI 2
AM (pe/Gd)! GdAI 2 T=4.2
gets a good agreement for high-angle reflections (sin 0/X > 0.25 A -1) but discrepancies for low-angle reflections. This is consistent with the general picture of the polarization of the conduction electrons superimposed on a 4f localized magnetization. The amplitudes, corresponding to the localized moment, extrapolate to 6.6#B. This result is very surprising; one expected 7.0/x B for the S state G d 3+ ion. A possible explanation of this low value would be that, like G d M g [12] for example, GdA12 is not a true ferromagnet and that the measured magnetic amplitudes do not correspond to the full moment. This hypothesis is supported by the anomalous behaviour of some physical properties of GdAI 2 such as: (a) the magnetic contribution to the specific heat which does not show a X anomaly [13]; (b) the temperature dependence of the bulk magnetization which does not decrease according to a Brillouin law [7]; and (c) the existence of an anisotropy in the magnetization curves
K
6.0 o
4.0
=l! I I |
2,0
k Jl
I illl
0.0 0.0
g m i
i
i
i
0.2
0.4
0.6
0.8
•
i
|
1,0 sine/MAq)
Fig. 1. Atomic magnetic amplitudes: experimental (solid circles) and calculated with a 6.6~B moment (open circles).
[10], but are more precise. They were introduced into the comparison of the flipping ratios measured at several wavelengths, a comparison which allows the extinction effects to be corrected for. The most accurate F M values were obtained from unpolarized neutron integrated intensities for those low angle reflections with 7 :~ 1, and from polarized neutron flipping ratios for the other reflections. These were measured on the thin crystal for stronger reflections where extinction may be large, and on the thick crystal for weaker reflections where counting statistics are more important. The atomic magnetic amplitudes are reported in fig. 1, as well as the bulk magnetization which corresponds to FM(0, 0, 0). Compared to the other rare earths, the magnetic amplitudes decrease much more rapidly and become negative at sin 0/X = 1 A - ] . This results from the S state of the G d 3+ ion: in such a case the magnetic form factor reduces to only the radial integral j0(sin 0 / ~ ) without contributions from J2, J4 or Jt. Because of this the experimental points are expected to lie on a monotonic curve: this is the case, as clearly shown in fig. 1. The magnetization distribution has a spherical symmetry around the G d nuclei. When comparing the experimental magnetic amplitudes with the radial integral
[6].
The spatial extension of the conduction electron magnetization is much like the other rare earths with a 5d character. Its value, greater than 0.6#B/atom, is much higher than was previously thought. It had been difficult to understand, assuming that the polarization of the conduction electrons is mainly due to spin interactions, why the rare earth ion with maximum spin (Gd 3+ ) only polarizes 0.25#B, much less than other rare earth ions. The value found here is more satisfactory.
References
[1] J.X. Boucherle, Thesis, Universit6 de Grenoble (1977). [2] J.X. Boucherle, D. Givord, A. Gregory and J. Schweizer, J. Appl. Phys. 53 (1982) 1950. [3] J.X. Boucherle and J. Schweizer, 3. Appl. Phys. 53 (1982) 1947. [4] E. Belorizky, J.J. Niez and P.M. Levy, Phys. Rev. B23 (1981) 3360. [5] R.M. Moon, W.C. Koehler, J.W. Cable and H.R. Child, Phys. Rev. B5 (1972) 997. [6] M.F. Rossignol, Thesis, Universit6 de Grenoble (1981). [7] E.W. Lee and J.F.D. Montenegro, J. Magn. Magn. Mat. 22 (1981) 282. [8] J.X. Boucherle and J. Schweizer, J. Magn. Magn. Mat. 24 (1981) 308. [9] B.N. Brockhouse, Can. J. Phys. 31 (1953) 440. [10] F. Vigneron, M. Bonnet, A. Herr and J. Schweizer, J. Phys. F 12 (1982) 223. [11] A.J. Freeman and J.P. Desclaux, J. Magn. Magn. Mat. 12 (1979) 11. [12] P. Morin, J. Pierre, D. Schmitt and D. Givord, Phys. Lett. 65A (1978) 156. [13] C. Dennadas, A.W. Thompson, R.S. Craig and W.E. Wallace, J. Phys. Chem. Solids 32 (1971) 1853.
NEUTRON
247
STUDY OF THE INTERMETALLIC
J.S. A B E L L *, J.X. B O U C H E R L E
t, R. O S B O R N
COMPOUND
*, B.D. R A I N F O R D
GdAI z
§ a n d J. S C H W E I Z E R
t*
* Centre for Material Science, POB 363, Birmingham B15 2TT, UK t DRF/DN, CENG, 85X, 38041 Grenoble Cedex, France * ILL, 156X, 38042 Grenoble Cedex, France § Dept, of Physics, University Southampton, S09 5NH, UK
We report the Gd magnetic form factor in GdAI 2. In order to avoid the strong absorption of neutrons by natural gadolium very short wavelenghts were used. The 4f part of the form factor agrees with the relativistic radial integral ~Jo) calculated for a free ion, with a moment of only 6.6#B instead of the 7.0#n expected. The value of the conduction electron polarization is consistent with values measured in other R A I 2 compounds. The rare earth properties have been much investigated in the intermetallic compounds RAI 2. Unlike pure rare earth metals, most of these c o m p o u n d s are ferromagnets at low temperature. It is therefore easier to compare their magnetic characteristics (such as the bulk magnetization or magnetization distribution [1]), from rare earth to rare earth. Such distributions are characterized by two contributions: one distribution well localized around the rare earth nucleus and due to 4f electrons and one more extended distribution due to the polarization of the conduction electrons and whose spatial extension is similar to that of 5d electrons [2]. The 4f electron magnetization is generally affected by the crystal field: the magnetization distribution loses spherical symmetry around the rare earth nuclei and the total magnetic moment is reduced with respect to the free R 3+ ion. It is therefore of importance to investigate the magnetic distribution of the particular compound G d A I 2. In this c o m p o u n d the G d 3+ ion is in an S state and no crystal field effect is expected. The magnitude of the conduction electron polarization varies throughout the series in a complex way: from the bulk magnetization it is only 0.25#B/atom in GdA12, whereas it is much larger in other compounds like H o A I 2 [3]. Orbital interactions have been proposed to explain these variations [4]. In GdA12 only spin interactions are present, and it is important to determine accurately the non 4f magnetization density. An important difficulty arises with gadolinium. For usual neutron wavelenghts, due to the proximity of several absorption peaks for two gadolinium isotopes ~55Gd and 157Gd, the G d absorption cross section is too high (o = 3000 barn at )~ = 1.3 A) for experiments to be possible. Only experiments made on J6°Gd isotope have been performed [5]. This problem has been overcome by the use of short wavelengths. In fact, the G d absorption cross section decreases very abruptly with wavelength falling to 760 barn at X = 0.50 ,~ and 280 barn at ~, = 0.42 ,g,. The
0304-8853/83/0000-0000/$03.00
experiment was performed on the polarized neutron diffractomater D5 located on a hot source beam of the ILL. Two GdA12 crystals, m a d e from natural gadolinium, were used with thicknesses 0.3 and 1.1 ram. The crystals were cooled to 4.2 K with their axis [110] vertical and parallel to a 16.5 kOe applied field. Two types of experiments were performed: (1) integrated intensities were recorded with the thin crystal and unpolarized neutrons at ~, = 0.453 ,~, and (2) flipping ratios were measured on both crystals at wavelengths 0.602, 0.502 and 0.442/k. Finally, the bulk magnetization was determined by the extraction method, with the same crystals and in the same conditions of field and temperature as for the neutron experiments. It was found to be 7.25(4)#B/mole, in good agreement with previous measurements [6,7]. As in the other RAI 2 investigations [8], the integrated intensities, together with the values of the ratios ~, = F M / F N obtained from the polarized neutron experiments, allowed us to determine the nuclear structure parameters. In the present case, due to the proximity of the absorption peaks, the scattering amplitude bed is not constant: bed = b 0 + b ' + i b " , with b' and b" varying with neutron wavelength according to the Breit-Wigner formulae [9]. We refined the scattering amplitude at ~, = 0.453 ,~ from the nuclear structure factors. Using the Breit-Wigner formulae we found the values given in table 1. These values agree with that determined previously, 1.08(5) 10-12 cm at X = 0.50 A
Tablle 1 Natural gadolinium scattering lengths ~(.~)
bo + b'(10 -12 cm)
b"(10 -12 cm)
0.422 0.453 0.502 0.602
0.999 1.026 (7) 1.072 1.180
-
© 1983 N o r t h - H o l l a n d
d
0.021 0.029 0.044 0.095
248
J.S. Abell et al. / Polarized neutron study of GdAI 2
AM (pe/Gd)! GdAI 2 T=4.2
gets a good agreement for high-angle reflections (sin 0/X > 0.25 A -1) but discrepancies for low-angle reflections. This is consistent with the general picture of the polarization of the conduction electrons superimposed on a 4f localized magnetization. The amplitudes, corresponding to the localized moment, extrapolate to 6.6#B. This result is very surprising; one expected 7.0/x B for the S state G d 3+ ion. A possible explanation of this low value would be that, like G d M g [12] for example, GdA12 is not a true ferromagnet and that the measured magnetic amplitudes do not correspond to the full moment. This hypothesis is supported by the anomalous behaviour of some physical properties of GdAI 2 such as: (a) the magnetic contribution to the specific heat which does not show a X anomaly [13]; (b) the temperature dependence of the bulk magnetization which does not decrease according to a Brillouin law [7]; and (c) the existence of an anisotropy in the magnetization curves
K
6.0 o
4.0
=l! I I |
2,0
k Jl
I illl
0.0 0.0
g m i
i
i
i
0.2
0.4
0.6
0.8
•
i
|
1,0 sine/MAq)
Fig. 1. Atomic magnetic amplitudes: experimental (solid circles) and calculated with a 6.6~B moment (open circles).
[10], but are more precise. They were introduced into the comparison of the flipping ratios measured at several wavelengths, a comparison which allows the extinction effects to be corrected for. The most accurate F M values were obtained from unpolarized neutron integrated intensities for those low angle reflections with 7 :~ 1, and from polarized neutron flipping ratios for the other reflections. These were measured on the thin crystal for stronger reflections where extinction may be large, and on the thick crystal for weaker reflections where counting statistics are more important. The atomic magnetic amplitudes are reported in fig. 1, as well as the bulk magnetization which corresponds to FM(0, 0, 0). Compared to the other rare earths, the magnetic amplitudes decrease much more rapidly and become negative at sin 0/X = 1 A - ] . This results from the S state of the G d 3+ ion: in such a case the magnetic form factor reduces to only the radial integral j0(sin 0 / ~ ) without contributions from J2, J4 or Jt. Because of this the experimental points are expected to lie on a monotonic curve: this is the case, as clearly shown in fig. 1. The magnetization distribution has a spherical symmetry around the G d nuclei. When comparing the experimental magnetic amplitudes with the radial integral
[6].
The spatial extension of the conduction electron magnetization is much like the other rare earths with a 5d character. Its value, greater than 0.6#B/atom, is much higher than was previously thought. It had been difficult to understand, assuming that the polarization of the conduction electrons is mainly due to spin interactions, why the rare earth ion with maximum spin (Gd 3+ ) only polarizes 0.25#B, much less than other rare earth ions. The value found here is more satisfactory.
References
[1] J.X. Boucherle, Thesis, Universit6 de Grenoble (1977). [2] J.X. Boucherle, D. Givord, A. Gregory and J. Schweizer, J. Appl. Phys. 53 (1982) 1950. [3] J.X. Boucherle and J. Schweizer, 3. Appl. Phys. 53 (1982) 1947. [4] E. Belorizky, J.J. Niez and P.M. Levy, Phys. Rev. B23 (1981) 3360. [5] R.M. Moon, W.C. Koehler, J.W. Cable and H.R. Child, Phys. Rev. B5 (1972) 997. [6] M.F. Rossignol, Thesis, Universit6 de Grenoble (1981). [7] E.W. Lee and J.F.D. Montenegro, J. Magn. Magn. Mat. 22 (1981) 282. [8] J.X. Boucherle and J. Schweizer, J. Magn. Magn. Mat. 24 (1981) 308. [9] B.N. Brockhouse, Can. J. Phys. 31 (1953) 440. [10] F. Vigneron, M. Bonnet, A. Herr and J. Schweizer, J. Phys. F 12 (1982) 223. [11] A.J. Freeman and J.P. Desclaux, J. Magn. Magn. Mat. 12 (1979) 11. [12] P. Morin, J. Pierre, D. Schmitt and D. Givord, Phys. Lett. 65A (1978) 156. [13] C. Dennadas, A.W. Thompson, R.S. Craig and W.E. Wallace, J. Phys. Chem. Solids 32 (1971) 1853.