Photon Factory Activity Report 2005 #23 Part B (2006)
Crystallography

3C3/2000S2-02, 2003G012

Spin form factor study of GdAl2
Hiromichi ADACHI*1, Hiroshi KAWATA1, Masahisa ITO2
1KEK-PF, Tsukuba, Ibaraki 305-0801, Japan
2
Gunma Univ., Kiryu, Gunma 376-8515, Japan

0.5

0.1

0.0

µSfS(888) (µB)

of reflections of (h00), (hh0), and (hhh) at several
temperatures. The details of the experiments are the sameas described in Ref. 3.
The spin form factors in medium through high sinθ/λregion were obtained and found to change in roughly3+
accordance with <j0> for the free Gd ion calculated with
the Hartree-Fock method or the density-functional-theory
one for each series of reflections. The values of the form
factors multiplied by the spin magnetic moment were,
however, lower in comparison with those estimated fromthe magnitude of the magnetization at the same
temperature. Similar phenomenon has been also reported
in the neutron case[4], but the reduction rate seems larger
in our x-ray case. Moreover, we found that the thermalvariation for the (hhh) series exhibits a broad maximum ataround 50 through 100K (Fig. 1), while the magnetization
varies monotonically in the ferromagnetically orderedregion (T ≤TC∼170K). Such a phenomenon was notobserved for the (h00) and (hh0) series.
The behavior described above might be related to theincomprehensible results found in some previous studiesof this compound.

µSfS(555) (µB)

Recently, we have developed the x-ray diffraction
method to obtain the atomic form factors of the electron
spin polarization in ferromagnetic crystals[1-3]. Since
given by this method is information about the electron
spin polarization rather than the magnetization, theobtained spin form factors for the rare earths or theactinides having large orbital magnetic moments shouldbe very different in shape from the neutron magnetic form
factors. This point will be advantageous when theexperiments are combined with the theoretical electronic
structure calculations, where the convincing prescription
for the treatment of the orbital magnetic moment has notbeen established yet.
The cubic Laves-phase compounds RAl2 (R = rareearth) are ferromagnetic for most of rare earths andsuitable for the present spin form factor study. We haveapplied this method to GdAl2. This study has a twofold
meaning. First, this was done as part of our systematic
study on the spin density distribution around the rareearth ions. From this point of view, the gadolinium ion isa key one, because the spin polarization of the localized
electrons is expected to be almost isotropic and theexperimental spin form factors can be compared with <j0>,
the numerical expectation value of the 0th-order sphericalBessel function with respect to the theoretical 4f radial
wave function. Second, according to the previous research
reports, the magnetic properties of GdAl2 are notnecessarily as understandable as expected, and wethought that the findings from our spin form factor study
could contribute to a better understanding of this material.
The polarized neutron study of GdAl2 has been done by
Abell et al. in the early 1980's and the Gd magnetic form
factors at 4.2K have been reported[4]. The polarized
neutron sees the orbital magnetic moment together, if any,
and detects the magnetic moment perpendicular to thescattering plane. In our experiment, on the other hand, theprobe photon sees the spin polarization parallel to thescattering vector. The magnetic parts of the atomic form
factors determined from these two experiments will beidentical when they arise solely from the spin polarizationand the spin density distribution does not depend on thedirection of the polarization.
The experiments were done at the station 3C3 with abending-magnet light source. The single-crystal samples
were prepared by the Bridgeman method at the Institutefor Solid State Physics, the University of Tokyo, and,prior to the measurements, the magnetic properties werechecked by a SQUID magnetometer at the Cryogenic
Center, the University of Tokyo. We measured three series

0.00100200Temperature (K)Fig. 1 The temperature dependence of the values of thespin form factors, fS, multiplied by the spin magnetic
moment, µS, for the (555) and (888) reflections of GdAl2,
which are marked with red and blue circles, respectively.
[1] H. Adachi, H. Kawata, and M. Ito, Phys. Rev. 63,054406 (2001).
[2] H. Adachi and H. Miwa, Phys. Rev. 66, 224428(2002).
[3] H. Adachi, H. Kawata, and M. Ito, Phys. Rev. 69,212409 (2004).
[4] J. S. Abell, et al., J. Mag. Mag. Mater. 31-34, 247(1983).
* hiromichi.adachi@kek.jp

Users' Report159