Photon Factory Activity Report 2004 #22 Part B (2005)
Crystallography

3C3/2000S2-02

Spin form factors of Pr and Dy in the dialuminides
Hiromichi ADACHI*1, Hiroshi KAWATA1, Masahisa ITO2
1
KEK-PF, Tsukuba, Ibaraki 305-0801, Japan
2
Gunma Univ., Kiryu, Gunma 376-8515, JapanSample
The single crystal samples of PrAl2 and DyAl2 wereprepared at the Institute for Solid State Physics, theUniversity of Tokyo, by the Bridgeman method using
sealed tungsten cruicibles. Preliminarily to theexperiments, the magnetic properties were examined witha SQUID magnetometer at the Cryogenic Center of theUniversity of Tokyo.
MethodThe experiments were done at the 3C3 station. The
incident x rays were elliptically polarized white x rays
emitted from a bending-magnet light source. The
diffraction angle was fixed to be 90 degrees. The sample
was set such that the easy direction of magnetization,<100>, should be parallel to the scattering vector, andseveral reflections of <h00> were simultaneously
measured by a Ge SSD. The sample magnetization wasswitched every ten seconds by a magnetic field of 8.4 kOe
generated by an electromagnet. The spin form factors of amagnetic ion can be obtained from a change in diffraction
intensity concomitant with a reversal of the magnetization.
The measurements were made at some temperatures
lower than the Curie temperatures. Data accumulation
lasted for about 2 days at each temperature.

Results
Figure 1 shows the spin form factors fs multiplied by
the spin magnetic moments µs for Pr and Dy in the
dialuminides, which were obtained from themeasurements at 14 K. The data on the lower-sinθ /λ side
have negative and positive values for Pr and Dy,respectively. These polarities correspond to those of the

1.5
PrAl2 , T = 14 K

DyAl2 , T = 14 K

0.0

exp.
calc.
µs<j0>µsc2<j2>µsc4<j4>µsc6<j6>

1.0

exp.
calc.
µs<j0>µsc2<j2>µsc4<j4>µsc6<j6>

-0.5

0.5

1.0

1.5
-1

sinθ /λ ( A )µs fs ( µB)

Experimental

spin magnetic moments with respect to the total magnetic
moments, being consistent with the fact that Pr is a lightrare-earth element and Dy is a heavy one.
The smooth lines are the theoretical estimates of thecontributions from the 4f electrons, which are analyzed tobe µs(<j0>+c2<j2>+c4<j4>+c6<j6>). Here, <jn> are theexpectation values of the spherical Bessel functions of thenth order with respect to the 4f radial wave function; <j0>
and <jn>(n=2, 4, 6) represent the spherical component
and the nth-order asphericities, respectively. The angular
distribution is reflected in the coefficients cn, which wereestimated in the LS-coupling scheme characterized bySLJM[1, 2]. As can be seen from the figure, an agreement
between the experiments and the theoretical results thus
estimated is fairly good, indicating that this method
properly approaches the spin density distribution.
Discussion about the thermal variation is found in Ref. 3.

µs fs ( µB)

Introduction
Spin is one of the basic attributes of the electron as
well as its electric charge. The technological applicationsuch as spin electronics has been also studied in recentyears. Different from the case of the electric-charge
distribution, the spatial distribution of the spin inmaterials is difficult to measure. We have recently
developed a concrete method to approach the spindistribution using the x-ray diffraction[1,2]. We haveapplied this method to the ferromagnetic Laves phasecompounds PrAl2 and DyAl2. Here we report the resultsof the experiments.

0.5

0.0

0.5

1.0

1.5
-1sinθ / λ ( A )Fig. 1 The spin form factors fs multiplied by the spin
magnetic moment µs for Pr and Dy in the dialuminides.
Displayed are the data for <h00>(h=8, 12, 16, 20, 24, and28), which are crystallographically allowed reflections.
References[1] H. Adachi, H. Kawata, and M. Ito, Phys. Rev. B 63,054406 (2001).
[2] H. Adachi and H. Miwa, Phys. Rev. B 66, 224428(2002).
[3] H. Adachi, H. Kawata, and M. Ito, Phys. Rev. B 69,212409 (2004).
* hiromichi.adachi@kek.jp

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