ARTICLE IN PRESS
K.S. Napolskii et al. / Physica B 397 (2007) 23–26
25
nickel framework (Fig. 1c). The average center-to-
center distance between close-packed voids is 450 nm,
suggesting no structure shrinkage during the fabrication
process.
Typical SAPNS diffraction pattern is shown in Fig. 2,
demonstrating several clearly resolved sets of hexagonally
arranged reflections. In similar laser diffraction experi-
ments, the patterns were interpreted considering each layer
of close-packed spherical voids in the PC as an individual
two-dimensional (2D) diffraction grating [4]. We can
introduce a 2D basis shown in Fig. 1b . For the consi-
dered geometry the interplanar spacings ðdh k 0Þ can be
calculated as
1
1
1
1
6000
4000
2000
0000
H = 0 mT
H = 26 mT
H = 67 mT
H = 135 mT
8
6
4
2
000
000
000
000
0
-
-
-
-
2000
4000
6000
8000
pffiffiffiffiffi
3
a
0.02
0.03
0.04
0.05
0.06
0.07
0.08
dh k 0 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi .
q, nm-1
2
2
2
h þ hk þ k
Using a ¼ 450 nm, we have found the interplanar distances
1
0000
000
6000
for the first diffraction maxima ({1 0 0}, {1 1 0}, etc.) and
calculated the corresponding values of q -vectors ðq
8
¼
h k 0
2
p=dh k 0Þ, which were used for plotting the theoretical
diffraction pattern (white circles in Fig. 2). It can be seen
that the calculated positions for the most intense {1 0 0}
and {1 1 0} reflections perfectly match the experimental
maxima. The other diffraction reflections are not so well-
resolved onto the diffuse scattering background. Mean-
while, high-order diffraction maxima can be seen in q-
dependences of the neutron intensity I(q) for defined
directions. For instance, q-dependence in [1 1 0]-direction
4
2
000
000
0
-
-
2000
4000
H = 10 mT
H = 40 mT
H = 80 mT
H = 135 mT
-6000
-8000
ꢀ
1
demonstrates diffraction peaks at q
ꢂ 0:028 nm and
1
1 0
ꢀ
1
q2 2 0 ꢂ 0:056 nm (Fig. 3). This result differs from the
common laser diffraction experiments, in which only
sixfold diffraction patterns are usually observed [3,4].
It is worth noting that the patterns, typical of single
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-1
q, nm
Fig. 4. q-Dependence of the nuclear–magnetic interference (a) and
magnetic contribution to the scattering I (q) (b).
H
crystals, were recorded using a large beam spot area (about
2
cm ), suggesting the well-ordering of Ni PCs on a
1
macroscale.
The increase in a magnetic field results in decrease in the
small-angle scattering from the multidomain structure
ꢀ
1
(
qo0.023 nm ; magnetic domain size more than 270 nm)
constrained by elementary blocks of Ni PC, while intensity
of Bragg peaks increases.
According to the polarization-dependent part of scatter-
(110)
ꢀ
+
1
00000
ing DI(q) ¼ (I (q)ꢀI (q)), nuclear and magnetic structures
are well-correlated (Fig. 4a). The two types of contribu-
tions to the interference scattering, the diffuse small angle
scattering and Bragg reflection, with domination of the
second one are clearly seen.
1
0000
The pure magnetic contribution to the scattering, also
referred to as field-induced scattering, was extracted as
(220)
I (q) ¼ I(q, H)ꢀI(q, 0) (Fig. 4b). In addition to the
H
1
000
decreasing of the small-angle scattering described above,
the magnetic reflections are clearly observed. It testifies to
transition from multi- to single-domain magnetic structure
at H450 mT. The nature of the several additional
magnetic reflections (indicated by arrows) with rather
small intensities and positions not connected to the Bragg
peaks demands the future investigation.
H = 0 mT
H = 680 mT
0
.02
0.03
0.04
0.05
q, nm-1
0.06
0.07
0.08
Fig. 3. SAPNS intensity profile for Ni PC in [1 1 0] direction.
Napolskii, Kirill S.
