Journal of the Physical Society of Japan
Vol. 78, No. 8, August, 2009, 084704
#2009 The Physical Society of Japan
Unquenched Geometric Frustration Effect on Spiral Spin Correlation
in Magnetically Ordered Phase
ꢀ
1
2
2
Keisuke TOMIYASU , Kazumasa HORIGANE , Toshio YOKOBORI , Yusuke KOUSAKA ,
3
4
2
1
Miwako TAKAHASHI , Haruhiro HIRAKA , Jun AKIMITSU , and Kazuyoshi YAMADA
Department of Physics, Tohoku University, Sendai 980-8578
WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577
1
2
Department of Physics and Mathematics, Aoyama-Gakuin University, Sagamihara, Kanagawa 229-8558
3Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573
4Institute for Materials Research, Tohoku University, Sendai 980-8577
(
Received August 29, 2008; accepted June 2, 2009; published July 27, 2009)
We studied magnetic phase diagram and x-dependence of spiral spin correlation in magnetically
ordered phase of (Co1ꢁxZnx)Cr2O4 by magnetization and neutron scattering experiments. The spiral
correlation survives in a wide x range from 0 to 0.9. As x increases, the correlation length decreases from
˚
˚
ꢀ
ꢂ 23 A at x ¼ 0, and saturates at ꢀ ꢂ 2:5 A at around x ¼ 0:75, which is close to the nearest
3
þ
3þ
neighboring Cr -Cr distance. The pitch is almost constant from x ¼ 0 to 0.75, then abruptly shortens
above around x ¼ 0:75. The correlation is isotropic at x ¼ 0:25 but anisotropic at x ¼ 0:75. We discuss
that the spiral correlation is of short-range owing to unquenched geometric frustration, and begins to
collapse with the minimization of correlation length above around x ¼ 0:75, possibly as the precursor of
dynamic spin hexamer caused by high geometric frustration.
In this paper, we study the spin correlations in
solid solution materials between CoCr2O4 and ZnCr2O4,
1
.
Introduction
The concept of geometric frustration was initially pointed (Co1ꢁxZnx)Cr2O4 (0 ꢃ x ꢃ 1), by magnetization and neu-
out for a system that spins exist only in a triangle-based tron scattering experiments for the first time. If the concept
lattice,1 as in spinel antiferromagnets AB2O4 with non- of geometric frustration can be expanded, the value of x will
,2)
2
þ
þ
2þ
3þ
2þ
2þ
2þ
magnetic A ¼ Mg , Zn , Cd , and Hg
ions and have great control of the degree of frustration; the weakly
ions (magnitude of spin S ¼ 3=2) frustrated CoCr O will gradually change towards the highly
3
magnetic B ¼ Cr
2
4
composing a corner-sharing tetrahedron lattice. These frustrated ZnCr O with increasing x. Magnetization experi-
2
4
materials exhibit complex magnetic long-range order with ments provide the x–T magnetic phase diagram (T: temper-
3
–6)
slight lattice deformation below Ne e´ l temperature,
but ature). Neutron experiments give the x-dependence of spiral
in a paramagnetic phase a antiferromagnetic spin hexamer correlation in lowest temperature phases. From the exper-
dynamically emerges in the B sites, a well-known emblem- imental results we validate and clarify the unquenched
7–14)
atic phenomenon for geometric frustration.
On the other hand, it was recently proposed that geometric magnetically ordered phase of this series of materials.
geometric frustration effect on spiral short-range order in
frustration effect coming from B-sites still survives in cubic
2þ
spinel ferrimagnets ACr O [magnetic A2 ¼ Co
þ
(S ¼
2. Experiments
2
4
2
þ
15)
3
=2) and Mn (S ¼ 5=2)] as explained below. These
Powder static magnetization measurements were carried
materials exhibit a conical spin structure resolved into an out in a full range of x ¼ 0 to 1 on a standard SQUID magne-
Ising-type ferrimagnetic component and an incommensurate tometer at Institute for Materials Research, Tohoku Univer-
spiral one. As the temperature decreases, although the sity, Japan. Powder neutron elastic scattering experiments
former component forms long-range order at TC ¼ 93 and were also carried out in a range of x ¼ 0 to 1 on a triple-axis
5
1
1 K, the latter one mainly starts to grow at TS ¼ 25 and spectrometer, AKANE (T1-2) of the same institute, installed
4 K and does not achieve long-range order even in the at the thermal guide tube of JRR-3 in Japan Atomic Energy
1
6)
lowest temperature phase (nm order correlation length). This Agency (JAEA). AKANE equips a Ge 311 monochroma-
result suggests that geometric frustration effect is surpris- tor and a PG 002 analyzer, and no filter was attached to
ingly robust for the existence of A-site spins.
eliminate higher-order contamination because of a Ge 622
However, the two types of spin correlations, spiral short- forbidden reflection. Incident energy was fixed at Ei ¼ 19:4
range order and hexamer, are too different from each other meV with horizontal collimation sequence of guide-open-
0
0
to be regarded as the same origin. Furthermore, the spiral 60 -blank (ꢂ180 ). Single-crystal neutron diffraction experi-
type belongs to a static spin structure in a magnetically ments were performed for x ¼ 0:25 and 0.75 on a time-of-
ordered phase, whereas the hexamer instantaneously appears flight Laue-type diffractometer at the beam line H1 (FOX)
in a paramagnetic phase. Therefore further examination is installed at the spallation neutron source, KENS, High
17)
needed to validate that the spiral short-range order comes Energy Accelerator Research Organization (KEK), Japan.
from geometric frustration.
Powder specimens of (Co1ꢁxZnx)Cr2O4 (0 ꢃ x ꢃ 1) were
synthesized from stoichiometric mixtures of ZnO, CoO, and
Cr2O3 by a solid reaction method. All the samples were
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E-mail: tomiyasu@m.tains.tohoku.ac.jp
084704-1