Magnetic structure of NiCr2O4 studied by neutron scattering and magnetization measurements

Article abstract of DOI:10.1143/JPSJ.73.2539

The magnetic ordering of the normal spinel ferrimagnet NiCr ₂O₄ below T_C = 74 K was reinvestigated by neutron scattering and magnetization measurements on a powder specimen. We found another magnetic transition at T_S = 31 K besides T_C in both experiments. The ordering of a ferrimagnetic (longitudinal) component and that of an antiferromagnetic (transverse) component occur at T_C and T_S, separately. A new magnetic structure model of NiCr ₂O₄ below T_S with a spontaneous magnetization of about 0.3 μ_B/formula is proposed based on experimental neutron scattering intensity. 2004 The Physical Society of Japan.

Full text of DOI:10.1143/JPSJ.73.2539

Journal of the Physical Society of Japan
Vol. 73, No. 9, September, 2004, pp. 2539–2542
#2004 The Physical Society of Japan
Magnetic Structure of NiCr O Studied by Neutron Scattering
2
4
and Magnetization Measurements
ꢀ
1
y
Keisuke TOMIYASU and Isao KAGOMIYA
Department of Applied Physics, School of Science and Engineering, Waseda University,
-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555
Advanced Research Center of Science and Engineering, Waseda University,
-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555
Received March 28, 2004)
3
1
3
(
The magnetic ordering of the normal spinel ferrimagnet NiCr2O4 below TC ¼ 74 K was reinvestigated
by neutron scattering and magnetization measurements on a powder specimen. We found another
magnetic transition at TS ¼ 31 K besides TC in both experiments. The ordering of a ferrimagnetic
(
longitudinal) component and that of an antiferromagnetic (transverse) component occur at TC and TS,
separately. A new magnetic structure model of NiCr2O4 below TS with a spontaneous magnetization of
about 0.3 ꢀB/formula is proposed based on experimental neutron scattering intensity.
KEYWORDS: NiCr2O4, chromite, normal spinel, magnetic structure, neutron scattering, magnetization measure-
ments
DOI: 10.1143/JPSJ.73.2539
1
.
Introduction
The ferrimagnets MnCr O , CoCr O and NiCr O
4
Ferrimagnetic spiral structure of CoCr O
2
4
2
4
2
4
2
crystallize into the normal spinel structure; magnetic
2þ
2þ
2þ
1.6
Mn , Co and Ni ions occupy A-sites and magnetic
3
1
.5
þ
Cr
ions occupy B-sites. Figure 1 shows the chemical
2
.4
2.6
primitive unit cell of a normal spinel structure and the
atomic sites in the cell.
3
.0
[ µ
B]
The lattices of MnCr2O4 and CoCr2O4 are cubic at all
temperatures.8,9) The magnetic moments of MnCr2O4 and
CoCr O are classified into a ferrimagnetic and a spiral
2
+
3+
3+
A1-A2 Ni
B1-B2 Cr
B3-B4 Cr
[
100]
2
4
components.8
,9,12)
Only the ferrimagnetic component exhib-
9)
Fig. 2. Ferrimagnetic spiral structure of CoCr2O4 below TS ¼ 25 K. The
spiral component is represented by propagation vector ð0:62; 0:62; 0Þ.
its ordering at T ¼ 43 K and 97 K, and a transition to a
C
ferrimagnetic spiral structure occurs at TS ¼ 18 K and 25 K,
respectively.8
,9,12)
The spiral components are described by
propagation vectors ð0:60; 0:60; 0Þ and ð0:62; 0:62; 0Þ, re-
On the other hand, the lattice of NiCr2O4 is elongated
spectively.8 As an example, the ferrimagnetic spiral tetragonally below 310 K. The value of ðc ꢁ aÞ=a is 4% at
,9)
9
)
6)
6)
structure of CoCr2O4 below TS is illustrated in Fig. 2.
Note that the B-sites are placed on two sublattices for both Bertaut and Dulac13,14) are summarized as follows. The
the ferrimagnetic and the spiral components. magnetic moments of NiCr O are composed of a ferrimag-
4.2 K. The magnetism of NiCr2O4 reported by Prince, and
2
4
netic (longitudinal) and an antiferromagnetic (transverse)
components, and ordering of the two magnetic components
occurs at TC ¼ 65 K simultaneously. The transverse compo-
nent is represented by propagation vector Q ¼ ð0; 0; 1Þ,
arising from the large tetragonal distortion. Figure 3 shows
the magnetic structure model of NiCr2O4. The B-sites are
regarded as a single sublattice (N e` el model) for the
longitudinal component, and are divided into semi-four
sublattices for the transverse component.
[
001]
B4
B3
B2
A1
[
010]
In fact, the magnetism of NiCr2O4 should be similar to
those of MnCr2O4 and CoCr2O4, because all these chromites
are similar normal spinel ferrimagnets and are characterized
by two magnetic components. However, NiCr2O4 was
reported to exhibit only a single magnetic transition at TC,
and the way to assort the B-sites in the magnetic structure
model also differs from that in MnCr O and CoCr O . In
B1
A2
A-sites
B-sites
[100]
Fig. 1. Sublattices A and B in a chemical primitive unit cell. Atomic sites
of oxygen ions are omitted.
2
4
2
4
particular, the magnetic structure model of NiCr O involves
2
4
ꢀ
y
a major defect which is that the magnitude of spontaneous
magnetization is 1.2 ꢀB/formula, which is too large com-
pared to that of about 0.3 ꢀB/formula estimated by magnet-
E-mail: k-tommy@aoni.waseda.jp
Present address: National Institute of Advanced Industrial Science and
Technology, Tsukuba, Ibaraki 305-8568.
2
539

2540
J. Phys. Soc. Jpn., Vol. 73, No. 9, September, 2004
K. TOMIYASU and I. KAGOMIYA
(
a) longitudinal component // [110]
Magnetization measurements were performed in a super-
conducting quantum interference device (SQUID) system at
the Materials Characterization Central Laboratory, Waseda
University, Japan. Neutron scattering experiments were
performed on the T1-1 triple axis spectrometer installed at
a thermal guide of JRR-3M, Tokai, Japan. The energy of the
incident neutrons was fixed at 13.5 meV. A pyrolytic
graphite filter efficiently eliminated higher-order contami-
nation. The sample was enclosed in a cylindrical vanadium
1
.40
1.64
[001]
[
µ
B]
[010]
B1=B2=B3=B4
A1=A2
[100]
(
b) transverse component [110]
4
B3
folder with a diameter of 10 mm with He exchange gas,
which was mounted on the cold head of a closed-cycle He
refrigerator.
B4
B2
B1
3. Results
A1=A2
Figure 5(a) shows the temperature dependence of magnet-
ization studied under field cooling condition. A magnetic
field of 100 Oe was applied. In addition to the Curie
temperature TC ¼ 74 K, another anomaly was observed at
TS ¼ 31 K. The anomaly is most likely identical to the
transition at 29 K reported by recent heat-capacity measure-
Fig. 3. Previous magnetic structure model of NiCr2O4 below TC proposed
by Bertaut and Durac.13,14) The ordering of the ferrimagnetic (longitu-
dinal) component is described by the N e` el model. The ordering of the
antiferromagnetic (transverse) component is represented by propagation
vector Q ¼ ð0; 0; 1Þ.
1
8)
ments. Figure 5(b) shows the hysteresis loop of magnet-
ization studied at 5 K. Spontaneous magnetization of the
ization measurements.3)
Klemme et al. recently found an unknown transition at present sample is also estimated to be about 0.3 ꢀB/formula
9 K by heat-capacity measurements, and presumed the by linearly extrapolating the high field magnetization to zero
2
ordering of the longitudinal component and that of the field.
1
8)
transverse component to occur at T and T , separately.
C
Figure 6 shows the neutron powder diffraction patterns at
S
The present paper confirms Klemme et al.’s speculation by 100 K, 50 K and 15 K. The fundamental reflections and the
magnetization and neutron scattering measurements. In Q ¼ ð0; 0; 1Þ superlattice reflections are observed at 15 K.
addition, based on experimental neutron magnetic scattering The former and latter reflections come from the ferrimag-
intensity, we propose a new magnetic structure model of netic and antiferromagnetic components, respectively.
NiCr2O4 with the spontaneous magnetization of about
The neutron scattering line profiles of the 111 fundamen-
.3 ꢀ /formula, in which the B-sites are grouped into two tal reflection and the 110 superlattice reflection at 100 K,
0
B
sublattices for both the longitudinal and the transverse
components like in MnCr O and CoCr O .
2
4
2
4
0
0
.25
.2
.15
.1
2
.
Experiments
(
a)
0
A powder specimen of NiCr2O4 was synthesized from a
ꢂ
stoichiometric mixture of NiO and Cr2O3 at 1200 C in air.
The sample used for Prince’s neutron powder diffraction
experiments was also prepared by the same method.
6
)
TS
0
Figure 4 shows an X-ray powder diffraction pattern of the
present sample at room temperature. No extra lines, which
cannot be explained by the spinel structure, are observed.
TC
0.05
0
0
20
40
60
80
100
Temperature [K]
4
3
2
1
000
000
000
000
0
0
0
0
0
.4
.3
.2
.1
0
(b)
~ 0.3 µB
-
-
-
-
0.1
0.2
0.3
0.4
-60
-40
-20
0
20
40
60
1
0
20
30
40
50
60
70
Magnetic Field [kOe]
Scattering angle [deg]
Fig. 5. (a) Temperature dependence of magnetization measured after field
cooling. A magnetic field of 100 Oe was applied. (b) Hysteresis loop at
5 K.
Fig. 4. X-ray powder diffraction pattern at room temperature. Several
peaks split into two owing to the tetragonal lattice elongation.

J. Phys. Soc. Jpn., Vol. 73, No. 9, September, 2004
K. TOMIYASU and I. KAGOMIYA
2541
2
1
1
000
500
000
1
1
2000
0000
1
1
11
10
300 K
TC
TS
8
6
4
2
000
000
000
000
0
5
00
50 K
0
0
20
40
60
80
100
Temperature [K]
Fig. 8. Temperature dependence of the peak intensity of the 111
fundamental and the 110 superlattice reflections.
15 K
intensity of these reflections. We can neglect uncertainty
coming from the shift of the peak position accompanied by
the thermal contraction of the lattice from 100 K to 15 K,
because the shift is within the instrumental resolution in this
temperature range. As the temperature decreases, only the
longitudinal component appears at TC ¼ 74 K, and the
1
0
20
30
40
50
Scattering angle [deg]
Fig. 6. Neutron powder diffraction patterns at 100 K, 50 K and 15 K. The
symbol (f) means fundamental reflection.
0
transverse component emerges at TS ¼ 35 K.
0
The value of TS is a little higher than that of T . This fact
S
2
2
1
1
500
000
500
000
can be explained by the difference between time scale in
neutron scattering and that in magnetization measurements.
Since dynamical spin correlation is observed through the
resolution window in neutron scattering, only the component
fluctuating slower than the energy-resolution limit is
(
a) 111
15 K
50 K
1
00 K
nuclear
+
magnetic
observed. The present resolution was of the order of
11
nuclear
10 Hz. In contrast, the time scale in magnetization
measurements is of the order of 10 Hz, because the
ꢁ
1
5
00
0
response is observed in a uniform and static magnetic field.
0
Therefore, the discrepancy between TS and T means that
S
2
7
28
29
30
31
32
the transverse component fluctuates dynamically retaining
0
Scattering angle [deg]
the correlation at TS and its static ordering occurs at TS with
1
000
decreasing temperature. This phenomenon is not a surprise
because very weak but finite diffuse magnetic scattering,
which is the sign of dynamical correlation, persists even at
(
b) 110
15 K
50 K
8
6
4
2
00
00
00
00
0
1
00 K
magnetic
liquid nitrogen temperature 77 K far above T determined by
S
8,9)
magnetization measurements in MnCr O and CoCr O .
4
2
4
2
It should also be mentioned that both the longitudinal
component below TC and the transverse component below
0
TS exhibit long-range order. Since the fundamental and the
superlattice reflection lines are as sharp as the instrumental
resolution, the correlation length is estimated to be longer
than the instrumental resolution limit of 20 nm.
Table I gives the experimental integrated intensity of
magnetic scattering. The experimental magnetic scattering
integrated intensity of the fundamental reflections was
obtained by subtracting the data at 100 K from those at
2
2
23
24
25
26
27
Scattering angle [deg]
Fig. 7. Neutron scattering line profiles of the 111 fundamental and the 110
superlattice reflections at 100 K, 50 K and 15 K.
15 K, and that of the superlattice reflections was obtained by
0 K and 15 K are magnified in Figs. 7(a) and 7(b), subtracting the data at 50 K from those at 15 K. To determine
5
respectively. As the temperature decreases, the magnetic the magnetic structure of NiCr2O4 at 15 K (T < TS), these
component of the 111 fundamental reflection appears at intensities at 15 K were calculated so as to best fit the
5
5
0 K, while the 110 superlattice reflection is not observed at observed values by varying the ratio of the magnitude of the
0 K within statistical uncertainty. The 111 fundamental transverse component to that of the longitudinal component
reflection at 100 K is due to nuclear scattering. Therefore, and the direction of each component in a least squares
only the order of the longitudinal component of magnetic method. In the calculations, we assumed both the longitu-
moments occurs at 50 K. dinal and the transverse components to be collinear (only up
Figure 8 shows the temperature dependence of the peak and down) structures, and fixed the magnitudes of the total

2542
J. Phys. Soc. Jpn., Vol. 73, No. 9, September, 2004
K. TOMIYASU and I. KAGOMIYA
Table I. Experimental and best-fit calculated magnetic scattering inten-
sity. The multiplicity of the tetragonal domains is also given. The symbol
N.O. means that no reflection was observed within statistical uncertainty.
the 3d-metal chromite normal spinel systems MCr O4
2
(
M ¼ Mn, Fe, Co, Ni, Cu).
The magnetic ordering of FeCr2O4 is also described by
two magnetic components, the ferrimagnetic one and the
spiral one.
been determined yet.
FeCr2O4 is contracted with a tetragonal distortion of 3% at
hkl
Multiplicity
Experimental
Calculated
1
0,11)
0
01
10
01
12
2
4
8
8
N.O. (< 70)
499
0
533
423
100
The more precise magnetic structure has not
1
0,11)
1
2
1
However, since the lattice in
429
1
1)
N.O. (< 80)
4.2 K, the four B sublattices are expected to be grouped
into the B1–B2 and B3–B4 pairs, as for MnCr O , CoCr O
0
02 þ 200
11
20 þ 202
R-factor
2 þ 4
8
N.O. (< 80)
1430
0
1426
149
2
4
2
4
and CuCr2O4. We intend to reinvestigate the magnetic
ordering of FeCr2O4 in the future.
1
2
4 þ 8
—
N.O. (< 150)
The KDLM theory and the LKDM theory predicted some
magnetic structures by solving the Heisenberg Hamiltonian
—
1.0%
5
,7)
for the 3d-metal MCr2O4. However, a structure with the
unique B-sublattice pairs obtained in the present magnetic
[001]
5,7)
structure of NiCr O was not proposed. The reason may
4
2
be that a plausible magnetic structure of NiCr O was not
2
4
determined at that time. More detailed theory is required to
explain the magnetic structures of the 3d-metal MCr2O4
systematically.
0.26
0.78
0
.21
3.0
2.9
3.0
Anderson proposed the concept of magnetic geometrical
frustration coming from the tetrahedron (pyrochlore lattice)
composed by the B-sites for the cubic normal spinel
[
µ
B
]
2
+
3+
3+
A1-A2 Ni
B1-B3 Cr
B2-B4 Cr
100]
[
1
)
systems. The antiferromagnetic short-range correlation,
which is the sign of magnetic geometrical frustration, was
Fig. 9. The new magnetic structure model of NiCr2O4 below TS ¼ 31 K.
The transverse component exhibits collinear (only up or down)
antiferromagnetic ordering described by propagation vector Q ¼ ð0; 0; 1Þ.
1
7)
actually observed in other 3d-metal chromite ZnCr2O4.
However, the magnetic ordering of NiCr2O4 exhibits long-
range order below TS. The reason is most likely the large
tetragonal distortion of NiCr2O4. This distortion removes the
and Cr ions at their condition that all B–B distances and B–O–B angles are the
2
þ
3þ
magnetic moments of the Ni
6)
1
theoretical values of 3 ꢀB. For the magnetic form factors same, and completely suppresses the magnetic geometrical
2þ
3þ
2)
of the Ni and Cr ions, the values reported by Watson frustration, as discussed in the case of CuCr O by Prince.
2
4
4
)
and Freeman were used. The multiplicity of the tetragonal
domains for each scattering and the best-fit calculated
intensity are given in Table I.
Acknowledgment
We thank Professor K. Kohn, Professor K. Siratori,
Figure 9 shows the new magnetic structure model. This Professor Y. Tsunoda and Dr. K. Kamazawa for their fruitful
new magnetic structure possesses a spontaneous magnet- advice and discussion. We also thank Mr. H. Suzuki for his
ization of 0.3 ꢀB/formula, which is consistent with the support in the experiments. This work was supported by
magnetization measurements. The summation of the longi- Waseda University Grand for Special Research Projects
tudinal component of the magnetic moments at the A-sites is (No. 2003A-589).
larger than that at the B-sites, which is compatible with other
1
6)
magnetization measurements. The longitudinal component
the spontaneous magnetization) is perpendicular to the c-
axis, agreeing with a M o¨ ssbauer spectroscopy study of
1
2
3
)
)
)
P. W. Anderson: Phys. Rev. 102 (1956) 1008.
E. Prince: Acta Crystallogr. 10 (1957) 554.
I. S. Jacobs: J. Phys. Chem. Solids 15 (1960) 54.
(
6
1
15)
Ni.
4) R. E. Watson and A. J. Freeman: Phys. Rev. 120 (1960) 1134.
)
5
T. A. Kaplan, K. Dwight, D. H. Lyons and N. Menyuk: J. Appl. Phys.
32 (1961) 13S.
E. Prince: J. Appl. Phys. 32 (1961) 68S.
4
.
Discussion
6
)
)
The new magnetic structure model of NiCr O is
4
2
7
D. H. Lyons, T. A. Kaplan, K. Dwight and N. Menyuk: Phys. Rev. 126
characterized by the fact that the four B sublattices are
classified into the B1–B3 and B2–B4 pairs for the sponta-
neous magnetization along the ½100ꢃ direction (or the B1–B4
and B2–B3 pairs for the spontaneous magnetization along
the ½010ꢃ direction). The ferrimagnetic spiral ordering of
cubic MnCr2O4 and CoCr2O4 is described by the B1–B2 and
B3–B4 pairs, as shown in Fig. 2. Furthermore, the Yafet–
Kittel triangular magnetic configuration in the normal spinel
system CuCr O , whose lattice is contracted with a
(
1961) 540.
8) J. M. Hastings and L. M. Corliss: Phys. Rev. 126 (1962) 556.
N. Menyuk, K. Dwight and A. Wold: J. Phys. (Paris) 25 (1964) 528.
9
)
1
1
1
1
0) G. L. Bacchella and M. Pinot: J. Phys. (Paris) 25 (1964) 537.
1) G. Shirane and D. E. Cox: J. Appl. Phys. 35 (1964) 954.
2) R. Plumier: J. Appl. Phys. 39 (1968) 635.
3) E. F. Bertaut and J. Dulac: Acta Crystallogr., Sect. A 28 (1972) 580.
14) E. F. Bertaut and J. Dulac: Acta Crystallogr., Sect. A 36 (1980) 157.
1
5) J. Nakamura et al.: RIKEN Rev. 16 (1997) 25.
6) A. N. Goryaga, L. G. Antoshina, A. I. Kokorev and D. A. Chursin:
Phys. Solid State 44 (2002) 663.
1
2
4
tetragonal distortion of 9% at 4.2 K, is also expressed by
1
7) S.-H. Lee et al.: Nature (London) 418 (2002) 856.
8) S. Klemme and J. C. Miltenburg: Phys. Chem. Miner. 29 (2002)
663.
2
)
the B1–B2 and B3–B4 pairs. Thus, we consider that such
combinations with respect to the B sublattices is due to the
tetragonal lattice elongation (not contraction) of NiCr2O4 in
1