Resonance-like magnetic excitations in spinel ferrimagnets FeCr 2O4 and NiCr2O4 observed by neutron scattering

Article abstract of DOI:10.1143/JPSJ.77.124703

We performed powder neutron scattering experiments on spinel ferrimagnets ACr₂O₄ with magnetic and Jahn-Teller A²⁺ ions (A = Fe, Ni, Cu). In both FeCr₂O₄ and NiCr ₂O₄, although geometric frustration had been expected to vanish so far, resonance-like magnetic excitation modes were discovered around Q ? 1.4 A^-1 and E ? 5 and 8 to 9 meV in a low-temperature magnetic order phase, similar to the local spin resonance modes early reported in highly frustrated spinel antiferromagnets ACr ₂O₄ with nonmagnetic and non-Jahn-Teller A²⁺ ions (A = Mg, Zn). In a high-temperature magnetic order phase the resonance-like inelastic scattering transformed into quasielastic scattering. In CuCr ₂O₄ no such diffusive scattering was observed. We interpret the resonance-like magnetic excitations as a dynamical spin-frustration effect, and discuss a necessary condition for the appearance of them. 2008 The Physical Society of Japan.

Full text of DOI:10.1143/JPSJ.77.124703

Journal of the Physical Society of Japan
Vol. 77, No. 12, December, 2008, 124703
#2008 The Physical Society of Japan
Resonance-Like Magnetic Excitations in Spinel Ferrimagnets
FeCr O and NiCr O Observed by Neutron Scattering
2
4
2
4
ꢀ
1
1
Keisuke TOMIYASU , Haruhiro HIRAKA , Kenji OHOYAMA , and Kazuyoshi YAMADA
WPI Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577
1Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577
(Received July 22, 2008; revised September 8, 2008; accepted September 19, 2008; published November 25, 2008)
We performed powder neutron scattering experiments on spinel ferrimagnets ACr2O4 with magnetic
and Jahn–Teller A2 ions (A = Fe, Ni, Cu). In both FeCr2O4 and NiCr2O4, although geometric
þ
frustration had been expected to vanish so far, resonance-like magnetic excitation modes were
ꢁ1
˚
discovered around Q ’ 1:4 A and E ’ 5 and 8 to 9 meV in a low-temperature magnetic order phase,
similar to the local spin resonance modes early reported in highly frustrated spinel antiferromagnets
2
þ
ACr2O4 with nonmagnetic and non-Jahn–Teller A ions (A = Mg, Zn). In a high-temperature magnetic
order phase the resonance-like inelastic scattering transformed into quasielastic scattering. In CuCr2O4
no such diffusive scattering was observed. We interpret the resonance-like magnetic excitations as a
dynamical spin-frustration effect, and discuss a necessary condition for the appearance of them.
KEYWORDS: geometric frustration, inelastic neutron scattering, neutron diffraction, spin molecule, hexamer
DOI: 10.1143/JPSJ.77.124703
suggests that, even if there is no usual geometric frustration
for ground states under lattice distortion and static magnetic
Since the Wannier and Anderson’s initial proposals of the order, an effect of the spin frustration dynamically survives
1
.
Introduction
concept of geometric spin frustration in 1950 and 1956,1,2) in excited states (dynamic spin frustration) and generates the
many researchers have studied the paramagnetic phases of spin molecules.
the lattices based on regular triangles/tetrahedra: e.g., C15-
In this paper, to study how generally such dynamic spin
Laves, spinel, pyrochlore, kagom e´ , and triangle systems. frustration emerges, we dare to select a magnetically ordered
Geometric spin frustration means macroscopic ground-state phase of spinel ferrimagnets ACr2O4 with magnetic and
2
þ
degeneracy for classic spins inhering in this kind of lattice, Jahn–Teller A ions (A = Fe, Ni, Cu), which are expected
and is expected to induce a novel paramagnetic state. to completely annihilate the usual geometric frustration
Therefore intensive neutron scattering studies have been among B sites (corner-sharing tetrahedra). Table I summa-
performed, and have revealed novel spin fluctuations in the rizes basic information on these ferrimagnets. The materials
3
–14)
2þ
paramagnetic phases.
Currently, the concept of geometric spin frustration is also Jahn–Teller Cr ions at B sites. All the ions exhibit no
are constructed by A ions at A sites and magnetic and non-
3þ
used as a guidance to exotic phenomena in a magnetically freedom of orbital and valence, and lattices are tetragonally
0–22)
2
ordered phase, such as fractional magnetization plateau in distorted below TJT ¼ 135, 310, and 854 K.
Figure 1
spinel antiferromagnets ACr2O4 (A = Mg, Zn, Cd, Hg) and schematically shows a magnetic structure in NiCr2O4 as a
2
3)
ferroelectrics in spinel ferrimagnets ACr2O4 (A = Co and representative. In a lowest temperature phase of FeCr2O4
Mn).1
5–17)
However, in a magnetically ordered phase, this and NiCr O the magnetic moments exhibit a canted
2 4
usual geometric spin frustration based on a regular triangle/ structure, as shown in Fig. 1(b), in which the ferrimagnetic
tetrahedron lattice is supposed to vanish owing to lattice (F) component and the antiferromagnetic (AF) component
distortion. In fact, few neutron studies on spin fluctuations form long-range order below TC ¼ 74 and 80 K (Curie
have been reported for a magnetically ordered phase. But temperature) and TS ¼ 31 and 35 K (temperature with a
among them, two powder inelastic neutron scattering studies superlattice structure), respectively.20,21,23,24) Hereinafter we
discovered novel spin-excitation modes with discrete ener- call the low-temperature F and AF order phase (T < TS)
˚
ꢁ1
gies (spin resonance levels): two modes of Q ¼ 1:5 A and and the high-temperature F order phase (TS < T < TC) as
E ¼ 4:5 and 9.0 meV in a spinel ZnCr O and the similar phase I and phase II, respectively. CuCr O consists of only
2
4
2
4
˚
ꢁ1
first level at around Q ¼ 1:5 A and E ¼ 4:7 meV in a a F component described by another type of F long-range
9
,18)
25)
spinel MgCr O ,
2
where Q is an absolute value of order (Yafet–Kittel structure) below T ¼ 135 K. Judged
4
C
scattering vector and E is energy transfer. These modes from the large tetragonal lattice distortion and the occur-
have been very recently identified to be spin hexamer and rence of magnetic long-range order, the three materials have
heptamer, defined as antiferromagnetic spin correlations not been recognized as geometrically frustrated magnets so
confined in the molecular units, by single-crystal inelastic far. However, in this paper, we report that resonance-like
neutron scattering.1 The spin hexamer excitation mode magnetic excitations are observed by powder inelastic
appears on a hexagon of a kagom e´ lattice perpendicular to neutron scattering in phase I of FeCr O and NiCr O .
9)
2
4
2
4
the [111] direction, and has the same spin correlation as
in the paramagnetic phase of ZnCr O and MgCr O , the
well-known prototype of geometric spin frustration. This
2.
Experiments
Neutron diffraction experiments were performed on the
2
4
2
5
4
,9)
powder diffractometer, HERMES (T1-3), of Institute for
Materials Research (IMR), Tohoku University, installed at
ꢀ
E-mail: tomiyasu@imr.tohoku.ac.jp
124703-1

J. Phys. Soc. Jpn., Vol. 77, No. 12
K. TOMIYASU et al.
Table I. Basic information on spinel chromites ACr2O4 (A = Fe, Ni, Cu, Mg, Zn). The vectors describe propagation vectors of the magnetic order. TS or
TN, TC, and TJT mean an AF ordering temperature, a F ordering one, and a Jahn–Teller tetragonal lattice distortion one. RT means room temperature.
TS or TN
K)
TC
TJT
A
Type of magnetic order
c=a
(
(K)
(K)
2
9Þ
20Þ
23Þ
20Þ
20Þ
20Þ
21Þ
Fe
Ni
F ð0; 0; 0Þ and AF ð1; 0; 1=2Þ
31
35
74
80
135
310
0.97 (4 K)
1.04 (4 K)
2
3Þ
23Þ
25Þ
21Þ
22Þ
F ð0; 0; 0Þ and AF ð0; 0; 1Þ
25Þ
25Þ
0.91 (RT)
Cu
F ð0; 0; 0Þ
—
135
854
2
3
8Þ
0Þ
24Þ
30Þ
31Þ
Mg
Zn
AF ð1; 0; 1=2Þ, ð0; 0; 1Þ, ð1=2; 1=2; 0Þ, ð1=2; 1=2; 1=2Þ
AF ð1; 0; 1=2Þ, ð0; 0; 1Þ, ð1=2; 1=2; 0Þ, ð1=2; 1=2; 1=2Þ
13
13
—
—
—
—
ꢃ0:999 (10 K)
30Þ
ꢃ0:999 (6 K)
analyzer, and no filter was attached to eliminate higher-order
contamination because of a Ge 622 forbidden reflection.
Incident energy was fixed at Ei ¼ 19:6 meV, typically with
(
a)
[
001]
B
3
horizontal collimation sequence of guide-open-sample-
B
4
A
1
0
60 -blank. Powder specimens of FeCr O , NiCr O , and
CuCr O were synthesized by solid reactions from a
2
4
2
4
2
4
ꢂ
B
stoichiometric mixture of Fe, Fe2O3, and Cr2O3 at 1000 C
in Ar with 5% H2 gas, from that of NiO and Cr2O3 at
2
ꢂ
ꢂ
[010]
1200 C in air, and from that of CuO and Cr2O3 at 1000 C
B
in O2 gas, respectively. Similar methods were used for the
preparations of samples in earlier neutron powder diffraction
1
A
20,21,23,25)
2
experiments.
in vanadium cylinders (10 mm-ꢀ) of aluminum containers
The samples of about 7 g were sealed
[
100]
F
A-sites
B-sites
4
with He exchange gas, which were mounted on cold fingers
4
of He closed-cycle refrigerators.
AF
AF
(
b)
F
3. Results
3
+
B =B Cr
Figures 2(a), 2(b), and 2(c) show the diffraction patterns
energy-integrated intensities) of FeCr2O4, NiCr2O4, and
1
3
AF AF
(
CuCr O , respectively. In FeCr O and NiCr O , at T ¼
2
4
2
4
2
4
1
5 K in phase I, very broad but appreciable diffuse scattering
˚
ꢁ1
F
F
is found from Q ¼ 0:8 to 2.0 A in addition to fundamental
Bragg reflections and magnetic superlattice Bragg reflec-
tions. The fundamental reflections consist of magnetic
scattering coming from a F component and nuclear scatter-
ing, and the superlattice reflections correspond to an AF
component. At T ¼ 50 K in phase II and at T ¼ 100 K in the
paramagnetic phase, the superlattice peaks disappear and the
diffuse scattering becomes stronger. In CuCr O , no diffuse
F
F
AF
B =B
AF
A =A
2
4
+
1
2
3
2+
Cr
Ni
2
4
scattering is observed at T ¼ 15 K.
Fig. 1. (a) Picture of the unit cell of crystal structure. The sublattices
A1, A2, B1, B2, B3, and B4 are defined. The oxygen sites are omitted.
Next, we studied the diffusive signal in FeCr2O4 and
NiCr2O4 by inelastic scattering. Figures 3(a) and 3(b) show
the maps of inelastic neutron scattering intensity, measured
at T ¼ 12, 50, and 100 K. The two materials exhibit almost
the same patterns at all the temperatures. At T ¼ 12 K,
resonance-like magnetic excitations are clearly observed
b) Schematic picture of magnetic structure in phase I of NiCr2O4.23) The
(
magnetic structure is described by three sets of sublattices, B1 ¼ B3,
B2 ¼ B4, and A1 ¼ A2. The diagonal solid arrows, the vertical dotted
arrows, and the horizontal dotted arrows show the ordered moments, the
F components, and the AF components, respectively. The F and AF
components are perpendicular to each other. In each sublattices the F
components are the same, and the AF components are alternatively
arranged in accordance with the propagation vector ð0; 0; 1Þ.
˚
ꢁ1
around Q ¼ 1:4 A and E ¼ 5 meV, as shown in the lower
panels. The Q range of resonance is consistent with the
diffraction patterns. Some signals below E ¼ 3 meV are due
to Bragg reflections, convoluted by instrumental resolution
functions, not due to inelastic components. In the insets,
the thermal guide tube of JRR-3 in Japan Atomic Energy other signals are also found above E ¼ 7 meV in addition to
Agency (JAEA).2 Incident neutrons with Ei ¼ 24:5 meV the main peaks around E ¼ 5 meV, suggesting the existence
were extracted by a 331 reflection of a Ge monochromator of higher-energy modes. A double Gaussian fitting with
6)
and horizontal collimation sequence of guide-blank-sample- constant background gives E ¼ 5:3 and 9.3 meV for
0
2
on the triple-axis spectrometer, AKANE (T1-2) of IMR, 50 and 100 K, the resonance-like inelastic scattering changes
2 . Inelastic neutron scattering experiments were carried out FeCr O and E ¼ 4:7 and 7.8 meV for NiCr O . At T ¼
2
4
2
4
2
7)
Tohoku University, installed at the same guide tube.
AKANE equips a Ge 311 monochromator and a PG 002 upper panels.
into quasielastic scattering, as shown in the middle and
124703-2

J. Phys. Soc. Jpn., Vol. 77, No. 12
K. TOMIYASU et al.
3
2
2
1
1
0000
5000
0000
5000
0000
4
.
Discussion
We revealed that (1) even the spinel ferrimagnets with
(
2
a) FeCr O4
111
no usual geometric frustration FeCr2O4 and NiCr2O4
exhibit resonance-like magnetic excitations around Q ’
˚
ꢁ1
1
:4 A and E ’ 5 and 8 to 9 meV in phase I, (2) there
2
2
20
02
is no resonance in phase II, and (3) no such magnetic
diffusive scattering was observed at the lowest temper-
ature in CuCr O . For result (1), the resonance-like
1
5 K
0 K
00 K
2
4
5
excitations are spectroscopically similar to the local spin
˚ ꢁ1
5
000
resonance modes with Q ’ 1:5 A
and E ’ 4:5 and
1
9
.0 meV in the highly frustrated spinel antiferromagnets
3
3
2
2
1
1
5000
0000
5000
0000
5000
0000
MgCr2O4 and ZnCr2O4, mentioned in the second para-
9
,18)
graph of Introduction.
This suggests that the reso-
(b) NiCr O4
2
111
nance-like excitations are also interpreted as the effect of
dynamic spin frustration, and the new concept of dynamic
spin frustration is quite general in a magnetically ordered
phase. If we unify the geometric and dynamic frustration
as comprehensive frustration, FeCr2O4 and NiCr2O4 will
be regarded as frustrated magnets for the first time
2
20
2
02
15 K
2þ
despite the existence of magnetic and Jahn–Teller A
ions.
5
0 K
Next, we discuss a necessary condition for the appear-
ance of the resonance-like excitations. Result (2) strongly
suggests that this condition is the ordering of AF
component. Table I summarizes propagation vectors de-
scribing the AF components in ACr2O4 (A = Fe, Ni, Mg,
Zn). The vectors of FeCr2O4 and NiCr2O4 are also
5
2
000
000
100 K
111
002
2
(
c) CuCr O4
2
20
202
identical to those in MgCr2O4 and ZnCr2O4 with multi-
1000
1
5 K
23,28–30)
Q AF components,
suggesting a close relation
between the AF ordering and the resonance-like excita-
tions. In addition, this criteria is consistent with result (3)
because CuCr O exhibits no AF component. On the other
no diffuse scattering
1.5
0
0
0.5
1
2
2.5
2
4
-1
Wave number Q [Å
]
hand, lattice distortion does not seem to be related to the
appearance in spinel chromites. As given in Table I, the
tetragonality of the lattice largely depends on the element
Fig. 2. Powder neutron diffraction patterns of ACr2O4 (A = Fe, Ni, Cu)
measured at T ¼ 15 K (phase I), 50 K (phase II), and 100 K (para-
magnetic phase). The zero points of intensity are shifted by 5000 and
2
0,21,25,30,31)
at A sites.
In contrast, the resonance energies
are almost independent of magnitude — of several per-
1
0000 counts in the data of T ¼ 50 and 15 K. The shaded portions show
the very broad diffuse scattering for guide to the eyes. In the panel (c), the
vertical scale is magnified to show that there is no diffuse scattering.
cent — and sign of the lattice distortion among ACr2O4
(A = Fe, Ni, Mg, Zn). These facts indicate that, although
it has been originally believed that remarkable properties
Figure 4 shows the constant-E scans of the resonance-like of geometric frustration are only observed on perfectly
magnetic excitations measured at E ¼ 5 meV and T ¼ 12 K regular triangles, the resonance-like excitations are rather
of FeCr2O4 and NiCr2O4. The strong peaks are commonly robust against lattice distortion of several percent. In
˚
ꢁ1
observed around Q ¼ 1:4 A , and are described by a full CuCr2O4 also, if the AF component can be extracted by
˚
ꢁ1
width at half maximum (FWHM) of ꢁ ¼ 0:54 A corre- a doping or an external field, resonance-like magnetic
˚
sponding to a correlation length ꢂ ¼ 5:1 A (FWHM) in a excitations might appear in the antiferromagnetically
Gaussian approximation. The line profiles exhibit fine ordered phase despite the large tetragonal lattice distortion
ꢁ1
˚
structures above Q ¼ 2 A , which are probably not due to of around 9%.
phonons standing from the Bragg reflections because no
dispersion relation is observed in the maps of overall
5.
Conclusions
scattering function SðQ; EÞ of Figs. 3(a) and 3(b). For
We performed powder neutron scattering on ACr2O4
reference, Fig. 4 also shows the calculated lines of the (A = Fe, Ni, Cu). In FeCr2O4 and NiCr2O4, two resonance-
representative spin molecules, antiferromagnetic spin dimer, like magnetic modes were discovered in phase I, similar to
5
,19)
hexamer, and heptamer composed of B-site spins.
The the local spin resonance modes in ZnCr2O4 and MgCr2O4,
line profiles of the molecular models are broader than the whereas only quasielastic scattering was observed in
experimental ones, meaning that the spatial correlations of phase II. In CuCr O no characteristic behavior was found.
2
4
resonance-like magnetic excitations extend beyond those These results indicate that the resonance-like magnetic
molecules. The larger spatial correlations are probably the excitations are surprisingly robust regardless of the magni-
2þ
effect of A ions. At present, it is difficult to precisely tude — of several percent — and sign of the lattice distortion,
determine the spatial correlation. and suggest that the only necessary condition for the
124703-3

J. Phys. Soc. Jpn., Vol. 77, No. 12
K. TOMIYASU et al.
1
2
0
8
6
4
2
12
10
8
(
a)
(b)
FeCr O
NiCr O4
3002
2
4
1
600
T=100 K
T=100 K
200
4
00
00
0
6
1
00
0
2
4
2
1
002
1020
10
8
FeCr O
T=50 K
NiCr O
2 4
2
4
300
T=50 K
1
0
8
6
4
2
6
00
2
00
00
0
4
2
00
00
0
6
1
4
2
1
002
1002
10
8
FeCr O4
N1 5i C0 r O4
2
2
1
0
8
6
4
2
0
T2 =0 10 2 K
T=12 K
1
00
100
6
5
0
0
4
0
2
0
100
Counts/170sec
0
100
res.
res.
Counts/170 sec
0
0
.0
0.5
1.0
1.5
2.0
2.5
0.0
0.5
1.0
1.5
2.0
2.5
-1
-1
Wave number Q [Å ]
Wave number Q [Å ]
Fig. 3. Maps of the inelastic neutron scattering intensity in the Q and E space, measured at T ¼ 12, 50, and 100 K on powder specimens of FeCr2O4 (a) and
NiCr2O4 (b). The vertical color gauges indicate the intensity scale in arbitrary units. The cross bars describe FWHM (full width at half maximum) of the
˚
ꢁ1
1
11 Bragg reflection around Q ¼ 1:3 A (ꢀQ) and FWHM of the incoherent scattering of vanadium standard sample (ꢀE) as typical Q and E
˚
ꢁ1
resolutions. The insets in the lower panels show constant-Q scans measured at Q ¼ 1:4 A . The symbols plot the experimental data, and the lines are
obtained by a double Gaussian fitting with constant background.
3
2
2
1
1
00
50
00
50
00
are frustrated magnets in the light of dynamic spin
frustration. Therefore, these results show that it could be
fruitful to investigate many magnets in connection with
geometric/dynamic spin frustration in the future, even if the
systems are not regarded as geometrically frustrated magnets
so far.
1
00
2
NiCr O4
FeCr O4
2
dimer
hexamer
heptamer
80
6
4
0
0
Acknowledgments
The author (K.T.) thanks Professor K. Kohn, Professor Y.
Tsunoda, Dr. K. Kamazawa, and Mr. T. Usa for discussions
and supports in Waseda University. We thank Mr. K.
Nemoto for supports on HERMES and AKANE. This work
was supported by Grants-in-Aid for Scientific Research on
Priority Area (16076204) and Scientific Research (B)
(19340090) from the Ministry of Education, Culture, Sports,
Science and Technology of Japan.
5
0
20
0
0
0
0.5
1
1.5
2
2.5
3
3.5
4
-
1
Wave number Q [Å
]
Fig. 4. Constant-E scans of FeCr2O4 and NiCr2O4, measured at
E ¼ 5 meV and T ¼ 12 K. The symbols represent the experimental data.
The dotted, solid, and broken curves show the form factors of a dimer, a
hexamer, and a heptamer with constant background and normalized scale
factors, respectively. The scale factors are adjusted so that the peak height
is the same as that of the experimental data.
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