Crystallographic, Electronic, and Magnetic Properties of Rock Salt Superstructure Sulfide Lu2CrS4 with Jahn-Teller Distortion

Article abstract of DOI:10.1021/acs.inorgchem.5b01511

A new chromium(II) sulfide, Lu₂CrS₄, with a novel structure was prepared by a solid-state reaction. The powder X-ray diffraction pattern could be indexed as a tetragonal system, with a = 7.46373(2) ?, c = 22.6338(2) ?, and space group I42d (No. 122). Rietveld analysis of the pattern provided the crystal structure consisting of CrS₆ and LuS₆ octahedra sharing edges and apexes and revealed a rock salt superstructure with new cation (vacancy) arrangements. The electrical resistivity indicates semiconducting behavior. The magnetic susceptibility and specific heat measurements showed that the Cr ions are in the high-spin d⁴ configuration and that their magnetic moments ordered antiferromagnetically at 55 K. The basic antiferromagnetic structure was determined using powder neutron diffraction data at 10 K. The band structure calculations demonstrate that the densities of states of Cr 3d electrons split into two spin-up e_g bands because of Jahn-Teller distortion.

Full text of DOI:10.1021/acs.inorgchem.5b01511

Article
pubs.acs.org/IC
Crystallographic, Electronic, and Magnetic Properties of Rock Salt
Superstructure Sulfide Lu CrS with Jahn−Teller Distortion
2
4
,†
‡
†
†
§
Keitaro Tezuka,* Makoto Wakeshima, Masataka Nozawa, Keita Oshikane, Kenji Ohoyama,
Yue Jin Shan, Hideo Imoto, and Yukio Hinatsu
†
†
‡
†Research Division of Functional Materials Design, Graduate School of Engineering, Utsunomiya University, Utsunomiya 321-8585,
Japan
‡
Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
§Institute of Materials Research, Tohoku University, Sendai 980-8577, Japan
*
S Supporting Information
ABSTRACT: A new chromium(II) sulfide, Lu CrS , with a novel
2
4
structure was prepared by a solid-state reaction. The powder X-ray
diffraction pattern could be indexed as a tetragonal system, with a =
7
̅
.46373(2) Å, c = 22.6338(2) Å, and space group I42d (No. 122).
Rietveld analysis of the pattern provided the crystal structure consisting
of CrS and LuS octahedra sharing edges and apexes and revealed a rock
6
6
salt superstructure with new cation (vacancy) arrangements. The
electrical resistivity indicates semiconducting behavior. The magnetic
susceptibility and specific heat measurements showed that the Cr ions are
4
in the high-spin d configuration and that their magnetic moments
ordered antiferromagnetically at 55 K. The basic antiferromagnetic
structure was determined using powder neutron diffraction data at 10 K.
The band structure calculations demonstrate that the densities of states of
Cr 3d electrons split into two spin-up e bands because of Jahn−Teller
g
distortion.
1
. INTRODUCTION
systems R CrS (R = Ho−Yb, Y) have the Er CrS -type
2
4
2
4
6
,14−17
structure.
the Y MnS -type structure, but there exist two long and four
4
The Er CrS -type structure is very similar to
Ternary sulfides R MS of trivalent rare-earth metal R and
2 4
2
4
divalent metal M show a variety of crystal structures. The
reported structures of these sulfides are grouped into several
three-dimensional structure types, i.e., the spinel type
2
short Cr−S bond lengths in the octahedral environment.
Because Jahn−Teller ordering prevents cation disordering, the
R and Cr atoms occupy independent crystallographic sites. The
1
5
5
−7
5,6,8−11
(
(
(
Fd3
Pnma),
̅
m),
the Th P type (I4
the Yb3S4 type (Pnma), the CaFe O type
̅
the olivine type
3
4
,6,12
5
2
4
1,5,6,13
CrS octahedra share corners and edges, forming a three-
6
Pnma), the Y MnS type (Cmcm or Cmc2 ),
and so on.
2
4
1
dimensional structure. In our previous studies, Y CrS showed a
The relative stability of these structures is determined by the
ionic sizes of the R and M atoms.
2
4
5
long-range antiferromagnetic (AFM) ordering of divalent Cr at
17
2
For transition metals except Cr, almost of all of the R MS4
65 K, and its collinear magnetic structure was determined. On
the other hand, as far as we know, the description of Lu CrS
phases crystallize in the spinel-, olivine-, and Y MnS -type
structures. The spinel- and olivine-type structures consist of
cubic closest packing (CCP) and hexagonal closest packing
2
4
2
4
has not been reported yet.
In this work, we succeeded in the synthesis of a new rare-
earth chromium sulfide, Lu CrS . This compound was found to
1
−7,12
(
HCP) of S atoms, respectively.
In both structures, the R
and M atoms occupy the octahedral and tetrahedral holes,
respectively. In the Y MnS -type structures, the R atoms adopt
two different coordination environments of 6-coordinated
octahedral sites and 7-coordinated polyhedral sites, and the
M atoms randomly share the octahedral sites with the R
2
4
crystallize in a novel CCP structure of S atom, in which both of
the Lu and Cr atoms occupy the octahedral holes, forming the
rock-salt-type superstructure with Jahn−Teller distortion. We
will report the synthesis, crystal structure, and electrical and
magnetic properties of Lu CrS .
2
4
1
,5,6,13
atoms.
4
For divalent Cr with a high-spin 3d electronic configuration,
the Jahn−Teller effect often plays an important role in
structural stabilization and electrical, magnetic, and optical
behavior. All of the reported compounds in the chromium
2
4
Received: July 6, 2015
Published: September 29, 2015
©
2015 American Chemical Society
9802
DOI: 10.1021/acs.inorgchem.5b01511
Inorg. Chem. 2015, 54, 9802−9809

Inorganic Chemistry
. EXPERIMENTAL SECTION
Article
2
Powder samples of Lu CrS were synthesized by solid-state reactions
2
4
of CrS with Lu S . Lutetium sesquesulfide (Lu S ) was prepared by
2
3
2 3
heating Lu O on a silica boat at 1150 °C in a flow of the mixed gas of
2
3
CS and N , which was obtained by bubbling N gas through liquid
2
2
2
CS2 at room temperature. Chromium monosulfide (CrS) was
prepared by heating a mixture of Cr and S at 1000 °C in an
evacuated silica tube (see the Supporting Information). The starting
materials were stoichiometrically mixed together and sealed in an
evacuated carbon-coated silica tube, and the tube was heated at 1300
°
C for 24 h.
Powder X-ray diffraction (XRD) patterns were measured with Cu
Kα radiation on a RINT2200 diffractometer (Rigaku) equipped with a
graphite monochromator. The crystal structure was determined using
Figure 1. Powder XRD pattern fitting for Lu
2
CrS
4
. The calculated and
1
8
19
EXPO2004 and refined with the program RIETAN-FP. The crystal
observed patterns are shown by the top solid line and cross markers,
respectively. The vertical marks in the middle show positions
calculated for Bragg reflections. The lower trace is a plot of the
difference between the calculated and observed intensities.
20
structures were visualized with the program VESTA. Powder neutron
diffraction (ND) measurements were performed on the Kinken
powder diffractometer for high-efficiency and high-resolution measure-
2
1
ments of the Institute for Materials Research at Tohoku University,
which was installed at the JRR-3 M Reactor of the Japan Atomic
Energy Agency, Tokai, Japan.The crystal and magnetic structures were
determined by the Rietveld method using the FullProf program.
systematic extinctions. Because the density of the Lu CrS
2 4
2
2
−3
powder was determined to be 5.5(2) g cm using a
pycnometer, the number of formula units in a unit cell, Z,
was estimated to be 8. From these data, the crystal structure
was solved by direct methods using EXPO2004. Although
The temperature dependence of the electrical conductivity was
measured by a direct-current (dc) four-probe method in the
temperature range between 300 and 400 K. The bar-shaped samples
for the resistivity measurements were sintered at 1300 °C for 12 h in
an evacuated carbon-coated silica tube. The relative density of the
sintered sample was 75.5%. Gold wires (0.030 mm) were used to
connect the sample to the stage with contacts made using silver epoxy,
while soldered contacts connected the stage to external cables leading
to the Keithley 2001 digital multimeter or the ADCMT 8252
electrometer. A dc two-probe method was used in the temperature
range between 260 and 350 K. The ohmic contacts were confirmed by
the current−voltage characteristics at room temperature.
The magnetic susceptibilities were measured under an applied field
of 0.1 T in the temperature range between 4.5 and 300 K by using a
SQUID magnetometer (Quantum Design, MPMS-5S). Specific heat
measurement was carried out using a relaxation technique supplied by
the commercial specific heat measurement system (Quantum Design,
PPMS) in the temperature range from 1.8 to 300 K. The sample in the
form of a pellet was mounted on an alumina plate with apiezon for
good thermal contact. UV−vis diffuse-reflectance spectra were
measured with a V-570 instrument (JASCO).
I4 md (No. 109) and I4
1
̅
group I4 md (No. 109). Then, it was determined that the Lu
1
atoms occupy the 8d and 8c sites, the Cr atoms occupy the 4a
and 8d sites, and the S atoms occupy two 8c sites and one 16e
site of the space group I42d (No. 122). The structure
̅
refinement using the program RIETAN-FP was converged to
Rwp = 8.81% and S = 1.29, and the lattice parameters were
determined to be a = 7.46373(3) Å and c = 22.6338(2) Å.
When the Cr atoms occupy all of the 4a and 8d sites, the molar
ratio of Lu/Cr/S becomes 4:3:8. Thus, the occupancies of the
Cr 4a and 8d sites were also refined, and the refined results
show that the Cr atoms occupy fully the 4a site and just half of
the 8d site within the error range. However, there is a strong
correlation between a site occupancy and an atomic displace-
ment parameter. Finally, the site occupancies of the Cr 4a and
Calculations of the electronic structure and density of states (DOS)
8
d sites were fixed to 1.0 and 0.5, respectively, and just the
23
were performed using the WIEN2k program package. This program
employs the full-potential linearized augmented plane wave + local
orbitals method based on density functional theory. We used the
generalized gradient approximation (GGA) + Hubbard U parameter
for the Cr 3d electrons. In the calculation, the convergence parameter
was set to RMTkmax = 7.0, and the muffin-tin (MT) spheres are
RMT(Lu) = 2.50 bohr, RMT(Cr) = 2.44 bohr, and RMT(S) = 2.10 bohr.
We used 6 × 6 × 2 meshes, which generated 36 k points in the first
Brillouin zone.
atomic displacement parameters of both sites were refined. The
final refined results are shown in Table 1 and Figure 1.
Figure 2 shows the crystal structure of Lu CrS . The Cr1 and
2
4
Cr2 atoms are 6-coordinated by S atoms, forming CrS6
octahedra. The Cr1S octahedra edge-share to Cr2S octahedra.
6
6
The Cr2S octahedra corner-share to each other in directions
6
perpendicular to the c axis. The S atoms form a slightly
distorted CCP arrangement parallel to {102}, as shown in
Figure 3a. It is well-known that the crystal structure is called a
rock salt (NaCl)-type structure if one kind of cationic atom
completely occupies the octahedral holes in the CCP
arrangement. In the case of Lu CrS , the Lu and Cr atoms
3
. RESULTS AND DISCUSSION
.1. Crystal Structure. Figure 1 shows the XRD pattern of
Lu CrS at room temperature. This pattern is not similar to any
3
2
4
2
4
1
1
of the known patterns of ternary sulfides including Lu MnS
fill / and / of their octahedral holes, respectively and
2
4
2 4
1
−7
with the spinel structure, although the divalent ionic radii of
orderly, and the rest holes remain as vacancies occupying the 4b
2+
1
1
Mn and Cr with high-spin states are very close (Mn , 0.97 Å;
site at ( / , / , 0) and half of the 8d site for Cr2. Figure 3b
2 2
2+
24
Cr , 0.94 Å). The difference in the XRD patterns (i.e., crystal
structures) between Lu MnS and Lu CrS is caused by Jahn−
shows a cationic atom arrangement between CCP sulfur layers.
The Lu and Cr (or vacancy labeled as □) atoms arrange
alternately in the sequence Lu2Cr1Lu2Cr1, Lu1Cr2Lu1Cr2,
and Lu2□Lu2□ along ⟨100⟩ but order successively in the
sequence Lu1Lu1Lu1Lu1, Lu2Lu2Lu2Lu2, Cr1□□Cr1 (or
Cr1□Cr1□), and Cr2Cr2Cr2Cr2 along ⟨201⟩. Consequently,
the Cr (or □) and Lu zigzag chains along ⟨201⟩ alternate
parallel to ⟨100⟩. In the case of rock-salt-type ionic compounds
2
4
2
4
Teller distortion of divalent Cr, as will be described later.
The peaks in the XRD pattern were indexed using both the
2
5
program JADE and the N-Treor algorithm implemented in
EXPO2004. The space group was determined to be a tetragonal
system I4 md (No. 109) or I4
̅
1
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Inorganic Chemistry
Article
Table 1. Crystallographic Data for Lu CrS at Room Temperature
2
4
space group
̅
I42d (No. 122, setting 1)
a/Å
c/Å
Rwp/%
S
7.46373(3)
22.6338(2)
8.81
1.29
atom
site
g
x
y
z
B/Å2
Lu1
Lu2
Cr1
Cr2
S1
8d
8c
1.0
1.0
1.0
0.5
1.0
1.0
1.0
0.2543(4)
1/4
0
1/8
1.07(6)
1.11(6)
1.6(3)
0
0.25031(9)
0
4a
0
0
1
1
8d
8c
0.758(3)
/4
/8
1.0(3)
0
0
0
0.3691(5)
0.1302(5)
0.0073(5)
0.3(2)
S2
8c
0
1.5(2)
S3
16e
0.2308(13)
0.2194(13)
1.07(13)
containing two or more kinds of cationic atoms, the cations
26
often occupy independent crystallographic sites. As far as we
know, no compound with the superstructure of Lu CrS exists.
2
4
However, β-NaMnO and β-Li CuZrO were reported to have
2
2
4
26−28
similar cation arrangements consisting of zigzag chains.
It
is interesting to note that the superstructures of both
compounds include Jahn−Teller distortions caused by the
4
9
trivalent Mn 3d and divalent Cu 3d electronic configurations,
4
as is the case with Lu CrS containing divalent Cr 3d . The
2
4
Er CrS -type structure is stable for R CrS (R = Ho−Tm) with
2
4
2
4
trivalent lanthanides but unstable for Yb CrS because of the
2
4
1
5
partially divalent Yb. Lu is also extremely stable in the
trivalent state, but Lu CrS does not have a Er CrS -type
2
4
2
4
structure. From these results, the difference in the crystal
structure between Tm CrS and Lu CrS is thought to be just
2
4
2
4
the difference between both the lanthanide ionic radii, although
3
+
the trivalent ionic radii of Tm and Lu are very close (Tm , 1.02
3+
24
Å; Lu , 1.00 Å).
Bond lengths between Cr and S calculated from the refined
data are shown in Figure 4 and Table 2. Two bonds along the c
Figure 2. Crystal structure of Lu CrS .
2
4
Figure 4. Coordination environments for CrS octahedra.
6
Table 2. Selected Bond Distances of Lu CrS
2
4
bond
distance (Å)
bond
distance (Å)
Lu1−S1
Lu1−S2
Lu1−S3
Lu2−S1
Lu2−S2
Lu2−S3
Lu2−S3
2.620(3) (×2)
2.664(3) (×2)
2.680(12) (×2)
2.689(10) (×1)
2.720(13) (×1)
2.596(10) (×2)
2.718(10) (×2)
Cr1−S2
Cr1−S3
2.946(13) (×2)
2.383(10) (×4)
Figure 3. (a) CCP arrangement of S atoms. (b) Cationic atom
arrangement adopted by Lu (blue spheres), Cr1 (red spheres), Cr2
Cr2−S1
Cr2−S2
Cr2−S3
2.686(14) (×2)
2.599(14) (×2)
3.003(12) (×2)
(
purple spheres), and vacancy (white spheres) between CCP sulfur
layers.
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Inorganic Chemistry
Article
axis for each Cr are obviously longer than the other four bonds,
for a Mott variable-range-hopping (VRH) conductor with
localized carriers was also examined, but we could not find
31
which indicates that the CrS octahedra are distorted because of
6
4
the Jahn−Teller effect of divalent Cr with the high-spin 3d
electronic configuration, like Er CrS and Y CrS . It is assumed
the most suitable model. As shown in the inset of Figure 5, the
−
1/4
ρ−T
plot for three-dimensional VRH is not a linear curve,
2
4
2
4
−1/3
−1/2
that the difference in the bond lengths is mainly due to the
deficiency in the Cr2 8d site, as described in the section about
the bond valence sum (BVS). The schematic diagram of the
orbital splitting is shown in the Supporting Information. Jahn−
Teller distortion of the orbital configurations will be described
exactly in the section 3.5. Although a decrease in the distortion
can induce a structural phase transition, the transition is not
observed below room temperature by the heat capacity (see
section 3.4) and ND (see section 3.5) measurements. At higher
temperature, the transition may occur as a result of a decrease
in the distortion. The Lu−S bond lengths are also shown in
Table 2. The BVS method was applied to estimate the valence
and the ρ−T
and ρ−T
plots were more bent than the
−1/4
ρ−T
curve, indicating that the temperature dependence of
resistivity does not follow the VRH model. Furthermore, the
resistivity is high at room temperature as the Cr2+ compounds.
There is a possibility that the peculiar temperature dependence
and high resistivities result from the disappearance of
conducting pathways because of the Cr2 site deficiency. It is
an obvious fact that this thermally activated behavior of the
4
electrical conductivity shows the localization of 3d electrons of
divalent Cr at their sites.
3
.3. Magnetic Susceptibility. The magnetic susceptibil-
ities for Lu CrS were measured in the temperature range
2
4
3
+
2−
29
between 4.5 and 300 K. Figure 6 and its inset show the
of Lu using r (Lu −S ) = 2.414 Å. The BVSs for Lu1 and
0
Lu2 were calculated to be +3.14 and +3.02, respectively,
indicating that Lu is in the trivalent state. When the valence of
Lu is trivalent, that of Cr is expected to be divalent by
considering the overall electroneutrality principle of Lu CrS .
2
4
2+
2−
30
Using r (Cr −S ) = 2.18 Å, the bond valences for Cr1 and
0
Cr2 were calculated to be +2.56 and +1.37, respectively,
showing large deviations between the prediction (+2) and
experiments. For the Er CrS -type structure with no Cr
2
4
deficiency, the valences of Cr for the Y CrS and Er CrS
2
4
2
4
phases were calculated to be ca. +2. On the other hand,
although Cr2 deficiencies exist in the Lu CrS structure, the
2
4
valence estimations for Cr1 and Cr2 were obtained from the
average structure and did not take into account structural
relaxation around the Cr2 deficiencies. The local displacements
of S atoms presumably lead to overestimation of the valence of
Cr1 and to underestimation of the valence of Cr2. The detail
discussion of the BVS method should need investigations of the
local Cr−S coordination environments. The valence of Cr
would be considered the divalent state, as described in the
following sections.
Figure 6. Magnetic susceptibility versus temperature for Lu CrS . The
inset shows the inverse magnetic susceptibilities as a function of the
temperature.
2
4
3
.2. Electrical Conductivity. The electrical resistivity (ρ)
temperature dependence of the magnetic susceptibilities (χ)
7
−1
for Lu CrS was ∼7 × 10 Ω m at room temperature. The
resistivity was measured in the temperature range between 260
and 400 K, and its Arrhenius plot is represented in Figure 5.
and inverse magnetic susceptibilities (χ ), respectively. A drop
2
4
due to long-range AFM ordering was observed at 55 K, and the
absence of divergence between the zero-field-cooled (ZFC) and
field-cooled (FC) magnetic susceptibilities indicates that the
The resistivity increases with decreasing temperature up to ∼2
2+
8
Cr ions are in an AFM state without any weak ferromagnetic
properties below 55 K. The peak shape of the anomaly is broad
in the temperature range between 60 and 100 K, suggesting the
existence of short-range magnetic ordering. The inverse
susceptibility obeys the Curie−Weiss law above 150 K. The
×
10 Ω m at 260 K and shows thermally activated
semiconducting (insulating) behavior. However, the temper-
ature dependence does not follow the Arrhenius plot (log ρ ∝
−1
−1/d+1
T
). The log ρ−T
curve (d = number of dimensions)
effective magnetic moment (μ ) was determined to be 4.93(1)
eff
μB from the Curie−Weiss fitting. The theoretical effective
2+
4
magnetic moments of Cr 3d with the high-spin state (S = 2)
and low-spin state (S = 1) are 4.90 and 2.83 μ , respectively. A
B
good agreement between the experimental and theoretical
values of S = 2 reveals that the Cr2+ ion is in the high-spin state.
The Weiss constant was determined to be a large negative value
of −142.6(9) K, indicating the existence of AFM interactions
between the Cr2+ ions.
3
.4. Specific Heat. We measured the specific heat (C ) of
p
Lu CrS and plotted the temperature dependence of C in
2
4
p
Figure 7a. A λ-type anomaly is observed at 54.5 K, so it is
2
+
corresponding to the long-range AFM ordering of the Cr
moments observed in the magnetic measurements (Figure 6).
Figure 5. Temperature dependence of the electrical resistivity (ρ).
−1/4
The inset shows the plot of ρ as a function of T
for three-
In order to estimate the magnetic contribution (Cmag) to C , we
p
dimensional VRH.
need to subtract the lattice contribution (C ) and the
lat
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Article
K are shown in Figure 7b. The high-temperature tail of the
magnetic specific heat above 55 K corresponds to the broad
anomaly in the temperature range between 55 and 100 K in the
χ−T curve (Figure 6), suggesting the existence of short-range
magnetic ordering due to frustration magnetic interactions as
described later. From the Smag−T curve, the S change due to
mag
2
+
the magnetic ordering of the Cr moments at 100 K is
estimated to be 13.1 J mol− K . This value of S is in good
1
−1
mag
−
1
−1
agreement with R ln 5 (=13.4 J mol K ) of the theoretical
value for the Cr2+ ion with S = 2.
3
.5. Electronic Structure. Figure 8 shows the UV−vis
diffuse-reflectance spectrum of Lu CrS . The absorption
2
4
Figure 8. Diffuse-reflectance spectrum of Lu CrS . The Tauc plot is
2
4
shown.
coefficients were calculated from the reflectance data with the
32
Kubelka−Munk function. The energy of the optical band gap
33
Figure 7. (a) Temperature dependence of the specific heat (C ) for
was determined to be 1.75 eV from the Tauc plot.
p
Lu CrS . The red solid line is a fit of the lattice contribution to the
Figure 9a displays the total and partial DOS of total electrons
2
4
specific heat according to the Debye and Einstein models as described
in the text. (b) Blue and red circle symbols representing the residual
of Lu, Cr1, Cr2, and S for Lu CrS obtained from the GGA + U
2
4
specific heat (Cp − C )/T and the corresponding entropy Smag,
lat
respectively.
electronic contribution (C ∼ 0 J mol K−1 for insulators)
−1
e
from the total C . The C data were fitted to the measured C
p
lat
p
data between 100 and 250 K using a linear combination of the
Debye and Einstein models. The analytical formula was
3
TD
/
T
4
x
⎛
⎞
⎟
T
x e
C(T) = n × 9N k ⎜
∫0
dx
2
D
A
B
x
⎝
T ⎠
(e − 1)
T /T
D
2
E1
⎛
T ⎞
E1
e
+
nE1
nE2
× 3NAkB⎜⎝
⎟
T /T
2
T ⎠
E1
(
e
− 1)
eTE2/T
2
⎛
T ⎞
E2
+
× 3NAkB⎜⎝
⎟
TE2/T
2
T ⎠
(e
− 1)
where N is Avogadro’s constant, k is Boltzmann’s constant,
A
B
TD is the Debye temperature, and TE is the Einstein
temperature. The sum of the scale factors n , n , and n
D
E1
E2
was restricted to the number of atoms per Lu CrS chemical
2
4
formula: n + n + nE2 = 7. We adopted the model using one
D
E1
T and two T because there was a disagreement between the
D
E
measured C data and the C data fitted by the simple model
p
lat
using one T and one T at high temperatures. The fit to the
D
E
data yielded T of 170 K, T of 254 K, TE2 of 408 K, n of
D
E1
D
1.95, nE1 of 2.39, and nE2 of 2.67, and this fitting result is also
plotted in Figure 7a.
The temperature dependences of C /T [=(C − C )/T]
and the magnetic entropy Smag (=∫ (C /T′) dT′) below 150
Figure 9. (a) Total and partial DOS of total electrons of Lu, Cr1, Cr2,
and S for Lu CrS (GGA + U with U = 5.0 eV). (b) Partial DOS of the
Cr 3d orbitals. The zero energy is placed at the highest occupied state.
mag
p
lat
2
4
T
0
mag
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calculations. In this calculation, the Cr deficiency was
considered by removing half of the Cr2 atoms at the 8d site
in a 2 × 2 × 1 supercell. The values of U for Hubbard-like
effective potentials of Cr1 and Cr2 were set to be 5.0 eV. In
Figure 9a, the occupied and unoccupied bands form a band gap
of ∼1.5 eV around the Fermi level and are consistent with the
result of the UV−vis spectra. The results from the GGA + U
calculations demonstrate that the Cr ions are in the divalent
state with the high-spin configuration and have the magnetic
moments of 3.37 μ per Cr1 atom and 3.45 μ per Cr2 atom.
B
B
Figure 9b shows the partial DOS of the Cr1 and Cr2 3d
2
2
orbitals. The energy levels of the unoccupied orbitals (dx −y
)
for the Cr spin-up states and all of the Cr spin-down orbitals
2
2
are located at 2−8 eV, which indicates that the spin-up d
x −y
2+
states correspond to one e hole for the spin-up Cr states. On
g
2
2
the other hand, the occupied spin-up d3
states are
r −z
delocalized over all of the S p bands and split up into two
peaks just below E and at around −3 eV, forming a bonding/
F
2
2
antibonding gap due to strong Cr d
These DOS for the spin-up d3
−S p σ bondings.
3
r −z
z
2
2
2
2
and d
states reveal that
r −z
x −y
the e bands of the Cr 3d electrons split into the occupied and
g
unoccupied states due to Jahn−Teller distortion for the Cr1S6
and Cr2S6 octahedra and suggest that the superexchange
2
2
2
2
interactions via the Cr d
−S p −Cr d
and/or Cr
3
r −z
z
3r −z
2
2
2
2
d3 −S p −S p −Cr d
paths play a key role in AFM
r −z
z
z
3r −z
ordering.
3.6. Magnetic Structure. Figure 10 shows the ND profiles
of Lu CrS at 10, 80, and 300 K using a wavelength of 1.8449 Å.
2
4
Only the nuclear Bragg reflections are observed at 80 and 300
K, and the crystal structure was refined by the Rietveld method.
The obtained parameters are in good agreement with those
obtained from the XRD measurement. The structural
parameters at 80 K are summarized in Table S1 in the
Supporting Information.
Figure 10. ND profiles for Lu CrS4 at 10, 80, and 300 K. The
2
calculated and observed diffraction profiles are shown as the top solid
line and the markers, respectively. The trace at the bottom is a plot of
the difference between the calculated and observed intensities. For the
profiles at 80 and 300 K, the set of vertical markers in the middle show
positions calculated from nuclear Bragg reflections. For the profile at
1
0 K, the upper set of vertical markers in the middle show positions
In the ND profile at 10 K, several additional Bragg reflections
appear. The temperature dependence of the magnetic
calculated from nuclear Bragg reflections. The lower set of vertical
markers in the middle show positions calculated from magnetic Bragg
reflections.
susceptibility of Lu CrS has a maximum around 60 K, and
2
4
the specific heat shows long-range AFM ordering at 55 K. It is
considered that these additional Bragg reflections at 10 K are
attributable to magnetic scatterings of long-range AFM
ordering of the Cr ions. The magnetic Bragg reflections are
components of these independent sites are listed in Table 3,
and the magnetic structures in the nuclear unit cell are
1
1
1
3
indexed to the ( / , / , l) and ( / , / , l) planes, which
2
2
2
2
Table 3. Possible Magnetic Structure Model for Lu CrS at
2
4
indicates that the propagation vector k in the magnetic ordered
10 K
1
1
state is k = ( / , / , 0).
2
2
atom
site
4a
g
x
a
y
z
mZ
+
The symmetry and directions of the magnetic moments
compatible with the crystal symmetry (I42d) were obtained
using the program SARAh. The decompositions of magnetic
Cr1
1.0
1.0
0.5
0.5
0.5
0.5
0
0
α
0
0
̅
34
1
1
/
1/
/
1/
1/8
7/8
7/8
+
2
4
4
(
2)
representations are Γ = 6Γ for both the 4a (Cr1) and 8d
Cr2
8d
8
0
mag
1
a
3/4
(
Cr2) sites. The constraint from the Landau theory requires six
−α
/4
3/4
−
−
0
1
a
possible magnetic structures for each Cr ion. In general, in the
case of the second-order magnetic phase transition, one
magnetic structure model should be obtained from the
combination of 12 possible directions of the magnetic moments
−α
a
α
a
α ∼ 0.76.
(
2)
(2)
Γ
= 6Γ1 (Cr1) + 6Γ (Cr2), but the magnetic peak profile
mag
1
fittings using the simple model did not agree with the observed
magnetic reflections.
illustrated in Figure 11. There exist 16 90° Cr1−S−Cr2 (J )
1
superexchange interactions and 4 180° Cr2−S−Cr2 (J )
2
Then, we attempted refinement using magnetic structures
with two sets of models constrained by the Landau theory. The
best results of the refinements indicated that most of the
components of the magnetic moments were the z components
as the following model. The Cr1 site has two magnetic
independent sites, and the Cr2 site has four magnetic
independent sites. The positive and negative signs of the z
superexchange interactions in the nuclear unit cell. For the
proposed model, because of quenching of the magnetic
moments of four Cr2 sites in the magnetic structure, eight J1
paths and all J paths vanish. Consequently, there remain eight
2
J1 paths between the nearest-neighbor magnetic moments, and
two arrays are parallel and the other six arrays are antiparallel.
According to the Goodenough−Kanamori rules, because the
9
807
DOI: 10.1021/acs.inorgchem.5b01511
Inorg. Chem. 2015, 54, 9802−9809

Inorganic Chemistry
Article
band-gap energy, divalent high-spin state of Cr, and Jahn−
Teller distortion were supported by the calculated results of the
DOS.
ASSOCIATED CONTENT
Supporting Information
■
*
S
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.5b01511.
CIF files giving structural data of Lu CrS at room
2
4
temperature (XRD) (CIF)
CIF files giving structural data of Lu CrS at 80 K (ND)
2
4
(CIF)
Synthesis of CrS, level splitting of the 3d orbitals in
Jahn−Teller distortion, and crystallographic data at 80 K
(PDF)
Figure 11. Possible magnetic structure models of the Cr moments: (a)
magnetic structure models constrained by the Landau theory; (b)
model of their combination. The z components of the magnetic
moments of blue and red spheres are antiparallel to each other. The
white Cr spheres mean quenching of the contribution to the magnetic
structure factors because of the offset between the up and down
moments.
AUTHOR INFORMATION
Corresponding Author
E-mail: ktez@cc.utsunomiya-u.ac.jp.
■
*
Notes
The authors declare no competing financial interest.
4
1
80° and 90° superexchange interactions between high-spin d
electrons are predicted to be quasistatic ferromagnetic and
ACKNOWLEDGMENTS
This work was partially supported by JSPS KAKENHI Grant
9750040.
■
1
35
quasistatic AFM, respectively, the magnetic interactions
between the Cr2+ ions are expected to be competitive. In
addition to the deficiency of the Cr2 sites, these competitive
interactions are reflected in the complicated magnetic structure.
Unfortunately, even refinements using the combination of two
sets of magnetic structure models could not achieve a good
agreement between the calculated and observed magnetic Bragg
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