Extended solid-state materials based on the hexagonal perovskite framework are typified by close competition between localized magnetic interactions and quasi-molecular electronic states. Here, we report the structural and magnetic properties of the new six-layer hexagonal perovskite Ba3CaMo2O9. Neutron diffraction experiments, combined with magnetic susceptibility measurements, show that the Mo2O9 dimers retain localized character down to 5 K and adopt nonmagnetic spin-singlet ground states. This is in contrast to the recently reported Ba3SrMo2O9 analogue, in which the Mo2O9 dimers spontaneously separate into a mixture of localized and quasi-molecular ground states. Structural distortions in both Ba3CaMo2O9 and Ba3SrMo2O9 have been studied with the aid of distortion mode analyses to elucidate the coupling between the crystal lattice and electronic interactions in 6H Mo5+ hexagonal perovskites.
Extended solid-state materials based on the hexagonal perovskite framework are typified by close competition between localized magnetic interactions and quasi-molecular electronic states. Here, we report the structural and magnetic properties of the new six-layer hexagonal perovskite Ba3CaMo2O9. Neutron diffraction experiments, combined with magnetic susceptibility measurements, show that the Mo2O9 dimers retain localized character down to 5 K and adopt nonmagnetic spin-singlet ground states. This is in contrast to the recently reported Ba3SrMo2O9 analogue, in which the Mo2O9 dimers spontaneously separate into a mixture of localized and quasi-molecular ground states. Structural distortions in both Ba3CaMo2O9 and Ba3SrMo2O9 have been studied with the aid of distortion mode analyses to elucidate the coupling between the crystal lattice and electronic interactions in 6H Mo5+ hexagonal perovskites.
Transition metal oxides (TMOs) display
a wealth of exotic physical
phenomena due to the intrinsic coupling between their lattice and
electronic degrees of freedom. In recent years, extended solid-state
TMOs containing closely spaced transition metal atoms have attracted
widespread interest for their ability to form clustered quasi-molecular
(QM) states.[1] Typically, these “orbital
molecules” manifest as a result of orbital ordering and direct
bonding between the metal atoms.[2] A pertinent
example is found in the naturally occurring mineral magnetite (Fe3O4), in which subtle contractions in the Fe2+–Fe3+ distances accompany the formation
of three-site Fe3+–Fe2+–Fe3+ bonded trimerons.[3,4] In general, such metal–metal
bonded clusters arise when the geometrical connectivity between neighboring
atoms imposes considerable overlap between the metal d orbitals; in
particular, materials with edge-sharing or face-sharing polyhedra
are promising in this regard,[5] with other
notable examples including TMOs such as VO2,[6,7] Li2RuO3,[8,9] and Y2Mo2O7.[10] Orbital molecules
are often formed in tandem with metal–insulator transitions
and are characterized by spin-gapped magnetic excitations. As such,
orbital molecules exhibit fundamentally interesting physical properties
that may hold future applications in spintronic or orbitronic technologies.In recent years, orbital molecules have been proposed to emerge
in hexagonal perovskites of the form Ba3B′Ru2O9 (B′ =
Na;[11] Y, In, and Lu;[12] and Ce[13]). These materials crystallize
in a six-layer hexagonal (6H) structure consisting of corner-sharing B′O6 octahedra and face-sharing M2O9 bioctahedral dimers (Figure a). The M2O9 dimers are characterized by short intradimer M–M distances that favor electronic
interactions between the metal atoms. When M is a
4d/5d transition metal (such as Ru or Ir), the spatially diffuse t2g orbitals can overlap, and with sufficiently
weak Hund’s coupling, direct M–M bonds can then form between the metal atoms.[14,15] However, some Ba3B′M2O9 compositions retain localized magnetic
moments on the metal atoms so that, in this case, the M2O9 dimers are better described as unbonded
cluster magnets (rather than orbital molecules).[16−19] This is due to the strong competition
between Hund’s coupling and M–M bonding in a face-sharing polyhedral geometry.[20,21] Such geometries are idiosyncratic motifs of hexagonal perovskites,
so these materials present a particularly promising phase space in
which to discover and study new orbitally molecular species.
Figure 1
Crystal structures
of Ba3CaMo2O9 at (a) 290 K (space
group: P63/mmc) and (b)
5 K (space group: Pnma). Projections
of the P63/mmc and Pnma structures down the long axes are provided in panels
(c) and (d), respectively.
Crystal structures
of Ba3CaMo2O9 at (a) 290 K (space
group: P63/mmc) and (b)
5 K (space group: Pnma). Projections
of the P63/mmc and Pnma structures down the long axes are provided in panels
(c) and (d), respectively.We have recently reported an unprecedented mechanism
of electronic
phase separation (EPS) in the 6H-perovskite Ba3SrMo2O9.[22] A single hexagonal P63/m phase is observed at room
temperature (P63/m-Ba3SrMo2O9), but upon cooling below 230
K, a new and electronically distinct monoclinic P21/m phase emerges (P21/m-Ba3SrMo2O9) and coexists with the primary phase down to 1.6 K. P63/m-Ba3SrMo2O9 features localized Mo2O9 spin dimers, while P21/m-Ba3SrMo2O9 contains a 50:50 mixture
of Mo–Mo bonded Mo2O9 orbital molecules
and localized spin dimers. The observed phase separation appears to
have an electronic origin related to competition between Mo–O–Mo
superexchange and direct Mo–Mo bonding. This contrasts established
electronic materials such as colossal magnetoresistant manganite perovskites,
where EPS appears to depend on the presence of some chemical disorder.[23,24] 6H-Ba3B′Mo2O9 compositions hence comprise a promising new system in which to study
how unusual electronic states emerge from competing orbital and magnetic
interactions.Here, we report the synthesis and characterization
of the new 6H-perovskite
Ba3CaMo2O9. Our neutron scattering
experiments reveal that Ba3CaMo2O9 undergoes a structural phase transition near 200 K, but, unlike
Ba3SrMo2O9, no phase separation is
observed down to 5 K. Magnetic susceptibility measurements, combined
with our neutron scattering experiments, show that the Mo2O9 dimers adopt a nonmagnetic ground state but do not
appear to have QM character. The diffraction data of both Ba3CaMo2O9 and Ba3SrMo2O9 have been further probed by distortion mode analysis to explore
the structural features that dictate orbital molecule formation in
this structure type.
Experimental Section
Polycrystalline samples of Ba3CaMo2O9 were synthesized via a standard
solid-state reaction. Stoichiometric
quantities of BaCO3 (99.999%, Aldrich), CaCO3 (Purity, Aldrich), and MoO3 (99.5 +%, Aldrich) were ground
and pressed into 13 mm pellets before being heated in air to 900 °C
for 10 h. The pellets were then reground and repressed before heating
under 5% H2/N2 at 1150 °C for 20 h, with
one intermittent regrinding after 10 h.X-ray diffraction (XRD)
measurements were recorded on a Panalytical
EMPYREAN diffractometer equipped with a Johansson monochromator (Cu
Kα1 radiation, λ = 1.5406 Å). Scans were recorded
for 1 h in the range of 10–100° with a 0.013° step
size. High-resolution neutron powder diffraction (NPD) data were collected
on a D2B diffractometer at the Institut Laue-Langevin (ILL) in Grenoble
(λ = 1.59432 Å). The sample was placed in an 8 mm vanadium
can and measured on heating at selected temperature intervals between
5 and 290 K. Scans were recorded for 2 h at each temperature. High-intensity
NPD data were also collected on the D20 diffractometer at the ILL
(λ = 2.40 Å) for 1.5 h at 5, 150, and 290 K to check for
long-range magnetic ordering.Rietveld refinements[25] were performed
using the GSAS/EXPGUI software.[26,27] The background was
modeled using a Chebyschev polynomial with 11 background coefficients,
while peak profiles were modeled using a pseudo-Voigt function. Distortion
mode analyses were performed using the ISODISTORT[28,29] and AMPLIMODES[30] programs.DC magnetization
measurements were performed on a Quantum Design
SQUID magnetometer between 2 and 400 K. Data were collected after
zero-field-cooling (ZFC) the sample in an applied field of 50 Oe.
Heat capacity measurements were recorded on a Quantum Design PPMS
from 2 to 300 K in 5 K intervals. DC resistivity measurements were
also performed on a PPMS using the four-probe method on a polycrystalline
bar between 4 and 300 K.
Results
Rietveld refinement from high-resolution XRD
and NPD data shows
that Ba3CaMo2O9 crystallizes in the
hexagonal P63/mmc space
group at room temperature (RT). The fit to the P63/mmc model at 290 K from NPD data collected
on D2B is shown in Figure S1, while selected
crystallographic data are reported in Table S1. An excellent fit to the P63/mmc structural model (Figure a) is observed, and there is no sign of any impurity
phases. The P63/mmc model
is the typical crystal structure adopted by 6H-Ba3B′M2O9 compositions.
Ba3CaMo2O9 then differs from the B′ = Sr analogue, which instead crystallizes in the P63/m space group at 290 K due
to in-phase tilting of the SrO6 octahedra about the hexagonal c axis.[22] The atomic site occupancies
could be refined to within ±1% of their nominal values and were
thus fixed at 1 for the remainder of the refinements. There is no
evidence of chemical disorder between the Ca and Mo sites; additionally,
the large difference in ionic radii between Ca2+ and Mo5+ (1.00 Å vs 0.61 Å, respectively[31]) makes this highly unlikely. Selected bond distances and
angles at 290 K are reported in Table S2. Bond valence sum (BVS) calculations gave a value of BVS(Mo) = 5.11(1),
which is in good agreement with the nominal +5 oxidation state.Variable-temperature NPD measurements recorded on D2B confirmed
that Ba3CaMo2O9 retains the P63/mmc structure down to 230
K. Below 200 K, a structural phase transition occurs as evidenced
by the appearance of new peaks in the diffraction pattern. It was
not possible to obtain a good fit to the previously reported structural
models for 6H-perovskites, such as Cmcm for Ba3CoRu2O9[16] or C2/c for Ba3CaIr2O9.[32] Attempts to perform
Rietveld fits with all direct subgroups of P63/mmc were also unsuccessful. However, very
good fits were obtained to two structural models described by the Pnma and P21/m space groups (Rwp = 4.34 and 4.28% for Pnma and P21/m, respectively, at 5 K). We found no evidence of any intermediate
phase transition that might favor one of these two options, and close
examination of the diffraction patterns found that the P21/m model offered no tangible improvement
to the peak positions, intensities, or profiles. Ultimately then, Pnma was selected as the correct space group assignment.The Rietveld fit and crystallographic data for the Pnma structural model at 5 K are provided in Figure and Table S3.
Selected bond lengths and angles for the Pnma phase
at this temperature are reported in Table S4. The Pnma structure (Figure b) accounts for tilting of the CaO6 octahedra along the orthorhombic [001] and [101] directions but
does not generate any additional Ca or Mo crystallographic sites.
This is in contrast to P21/m-Ba3SrMo2O9, in which there are
two crystallographically inequivalent Sr and Mo sites. The Pnma structure is retained down to 5 K.
Figure 2
Rietveld fit to the Pnma structural model from
NPD data collected on D2B at 5 K for Ba3CaMo2O9.
Rietveld fit to the Pnma structural model from
NPD data collected on D2B at 5 K for Ba3CaMo2O9.No magnetic diffraction peaks were detected on
the high-intensity
D20 diffractometer down to 5 K. Ba3CaMo2O9 was too resistive to measure from our DC resistivity measurements,
showing that it is an insulator below 300 K. Heat capacity measurements
confirmed that the structural transition occurs at 220 K (Figure S2). Variable-temperature magnetic susceptibility
(χ(T)) measurements (Figure ) corroborated the lack of long-range magnetic
ordering down to 4 K so that the structural transition at 220 K is
not tied to magnetic ordering of the Mo5+ moments. At low
temperatures, a paramagnetic Curie tail is observed, while above 44
K, χ(T) weakly increases as a function of temperature.
A small Curie constant of 3.55(2) × 10–3 emu
K Oe–1 mol–1 was extracted from
an initial Curie–Weiss fit of the data below 44 K (shown in Figure a); we attribute
this to minor magnetic impurities or structural defects in the sample.
A subtraction of the Curie–Weiss contribution from χ(T) shows that the residual magnetic contribution tends to
zero with cooling. This response is reminiscent of spin-gapped materials
such as La4Ru6O19[33] or SrCu2O3[34] and shows that Mo2O9 dimers in Ba3CaMo2O9 have a spin-gapped nonmagnetic ground
state.
Figure 3
(a) Variable-temperature magnetic susceptibility (χ(T)) measurements of Ba3CaMo2O9. The initial Curie–Weiss (C-W) fit is shown by the
solid black line, and its subtraction from χ(T) is shown in purple. (b) Fit to the spin-gap function listed in
the main text, with additional temperature-independent (χ0) and C-W terms.
(a) Variable-temperature magnetic susceptibility (χ(T)) measurements of Ba3CaMo2O9. The initial Curie–Weiss (C-W) fit is shown by the
solid black line, and its subtraction from χ(T) is shown in purple. (b) Fit to the spin-gap function listed in
the main text, with additional temperature-independent (χ0) and C-W terms.Prior to the fit, a diamagnetic correction was
performed. To fit
the full susceptibility response χ(T), we used
a modified spin gap expression of the form χSG = a(T) exp(−Δ/kBT)[35] (Figure b). This expression
accounts for spin-gapped Mo2O9 dimers in which
there is a gap between a nonmagnetic singlet state and a triplet excited
state. Similar functions have been used to model spin gaps in previous
6H-perovskites such as Ba3BiRu2O9[36,37] and Ba3BiIr2O9.[38] In Ba3CaMo2O9, the spin gap expression—including additional temperature-independent
and C-W terms—gives an excellent fit to χ(T) up to 320 K. From the fit, the following parameters were extracted:
χ0 = 3.571(1) × 10–4 emu Oe–1 mol–1, Cimp = 3.35(1) × 10–3 emu K Oe–1 mol–1, θ = −0.23(1) K, a = 6.54(1) × 10–3 emu Oe–1 mol–1 K–0.5, and Δ/kB = 233(1) K.
Discussion
The structural and physical properties of
Ba3CaMo2O9 are surprisingly different
from Ba3SrMo2O9. Most notably, no
phase separation
is observed in Ba3CaMo2O9 down to
5 K as demonstrated by our high-resolution diffraction measurements.
The Mo2O9 dimers are described well by a simple
model of spin-gapped dimers, and there is no pronounced asymmetry
in the χ(T) curve that would suggest that a
more complex mixture of dimers forms (as previously observed for Ba3SrMo2O9). The properties of the spin
dimers do not appear to be affected by the structural transition near
200 K, and there is also no marked lattice contraction (Figure S3). Therefore, the spin dimers in Ba3CaMo2O9 are not strongly coupled to
the crystal lattice.Figure compares
the Mo–Mo distances in Ba3SrMo2O9 and Ba3CaMo2O9. Close inspection
of the Mo–Mo distances in the Ca analogue (Figure S4) reveals that no Mo–Mo bond forms upon cooling.
The Mo–Mo separation in Ba3CaMo2O9 is 2.523(3) Å at 290 K and remains largely similar with
cooling so that the Mo–Mo separation is 2.527(3) Å at
5 K. This is in contrast to the QM Mo2O9 dimers
in P21/m-Ba3SrMo2O9, where the Mo–Mo distances contract
by ∼4% below 230 K due to the formation of a Mo–Mo bond.
The Mo t2g orbitals in Ba3CaMo2O9 are hence too far apart to hybridize and form
a quasi-molecular electronic state. Competition between Mo–Mo
bonding and Mo–O–Mo superexchange is therefore less
pronounced in Ba3CaMo2O9 than in
Ba3SrMo2O9.
Figure 4
Comparison of the Mo–Mo
distances in Ba3B′Mo2O9 (B′ = Ca and Sr22). “AFM” and “QM”
refer to the antiferromagnetic spin dimers and quasi-molecular Mo2O9 clusters, respectively, in Ba3SrMo2O9.
Comparison of the Mo–Mo
distances in Ba3B′Mo2O9 (B′ = Ca and Sr22). “AFM” and “QM”
refer to the antiferromagnetic spin dimers and quasi-molecular Mo2O9 clusters, respectively, in Ba3SrMo2O9.Due to the differing structural and magnetic properties
of Ba3CaMo2O9 and Ba3SrMo2O9, we explored sources of structural coupling
in these
materials that may influence whether localized spin dimers are obtained
over quasi-molecular clusters. We performed distortion mode analyses
using the ISODISTORT[28,29] and AMPLIMODES[30] programs to examine the behavior of structural degrees
of freedom in both compositions. Distortion modes comprise symmetry-adapted
linear combinations of irreducible representations that relate a high-symmetry
crystal structure to a lower-symmetry counterpart. In particular,
distortion modes describe symmetry-related sets of collective atomic
displacements that represent distinct structural degrees of freedom
(for example, octahedral rotations or ferroelectric polarizations).
Each mode is quantified by an amplitude that describes the magnitude
of the deviation from the high-symmetry structure and denotes its
contribution to the total distortion observed. Hence, the advantage
of this approach is that it can identify and characterize distinct
structural degrees of freedom that produce a structural distortion.
For Ba3CaMo2O9, the amplitudes of
each distortion mode were derived and normalized with respect to the
parent P63/mmc unit cell.
Three distortion modes are active in the low-temperature Pnma structure, corresponding to the irreducible representations Γ1+, Γ5+, and Μ2+. Their amplitudes are shown in Figure a, while the effects of the
Γ5+ and Μ2+ modes on the crystal structure are depicted in Figure b and Figure c, respectively. The Γ1+ mode is a minor strain mode resulting from the overall compression
of the unit cell along c with cooling. The Γ1+ mode shows no abrupt variation across the structural
transition and is not associated with any octahedral tilting distortion.
The Γ5+ mode consists of an in-phase tilting
distortion of the CaO6 octahedra about the orthorhombic
[001] direction, while the Μ2+ mode consists
of an out-of-phase tilt of the CaO6 octahedra about the
[101] direction. Overall, these tilting modes serve to “buckle”
the Mo2O9 dimers; despite this disruption to
the local MoO6 octahedral environment below the structural
transition, the lack of any accompanying change in the magnetic susceptibility
(Figure b) shows that
the magnetic properties of the Mo2O9 dimers
are largely insensitive to the structural distortion. As this distortion
does not appear to be tied to any specific electronic instability,
it is instead driven by purely structural fluctuations. This substantiates
the lack of Mo–Mo bond formation at the transition and ultimately
reflects the localized character of the Mo2O9 spin dimers. This is a notable contrast to Ba3SrMo2O9, where distinct changes in the magnetic susceptibility
can be identified at the phase separation temperature[22] so that the magnetic and electronic properties of the dimers
are more sensitive to the distortion of the local MoO6 environment.
Figure 5
Distortion
mode analysis of the structural transition to the Pnma phase in Ba3CaMo2O9. (a) Variable-temperature
mode amplitudes, normalized with respect
to the parent P63/mmc structure; error bars are too small to be visible. (b) Γ5+ distortion mode, corresponding to an in-phase
rotation of the CaO6 octahedra about the orthorhombic [001]
direction. (c) Μ2+ distortion mode, corresponding
to an anti-phase rotation of the CaO6 octahedra about the
orthorhombic [101] direction. The arrows in panels (b, c) highlight
the rotations of the CaO6 octahedra and Mo2O9 dimers.
Distortion
mode analysis of the structural transition to the Pnma phase in Ba3CaMo2O9. (a) Variable-temperature
mode amplitudes, normalized with respect
to the parent P63/mmc structure; error bars are too small to be visible. (b) Γ5+ distortion mode, corresponding to an in-phase
rotation of the CaO6 octahedra about the orthorhombic [001]
direction. (c) Μ2+ distortion mode, corresponding
to an anti-phase rotation of the CaO6 octahedra about the
orthorhombic [101] direction. The arrows in panels (b, c) highlight
the rotations of the CaO6 octahedra and Mo2O9 dimers.In Ba3CaMo2O9,
the Μ2+ mode forms the dominant contribution
to the observed
distortion. Analysis of the group–subgroup relations between
the P63/mmc and Pnma space groups confirms that the Μ2+ mode forms the primary order parameter of the transition
as it is the only mode capable of producing the final Pnma symmetry. Pnma is not a direct subgroup of P63/mmc, so the transition is
necessarily first order. Despite this, the unit cell volume shows
no clear contraction upon cooling below the phase transition temperature
(Figure S5), which would appear to be inconsistent
with a first-order transition. However, Figure shows that the Μ2+ mode amplitudes (X) can be fit to a critical equation
of the following form:where Xu and X0 are the amplitudes at
the transition temperature (Tu) and 0
K, respectively, W is a fitting parameter
(W ≈ 2), and tu is the reduced temperature defined as tu = (Tu – T)/Tu. This empirical expression describes the critical
variation of order-parameter-like structural quantities below a phase
transition.[39]Equation is particularly successful in describing
the variations of such quantities at temperatures well below the transition
temperature (T ≪ Tu); hence, it can be used to model the behavior of distortion modes
across extended temperature ranges. Equation has been used previously to model the behavior
of structural quantities that vary as order parameters in materials
featuring quasi-molecular clusters such as Fe3O4[39] and GaV2O4.[40] Here, a transition temperature of Tu = 225 K was extracted from the fit (Figure ), which is in excellent agreement
with the temperature determined from our heat capacity measurements.
The parameters X0 and Xu can also be compared to characterize the behavior of
the transition, that is, whether the structural distortion is largely
frozen below Tu (Xu/X0 ≈ 1), or whether it
is quasi-continuous in character (Xu/X0 ≈ 0).[39] Frozen
transitions feature largely temperature-invariant structural changes
below Tu, whereas quasi-continuous transitions
display more temperature-dependent behavior. In the case of Ba3CaMo2O9, the ratio Xu/X0 ≈ 0.45 tends toward
the quasi-continuous limit over the frozen limit. This explains the
lack of any notable discontinuity in unit cell volume upon cooling
below the structural transition. It appears then that thermal effects
largely dictate the structural behavior of Ba3CaMo2O9, and the transition does not appear to be tied
to any specific electronic instability. This substantiates the lack
of Mo–Mo bond formation at the transition and ultimately reflects
the localized character of the Mo2O9 spin dimers.
Figure 6
Temperature
dependence of the Μ2+ distortion
mode in Ba3CaMo2O9. The solid cyan
line depicts the fit to the order-parameter-like expression given
in the main text.
Temperature
dependence of the Μ2+ distortion
mode in Ba3CaMo2O9. The solid cyan
line depicts the fit to the order-parameter-like expression given
in the main text.We performed a comparative distortion mode analysis
on Ba3SrMo2O9 based on our previously
reported NPD
data.[22] The distortion mode amplitudes
for both phases of Ba3SrMo2O9 are
shown in Figure .
Here, the distortion modes have been labeled with respect to the parent P63/m symmetry as the P63/mmc phase has not been reported
for Ba3SrMo2O9. For the P63/m phase, the low-temperature distortion
is described by a single Γ1+ mode. Predominantly,
the Γ1+ mode corresponds to in-phase tilting
of the SrO6 octahedra and Mo2O9 dimers
about the hexagonal c axis; in 6H-perovskites, this
distortion has been canonically attributed to the size mismatch between
the B′ and M sites.[41] The amplitude of the Γ1+ mode in P63/m-Ba3SrMo2O9 shows a discontinuous
increase below 210 K (Figure a). Interestingly, this discontinuity overlaps with a previously
identified lattice anomaly in this phase, where there is an abrupt
contraction of the lattice along c below 210 K without
any accompanying structural transition.[22] We previously showed that the phase fractions of the P63/m and P21/m phases in Ba3SrMo2O9 were sensitive to this lattice anomaly: the weight fraction
of the P21/m phase attains
a maximum of 47.6% at 210 K, but this fraction gradually decreases
below this temperature so that the lattice anomaly promotes the P63/m phase instead. The distortion
stemming from the Γ1+ mode is then associated
with the anomalous lattice contraction in this phase. We also note
that the amplitude of this mode correlates with the Mo–O(1)–Mo
bond angles (Figure S6), where the Mo–O(1)–Mo
bond angles tend toward the ideal angle for magnetic superexchange
interactions. This structural correlation suggests that the lattice
anomaly serves to promote intradimer superexchange pathways in P63/m-Ba3SrMo2O9 so that this is the mechanism by which the P63/m phase becomes favored
over the P21/m phase
upon further cooling.
Figure 7
Distortion mode analyses of the (a) P63/m and (b) P21/m phases of Ba3SrMo2O9.
Mode amplitudes were derived and normalized with respect to their
respective parent unit cells. Where not apparent, error bars are smaller
than the data points. Data for the P21/m phase at 230 K have been omitted as the small
phase fraction at this temperature did not allow for a reliable quantification
of the mode amplitudes.
Distortion mode analyses of the (a) P63/m and (b) P21/m phases of Ba3SrMo2O9.
Mode amplitudes were derived and normalized with respect to their
respective parent unit cells. Where not apparent, error bars are smaller
than the data points. Data for the P21/m phase at 230 K have been omitted as the small
phase fraction at this temperature did not allow for a reliable quantification
of the mode amplitudes.For P21/m-Ba3SrMo2O9, there are three distortion
modes active
in the low-temperature regime. The Γ1+ and Γ3,5+ modes predominantly correspond to in-phase tilting distortions of
the SrO6 octahedra about the pseudohexagonal c and a axes, respectively, while the M1+ distortion mode corresponds to an out-of-phase tilt
of the SrO6 octahedra about the pseudohexagonal b axis. The structural distortions in Ba3SrMo2O9 and its Ca analogue are hence largely similar,
with the notable exception of the SrO6 tilting associated
with the Γ1+ mode in Ba3SrMo2O9. The M1+ mode comprises
the dominant contribution to the structural distortion in P21/m-Ba3SrMo2O9 at lower temperatures (Figure b) so that it is the primary order parameter
for the transition. Although the Γ1+ mode
also has a significant amplitude in this phase, its amplitude shows
no apparently critical variation with cooling. This suggests that
this mode behaves as a secondary order parameter so that it is coupled
to the primary M1+ distortion. In contrast,
the M1+ mode shows an overall increase upon
cooling (Figure S7). The temperature variation
of the M1+ amplitude can be fit with the critical
expression given in eq , as shown in Figure S8. A transition
temperature of Tu = 241 K was extracted
from the fit, which is in agreement with the experimental temperature
previously identified from neutron diffraction and heat capacity measurements.
The transition is also characterized by the ratio Xu/X0 = 0.80, suggesting that
Ba3SrMo2O9 tends toward the frozen
limit over the quasi-continuous limit.Closer examination of
the individual atomic displacements for Ba3SrMo2O9 reveals a subtle distinction
to its B′ = Ca counterpart. The M1+ mode in P21/m-Ba3SrMo2O9 changes the intradimer
Mo–Mo distances according to the [Mo:f]A(a) displacement (Figure ). The two crystallographically
distinct Mo2O9 dimers in this phase feature
an antiferrodistortive displacement of the Mo atoms along c so that they displace toward each other within the QM
clusters and away from each other within the AFM spin dimers. In contrast,
the displacement of the Mo atoms in Ba3CaMo2O9 is limited by symmetry to the Μ2+ [Mo:f]E(a) distortion, which corresponds to an antiferrodistortive
displacement within the pseudohexagonal basal plane; as the intradimer
Mo–Mo distances lie parallel to the crystallographic long axis,
there is hence no contraction of the intradimer Mo–Mo distances
in Ba3CaMo2O9. Mo–Mo bonding
is therefore strongly coupled to the crystal lattice in P21/m-Ba3SrMo2O9, and the near-frozen character of the structural transition
in this phase reflects the crystallization of the QM dimer network.
In contrast, there appears to be no such behavior in Ba3CaMo2O9 so that orbital molecules do not form
in this composition and the electrons remain entangled in a localized
spin state. It is likely that the more covalent Ca–O bond draws
electron density away from the Mo2O9 dimers
so that Mo–Mo bonding is less favored than in the B′ = Sr counterpart.
Figure 8
Asymmetric M1+ [Mo:f]A(a)
displacement in
Ba3SrMo2O9. Quasi-molecular dimers
are shown in pink, while the localized spin dimers are shown in blue.
Asymmetric M1+ [Mo:f]A(a)
displacement in
Ba3SrMo2O9. Quasi-molecular dimers
are shown in pink, while the localized spin dimers are shown in blue.
Summary
Ba3CaMo2O9 is a novel 6H-perovskite
featuring localized Mo2O9 spin dimers below
320 K. A structural transition is observed near 200 K, but the electronic
and magnetic properties of the Mo2O9 dimers
appear to be largely insensitive to the resulting distortion so that
the transition does not produce Mo–Mo bonding. Our distortion
mode analyses suggest that tilting of the B′O6 octahedra along c in 6H-perovskites is correlated
with the intradimer superexchange pathways. Size mismatch between
the B′ and M sites could
hence constitute an appropriate chemical parameter to tune intradimer
exchange interactions and discover new ground states in new or existing
6H-perovskites. This approach could also be extended to other materials
featuring orbital molecules to probe the sensitive interplay between
bonding interactions and magnetic exchange.
Authors: Qiang Chen; Shiyu Fan; Keith M Taddei; Matthew B Stone; Alexander I Kolesnikov; Jinguang Cheng; Janice L Musfeldt; Haidong Zhou; Adam A Aczel Journal: J Am Chem Soc Date: 2019-06-12 Impact factor: 15.419
Authors: Wojciech Miiller; Maxim Avdeev; Qingdi Zhou; Brendan J Kennedy; Neeraj Sharma; Ramzi Kutteh; Gordon J Kearley; Siegber Schmid; Kevin S Knight; Peter E R Blanchard; Chris D Ling Journal: J Am Chem Soc Date: 2012-02-06 Impact factor: 15.419
Authors: Peter M M Thygesen; Joseph A M Paddison; Ronghuan Zhang; Kevin A Beyer; Karena W Chapman; Helen Y Playford; Matthew G Tucker; David A Keen; Michael A Hayward; Andrew L Goodwin Journal: Phys Rev Lett Date: 2017-02-08 Impact factor: 9.161
Authors: Simon A J Kimber; Mark S Senn; Simone Fratini; Hua Wu; Adrian H Hill; Pascal Manuel; J Paul Attfield; Dimitri N Argyriou; Paul F Henry Journal: Phys Rev Lett Date: 2012-05-24 Impact factor: 9.161
Authors: Struan Simpson; Michael Milton; Sacha Fop; Gavin B G Stenning; Harriet Alexandra Hopper; Clemens Ritter; Abbie C Mclaughlin Journal: Inorg Chem Date: 2022-07-19 Impact factor: 5.436