Crystal structure, physical properties, and electronic and magnetic structure of the spin S = 5/2 zigzag chain compound Bi2Fe(SeO3)2OCl3

Article abstract of DOI:10.1021/ic500706f

We report the synthesis and characterization of the new bismuth iron selenite oxochloride Bi₂Fe(SeO₃)₂OCl ₃. The main feature of its crystal structure is the presence of a reasonably isolated set of spin S = ⁵/₂ zigzag chains of corner-sharing FeO₆ octahedra decorated with BiO₄Cl ₃, BiO₃Cl₃, and SeO₃ groups. When the temperature is lowered, the magnetization passes through a broad maximum at T_max ≈ 130 K, which indicates the formation of a magnetic short-range correlation regime. The same behavior is demonstrated by the integral electron spin resonance intensity. The absorption is characterized by the isotropic effective factor g ≈ 2 typical for high-spin Fe³⁺ ions. The broadening of ESR absorption lines at low temperatures with the critical exponent β = ⁷/₄ is consistent with the divergence of the temperature-dependent correlation length expected for the quasi-one-dimensional antiferromagnetic spin chain upon approaching the long-range ordering transition from above. At T_N = 13 K, Bi ₂Fe(SeO₃)₂OCl₃ exhibits a transition into an antiferromagnetically ordered state, evidenced in the magnetization, specific heat, and Moessbauer spectra. At T < T_N, the ⁵⁷Fe Moessbauer spectra reveal a low saturated value of the hyperfine field H_hf ≈ 44 T, which indicates a quantum spin reduction of spin-only magnetic moment δS/S ≈ 20%. The determination of exchange interaction parameters using first-principles calculations validates the quasi-one-dimensional nature of magnetism in this compound.

Full text of DOI:10.1021/ic500706f

Article
pubs.acs.org/IC
Crystal Structure, Physical Properties, and Electronic and Magnetic
5
Structure of the Spin S = /2 Zigzag Chain Compound
Bi2Fe(SeO3)2OCl3
Peter S. Berdonosov,*,† Elena S. Kuznetsova,† Valery A. Dolgikh,† Alexei V. Sobolev,† Igor A. Presniakov,†
Andrei V. Olenev,‡,$ Badiur Rahaman,§ Tanusri Saha-Dasgupta,§ Konstantin V. Zakharov,∥
Elena A. Zvereva,∥ Olga S. Volkova,∥,⊥ and Alexander N. Vasiliev∥,⊥,#
†Faculty of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
‡Department of Chemistry, University of California, Davis, California 95616, United States
§S. N. Bose National Centre for Basic Sciences, Kolkata 700098, India
∥Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
⊥Theoretical Physics and Applied Mathematics Department, Ural Federal University, Ekaterinburg 620002, Russia
#National University of Science and Technology “MISiS”, Moscow 119049, Russia
S
* Supporting Information
ABSTRACT: We report the synthesis and characterization of
the new bismuth iron selenite oxochloride Bi2Fe(SeO3)2OCl3.
The main feature of its crystal structure is the presence of a
reasonably isolated set of spin S = 5/2 zigzag chains of corner-
sharing FeO6 octahedra decorated with BiO4Cl3, BiO3Cl3, and
SeO3 groups. When the temperature is lowered, the magnet-
ization passes through a broad maximum at Tmax ≈ 130 K,
which indicates the formation of a magnetic short-range
correlation regime. The same behavior is demonstrated by the
integral electron spin resonance intensity. The absorption is
characterized by the isotropic effective factor g ≈ 2 typical for
high-spin Fe3+ ions. The broadening of ESR absorption lines at low temperatures with the critical exponent β = 7/4 is consistent
with the divergence of the temperature-dependent correlation length expected for the quasi-one-dimensional antiferromagnetic
spin chain upon approaching the long-range ordering transition from above. At TN = 13 K, Bi2Fe(SeO3)2OCl3 exhibits a
transition into an antiferromagnetically ordered state, evidenced in the magnetization, specific heat, and Mossbauer spectra. At T
̈
< TN, the 57Fe Mossbauer spectra reveal a low saturated value of the hyperfine field H ≈ 44 T, which indicates a quantum spin
̈
hf
reduction of spin-only magnetic moment ΔS/S ≈ 20%. The determination of exchange interaction parameters using first-
principles calculations validates the quasi-one-dimensional nature of magnetism in this compound.
was seen in the sawtooth chain Rb2Fe2O(AsO4)2.13 All of these
compounds undergo three-dimensional ordering at low
temperatures resulting from the interchain coupling. The
more isolated the chains in a given compound, the more
INTRODUCTION
■
Magnetism in quasi-one-dimensional magnetic systems, which
are quantum in nature, is currently a hot topic due to the
diversity of exciting physical phenomena exhibited by them. To
mention a few, we note the observation of the spin-Peierls
transition in CuGeO3,1 the charge-driven and orbital-driven
pronounced the quantum aspect in properties is expected to be.
5
In the case of the S =
/ compound Mn2(OD)2(C4O4),
2
spin-Peierls-like transitions in NaV2O5 and NaTiSi2O6,3 the
2
inelastic neutron scattering measurements have revealed the
characteristic behavior of a spin liquid coexisting with a valence
bond solid. The departure from classical behavior observed in
the high-spin systems is generally assumed to originate from
low dimensionality and geometrical frustration.14
Compounds with magnetic ions distributed in low-dimen-
sional or layered structures are promising objects for observing
such effects. It is well-known that compounds containing
Bose−Einstein condensation of magnons in TlCuCl3,4 and the
spiral spin structures in LiCuVO4 and LiCu2O2.7−9 All of
5,6
these compounds are based on ions with a low spin value, i.e. S
= /2, where the quantum effects on physical properties are
most pronounced.
Less studied are classical quasi-one-dimensional magnetic
1
5
systems based on ions with high spin values: e.g., S = /2. The
low-dimensional behavior in classical magnetic systems was
found in particular in FeOHSO4,10 N2H6FeF5,11 and
SrMn2V2O8;12 however, no evidence of reduced dimensionality
Received: March 26, 2014
Published: May 13, 2014
© 2014 American Chemical Society
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elements with lone electron pair ions (I5+, Se4+, Te4+, As3+, Sb3+,
Bi3+, Pb2+, etc.) enhance the possibility to form low-
dimensional structures.15 The introduction of halide ions as
spacers into selenite(IV) or tellurite(IV) may increase the trend
to form low-dimensional crystal structure. Up to now, there
have been many prepared and characterized selenite and
tellurite halides. The most explored systems contain Cu2+ and
anisotropic atomic displacement parameters for all atoms. The
pertinent information related to unit cell parameters, data collection,
and refinement is provided in Table 1. Selected bond distances are
given in Table 2.
Table 1. Data Collection and Structure Refinement
Parameters for Bi2Fe(SeO3)2OCl3
1
Ni2+, due to the interest in spin /2 or 1 lattices or to the
composition
Bi2Fe(SeO3)2OCl3
monoclinic
formation of different coupling regimes.16 Systems with much
higher spin states have not yet been explored. Only
Cr3Te5O13Cl3,17 Fe6Ca2(SeO3)9Cl4,18 and Fe3+ tellurite hal-
ides19 are known up to now. To the best of our knowledge,
Fe6Ca2(SeO3)9Cl4 is the only known selenite halide that
contains Fe(III) ions. When this work was considered for
publication, the new iron selenite fluoride FeSeO3F was
described.19e In the crystal structure of this compound cis-
[FeO4F2] octahedra form Heisenberg antiferromagnetic
chains.19e
cryst syst
space group
P21/m (No. 11)
unit cell dimens
a, Å
8.570 (2)
7.137(2)
8.604(2)
107.090(3)
503.1(2)
2
b, Å
c, Å
β, deg
V, Å3
Z
calcd density, g/cm3
abs coeff, mm−1
temp, K
5.612
In the present study, we report the synthesis and crystal
structure determination of a new quasi-one-dimensional
compound, the bismuth iron selenite oxochloride Bi2Fe-
(SeO3)2OCl3, and its characterization through magnetization,
44.355
90(2)
wavelength, Å
θ range for data collection, deg
no. of rflns collected
no. of unique rflns
no. of params refined
R1, wR2 (I > 2σ(I))
R1, wR2 (all data)
largest diff peak and hole, e/Å3
goodness of fit on F2
0.710 73
2.4827.31
5393
specific heat, electron spin resonance, and 57Fe Mossbauer
̈
spectroscopy measurements. Significant quantum reduction of
1214
the spin-only value of the iron magnetic moment is found
78
through the analysis of the low-temperature Mossbauer spectra.
̈
0.0381, 0.0817
0.0540, 0.0889
3.111 and −3.543
0.999
The electronic and magnetic structures of Bi2Fe(SeO3)2OCl3
have been obtained through first-principles calculations. The
calculated parameters of nearest-neighbor intrachain J∥ and
next-nearest-neighbor intrachain J∥′ exchange interactions, as
well as interchain J⊥ exchange interactions, agree with
experimental data, supporting the quasi-one-dimensional nature
of the compound.
Table 2. Bond Lengths (Å) for Bi2Fe(SeO3)2OCl3
bond
Bi1−O3
distance
bond
Bi2−O3
distance
2.21(1)
2.70(1)
EXPERIMENTAL DETAILS
Bi1−O4
Bi1−O1 (×2)
Bi1−Cl1
Bi1−Cl2 (×2)
Bi2−O5
Bi2−O2 (×2)
Bi2−Cl1 (×2)
Bi2−Cl2
2.25(1)
Se1−O5
Se1−O1 (×2)
Se2−O4
Se2−O2 (×2)
Fe−O3 (×2)
Fe−O2 (×2)
Fe−O1 (×2)
1.67(1)
■
2.384(8)
2.869(4)
3.237(4)
2.43(1)
1.751(8)
1.68(1)
Originally single crystals of the new compound were found in the
reaction mixture of chemically pure BiOCl (0.2341 g, 0.899 mmol),
FeOCl (0.098 g, 0.913 mmol) and anhydrous SeO2 (0.202 g, 1.82
mmol) which was heated in a sealed quartz tube to 300 °C for 168 h.
FeOCl was obtained from a mixture of Fe2O3 (1.3457 g , 8.427 mmol)
and anhydrous FeCl3 (1.3620 g, 8.397 mmol) in a sealed, evacuated
quartz tube at 370 °C for 48 h similarly to the procedure in ref 20.
After a structure determination the composition of the compound
was confirmed by directed synthesis from a mixture of chemically pure
Bi2O3 (0.4792 g, 1.028 mmol), SeO2 (0.229 g, 2.064 mmol), and
FeCl3 (0.165 g, 1.017 mmol) at 300 °C for 60 h according to the
reaction
1.718(8)
1.980(5)
2.020(8)
2.041(8)
2.539(8)
2.589(4)
2.685(3)
Thermal decomposition of Bi2Fe(SeO3)2OCl3 was studied on a
NETZSCH STA 409 PC instrument under an argon atmosphere.
Samples (approximately 16 mg) were heated in an alumina crucible
from room temperature up to 1000 °C at a rate of 10 °C/min. The
resulting graph is presented in Figure S1 (Supporting Information).
The electron spin resonance (ESR) study was carried out using
using a CMS 8400 (ADANI) X-band ESR spectrometer (frequency
∼9.4 GHz, B ≤ 0.7 T) equipped with a low-temperature mount,
operating in the range 6−470 K. The effective g factor of the powder
sample of Bi2Fe(SeO3)2OCl3 was calculated with respect to the
external reference for the resonance field using BDPA (α,γ-
bis(diphenylene)-β-phenylallyl) as a reference material (get = 2.00359).
The thermodynamic properties of the Bi2Fe(SeO3)2OCl3 ceramic
sample, i.e. magnetization and specific heat, were measured with a
Quantum Design PPMS-9T Physical Property Measurement System.
Bi2O3 + 2SeO2 + FeCl3 = Bi2Fe(SeO3)2OCl3
The powder XRD pattern was indexed in the monoclinic space
group P21/m with cell constants a = 8.575(5) Å, b = 7.133(4) Å, c =
8.603(6) Å, and β = 107.04(3)°. These values are in good agreement
with single-crystal experimental results.
We have tried to prepare the bromide analogue of Bi2Fe-
(SeO3)2OCl3 by the same technique. All our attempts to do this
were unsuccessful.
The single crystal selected for the structure determination was
analyzed on a KAPPA APEX II diffractometer equipped with a CCD
detector. The data set was recorded as ω scans at 0.3° step width and
integrated with the Bruker SAINT software package.21 The data set
was indexed in the monoclinic primitive unit cell. The absorption
correction was based on fitting a function to the empirical transmission
surface as sampled by multiple equivalent measurements (SADABS).22
The solution and refinement of the crystal structure were carried out
using the SHELX suite of programs.23 It was solved in the space group
P21/m (No. 11), and the final refinement was performed with
The 57Fe Mossbauer spectra were recorded in the temperature
̈
range 4.6−300 K using a conventional constant-acceleration
spectrometer. The radiation source, 57Co(Rh), was kept at room
temperature. All isomer shifts refer to α-Fe at 300 K. The experimental
spectra were processed and analyzed using methods of spectral
simulation implemented in the SpectrRelax program.24
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Figure 1. Coordination surroundings of Bi(1), Bi(2), and Fe atoms in the crystal structure of Bi2Fe(SeO3)2OCl3.
First-principles calculations on a plane wave basis, as implemented
in VASP,25 were used to arrive at a self-consistent description of the
electronic structure of Bi2Fe(SeO3)2OCl3 within the framework of
density functional theory (DFT). The exchange-correlation functional
was chosen to be that of the generalized gradient approximation
(GGA).26
RESULTS AND DISCUSSION
■
Crystal Structure. In Bi2Fe(SeO3)2OCl3, the bismuth
atoms have mixed oxygen and chlorine surroundings (Figure
1). The bond valence sum (BVS) calculation27 with R0 and B
parameters taken from ref 28 according to the formula
BVS =
exp((R − R )/B)
∑
0
i
i
leads to 2.64 for Bi1 atoms in case of a strongly asymmetric
BiO4Cl polyhedron. The addition of two Bi1−Cl2 bonds with
lengths of more than 3 Å increases this value to 2.90. Therefore,
the coordination surroundings for Bi1 atoms may be
represented as the seven-vertex polyhedron Bi1O4Cl3. The
lone pair activity of the Bi1 atom may be the reason for such
asymmetrical surroundings. Bi2 atoms have six nearest
neighbors: i.e., three oxygen atoms at distances of 2.42−2.54
Å and three chlorine atoms at distances of 2.58−2.68 Å. The
BVS value for this polyhedron is 3.07. The polyhedron for the
Bi2 atom is a distorted Bi2O3Cl3 octahedron with the Bi2 atom
situated in the plane formed by two O2 and two Cl2 atoms
(Figure 1, Table 2). Fe(III) atoms are surrounded by six oxygen
atoms in the FeO6 octahedron with bond lengths in the range
1.98−2.04 Å (Figure 1, Table 2). The BVS value for this
polyhedron is 3.02. Selenium atoms are surrounded by oxygen
atoms only and form SeO3 groups with the pyramidal shape
SeO3E, where E is the lone pair of Se(IV). Se−O distances are
in the usual range: 1.67−1.75 Å (Table 2) (see for example refs
16 and 18). The BVS values are 3.84 and 4.02 for Se1 and Se2,
respectively.
FeO6 octahedrons are connected into zigzag chains by
common O3 vertexes. FeO6 octahedrons share O1−O3 edges
with the Bi1O4Cl3 polyhedron and O2 vertexes with the
Bi2O3Cl3 polyhedron. These Bi polyhedrons are connected by
common Cl1 and Cl2 vertexes. FeO6 octahedrons share O2 and
O1 vertexes with Se1O3 and Se2O3 groups. The third oxygen
atoms of Se1 and Se2 groups, i.e. O4 and O5, are shared with
Bi1 and Bi2 polyhedrons. Therefore, SeO3 groups additionally
stitch Fe−Bi−O chains. A polyhedral representation of the
Bi2Fe(SeO3)2OCl3 crystal structure is shown in Figure 2.
According to this description, the crystal structure of
Bi2Fe(SeO3)2OCl3 can be considered as layered. The FeO6
octahedron chains running along the b axis form layers
perpendicular to the c axis. The distance between Fe atoms
in the chain is 3.569(1) Å, whereas the distances between Fe
atoms from different chains are 8.570(2) and 8.604(2) Å. On
Figure 2. Polyhedrons of Bi1, Bi2, and Fe atoms in the crystal
structure of Bi2Fe(SeO3)2OCl3 (upper panel). Polyhedral representa-
tion of Fe−Bi−O−Cl layer along the c axis (upper panel) and a axis
(lower panel). Bi1 polyhedrons are drawn as dark and Bi2 polyhedrons
as light. SeO3 groups stitch FeO6 and BiO4Cl3 polyhedrons.
the basis of this fact the magnetic sublattice may be suggested
as being quasi-one-dimensional.
Thermal Stability Study. As follows from our experiment
Bi2Fe(SeO3)2OCl3 is stable up to 400 °C. At higher
temperatures, decomposition begins within at least four steps
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with DSC peaks at 440, 500, 825, and 915 °C. The weight loss
does not end at 1000 °C and amounts to a total of about 60%
from the starting amount of the substance. It is possible to
suggest that the first step of decomposition with an illegible
plateau in the range 440−500 °C corresponds to loss of a
SeOCl2 molecule. The observed weight loss of about 20% is in
good agreement with the calculated value, 19.6%. The plateau
in the 500−750 °C temperature range may be attributed to loss
of all chlorine atoms and two molecules of SeO2 (observed
41%, calculated 38.7%).
orders of magnitude more intense than the additional weak line
L2. One can assume that the line L1 originates presumably from
a quasi-one-dimensional subsystem of Fe3+ ions, while the latter
line L2 possibly refers to a small amount of paramagnetic
defects or impurities. The results of ESR line shape fitting in
accordance with eq 1 are shown by solid lines in Figure 3.
Apparently, the fitted curves are in good agreement with the
experimental data over the whole temperature range studied.
The main resonance line L1 is characterized by the effective g
factor g = 1.999 0.005, which is typical of S-type Fe3+ ions in
octahedral coordination (Figure 4). The quasi-one-dimensional
Electron Spin Resonance. The evolution of the X-band
ESR spectra with temperature for a powder sample of
Bi2Fe(SeO3)2OCl3 is shown in Figure 3. A qualitative analysis
Figure 4. Temperature dependence of the effective g factor, the ESR
line width ΔB, and the integral ESR intensity χESR for Bi2Fe-
(SeO3)2OCl3 derived from fitting of ESR spectra in accordance with
eq 1 for the main resonance mode L1 related to the signal from a
quasi-one-dimensional chain of Fe3+ cations. The red solid line is the
fit according to eq 2.
behavior of the ESR signal in Bi2Fe(SeO3)2OCl3 is clearly seen
in the temperature dependence of the ESR integral intensity
χESR of the L1 line, which is proportional to the number of
magnetic spins and was estimated by double-integration of the
first-derivative ESR spectra (Figure 4). Similarly to the static
magnetic susceptibility (as shown below) this value passes
through a broad maximum at about Tmax ≈ 130 K. The line
width of this component, ΔB, increases progressively at
decreasing temperature, and a pronounced degradation of the
ESR absorption line occurs at low temperature (Figure 3). This
low-T signal fading could be due to a shortening of spin−spin
Figure 3. Temperature evolution of the first-derivative ESR absorption
line for a powder sample of Bi2Fe(SeO3)2OCl3: (black points)
experimental data; (solid lines) fitting by the sum of two Lorentzians
(eq 1). The top panel represents an example of the spectrum
decomposition along with two resolved lines at room temperature.
of the line shape was performed, taking into account two
circular components of the exciting linearly polarized micro-
wave field by fitting of the experimental spectra in accordance
with the sum of two Lorentzian functions in the form
correlations as the temperature approaches the Nee
́
l temper-
ature TN from above.
Anomalous broadening of the line upon approaching the
long-range ordering transition from above has been observed
earlier for a wide class of antiferromagnetic, spin-glass, diluted
magnetic, and lower dimensional systems29 including a great
number of antiferromagnetic compounds with trivalent iron.30
It has been treated as critical behavior due to the slowing down
of spin fluctuations on approaching the critical temperature.
This causes the divergence of the spin correlation length, which
in turn affects the spin−spin relaxation time, resulting in
broadening of the ESR line. According to Huber’s formula,31
which evolved from the theory of Mori and Kawasaki,32,33 the
⎡
⎢
⎣
⎤
⎥
⎦
dP
dB
d
dB
ΔB
ΔB
∝
+
ΔB2 + (B − B )2
ΔB2 + (B + Br)2
r
(1)
This formula describes a symmetric line, where P is the
power absorbed in the ESR experiment, B is the magnetic field,
Br is the resonance field, and ΔB is the the line width. It was
found that a proper description of the ESR spectra requires
including the two spectral components L1 and L2. The upper
panel in Figure 3 represents an example of the spectrum
decomposition along with the two resolved lines L1 and L2 at
room temperature. Obviously, the line L1 appears to introduce
the main contribution to the absorption signal and is at least 2
ESR line width varies with temperature near the Nee
́
l point in
accordance with34
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β
upturn interrupted by a sharp anomaly at TN = 13 K. This
anomaly is seen also in specific heat, as shown in the inset to
Figure 5, despite the fact that it is rather weak. Overall, the
temperature dependence of χ in Bi2Fe(SeO3)2OCl3 can be
treated as formation of the short-range correlation regime at
elevated temperatures with subsequent three-dimensional long-
ESR
⎡
⎢
⎣
⎤
⎥
⎦
TN
T − T
ΔB(T) = ΔB * + A
ESR
(2)
N
where ΔB denotes the ESR line width, A is an empirical
parameter, ΔB* is the limiting minimum value of the narrowed
line width, which is temperature independent, while the second
́
range order at the Neel temperature. Note that Tmax and TN
ESR
term reflects the critical behavior with TN
being the
differ by 1 order of magnitude, signifying the quasi-low-
dimensional nature of magnetism in Bi2Fe(SeO3)2OCl3.
In accordance with the structural features of Bi2Fe-
(SeO3)2OCl3, the dominant magnetic exchange interaction J∥
in this compound is realized within the chains of corner-sharing
FeO6 octahedrons. The interaction through apical oxygen
atoms is assumed to be antiferromagnetic for both 90 and 180°
angles of Fe3+−O2−−Fe3+ bonds.38 Thus, quasi-isolated
temperature of the order−disorder transition and β the critical
exponent. In Figure 4, the solid red line superimposed on
experimental data represents a least-squares fit of experimental
data for the main absorption line according to eq 2. Apparently,
this formula remains valid for Bi2Fe(SeO3)2OCl3 in a wide
temperature range: 35−300 K. The best fit of the X-band ESR
experimental data according to eq 2 resulted in the values ΔB*
= 10 1 mT, A = 42 1 mT, TNESR = 13 2 K, and β = 1.75
0.05. In the frame of the Kawasaki approach, the critical
exponent can be expressed as β = −[1/2(7 + η)ν − 2(1 − α)],
where ν describes the divergence of correlation length, η is the
critical exponent for the divergence of static correlations, and α
relates to divergence of the specific heat, respectively. Using the
5
antiferromagnetic S = /2 chains define the magnetic behavior
of Bi2Fe(SeO3)2OCl3 at high temperatures: i.e., produce the
correlation maximum in χ(T) dependence. The calculations of
5
thermodynamic properties of the Heisenberg S =
/
2
antiferromagnetic chain define the ratio for the value of
magnetic susceptibility in the maximum χmax, its temperature
T(χmax) ,and g factor through the expression39
2
values η = α = 0 and ν = /3 for a three-dimensional (3D)
Heisenberg antiferromagnet,32 β becomes equal to 1/3, which is
essentially lower than the experimental value. In case of
magnetic systems with lower dimensionality the critical
exponent is expressed as β = −(3 − 2η)ν and β = −(3.5 −
2η)ν for two-dimensional (2D) and one-dimensional (1D)
systems, respectively.35,36 The corresponding values β using the
values η = 0 and ν = 1/2 result in β = 3/2 and β = 7/4 for 2D and
1D systems, respectively. Obviously, the latter value is in good
agreement with the experimentally observed value.
χ
max [T(χmax )]
= 0.38
g2
(3)
In Bi2Fe(SeO3)2OCl3, this quantity is only 0.26. This low
value indicates either reduction of the spin-only magnetic
moments of the iron atoms or frustration of the dominant
nearest-neighbor exchange interaction within the chains.
In the simplified model of unique nearest-neighbor exchange
interaction, the position of the maximum of magnetic
susceptibility defines the exchange interaction parameter J∥
through the expression
Thermodynamics. The temperature dependence of
magnetic susceptibility χ of Bi2Fe(SeO3)2OCl3 taken in the
field-cooled regime at B = 0.1 T is shown in Figure 5. At
kB[T(χmax )]
= 10.6
|J |
(4)
The estimation of antiferromagnetic exchange interaction
parameter according to eq 4 gives J∥ = 12 K.
It can be determined more precisely using Fisher’s model of
S = ∞ infinite chains:39
N g2S(S + 1)μ
2 1 + u
1 − u
A
B
χ
=
chain
3kBT
⎛
⎝
⎞
⎠
2J S(+1)
kBT
kBT
2J S(+1)
⎜
⎜
⎟
⎟
u = coth
−
(5)
Figure 5. Temperature dependence of magnetic susceptibility in
Bi2Fe(SeO3)2OCl3. The solid line represents the fit in a Heisenberg S
= ∞ antiferromagnetic chain model. The inset represents the
temperature dependence of specific heat on the C/T vs T2 scale.
where NA, μB, and kB are Avogadro, Bohr, and Boltzmann
constants. As is shown in Figure 5, the χ(T) dependence can be
fitted by the sum of the temperature-independent term χ0, the
Curie−Weiss term related to the defects C/T, and Fisher’s
magnetic susceptibility of the chain χchain
:
elevated temperatures, the field-cooled and zero-field-cooled
curves coincide but slightly deviate from each other at low
temperatures. This divergence is ascribed routinely to defects
and/or impurities; we neglect it in further discussion. However,
the increase of magnetic susceptibility at the lowest temper-
atures could be of intrinsic origin. In zigzag chains of FeO6
octahedra the Dzyaloshinskii−Moriya interaction results in
canting of magnetic moments, seen as the rise of magnetic
susceptibility at low temperatures.37 On cooling, the magnetic
C
T
χ = χ0 +
+ αχ
chain
(6)
Here, the temperature-independent term was estimated from
the summation of Pascal’s constants of the atoms forming
Bi2Fe(SeO3)2OCl3 as χ0 = −2.1 × 10−4 emu/mol.40 The Curie
constant C = 4.7 × 10−2 emu K/mol gives an estimation of the
5
impurities/defects concentration (S = /2) as about 1%. The
susceptibility passes through a broad maximum at about Tmax
130 K. Well below this maximum, χ demonstrates a Curie-like
≈
coefficient α = 0.92 highlights the deviation from the one-
dimensional model. In this case, the estimation of the
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antiferromagnetic intrachain exchange interaction parameter
amounts to J∥ ≈ 17 K.
shown in Figure 6. The approximated saturation value of the
hyperfine field Hhf(T→0) ≈ 44 T is anomalously low for a
high-spin iron atom in octahedral oxygen coordination, for
which Hhf is usually about 56 T.42 The spin reduction of about
∼20% cannot be accounted for by crystal field or covalency
effects and can be attributed only to quantum spin reduction,
predicted to be large in quasi-one-dimensional antiferromag-
nets.43 The quantum spin reduction is the function of the ratio
HA/HE (where HA and HE are crystal anisotropy and exchange
fields, respectively) and of the ratio ξ = J⊥/J∥ of the interchain
to intrachain exchange interaction parameters. Following spin-
wave theory for an antiferromagnetic systems,43 the zero-point
spin reduction ΔS(0) = (5/2 − ⟨S(0)⟩) at each magnetic
sublattice can be given by
The interchain interaction in Bi2Fe(SeO3)2OCl3, J⊥, can be
calculated from the equation41
⎛
⎝
⎞
⎠
2|J |
4 + Zη
Zη
⎜
⎜
⎟
⎟
exp
=
kT
N
(7)
where η = J⊥/J∥ and Z is the number of nearest-neighboring
chains (Z = 4). This expression gives the estimates η = 0.08 and
J⊥ ≈ 1.4 K.
57
Fe Mossbauer Spectroscopy. The 57Fe Mossbauer
̈
̈
spectra of Bi2Fe(SeO3)2OCl3 were recorded both below and
́
above the Neel temperature TN = 13 K. As shown in Figure 6,
π/2a
π/2b
4abc ∫ ∫ ∫
ΔS(0) =
π/2c [(1 − αγ 2)−1/2 − 1]
k
π3
dkx dky dkz
0
0
0
(8)
where α = (1 + HA/HE)−2 and γk is the structure factor defined
by
cos kyb + ξ[(cos kxa + cos kzc)]
γk =
1 + 2ξ
(9)
Here, b is the lattice constant along the iron chains, a and c are
the lattice constants perpendicular to the chains, and kx, ky, and
kz are the components of the wavevector k along principal
lattice vectors. Spin fluctuations (8) or spin waves are present
even at absolute zero temperature. These fluctuations reduce
5
the mean value ⟨S(0)⟩ of the Fe3+ ions below S(0) = /2. This
reduction is directly measurable from the Mossbauer spectra,
̈
since the magnitude of the magnetic hyperfine field Hhf is
proportional to ⟨S(0)⟩. We evaluated numerically the integral
(8) for various values of α and ξ. The result of ΔS(0)
evaluation is shown in Figure 7. The values of the hyperfine
field Hhf(0) corresponding to the spin reduction are indicated
on the right-hand scale axis of Figure 7. For ΔS(0) we assumed
a saturation Hhf(0) value of 54 T for Fe3+ ions in FeO6
octahedral coordination, corrected for covalence effects.44
Figure 6. Representative 57Fe Mossbauer spectra of powder−crystal
̈
Bi2Fe(SeO3)2OCl3 recorded both above (upper panel) and below
́
(lower panel) the Neel temperature.
the spectrum at room temperature can be fitted by a
quadrupole doublet with isomer shift value δ300 K = 0.39
0.01 mm/s, which falls in the range for high-spin Fe3+ ions in an
octahedral oxygen environment.24 The quadrupole splitting
value Δ300 K = 0.20
0.01 mm/s is rather high for a 6S
electronic state of Fe3+ ions. This might be due to the distortion
of oxygen octahedrons FeO6 within the isolated iron chains in
the Bi2Fe(SeO3)2OCl3 structure. No visible anomalies in the
δ(T) and Δ(T) dependences were seen on cooling, thus
indicating that there are no structural transitions below room
temperature.
Figure 7. Diagram of calculated zero-point spin reduction ΔS(0) and
corresponding hyperfine field Hhf(0) as a function of the anisotropy
ratio HA/HE and the ratio ξ = J⊥/J∥ of the interchain to intrachain
exchange interaction parameters.
In the antiferromagnetic phase (T = 4.6 K) the 57Fe
Mossbauer spectrum consists of a magnetic Zeeman sextet, as
̈
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According to this figure, the ΔS(0) value increases rapidly when
the magnetic dimensionality ξ and anisotropy HA/HE are
reduced. Using the usually observed values for HA/HE = (1−5)
× 10−3,43 we estimated ξ ≈ 0.01−0.03. This is in good
assumption with the notion that the Bi2Fe(SeO3)2OCl3
compound is a quasi-one-dimensional spin system.
for dominant magnetic interactions are shown in Figure 9. We
see that J∥ is mediated by an Fe−O−Fe superexchange path
First-Principles Electronic Structure Calculations. The
spin-polarized density of states, projected onto Fe d, O p, Cl p,
Se p, and Bi p states, are shown in Figure 8. We find that
Figure 9. Exchange paths for various magnetic interactions J∥ (in
black), J∥′ (in cyan), and J⊥ (in gold).
where the Fe−O−Fe bond angle is 128.6°, whereas J∥′ is
mediated by a supersuperexchange path, involving Fe, O, Se,
and Bi. The interchain interaction J⊥ is mediated by a long-
range Fe−O−Bi1−Cl−Bi2−O−Fe path. All of the calculated J
values turned out to be of antiferromagnetic nature, in
agreement with the experimental prediction. The J values
using the superexchange formula, and taking a Hubbard U value
of 8 eV, turned out to be J∥ ≈ 21 K, J∥′ ≈ 4.6 K, and J⊥ ≈ 0.6 K,
which shows the dominance of the nearest-neighbor intrachain
Fe−Fe interaction, proving the quasi-one-dimensional nature of
the underlying spin model of the compound. The ratio κ of the
next-nearest-neighbor exchange interaction parameter to the
nearest-neighbor interaction parameter, J∥′/J∥ ≈ 0.22, is close
to the critical value (κcr ≈ 0.25) separating the collinear
magnetic structures (κ < κcr) from the helical structures (κ >
κcr).48 Thus, the magnetic structure in Bi2Fe(SeO3)2OCl3 is
expected to be collinear.
Figure 8. Spin-polarized density of states for Bi2Fe(SeO3)2OCl3
projected onto Fe d, O p, Cl p, Se p, and Bi p states. Zero energy
is set at the GGA Fermi energy. The states in majority and minority
spin channels are shown as positive and negative values.
octahedral crystal field split Fe t2g and eg states are completely
filled in the majority spin channel and completely empty in the
minority spin channel, suggesting the nominal Fe3+ or d5
valence of Fe. Both Bi p and Se p are found to be nearly
empty, suggesting the nominal Bi3+ and Se4+ valences, while the
O p and Cl p states are found to be mostly occupied, suggesting
the nominal 2− and 1− valence states, respectively. The O p
and Cl/Se p states show finite, nonzero hybridization with Fe d
states close to the Fermi energy, which contributes to the
superexchange path of the magnetic interaction between two Fe
sites. The magnetic moment, calculated with the single-electron
approximation of DFT, at the Fe site is found to be 4.33 μB,
with rest of the moment sitting at neighboring O and Cl sites,
with a total magnetic moment of 5 μB per formula unit.
In order to estimate the various Fe−Fe magnetic exchange
interactions present in the compound, the nth-order muffin tin
orbital (NMTO) based downfolding technique45 was applied to
construct Fe d only Wannier orbitals by downfolding all the
degrees of freedom associated with O, Cl, Se, and Bi and
keeping active only the Fe d degrees of freedoms. This
procedure provides renormalization of Fe d orbitals due to
hybridization from O p, Cl p, Se p, and Bi p. The effective Fe−
Fe hopping interactions were obtained by the real-space
representation of the Hamiltonian in the effective Fe d Wannier
function basis. The dominant hopping interactions are found to
be the nearest-neighbor intrachain t∥, next-nearest-neighbor
intrachain t∥′, and interchain t⊥. The magnetic exchange
interactions, J∥, J∥′, and J⊥, can be obtained from the knowledge
of hopping interactions and the on-site energies of various Fe d
states through a superexchange formula,46 with a choice of the
appropriate Hubbard U parameter. Such an approach is found
to be highly successful in a number of applications.47 The paths
CONCLUSIONS
■
The new bismuth iron selenite oxochloride Bi2Fe(SeO3)2OCl3
was synthesized and its crystal structure determined. The new
compound possesses a unique crystal structure with nearly
isolated zigzag chains of corner-sharing FeO6 octahedrons
decorated by BiO4Cl3 and BiO3Cl3 polyhedrons and SeO3
groups. The physical properties of the new compound are
closely related to its crystal structure. At elevated temperatures,
the magnetization of the title compound passes through the
broad maximum Tmax ≈ 130 K, which indicates the formation
of a short-range correlation regime and defines the scale of
magnetic exchange interactions J∥ ≈ 17 K within the chains.
The electron spin resonance data corroborate well the static
magnetization results and reveal an extended region of short-
range order correlations in the compound studied. The critical
broadening of ESR absorption lines at low temperatures is
consistent with the divergence of temperature-dependent
correlation length expected for a quasi-one-dimensional
antiferromagnetic spin chain upon approaching the long-
range order from above. The 57Fe Mossbauer spectra recorded
̈
at T > Tmax are characteristic for Fe3+ ions located in distorted
FeO6 octahedra. At T = 13 K, Bi2Fe(SeO3)2OCl3 exhibits a
phase transition to the long-range antiferromagnetic state
evidenced in specific heat and magnetization measurements.
The Mossbauer spectrum at low temperature shows a low
̈
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saturated value of the hyperfine field, Hhf = 44 T, expected for
quasi-one-dimensional systems with a substantial quantum spin
reduction ΔS/S(0) of about 20%. The first-principles
calculations, within the framework of density functional theory,
allow for estimating both nearest-neighbor J∥ and next-nearest-
neighbor J∥′ exchange interaction parameters within the chains,
as the interchain interaction J⊥. These values are found to be in
good correspondence with estimates based on the simplified
description of magnetism in quasi-one-dimensional systems.
For the ratio of intrachain to interchain exchange interaction
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ASSOCIATED CONTENT
■
S
* Supporting Information
CIF file giving crystallographic data for Bi2Fe(SeO3)2OCl3 and
a figure giving the results of thermal analysis. This material is
available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
■
Corresponding Author
*P.S.B.: e-mail, berdonosov@inorg.chem.msu.ru; tel, +7(495)
939-3504; fax, +7(495)939-0998.
Present Address
$Sine Theta LTD, Moscow 119991, Russia.
Author Contributions
The manuscript was written through contributions of all
authors. All authors have given approval to the final version of
the manuscript
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ACKNOWLEDGMENTS
■
We are grateful to Prof. K. Kovnir (UC Davis) for his help with
the structural experiment arrangement and to Prof. V.S.
Rusakov (Lomonosov Moscow State University) for MS
spectrum measuring at 4.6 K. This work was supported in
part from the Ministry of Education and Science of the Russian
Federation in the framework of Increase Competitiveness
Program of NUST “MISiS” (No. K2-2014-036), by Russian
Foundation for Basic Research grants 12-03-00665, 13-02-
00174, 14-02-00245, and 14-02-92693 and by the President of
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