Synthesis and characterization of the crystal structure and magnetic properties of the ternary manganese vanadate NaMnVO4

Article abstract of DOI:10.1021/ic101180h

A new ternary manganese vanadate, NaMnVO₄, was synthesized by solid state reaction route, and its crystal structure and magnetic properties were characterized by X-ray diffraction, magnetic susceptibility and specific heat measurements, and by density functional calculations. NaMnVO₄ crystallizes in the maricite-type structure with space group Pnma, a = 9.563(1) A, b = 6.882(1) A, c = 5.316(1) A, and Z = 4. NaMnVO ₄ contains MnO₄ chains made up of edge-sharing MnO ₆ octahedra, and these chains are interlinked by VO₄ tetrahedra. The magnetic susceptibility has a broad maximum at T_max = 24 K and follows the Curie-Weiss behavior above 70 K with θ = -62 K. NaMnVO₄ undergoes a three-dimensional antiferromagnetic ordering at T_N = 11.8 K. The spin exchanges of NaMnVO₄ are dominated by the intrachain antiferromagnetic exchange, and the interchain spin exchanges are spin-frustrated. The most probable magnetic structure of the ordered magnetic state below T_N was predicted on the basis of the extracted spin exchanges.

Full text of DOI:10.1021/ic101180h

8578 Inorg. Chem. 2010, 49, 8578–8582
DOI: 10.1021/ic101180h
Synthesis and Characterization of the Crystal Structure and Magnetic Properties
of the Ternary Manganese Vanadate NaMnVO4
Hamdi Ben Yahia,*,† Etienne Gaudin,† Khalid Boulahya,‡ Jacques Darriet,† Won-Joon Son,§ and
Myung-Hwan Whangbo§
†
ꢀ
ICMCB, CNRS, Universite Bordeaux 1, 87 Avenue du Docteur Schweitzer, 33608 Pessac Cedex, France,
‡
´
ꢀ
´
Departamento de Quımica Inorganica Facultad de Quımicas Universidad Complutense, 28040 Madrid, Spain,
and §Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, USA
Received June 11, 2010
A new ternary manganese vanadate, NaMnVO4, was synthesized by solid state reaction route, and its crystal structure
and magnetic properties were characterized by X-ray diffraction, magnetic susceptibility and specific heat measure-
ments, and by density functional calculations. NaMnVO4 crystallizes in the maricite-type structure with space group
˚
˚
˚
Pnma, a = 9.563(1) A, b = 6.882(1) A, c = 5.316(1) A, and Z = 4. NaMnVO4 contains MnO4 chains made up of edge-
sharing MnO6 octahedra, and these chains are interlinked by VO4 tetrahedra. The magnetic susceptibility has a broad
maximum at Tmax = 24 K and follows the Curie-Weiss behavior above 70 K with θ = -62 K. NaMnVO4 undergoes a
three-dimensional antiferromagnetic ordering at TN = 11.8 K. The spin exchanges of NaMnVO4 are dominated by the
intrachain antiferromagnetic exchange, and the interchain spin exchanges are spin-frustrated. The most probable
magnetic structure of the ordered magnetic state below TN was predicted on the basis of the extracted spin exchanges.
1. Introduction
crystallizing intheolivine-typestructure, however, LiMnVO4
is not a good cathode material for rechargeable Li-ion bat-
teries.8 Recently, the AMnVO4 vanadate series have been
extended with AgMnVO4,9 CuMnVO4,10 KMnVO4,11 and
RbMnVO4.9 AgMnVO4 crystallizes in the maricite-type struc-
ture and contains MnO4 chains made up of edge-sharing
MnO6 octahedra. CuMnVO4 crystallizes in the Na2CrO4-
type structure and also contains MnO4 chains made up of
edge-sharing MnO6 octahedra. The spin exchange interac-
tions within such MnO4 chains and between them were found
to be antiferromagnetic. Surprisingly, KMnVO4 crystallizes
in a new type of oxygen-deficient perovskite, and RbMnVO4
is the first vanadate crystallizing in the stuffed tridymite-type
structure.9
Toward completing the AMnVO4 series with A = alkali, it
is highly desirable to prepare the missing phase NaMnVO4.
In the present work, we successfully synthesized this phase,
determined its crystal structure by X-ray diffraction, exam-
ined its magnetic properties by magnetic susceptibility and
specific heat measurements, and analyzed its spin exchange
interactions by density functional calculations. Results of our
studies are presented in the following section.
Many phosphates with the general formula ABPO4 (A =
alkali, Cu, Ag; B = transition metal) crystallize mainly in
four different structural types, i.e., olivine, maricite, stuffed-
tridymite, and zeolite-ABW. The stuffed-tridymite and zeo-
lite-ABW structure types are observed with large alkali
metals such as K, Rb, and Cs. In these structures, the transi-
tion metal is found mainly at tetrahedral sites and sometimes
at trigonal bipyramidal sites. In the more condensed phases
with olivine and maricite-type structures, the transition metal
is located at an octahedral site. It is of interest to compare the
structural evolution between homologous phosphates and
vanadates, AMnPO4 and AMnVO4, respectively. In the AMn-
PO4 phosphates series, LiMnPO4,1 NaMnPO4,2 KMnPO4,3
4
and CsMnPO4 were studied in the past and their structures
determined. Recently, we reported the structural and magnetic
properties of RbMnPO45 and AgMnPO4.6 In the homologous
AMnVO4 vanadates, LiMnVO47 is known to crystallize in the
Na2CrO4-type structure. In contrast to the case of LiFePO4
*Author to whom correspondence should be addressed. E-mail:
benyahia.hamdi@voila.fr.
(1) Geller, S.; Durand, J. L. Acta Crystallogr. 1960, 13, 325.
(2) Moring, J.; Kostiner, E. J. Solid State Chem. 1986, 61, 379.
(3) Lujan, M.; Kubel, F.; Schmid, H. Z. Naturforsch. 1995, 50b, 1210.
(4) Yakubovich, O. V.; Simonov, M. A.; Mel’nikov, O. K. Kristallografiya
1990, 35, 42.
(5) Ben Yahia, H.; Gaudin, E.; Darriet, J. J. Alloys Compd. 2007, 442, 74.
(6) Ben Yahia, H.; Gaudin, E.; Darriet, J. Z. Naturforsch. 2009, 64b, 875.
(7) Padhi, A. K.; Archibald, W. B.; Nanjundaswamy, K. S.; Good-
enough, J. B. Solid State Chem. 1997, 128, 267.
(8) Chung, S.-Y.; Bloking, J. T.; Chiang, Y.-M. Nat. Mater. 2002, 1, 123.
(9) Ben Yahia, H.; Gaudin, E.; Darriet, J. J. Solid State Chem. 2008, 181,
3103.
(10) Ben Yahia, H.; Gaudin, E.; Darriet, J.; Banks, M.; Kremer, R. K.;
Villesuzanne, A.; Whangbo, M. H. Inorg. Chem. 2005, 44, 3087.
(11) Ben Yahia, H.; Gaudin, E.; Lee, C.; Whangbo, M. H.; Darriet, J.
Chem. Mater. 2007, 19, 5563.
r
pubs.acs.org/IC
Published on Web 08/23/2010
2010 American Chemical Society

Article
Inorganic Chemistry, Vol. 49, No. 18, 2010 8579
Figure 1. Observed, calculated, and difference plots for the X-ray powder diffraction profile refinement (Cu KR1-R2 radiation) of NaMnVO4.
Table 1. Atomic Positions and Isotropic Displacement Parameters for NaMnVO4
2. Experimental Section
2
Ueq (A )
˚
Synthesis. Pure NaMnVO4 was prepared by solid state reac-
tions from a stoichiometric mixture of NaVO3 and MnO (NaVO3
was obtained by heating a 1:1 mixture of Na2CO3 and V2O5 at
600 ꢀC for 6 h). The mixture was put in a gold tube, which was
sealed under vacuum in a silica tube, and then heated at 500 ꢀC for
120 htoavoidthe meltingofNaVO3 (melting point = 610 ꢀC) and
at 650 ꢀC for 24 h. After grinding, the mixture is pelletized, fired
at 650 ꢀC for 12 h under argon flow, and then quenched in water
in order to avoid decomposition of the phase and to clean the
sample from traces of NaVO3, which are soluble in water. Single
crystals of NaMnVO4 were prepared under vacuum by a fast
heating of the pure sample at 950 ꢀC (melting point ≈ 900 ꢀC)
and then by slowly decreasing the temperature at the rate of
2 ꢀC h-1 to room temperature. The obtained crystals are yellow
in color.
atom sites
x
y
z
Na
Mn
V
4c
4a
4c
4c
4c
8d
0.14622(12) 3/4
1/2
0.18090(3)
0.36336(15) 1/4
0.12308(15) 1/4
0.51349(15) 0.0161(2)
0
1/4
1/2
0.01109(8)
0.00618(7)
0.0100(3)
0.0121(4)
0.52042(5)
0.5585(3)
0.2112(3)
O1
O2
O3
0.11606(11) 0.44536(16) 0.67228(18) 0.0138(3)
KR radiation. Full pattern matching refinements were perfor-
med with the Jana2000 program package12 (Figure 1). The back-
ground was estimated by a Legendre function, and the peak
shapes were described by a pseudo-Voigt function. The refine-
ment of peak asymmetry was performed using four Berar-
Baldinozzi parameters.13 The diffraction pattern of the powder
obtained by melting NaMnVO4 under vacuum has shown an
important difference compared to that of the pure NaMnVO4
phase. Most of the diffraction peaks were indexed using NaMn-
VO4, Na3MnV2O7.5, and Mn3O4 cell parameters (Figure S2 of
the Supporting Information). The same powder pattern is ob-
tained after melting the pure sample under Argon atmosphere.
Single Crystal X-ray Diffraction. NaMnVO4 single crystals
suitable for single crystal X-ray diffraction were selected on the
basis of size and sharpness of the diffraction spots. The data
collections were carried out on an Enraf-Nonius Kappa CCD
diffractometer using Mo KR radiation. Data processing and all
refinements were performed with the Jana2000 program pack-
age.12 A Gaussian-type absorption correction was applied, and
the shape was determined with the video microscope of the
Kappa CCD. For the NaMnVO4 data collection details, see
Table S1 of the Supporting Information. The extinction condi-
tions observed for single crystal NaMnVO4 agree with the Pnma
and Pn21a space groups. The refinement was performed taking
into account the centrosymmetric space group Pnma. Most of
the atomic positions were found by Direct Methods using
Sir97.14 With anisotropic displacement parameters, the final resi-
dual factors converged to the value R(F) = 0.0304 and wR(F2) =
0.0538 for 41 refined parameters, 807 observed reflections, and
Electron Microprobe Analysis. Semiquantitative EPMA ana-
lyses of many crystals, including the one investigated on the
diffractometer, were carried out with a CAMECA SX-100 in-
strument. The experimentally observed compositions were close
to the compositions obtained from the single crystal refinement.
Traces of an impurity with the mean composition of Na3.08
-
Mn0.9V2.02O7.5 have been also observed. This indicates a partial
decomposition of NaMnVO4. No traces of manganese oxides or
NaVO3 have been detected.
Differential Thermal Analysis (DTA). DTA of the NaMnVO4
sample was carried out under argon atmosphere between 25 and
950 ꢀC using a Setaram thermal analyzer at a heating and cool-
ing rate of 5 ꢀC min-1. In a platinum tube, about 60 mg of
NaMnVO4 sample was used. From the heating curve, the melt-
ing temperature of NaMnVO4 was estimated to be about 900 ꢀC.
The two additional transitions observed on the cooling curve
might correspond to the melting of binary sodium vanadates
(Figure S1 of the Supporting Information).
Powder X-ray Diffraction. To ensure the purity of NaMnVO4
powders, we performed high precision X-ray powder diffraction
measurements. The data were collected at room temperature
over the 2θ angle range 5ꢀ e 2θ e 120ꢀ with a step size of 0.02 or
0.008ꢀ using a Philips X-pert diffractometer operating with Cu
(13) Berar, J. F.; Baldinozzi, G. J. Appl. Crystallogr. 1993, 26, 128.
(14) Altomare, A.; Burla, M. C.; Camalli, M.; Cascarano, G. L.;
Giacovazzo, C.; Guagliardi, A.; Moliterni, A. G. G.; Polidori, G.; Spagna,
R. J. Appl. Crystallogr. 1999, 32, 115.
(12) Petricek, V.; Dusek, M.; Palatinus, L. Jana2006: The Crystallo-
graphic Computing System; Institute of Physics: Praha, Czech Republic, 2006.

8580 Inorganic Chemistry, Vol. 49, No. 18, 2010
Ben Yahia et al.
Figure 2. (a) Perspective view of NaMnVO4 structure. (b) Surrounding of sodium atoms. (c) Perspective view of CuMnVO4 structure.
˚
Table 2. Interatomic Distances (A), Bond Valence, and Bond Valence Sum
(*BVS) for NaMnVO4
difference-Fourier residues in the range between -1.41 and
þ1.40 eA-3. The Na atoms have a somewhat large anisotropic
˚
2
displacement parameter [U11 = 0.0203(5) A ]. One might con-
˚
distances
BVS
sider this to arise from a partial substitution of Mn for Na.
However, the occupancies of all the atoms do not show any
significant deviation from the ideal stoichiometric composi-
tion. Thus the large anisotropic displacement parameter of Na
is due probably to the mobility of the Na atoms. The refined
atomic positions and anisotropic displacement parameters
(ADPs) are given in Table 1 and Table S2 of the Supporting
Information, respectively.
Na-O1 (ꢀ1)
Na-O1 (ꢀ1)
Na-O2 (ꢀ1)
Na-O2 (ꢀ1)
Na-O3 (ꢀ2)
2.421(2)
2.899(2)
2.963(2)
2.444(2)
2.2784(11)
<2.355>*0.92(1) [C.N. = 4]
<2.547>*1.01(1) [C.N. = 6]
2.1828(9)
2.3678(10)
2.0995(10)
<2.216>
1.7565(15)
1.7342(14)
1.6866(11)
<1.716>
0.189
0.052
0.044
0.177
0.277 (ꢀ2)
Mn-O1 (ꢀ2)
Mn-O2 (ꢀ2)
Mn-O3 (ꢀ2)
0.346 (ꢀ2)
Magnetic Susceptibility and Specific Heat Measurements.
Magnetic susceptibility measurements for NaMnVO4 were car-
ried out with a Quantum Design SQUID magnetometer. The
susceptibility was recorded at 5 kOe for NaMnVO4 in the whole
temperature range 2-300 K. The data were collected during the
warm-up cycle at 5 kOe, after the sample was cooled in the zero
applied field. The diamagnetic corrections were carried out on
the basis of Pascal’s tables.15 Heat capacity measurements were
performed on NaMnVO4 pellets using a PPMS Quantum De-
sign in a temperature range from 2 to 100 K.
0.21 (ꢀ2)
1.433 (ꢀ2)
*1.97(1) [C.N. = 6]
1.132
V-O1 (ꢀ1)
V-O2 (ꢀ1)
V-O3 (ꢀ2)
1.205
1.372 (ꢀ2)
*5.08(1) [C.N. = 4]
The crystal structures of NaMnVO4 and CuMnVO4 are
very similar. Indeed, in these two different structures, the
maricite- and the Na2CrO4-type, respectively, the cation
arrays are similar (Figure 2a,c), but the oxygen arrays are
different. This explains the difference in the connectivity bet-
ween the chains of edge-sharing octahedra and in the other
cation coordination polyhedra. The structural transition from
the maricite- to the Na2CrO4-type structure is possible. Peltier
et al. have evidenced this in their studies of R- and β-InPO4
phases.17 This makes NaMnVO4 and CuMnVO4 strongly
related from the structural and magnetic points of view.
3. Crystal Structure of NaMnVO4
NaMnVO4 is isostructural with NaMnPO4 of maricite-
type structure. The structure consists of edge-sharing chains
of MnO6 octahedra running along the b axis. The MnO6
octahedra are cross connected by the VO4 tetrahedra, giving
rise to large cavities in which the sodium atoms are located
(Figures 2a,b). The interatomic distances and the bond
valence sum (BVS) are given in Table 2. The Mn-O distances
˚
range from 2.099 to 2.368 A, with an average distance of
4. Magnetic Susceptibility and Specific Heat of NaMnVO4
˚
2.216 A. This is very similar to the results found for
The plot of the magnetic susceptibility versus temperature
(χ vs T) and the corresponding χ-1 versus T plot for
NaMnVO4 are shown in Figure 3. The χ-1 versus T plot
reveals that NaMnVO4 exhibits a Curie-Weiss behavior in
the temperature range 70 - 300 K, leading to the Curie-
Weiss law with θ = -62(1) K and C = 4.31 mol-1 cm3 K.
The negative θ indicates that the predominant spin exchange
interactions are antiferromagnetic. The effective magnetic
moment μeff calculated from the Curie constant is 5.87(1) μB,
which is close to the spin only value of 5.92 μB expected for a
high-spin Mn2þ (d5) ion. The χ versus T plot has a broad
maximum (at Tmax = 24 K), indicating the occurrence of
short-range antiferromagnetic order around Tmax and a local
minimum at 11.8 K. The specific heat of NaMnVO4 exhibits
a lambda-type anomaly at 11.8 K (Figure 4), which shows
that NaMnVO4 undergoes a three-dimensional antiferro-
magnetic ordering at 11.8 K. Thus, Tmin corresponds to the
NaMnPO4,2 in which the Mn-O distances range from 2.077
˚
˚
to 2.397 A, with an average distance of 2.229 A. The BVS of
1.97 is in good agreement with the expected value of þ2 for
Mn2þ (d5).16 The vanadium tetrahedron is quite regular with
˚
distances ranging from 1.68 to 1.75 A, with an average value
˚
of 1.71 A. The BVS of 5.08 is in agreement with the expected
value of þ5 for Vþ5. The Naþ ion is bonded to four O atoms
belonging to four different MnO6 groups to form an irregular
tetrahedron. The O-Na-O angles range from 87.42(4)ꢀ to
˚
124.92(5)ꢀ, and the average Na-O distance is 2.355 A. The
BVS is calculated to be 0.92 by using the four shortest Na-O
contacts. When the coordination sphere of Na is increased to
six (Figure 2b), the BVS becomes 1.016. Thus, the sodium
atoms are best considered to be 4 þ 2 coordinate (see the
Na-O distances listed in Table 2).
(15) Mabbs, F. E.; Machin, D. J. Magnetism and Transition Metal
Complexes; Chapman and Hall: London, 1973.
(16) Brown, I. D.; Altermatt, D. Acta Crystallogr., Sect. B: Struct. Sci.
1985, 41, 244.
(17) Peltier, V.; Deniard, P.; Brec, R.; Marchand, R. C. R. Acad. Sci., Ser.
II 1998, 1, 57.

Article
Inorganic Chemistry, Vol. 49, No. 18, 2010 8581
Figure 3. Magnetic susceptibility χ vs temperature and the correspond-
ing χ-1 vs T plots of NaMnVO4 measured in the applied field H = 5 kOe.
Figure 5. (a) Schematic representation of the spin exchange paths J1-J4
in NaMnVO4, where the circles represent the Mn2þ (S = 5/2) spin sites
while the numbers 1-4 represent J1 - J4, respectively. The J1 magnetic
bonds along the b-direction are represented by the cylinders. (b) The
occurrence of four spin exchanges J3 at a given Mn2þ site. (c) The magetic
structure of the magnetic ground state expected below TN, where the
unshaded and shaded circles represent the Mn2þ ions with up-spin and
down-spin, respectively.
Table 3. Geometrical Parameters Associated with Spin Exchanges J1-J4 in
NaMnVO4 and Values of J1-J4 Determined from GGAþU Calculations
˚
distance (A)
J/kB (K)
exchange
Mn Mn
O
O
U = 4 eV
U = 5 eV
3 3 3
3 3 3
Figure 4. Specific heat Cp vs T plot of NaMnVO4. The inset displays
Cp/T in the region of the magnetic transition at 11.8 K.
J1
J2
J3
J4
3.441a
5.471
6.463
5.316
-6.13
-0.64
-0.52
-1.25
-4.84
-0.51
-0.41
-1.00
2.787
2.787
2.975
ꢀ
Neel temperature TN = 11.8 K. It is noted that CuMnVO4
has the same type of edge-sharing MnO4 chains (Figure 2c)
and exhibits a similar magnetic behavior with Tmax = 28 K and
Tmin = TN = 20 K.10
a The —Mn-O-Mn = 104.04ꢀ.
consider the four spin-exchanges J1-J4 between the Mn2þ
ions; J1 is the Mn-O-Mn superexchange between adjacent
Mn2þ ions along each edge-sharing MnO4 chain along the
Given that θ = -62 K and TN = 11.8 K, the spin exchanges
of NaMnVO4 are frustrated (|θ|/TN > 5).18 We fitted the
magnetic susceptibility curve of NaMnVO4 above TN in terms
of the interacting uniform chain model (with the intra- and
interchain spin exchanges Jintra and Jinter, respectively), as
carried out for CuMnVO4 in ref 10, without considering the
contribution of paramagnetic impurities. This fitting analysis
leads to a very good agreement between the calculated and
experimental susceptibilities. Unlike the case of CuMnVO4
(Jinter/Jintra ≈ 0.29),10 but Jinter is found to be comparable in
magnitude to Jintra for NaMnVO4 (i.e., Jinter/Jintra ≈ 1). Thus,
the use of the interacting uniform chain model is not appro-
priate for NaMnVO4 because it requires that Jinter/Jintra , 1.
Therefore, we attempted to fit the magnetic succeptibility data
using a classical antiferromagnetic Heisenberg chain with spin
S = 5/2 and intrachain exchange Jintra (see eq 2 in ref 10), but
this model does not adequately describe the data. This is most
probably because of the presence of significant interchain
exchange interactions (see below).
b-direction, while J2-J4 are Mn-O O-Mn supersuper-
3 3 3
exchanges between adjacent MnO4 chains, which are medi-
ated by VO4 units. It should be noted that a Mn2þ site of each
MnO4 chain gives rise to four J3 exchanges with the neigh-
boring MnO4 chains as depicted in Figure 5b. The Mn Mn
and O O distances associated with these spin exchanges
are summarized in Table 3. To determine the values of these
exchanges, we first examine the five ordered spin states,
defined in Figure 6 in terms of a (a, b, 2c) supercell containing
eight formula units (FUs). The total spin exchange energies
3 3 3
3 3 3
of these states can be expressed in terms of the spin
P
^
^
^
Hamiltonian H ¼ -
applying theenergy expressionsobtainedfor spin dimers with
N unpaired spins per spin site (in the present case, N = 5),19
the total spin exchange energies (per 4 FUs, i.e., per one
chemical unit cell) of the five ordered spin states are written as
JijSi ꢀ Sj, where Jij = J1 - J4. By
i<j
5. Spin Exchange Interactions
In NaMnVO4, only the high-spin Mn2þ (S = 5/2) ions are
FM : ð - 4J1 - 8J2 - 8J3 - 4J4ÞðN2=4Þ
AF1 : ð þ 4J1 - 8J2 þ 8J3 - 4J4ÞðN2=4Þ
magnetic ions. As depicted in panels a and b of Figure 5, we
AF2 : ð þ 4J1 þ 8J2 - 8J3 - 4J4ÞðN2=4Þ
AF3 : ð - 4J1 þ 8J2 þ 8J3 - 4J4ÞðN2=4Þ
AF4 : ð þ 4J3ÞðN2=4Þ
ð1Þ
(18) (a) Greedan, J. E. J. Mater. Chem. 2001, 11, 37. (b) Dai, D.; Whangbo,
M.-H. J. Chem. Phys. 2004, 121, 672.

8582 Inorganic Chemistry, Vol. 49, No. 18, 2010
Ben Yahia et al.
quantum number of each spin site (i.e., S = 5/2 in the present
case). Thus, for NaMnVO4, θ can be approximated by
35ð2J1 þ 4J2 þ 4J3 þ 2J4Þ
θ ꢁ
ð3Þ
12kB
The θ value is estimated to be -56.6 and -44.8 by using the
spin exchange parameters from the GGAþU calculations
with U = 4 and 5 eV, respectively. This is in good agreement
with experiment (i.e., -62 K), given that GGAþU electronic
structure calculations generally overestimate the magnitude
of spin exchange interactions by a factor approximately up to
four.25
In NaMnVO4, the intrachain exchange J1 is by far the
strongest exchange, which forms uniform antiferromagnetic
chains along the b-direction. This explains the occurrence of a
broad maximum in the magnetic susceptibility at 24 K. The
spin exchanges J1-J4 are all antiferromagnetic. Therefore,
the exchanges in the (J1, J2, J3) and (J2, J2, J4) triangles are
spin-frustrated (Figure 5a,b), namely, the interchain spin
exchanges are spin-frustrated. This explains why TN is con-
siderably smaller than |θ| in NaMnVO4 (11.8 vs 62 K). It is of
interest to consider the probable magnetic structure for the
ordered antiferromagnetic state below TN. Among the inter-
chain spin exchanges, J4 is stronger than J2 and J3 by a factor
of ∼2. Thus, the magnetic structure shown in Figure 5c, in
which the spins are antiferromagnetically coupled in all J1
and J4 magnetic bonds, is energetically most favorable and
hence is expected to represent the ordered magnetic structure
of NaMnVO4 below TN.
Figure 6. Five ordered spin states of NaMnVO4 employed to extract the
spin exchanges J1-J4 by using a (a, b, 2c) supercell. The unshaded and
shaded circles represent the Mn2þ ions with up-spin and down-spin,
respectively. The two numbers in the parentheses (from left to right) for
each state are the relative energies (in meV per 4 FUs) obtained from the
GGAþU calculations (with U = 4 and 5 eV, respectively).
To determine the values ofJ1-J4, we determine the relative
energies of the five ordered spin states on the basis of density
functional calculations. Our calculations employed the fro-
zen-core projector augmented wave method20 encoded in the
Vienna ab initio simulation packages21 and the generalized-
gradient approximation (GGA)22 with the plane-wave-cutoff
energy of 500 eV and a set of 36 k points for the irreducible
Brillouin zone. To properly describe the effect of electron
correlation in the Mn 3d states, the GGA plus on-site
repulsion method (GGAþU)23 was used with the effective
U values of 4 and 5 eV. The relative energies (per 4 FUs) of
the five ordered spin states obtained from GGAþU calcula-
tions are summarized in Figure 6. Thus, by mapping the
relative energies of the five spin ordered states onto the
corresponding energies expected from the total spin exchange
energies listed in eq 1, we obtain the values of J1-J4
summarized in Table 3.
6. Concluding remarks
NaMnVO4 crystallizes in the maricite-type structure as
does NaMnPO4 and undergoes a three-dimensional antifer-
romagnetic ordering at TN = 11.8 K, with a broad maximum
in the magnetic susceptibility at Tmax = 24 K. The broad
maximum reflects the fact that the strongest spin exchange J1
forms uniform antiferromagnetic chains, and TN is consider-
ably smaller inmagnitude than the Curie-Weiss temperature
of -62 K because the interchain spin exchanges are spin-
frustrated. Our study predicts that, in the ordered magnetic
structure below TN, the spins are antiferromagnetically
coupled in all J1 and J4 magnetic bonds. It would be
interesting to verify this prediction by neutron diffraction
measurements.
To see how reasonable the extracted spin exchanges are, we
calculate the Curie-Weiss temperature θ, which in the mean
field theory24 is related to spin exchanges as
X
SðS þ 1Þ
θ ¼
ziJi
ð2Þ
3kB
i
Acknowledgment. The authors acknowledge the work
that occurred at NCSU funded by the Office of Basic
Energy Sciences, Division of Materials Sciences,
U.S. Department of Energy, under Grant DE-FG02-
86ER45259, and also the computing resources of the
NERSC center and the HPC center of NCSU.
where the summation runs over all nearest neighbors of a
given spin site, zi is the number of nearest neighbors con-
nected by the spin exchange parameter Ji, and S is the spin
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Supporting Information Available: X-ray diffraction details
(CIF) as well as Tables S1 and S2 and Figures S1 and S2. This
material is available free of charge via the Internet at http://
pubs.acs.org.
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