KV6O11: A magnetic metal synthesized at high pressure

Article abstract of DOI:10.1103/PhysRevB.60.3764

An AV₆O₁₁-type magnetic metal KV₆O₁₁ was discovered by a high-pressure synthesis. It crystallizes in hexagonal P6₃/mmc at 295 K, whereas in hexagonal P6₃mc at 154 K. KV₆O₁₁ shows three magnetic transitions at 190, 66.8, and 35.1 K. KV₆O₁₁ is paramagnetic above 66.8 K. Its inverse magnetic susceptibility is slightly concave upward with respect to temperature above 190 K, but the relationship is significantly concave upward below 190 K. KV₆O₁₁ shows uniaxial magnetic anisotropy with an easy axis of magnetization parallel to the [001] direction below 66.8 K. The magnetization shows an anomaly at 35.1 K. The resistivity normal to [001] is of the order of 10^-4 Ω cm^-1. The resistivity versus temperature shows a positive slope above 190 K, a broad maximum at around 90 K, a linear relationship with a positive slope between 35.1 and 66.8 K, and Fermi-liquid-type behavior below 35.1 K. The paramagnetic state below 190 K is discussed on the basis of two types of spin-gap models. Problems of the models are also pointed out. The saturated magnetization versus temperature shows a hyperbolic relationship. The magnetization cannot be explained by the well-known mean field theory or the spin fluctuation mechanism. 1999 The American Physical Society.

Full text of DOI:10.1103/PhysRevB.60.3764

PHYSICAL REVIEW B
VOLUME 60, NUMBER 6
1 AUGUST 1999-II
KV O : A magnetic metal synthesized at high pressure
6
11
Yasushi Kanke
National Institute for Research in Inorganic Materials, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
Received 17 December 1998͒
͑
An AV O -type magnetic metal KV O was discovered by a high-pressure synthesis. It crystallizes in
6
11
6
11
hexagonal P6 /mmc at 295 K, whereas in hexagonal P6 mc at 154 K. KV O shows three magnetic
3
3
6
11
transitions at 190, 66.8, and 35.1 K. KV O is paramagnetic above 66.8 K. Its inverse magnetic susceptibility
6
11
is slightly concave upward with respect to temperature above 190 K, but the relationship is significantly
concave upward below 190 K. KV O shows uniaxial magnetic anisotropy with an easy axis of magnetization
6
11
parallel to the ͓001͔ direction below 66.8 K. The magnetization shows an anomaly at 35.1 K. The resistivity
normal to ͓001͔ is of the order of 10Ϫ4 ⍀ cm . The resistivity versus temperature shows a positive slope
above 190 K, a broad maximum at around 90 K, a linear relationship with a positive slope between 35.1 and
Ϫ1
66.8 K, and Fermi-liquid-type behavior below 35.1 K. The paramagnetic state below 190 K is discussed on the
basis of two types of spin-gap models. Problems of the models are also pointed out. The saturated magneti-
zation versus temperature shows a hyperbolic relationship. The magnetization cannot be explained by the
well-known mean field theory or the spin fluctuation mechanism. ͓S0163-1829͑99͒01630-6͔
I. INTRODUCTION
The P6 /mmc-P6 mc transition is of second order, and the
3 3
8
,14
P6 mc-Cmc21 transition is of first order.
The V͑1͒
3
Various V3ϩ-V4ϩ mixed valence oxides show metal-
insulator transitions as functions of temperature. They are
relevant substances to understand the nature of 3d electrons
in states between localized and itinerant. A series of hexago-
kagome
´
lattice consists of a unique regular triangle in the
P63 /mmc phase. In the P63mc phase, the triangle main-
tains regularity, but branches into larger and smaller types,
and the V͑1͒ atoms form a kagom e´ trimer. In the Cmc21
phase, the shape of the kagom e´ trimer is transformed into an
isosceles triangle, and the V͑1͒ atoms branch into two types.
A pair of the V͑2͒ atoms forming the dimer are no longer
3
ϩ
4ϩ
nal V -V oxides, AV O ͓AϭNa ͑Ref. 1͒ Sr ͑Ref. 2͒ Pb
6
11
͑
Ref. 3͔͒ have become of interest because of their unusual
magnetism, electric conductivity, and structural phase
transitions.
NaV O is paramagnetic above 64.2 K (ϭT ). Its mag-
4
–15
equivalent in both P6 mc and Cmc21 phases. The V͑3͒
3
5
atoms are unique in all of the three phases.
6
11
C
51
Two V NMR absorption peaks of NaV O are detected
6
11
netic susceptibility ␹ obeys the Curie-Weiss law above 240
6
5
at 300 K. One exhibits a small Knight shift, Ϫ0.1%, and the
shift is almost independent of temperature. The Knight shift
of the other is Ϫ2% at 300 K, and the negative shift in-
K (ϭT ), but below T . NaV O shows uniaxial magnetic
t
t
6
11
anisotropy with an easy axis of magnetization parallel to
5
͓
001͔ below T . The resistivity of NaV O is also
C 6 11
4
,5
anisotropic. In what follows, ␳
ity parallel to ͓001͔ and that perpendicular to ͓001͔, respec-
tively. Between 5 and 300 K, ␳ shows normal metallic char-
acter without any anomaly. ␳ is of the order of
/ץT is positive, whereas ␳Ќ is
ʈ
and ␳Ќ represent resistiv-
ʈ
ʈ
Ϫ5
Ϫ6
1
0
–10 ⍀ cm, and ץ␳
ʈ
approximately one order of magnitude larger than ␳
shows anomalies at T , T , and 80 K.
ʈ
and
C
t
AV O compounds are essentially isostructural with
6
11
1
6–18
18,19
20
BaTi Fe O ,
BaSn Fe O ,
and BaFe Ru O .
A
2
4
11
2
4
11
2
4
11
homologous structure of the spinel structure and AV O one
6
11
corresponds to the magnetoplumbite structure ͑Fig. 1͒.
BaFe O ͑Refs. 21 and 22͒ and NaFe V O , ͑Ref. 23–25͒
1
2
19
3
9
19
crystallize in magnetoplumbite type. The former is a well-
known permanent magnet material, and the latter shows
spontaneous magnetization below 240 K. AV O phases
FIG. 1. ͑111͒ sectional view of cubic Fe O ͑left͒ and ͑110͒
3
4
6
11
sectional views of hexagonal BaFe O ͑middle͒ and hexagonal
1
2
19
consist of three types of V atoms, V͑1͒O and V͑2͒O octa-
6
6
NaV O ͑right͒. S and R represent spinel block and R block, re-
6
11
hedra and V͑3͒O trigonal bipyramid. The V͑1͒O octahedra
5
6
spectively. Thin vertical lines and dashed horizontal lines ͑m͒ indi-
cate threefold axes and mirror planes, respectively. Large open
circles, large shaded circles, and small circles indicate O atoms, Ba
or Na atoms, and Fe or V atoms, respectively. Patterns in small
circles represent types of the Fe/V atoms. Two types of the octahe-
dral Fe sites in Fe O are equivalent due to the cubic crystal system.
form a kagom e´ lattice normal to the hexagonal ͓001͔ direc-
tion by edge sharing. The V͑2͒O octahdedra form a face-
6
sharing dimer parallel to ͓001͔. NaV O crystallizes in hex-
6
11
agonal P6 /mmc above T , in hexagonal P6 mc between
3
t
3
7
–9,15
8
0 K and T , and in orthorhombic Cmc2 below 80 K.
t
1
3
4
0
163-1829/99/60͑6͒/3764͑13͒/$15.00
PRB 60
3764
©1999 The American Physical Society

PRB 60
creases on cooling. The latter peak split into two in the
3765
KV O : A MAGNETIC METAL SYNTHESIZED AT . . .
6
11
5
1
P6 mc state. A zero-field V NMR study of NaV O at 4.2
3
6
11
1
0
K detected three lines, but without assignment so far.
The paramagnetic state of SrV O shows qualitatively
6
11
the same behavior as that of NaV O , showing a transition
6
11
6
at 320 K (ϭT ). However, SrV O is insulating in its mag-
t
6
11
netically ordered state below 70 K (ϭT ) and shows meta-
C
6
magnetism below 35 K. The crystal structure of SrV O at
6
11
room temperature was described in P6 /mmc with rather
3
7
high R factors. Recently, the P6 /mmc-P6 mc transition
has been observed between room temperature and 353 K,
as in the case with NaV O .
3
3
2
6,27
6
11
1
3,28
PbV O is paramagnetic above 90 K (ϭT ).
Its ␹
6
11
C
shows qualitatively same temperature dependence as those of
2
8
NaV O and SrV O with an anomaly at 560 K (ϭT ).
6
11
6
11
t
PbV O exhibits spin-glass-type behavior with a freezing
6
11
1
3
temperature of 50 K and is insulating below 50 K. It crys-
tallizes in P6 mc at room temperature.
1
3
3
The three AV O compounds exhibit a common charac-
6
11
ter at their paramagnetic states, but, especially NaV O ,
6
11
show drastic differences below T . An itinerant electron
C
1
2
model is proposed for NaV O . The model attributes the
6
11
spontaneous magnetization of NaV O to spin polarization.
6
11
However, the origin of their unusual magnetism has not been
revealed so far.
The three AV O compounds are synthesized at ambient
6
11
pressure whose A and O atoms form hexagonal close packed
layers. Trials to prepare AV O (AϭCa, Ba, La, Nd, Bi, Tl)
6
11
,13
at ambient pressure have failed.2 High-pressure synthesis
would be relevant to dense packing and simple and high-
symmetrical crystal structures. The characters would be ad-
vantageous to magnetic order and metallic conductivity. In
this study, KV O is prepared at 5.5–6.0 GPa and at 1473–
6
11
2
273 K. The structural phase transition, magnetism, and
FIG. 2. The cell assemblies for high-pressure synthesis at 1573
K ͑upper͒, at 1973 K ͑middle͒, and at 2273 K ͑lower͒. ͑1͒ steel ring,
electric conductivity of KV O are studied.
6
11
͑
2͒ graphite heater, ͑3͒ NaClϩ10 wt. % ZrO , ͑4͒ Pt capsule, ͑5͒
II. EXPERIMENT
A. Synthesis
2
NaCl, ͑6͒ sample, ͑7͒ NaClϩ20 wt. % ZrO , ͑8͒ NaClϩ10 wt. %
ZrO , ͑9͒ NaClϩ20 wt. % ZrO , ͑10͒ NaClϩ20 wt. % ZrO , and
2
2
2
2
͑11͒ Ta foil.
The starting materials V O ͑99.9%͒ and K CO ͑99.9%͒
2
5
2
3
were dried at 873 and 573 K immediately before using, re-
spectively. V O was prepared by reducing V O in a H /N
2
in a platinum capsule. Two capsules were assembled in a cell
with a graphite heater ͑Fig. 2͒. The assembly for higher tem-
perature was modified to maintain temperature stability.3
The cell was pressed at the target pressure and heated at
1573 K for 60–120 min ͑preliminary study͒ or for 5–10 min
to wait melting the sodium chloride inside the graphite heater
͑crystal synthesis͒. For crystal synthesis, the temperature was
then increased to the target temperature. Finally, the cell was
quenched to room temperature and was gradually released to
ambient pressure to avoid a blowout.
2
3
2
5
2
0,31
atmosphere at 1073 K for 2 h. V O was obtained by heating
2
4
an equimolar mixture of V O and V O in a sealed silica
2
5
2
3
tube at 1273 K for 3 days. KVO was synthesized by heating
3
an equimolar mixture of K CO and V O at 773 K for 5
2
3
2
5
days with several intermediate grindings.
High-pressure synthesis was performed at 5.5–6.0 GPa
and at 1473–2273 K using two belt-type presses, FB30H
͑Ref. 29͒ with a bore diameter of 32 mm and FB40H with
that of 44 mm. The pressure was calibrated at room tempera-
ture by means of the known pressure-induced phase transi-
tions in Bi, Tl, and Ba.30,31 The temperature was estimated
from the extrapolated relations between the input electric
power and the temperature, which had been obtained in ad-
KV O was synthesized at 6.0 GPa and at 1573 K
6
11
using the FB30H press. Successful experiments gave the
weight change of the capsule less than 0.4 mg. The typical
weight of the capsule including the mixture was 1.2 g.
A couple of three-phase regions, KV O -V O -V O and
6
11
2
3
3
5
vance by measuring the temperature up to 1773–2073 K
KV O -K -V O ͑Refs. 32 and 33͒-V O were observed.
Powder x-ray diffraction detected no solid solution in
6 11 2Ϫx 8 16 2 4
with a W͑5% Re͒-W͑26% Re͒ thermocouple.3
0,31
The pres-
sure effect on the electromotive force of the thermocouple
was not corrected.
KV O . Trials to obtain ATi O ͑AϭNa, K, Ca, Sr, Ba͒
6
11
6
11
compounds failed in this study.
Single crystals of KV O were prepared from stoichio-
About 0.3 g ͑for FB30H͒ or about 2.5 g ͑for FB40H͒ of a
mixture of KVO , V O , and V O was mechanically sealed
6
11
metric mixtures ͑1͒ at 6.0 GPa and 1973 K for 60 min
3
2
3
2
4

3766
YASUSHI KANKE
PRB 60
Chromel-Alumel thermocouple with a water-ice standard.
Lattice parameters were determined from Bragg angles of 22
reflections in the region 86°Ͻ2␪Ͻ89° at both temperatures.
Reflections for hу0, kу0, lу0, and
and those for hр0, kр0, lрϪ1, and
were measured at both temperatures.
͉
h
͉
р
͉
k
͉
with 2␪р90°
with 2␪р90°
͉
h
͉
р
͉
k
͉
Of the resulting 1280/1272 reflections, 167/45 ones were
unobserved ͑295 K/154 K hereafter in this paragraph͒. Three
¯
standard reflections 600, 240, and 0012 were measured every
4
h. Deviation of intensity was within 0.2%/0.7% during the
total exposure time of 84.3 h/123.9 h. No decay correction
3
4
was applied. An absorption correction was applied with
Ϫ1
correction factors (␮ϭ75.668 cm ) for F ranging from
FIG. 3. Powder x-ray diffraction profile of KV O (Cu K␣).
1.475/1.477 to 1.764/1.833. 1106/1222 reflections with I
Ͼ1.5␴(I) were used for structural model determination.
Structural parameters including one ͑single domain
model͒ or two ͑twin model͒ scale factor͑s͒ and one free pa-
rameter for extinction correction were refined by an anony-
mous twin refinement program.35 Atomic scattering factors
for neutral atoms and their dispersions were taken from In-
ternational Tables for X-ray Crystallography.36
6
11
Hexagonal, P6 /mmc, aϭ5.7209(5) Å, and cϭ13.2236(8) Å.
3
͑
FB30H͒ for structural analysis, ͑2͒ at 5.5 GPa and 2273 K
for 30 min, then 1473 K for 30 min ͑FB30H͒ for magnetism
measurement, and ͑3͒ at 5.5 GPa and 2273 K for 120 min
͑
FB40H͒ for resistivity measurement. The capsules of ͑1͒
always showed about 1 mg of weight gain after the synthesis.
It was impossible to check the weight change of the capsules
of both ͑2͒ and ͑3͒ because of alloy formation between Pt
and Ta. Surfaces of the as-obtained products were slightly
oxidized; however, the bulk was not affected.
C. Magnetic and electric properties measurement
Magnetic properties were measured using a superconduct-
ing quantum interference device ͑SQUID͒ magnetometer
͑
1͒ About 0.2-mm-diam black crystals with hexagonal-
͑Quantum Design, MPMS͒. Magnetic susceptibility was
plate shape were obtained. Quantitative x-ray microanalysis
of the crystals, using K Ti O and NaV O as references,
measured using the crushed specimen ͑61.87 mg͒ up to 390
K with external magnetic field of 1000 Oe. The magnetiza-
tion was studied on the single-crystal specimen ͑0.07
mg͒ down to 5 K with an external magnetic field of
2
6
13
6
11
determined the K/V ratio of 1/͑6.00Ϯ0.15͒, which supports a
composition of KV O . The specimen for diffraction study
6
11
was cut into 110, 310, and 150 ␮m parallel to ͓001͔, ͓010͔,
4
4
¯
Ϫ5.5ϫ10 –5.5ϫ10 Oe. The resistivity ␳ was measured
and ͓210͔ directions, respectively.
2͒ and ͑3͒ X-ray microanalysis of the crystals detected no
Ќ
by a standard four-probe method at 5–246.5 K using a Physi-
cal Property Measurement System ͑Quantum Design͒. The
electrodes were made on the 0.15 mmϫ1.00 mm surface of
the 0.15 mmϫ0.20 mmϫ1.00 mm specimen using Au wires
͑
possible impurities such as Pt, Ta, Na, Cl, Zr, or Fe. The
single-crystal specimens for the measurements were checked
by oscillation and Weissenberg photographs. ͑2͒ Obtained
crystals were about 0.5 mm in diameter with hexagonal-plate
shape. The specimen for the magnetism measurement was
͑0.033 mm in diameter͒ and Ag paste ͑EPO-TEK H20F͒.
0
.07 mg. About 100 crystals were selected and crushed for
III. RESULTS
A. Structural analysis
magnetic susceptibility measurement. ͑3͒ Microscopic obser-
vation indicated that the product passed through a partially
molten state and contained columnar crystals instead of the
hexagonal-plate ones. Typical size was 0.1 mmϫ0.15
mmϫ0.8 mm. The specimen for the resistivity measurement
was 0.15 mmϫ0.20 mmϫ1.00 mm. The 0.15 mmϫ1.00 mm
surfaces were perpendicular to ͓001͔ direction. The 0.20
mmϫ1.00 mm surfaces were much more lustrous than the
others. About 1.00 mm diameterϫ0.20 mm thick single crys-
tals may have formed, but broken into pieces during quench-
ing to room temperature or during releasing pressure. Dozens
of the crystals were selected and crushed for powder x-ray
diffraction ͑Fig. 3͒
At both temperatures, diffraction data showed hexagonal
symmetry and an extinction rule, lÞodd for hhl, indicating
¯
possible space groups of P6 /mmc, P62c, and P6 mc.
3
3
P6 /mmc is centrosymmetric and gives a unique structural
model. But the other two are not centrosymmetric, and each
of the two gives two single-domain models and one twin
3
¯
model. P62c provides a single-domain model ͓͑x,y,z͒
model͔, its ͑110͒ mirror image ͓(Ϫy,Ϫx,z) model͔, and a
twin model consisting of the two ͓(x,y,z)ϩ(Ϫy,Ϫx,z)
model͔. P6 mc gives a single-domain model ͓͑x,y,z͒ model͔,
3
its ͑001͒ mirror image ͓(x,y,Ϫz) model͔, and a twin model
consisting of the two ͓(x,y,z)ϩ(x,y,Ϫz) model͔. The
B. Structural analysis
(
x,y,z) and (Ϫy,Ϫx,z) models and the (x,y,z) and (x,y,
Diffraction data for KV O were collected at 295 and
54 K on an Enraf-Nonius CAD4 diffractometer with
graphite-monochromatized Mo K␣ radiation ͑␭ϭ0.7093 Å͒
using ␻-␪ scan with ⌬␻ϭ͑0.8ϩ0.35 tan ␪͒°. The measure-
ment at 154 K was carried out by blowing cold nitrogen gas
onto the specimen. The temperature was calibrated by a
Ϫz) models are essentially congruent, but differently related
to the external form of the specimen. All of the seven models
are examined using the same data set for each temperature.
To test twin models as well as single-domain models, all of
the refinements are carried out on the basis of I instead of F.
The results are summarized in Table I.
6
11
1

PRB 60
3767
KV O : A MAGNETIC METAL SYNTHESIZED AT . . .
6
11
TABLE I. Structural model examination on KV O at 295 and at 154 K.a
6
11
T ͑K͒
Space group
Model
Nr
Np
R ͑%͒
Rw ͑%͒
2
2
95
95
P6 /mmc
¯
P62c
unique
(x,y,z)
1106
1106
26
32
2.95
2.91
4.54
4.45
3
2
95
95
¯
(Ϫy,Ϫx,z)
(x,y,z)ϩ(Ϫy,Ϫx,z)
(x,y,z)b
1106
1106
32
33
2.91
2.91
4.46
4.44
P62c
2
¯
P62c
295
295
295
154
154
P6 mc
1106
1106
1106
1222
1222
43
43
44
26
32
3
b
P6 mc
(x,y,Ϫz)
3
b
P6 mc
(x,y,z)ϩ(x,y,Ϫz)
3
P6 /mmc
uniquec
7.07
6.87
18.81
18.49
3
d
¯
P62c
¯
P62c
¯
P62c
(x,y,z)
1
1
54
54
(Ϫy,Ϫx,z)d
(x,y,z)ϩ(Ϫy,Ϫx,z)d
1222
1222
32
33
6.86
6.98
18.48
18.39
154
154
154
P6 mc
(x,y,z)
(x,y,Ϫz)
(x,y,z)ϩ(x,y,Ϫz)
1222
1222
1222
43
43
44
2.80
2.81
2.70
4.73
4.77
4.39
3
P6 mc
3
P6 mc
3
aTo examine twin models as well as single-crystal models, all of the refinements are carried out on the basis
of I.
b
Structural parameters do not converge.
c
Temperature factors of V͑1͒, V͑3͒, and O͑2͒ are negative.
d
Temperature factors of V͑3͒, O͑1͒, and O͑2͒ are negative.
1
. 295 K
1280 of reflections are averaged into 640 unique ones for
P6 /mmc (R ϭ0.010). Here 542 reflections among the
3
int
The three P6 mc models provide low enough Rw values
as well as the others. But structural parameters of the three
models are oscillating with large amplitudes and do not con-
3
6
40 ones satisfy the condition IϾ1.5␴(I). The final refine-
ment is carried out on the basis of F using the 542 reflections
Table II͒.37 Interatomic distances and bond angles are listed
in Table III.
͑
verge. So the three P6 mc models are excluded. The three
3
¯
P62c models give slightly smaller Rw values compared to
the P6 /mmc one. Among the four possible models, the
3
2
. 154 K
P6 /mmc one provides the highest R value of 0.0454 and
3
w
¯
All of the P6 /mmc and P62c models result in signifi-
3
¯
the P62c twin model the lowest Rw value of 0.0444. How-
ever, the difference in Rw for the two models cannot be
regarded as significant, taking into account the number of
parameters, N . Hence the P6 /mmc model with the high-
cantly high Rw values compared to the remaining P6 mc
models. In addition, several temperature factors converge to
3
¯
negative in all of the P6 /mmc and P62c models. Among
p
3
3
est symmetry is selected for the 295 K structure. A total
the three possible P6 mc models, the twin model gives the
3
2
TABLE II. Atomic coordinates and equivalent thermal parameters ͑Å ͒ in KV O at 295 and 154 K. For both temperatures: M
6
11
8
2
ϭ520.7407, hexagonal, Zϭ2, F(000)ϭ490, and B ϭ ␲ (4U ϩ4U ϩ3U Ϫ4U ). 295 K: P6 /mmc, aϭ5.7233(1) Å, c
eq
Ϫ3
9
11
22
33
12
3
3
2
ϭ13.2282(2) Å, Vϭ375.25(2) Å , d ϭ4.609 g cm . Refined on F as a single-crystal specimen, Rϭ0.016, R ϭ0.019, wϭ1/␴ (F),
/␴Ͻ0.006, and Ϫ1.147Ͻ⌬␳р0.757 e Å . 154 K: P6 mc, aϭ5.7137(2) Å, cϭ13.1947(3) Å, Vϭ373.05(2) Å , dcalcϭ4.636 g cm
Refined on I as a twin specimen, Rϭ0.026, R ϭ0.043, wϭ1/␴ (I), ⌬/␴Ͻ0.006, and volume fraction (x,y,z): (x,y,Ϫz)
calc
w
3
3
Ϫ3
⌬
.
3
2
w
ϭ1.00(6):0.95(6).
2
95 K (P6 /mmc)
154 K (P6 mc)
3
3
Atom
Position
x
y
z
Beq
Atom
K
Position
x
y
z
Beq
K
V͑1͒
V͑2͒
2c
6g
4e
1/3
1/2
0
2/3
0
0
1/4
0
0.680͑7͒
0.487͑4͒ V͑1͒
2b
6c
2a
2a
2b
6c
6c
6c
2b
2b
1/3
0.493 98͑2͒
2/3 0.252 86͑11͒ 0.359͑8͒
2x
0
0
0.271͑3͒
0.146 907͑18͒ 0.417͑4͒ V͑21͒
V͑22͒
3/4
0.078 91͑5͒
0
0
1/3
0.147 90͑11͒ 0.249͑13͒
0.353 89͑10͒ 0.290͑14͒
0
V͑3͒
O͑1͒
2d
12k
1/3
0.169 30͑7͒
2/3
2x
0.539͑6͒ V͑3͒
0.502͑8͒ O͑11͒
O͑12͒
0.544͑11͒ O͑2͒
0.480͑14͒ O͑31͒
O͑32͒
2/3 0.744 62͑10͒ 0.313͑8͒
0.169 55͑11͒ 2x 0.079 88͑13͒ 0.343͑18͒
0.168 55͑10͒ 2x 0.421 59͑12͒ 0.350͑16͒
0.152 82͑10͒ 2x 0.749 48͑13͒ 0.392͑11͒
O͑2͒
O͑3͒
6h
4f
0.152 71͑10͒ 2x
1/3 2/3
3/4
0.590 37͑9͒
1/3
1/3
2/3 0.586 89͑16͒ 0.29͑2͒
2/3 0.904 63͑17͒ 0.27͑3͒

3768
YASUSHI KANKE
PRB 60
TABLE III. Interatomic distances ͑Å͒ and bond angles ͑deg͒ in KV O at 295 and 154 K. Symmetry
6
11
codes: ͑i͒ x,y,z; ͑ii͒ 1Ϫy, 1ϩxϪy, z; ͑iii͒ Ϫxϩy, 1Ϫx, z; ͑iv͒ 1Ϫy, 1Ϫx, 1/2Ϫz; ͑v͒ Ϫxϩy, y, 1/2
Ϫz; ͑vi͒ x, 1ϩxϪy, 1/2Ϫz; ͑vii͒ Ϫx, 1Ϫy, Ϫ1/2ϩz; ͑viii͒ 1Ϫx, 1Ϫy, Ϫ1/2ϩz; ͑ix͒ y, Ϫxϩy,
Ϫ1/2ϩz; ͑x͒ y, 1Ϫxϩy, Ϫ1/2ϩz; ͑xi͒ xϪy, x, Ϫ1/2ϩz; ͑xii͒ 1ϩxϪy, 1ϩx, Ϫ1/2ϩz; ͑xiii͒ 1Ϫy, x
Ϫy, z; ͑xiv͒ Ϫxϩy, Ϫx, z; ͑xv͒ y, x Ϫz; ͑xvi͒ 1Ϫx, Ϫxϩy, Ϫz; ͑xvii͒ x, xϪy, 1/2Ϫz; ͑xviii͒ Ϫy, x
Ϫy, z, ͑xix͒ Ϫx, Ϫy, Ϫ1/2ϩz; ͑xx͒ Ϫxϩy, y, 3/2Ϫz; ͑xxi͒ 1Ϫxϩy, 1Ϫx, z; ͑xxii͒ x, Ϫ1ϩy, z; ͑xxiii͒
1
ϩxϪy, x, Ϫ1/2ϩz; ͑xxiv͒ x, Ϫ1ϩy, Ϫ1ϩz.
2
95 K (P6 /mmc)
154 K (P6 mc)
3
3
K-O͑1i,ii,iii,iv,v,vi
͒
2.7868͑6͒
K-O͑11i,ii,iii͒
O͑12i,ii,iii
O͑2vii,viii,ix,x,xi,xii
V͑1xxii͒-O͑11xiii,xiv
O͑12ix,xxiii
O͑31viii
O͑32xxiv
V͑21͒-O͑11i,xiv,xviii͒
O͑2ix,xi,xix
V͑22͒-O͑12i,xiv,xviii͒
O͑2ix,xi,xix
2.799͑2͒
2.760͑2͒
͒
O͑2vii,viii,ix,x,xi,xii
V͑1͒-O͑1xiii,xiv,xv,xvi
͒
2.8650͑1͒
1.9434͑4͒
͒
2.8605͑1͒
1.9206͑10͒
1.9655͑10͒
2.0580͑12͒
2.0276͑14͒
1.9029͑13͒
2.0208͑16͒
1.8922͑13͒
2.0459͑16͒
1.7876͑10͒
2.081͑3͒
͒
͒
͒
O͑3viii,xvii
͒
2.0393͑7͒
͒
͒
V͑2͒-O͑1i,xiv,xviii͒
1.9041͑6͒
2.0375͑7͒
O͑2ix,xi,xix
͒
͒
͒
V͑3͒-O͑2i,ii,iii͒
1.7905͑9͒
V͑3͒-O͑2i,ii,iii
͒
O͑3i,xx
͒
2.1116͑12͒
O(31)
O(32)
2.111͑2͒
V͑1͒-V͑1xxi
V͑2͒-V͑2v͒
͒
2.861 65͑5͒
V͑1xxii͒-V͑1
xiv a
͒
2.7536͑4͒
2.9601͑4͒
2.7180͑5͒
93.92͑8͒
iii b
V͑1 ͒
2.7275͑5͒
92.88͑4͒
V͑21͒-V͑22͒
O͑1xiii͒-V͑1͒-O͑1xiv
͒
͒
O͑11 ͒-V͑1xxii͒-O͑11xiv͒
xiii
O͑12 ͒-V͑1 ͒-O͑12xxiii
ix
xxii
͒
91.86͑7͒
O͑1xiii͒-V͑1͒-O͑1xvi
O͑1xiii͒-V͑1͒-O͑3viii
87.13͑4͒
92.00͑2͒
O͑11 ͒-V͑1xxii͒-O͑12xxiii͒
xiii
87.03͑4͒
xiii
͒
O͑11 ͒-V͑1xxii͒-O͑31viii͒
91.79͑5͒
O͑12 ͒-V͑1xxii͒-O͑32xxiv
ix
͒
91.71͑6͒
O͑1xiii͒-V͑1͒-O͑3xvii
O͑1͒-V͑2͒-O͑1xiv͒
͒
88.00͑2͒
O͑11 ͒-V͑1xxii͒-O͑32xxiv͒
xiii
91.28͑4͒
O͑12 ͒-V͑1xxii͒-O͑31viii
ix
͒
85.16͑4͒
99.51͑2͒
89.356͑19͒
80.10͑3͒
O͑11͒-V͑21͒-O͑11xiv͒
99.57͑7͒
ix
ix
O͑1͒-V͑2͒-O͑2 ͒
O͑11͒-V͑21͒-O͑2 ͒
89.02͑3͒
ix
xi
ix
xi
O͑2 ͒-V͑2͒-O͑2 ͒
O͑2 ͒-V͑21͒-O͑2 ͒
O͑12͒-V͑22͒-O͑12xiv͒
80.80͑8͒
99.54͑7͒
ix
O͑12͒-V͑22͒-O͑2 ͒
89.55͑4͒
ix
xi
O͑2 ͒-V͑22͒-O͑2 ͒
O͑2͒-V͑3͒-O͑2ii͒
O͑2͒-V͑3͒-O͑31͒
O͑2͒-V͑3͒-O͑32͒
79.61͑7͒
O͑2͒-V͑3͒-O͑2ii͒
O͑2͒-V͑3͒-O͑3͒
120
119.873͑9͒
92.05͑7͒
90
87.95͑7͒
V͑1͒-O͑1 ͒-V͑1xxi͒
xv
94.83͑3͒
89.12͑4͒
V͑1 ͒-O͑11 ͒-V͑1
xxii
xiii
xiv a
͒
91.59͑6͒
xxii
ix
iii b
V͑1 ͒-O͑12 ͒-V͑1 ͒
97.70͑7͒
V͑1͒-O͑3viii͒-V͑1xxi
͒
V͑1xxii͒-O͑32 ͒-V͑1
xxiv
xiv a
͒
85.54͑7͒
V͑1xxii͒-O͑31 ͒-V͑1 ͒
viii
iii b
91.97͑7͒
ix
v
ix
V͑2͒-O͑2 ͒-V͑2 ͒
V͑1͒-O͑1xiv͒-V͑2͒
84.03͑4͒
V͑21͒-O͑2 ͒-V͑22͒
83.88͑4͒
xxii
xiv
128.06͑2͒
V͑1 ͒-O͑11 ͒-V͑21͒
129.65͑4͒
126.63͑3͒
123.86͑5͒
128.36͑5͒
136.40͑11͒
139.72͑11͒
xxii
ix
ix
V͑1 ͒-O͑12 ͒-V͑22 ͒
V͑1xxii͒-O͑31viii͒-V͑3viii
͒
V͑1͒-O͑3viii͒-V͑3viii
V͑2͒-O͑2 ͒-V͑3viii͒
͒
125.89͑3͒
V͑1xxii͒-O͑32xxiv͒-V͑3xxiv
V͑21͒-O͑2 ͒-V͑3viii͒
V͑22͒-O͑2 ͒-V͑3viii͒
͒
ix
ix
137.986͑17͒
ix
a
Intratrimer.
Intertrimer.
b

PRB 60
3769
KV O : A MAGNETIC METAL SYNTHESIZED AT . . .
6
11
TABLE IV. Electrostatic potentials ͑␸͒ and Madelung energies (⌬E) of KV O for possible charge
6
11
distributions. The V͑21͒ and V͑22͒ atoms are equivalent in the P6 /mmc form.
3
2
95 K (P6 /mmc)
154 K (P6 mc)
3
3
V͑1͒
ϩ4
ϩ3
ϩ3
ϩ3
ϩ3.5
ϩ3.5
ϩ3.5
ϩ3
ϩ4
ϩ4
ϩ4
ϩ4
ϩ3
ϩ3
ϩ3
ϩ3.5
ϩ3.5
ϩ3.5
ϩ3
ϩ4
ϩ4
ϩ4
V͑21͒
V͑22͒
V͑3͒
ϩ3.5
ϩ3.5
␸
␸
␸
␸
͓V͑1͔͒͑V͒
Ϫ38.92
Ϫ38.56
Ϫ38.56
Ϫ40.03
Ϫ5.631
Ϫ37.50
Ϫ41.14
Ϫ41.14
Ϫ42.04
Ϫ5.656
Ϫ36.08
Ϫ43.73
Ϫ43.73
Ϫ44.05
Ϫ5.727
Ϫ38.73
Ϫ38.71
Ϫ38.70
Ϫ40.24
Ϫ5.629
Ϫ37.31
Ϫ41.25
Ϫ41.33
Ϫ42.26
Ϫ5.658
Ϫ35.90
Ϫ43.79
Ϫ43.96
Ϫ44.28
Ϫ5.733
͓V͑21͔͒͑V͒
͓V͑22͔͒͑V͒
͓V͑3͔͒͑V͒
⌬
E(MJ molϪ1
)
lowest R value. The difference should be significant even if
However, both KV O and NaV O are metallic and show
6 11 6 11
w
the number of parameters, N , is considered. The twin
similar resistivity above T . So the two compounds prob-
p
C
ϩ
ϩ
P6 mc model is selected for the 154 K data. A pair of hk0
ably show comparable ␹ . The difference, K or Na , does
3
P
and hk0 reflections are averaged into an hk0 reflection. As a
result, a total of 1272 reflections are averaged into 1236
unique ones for P6 mc (R ϭ0.005). Here 1189 reflections
not appear to cause so large difference in ␹ or ␹ . A large
VV
L
Ϫ3
Ϫ1
␹const of KV O , 1.89ϫ10 emu mol , may be question-
6
11
able. ␹ data of KV O at 190–270 K are reanalyzed by
3
int
6
11
among the 1236 ones satisfy the condition IϾ1.5␴(I). The
final refinement was carried out on the basis of I using the
1
fixing ␹const of KV O at ␹const of NaV O ͓Table V, spin-
6 11 6 11
free V͑1͒ model͔. The Curie constant of KV O obtained in
6
11
189 reflections ͑Table II͒.37 Interatomic distances and bond
this way is close to that of NaV O . The latter analysis is
6 11
angles are listed in Table III.
used for the spin-free V͑1͒ model described later.
Madelung energies are calculated by the Fourier method
using an unpublished computer program38 for both structures
at 295 and 154 K. At both temperatures, the V͑1͒ atom pre-
fers the trivalent state and both V͑2͒ and V͑3͒ atoms the
tetravalent state ͑Table IV͒.
2. Below Tt
Ϫ1
Below T , ␹ versus T is significantly concave upward
t
in KV O as well as in NaV O ͑Ref. 5͒ and SrV O ͑Ref.
6
11
6
11
6
11
Ϫ1
6
͒ ͑Fig. 4͒. The relationship of ␹
versus T approaches
being linear with decreasing temperature. An additional ␹
B. Magnetic susceptibility
term appears to contribute which decreases with decreasing
Ϫ1
temperature. ␹ versus T is analyzed on the assumption that
1
. Above Tt
the additional term is an energy-gap term as follows:
Ϫ1
Figure 4 shows ␹
versus temperature of KV O ,
6
11
5
6
Ϫ1
NaV O , and SrV O . The ␹
of KV O shows an
6
11
6
11
6 11
anomaly at 190 K (ϭT ) and is concave upward both above
t
Ϫ1
and below T . Above T , ␹ versus temperature is linear in
t
t
Ϫ1
both NaV O and SrV O , whereas ␹ is concave upward
6
11
6
11
in KV O . The specimen of KV O is obtained by crushing
6
11
6
11
single crystals and is confirmed to be phase pure by powder
x-ray diffractometry. The nature of ␹ in KV O is believed
6
11
to be intrinsic.
Above T , ␹ data of the three compounds are analyzed,
t
considering that ␹ consists of the Curie-Weiss paramagnetic
term and temperature-independent term as follows:
␹
ϭC/͑TϪ␪͒ϩ␹const
.
͑1͒
C and ␪ represent the Curie constant and Weiss temperature,
respectively. ␹const includes the Pauli paramagnetic term
(
␹ ), Van-Vleck paramagnetic term (␹VV), and Landau dia-
P
magnetic term (␹ ). The parameters obtained are shown in
L
Table V. ␹const of NaV O agrees well with that obtained
6
11
3
9
Ϫ4
Ϫ1
from a Knight shift versus ␹ plot, 4ϫ10 emu mol . The
parameters for SrV O do not converge, probably due to the
FIG. 4. Inverse magnetic susceptibility vs temperature for
6
11
KV O ͑circle͒, NaV O ͑Ref. 5͒ ͑triangle͒, and SrV O ͑Ref. 6͒
6
11
6
11
6
11
narrow temperature range of the data. So the analysis is car-
͑
square͒. The fitting curve above T for KV O is on the basis of
t 6 11
ried out by fixing ␹
of SrV O at ␹const of NaV O ,
const
.
6 11 6 11
the spin-gap V͑1͒ model ͑see text͒. Those for both NaV O and
6 11
SrV O are on the basis of the spin-free V͑1͒ model. The fitting
6 11
Ϫ4
Ϫ1
3
1
.6ϫ10 emu mol
.89ϫ10 emu mol , which is much larger than that of
␹const of KV O
converges to
6
11
Ϫ3
Ϫ1
curves below T for the three compounds are on the basis of Eq. ͑2͒
t
Ϫ1
NaV O . This reflects different curvature in ␹ versus T.
͑see text͒.
6
11

3770
YASUSHI KANKE
PRB 60
TABLE V. Parameters characterizing the paramagnetic states of AV O compounds.
6
11
KV O
NaV O
SrV O
6 11
6
11
6
11
TрTt
C ͑emu K molϪ1
͒
1.20͑3͒
1.79
2.19
0.968͑5͒
1.61
1.97
1.431͑5͒
1.95
2.39
peff(nϭ3)
peff(nϭ2)
peff(nϭ1)
3.10
2.78
3.38
␪
͑K͒
70.1͑4͒
0.0148͑18͒
200͑28͒
3.6ϫ10Ϫ4
65.57͑13͒
0.0255͑15͒
494͑15͒
3.6ϫ10Ϫ4
79.20͑15͒
0.0144͑3͒
472͑8͒
A ͑emu molϪ1͒
⌬
͑K͒
␹const ͑emu molϪ1͒
3.6ϫ10Ϫ4
T рT ͓spin-free V͑1͒ model͔
t
Ϫ1
C ͑emu K mol
peff(nϭ3)
͒
2.733͑7͒
2.70
2.670͑11͒
2.67
3.142͑14͒
2.89
peff(nϭ2)
3.30
3.27
3.54
peff(nϭ1)
4.67
4.62
5.01
␪
͑K͒
12.5͑5͒
3.6ϫ10Ϫ4
Ϫ58͑7͒
Ϫ17.1͑17͒
3.6ϫ10Ϫ4
␹const ͑emu molϪ1͒
3.6(14)ϫ10Ϫ4
T рT ͓spin gap V͑1͒ model͔
t
Ϫ1
C ͑emu K mol
1
͒
2.301͑18͒
2.48
2.99͑7͒
2.82
2.68͑9͒
2.67
peff(nϭ3)
␪1
͑K͒
Ϫ236͑4͒
Ϫ608͑24͒
Ϫ469͑28͒
␹
ϭC/͑TϪ␪͒ϩA exp͑Ϫ⌬/T͒ϩ␹const
.
͑2͒
␹hfϭpTϩq.
͑3͒
However, the slope p is smaller below 35 K ͓p
A is a constant and ⌬ corresponds to the energy gap. The gap
Ϫ1 Ϫ2
Ϫ1 Ϫ1
4
0
ϭ0.065(3) emu mol
and larger above 35 K ͓pϭ0.321(8) emu mol
K
,
qϭ4.66(6) emu mol
K
K
͔
term has been applied for Ni͑C H N ͒ NO ͑ClO ͒, a typi-
2
8
2 2
2
4
Ϫ1
Ϫ2,
4
1
cal Haldane gap system. Equation ͑2͒ fits well the data
Ϫ1 Ϫ1
qϭϪ4.3(4) emu mol
intersect each other at 35.2 K.
The initial magnetization curves ͑Fig. 6͒ are analyzed by
K ͔. The two fitting lines in Fig. 7
͑
3
AT
Fig. 4͒. Analyses are performed by fixing ␹
at
const
Ϫ4
Ϫ1
.6ϫ10 emu mol
͑Table V͒. Other forms such as
Ϫ1/2
Ϫ1
exp(Ϫ⌬/T) and AT exp(Ϫ⌬/T) are tried as well.
2
5/2
3/4
means of an M versus H/M plot, M versus (H/M)
4
2
The former has been applied for two-leg spin ladder sys-
tems, SrCu O ͑Ref. 43͒ and CaV O . The latter has been
applied for the spin gap in CaCuGe O . However, quality
plot,5 and M versus H/M one ͑Fig. 8͒. The first one has
been derived from the mean field theory and is well known
as the Arrot plot. The second one is relatively empirical and
,46
4
47
4
4
2
3
2
5
4
5
2
6
of the fitting is essentially independent of the form of the gap
term. The parameters A and ⌬ vary significantly depending
on the form, but the parameters C and ␪ are almost indepen-
dent of the form. So the simplest form A exp(Ϫ⌬/T) is
adopted.
5
has been applied for Ni ͑Ref. 46͒ and NaV O . The third
6
11
one has been derived from the self-consistent renormaliza-
48
tion ͑SCR͒ theory and has been applied for the weakly
49
itinerant ferromagnetism of Fe0.83Co0.17Si. Arrott plots are
5
/2
concave upward at 55–75 K ͓Fig. 8͑a͔͒. M
(
versus
H/M)3 plots are slightly concave downward below 60 K,
/4
C. Magnetization
but linear above 62 K. Their slopes increase with increasing
temperature. M4 versus H/M plots are slightly concave
downward below 25 K, linear at 30–64 K, and concave
downward again above 65 K. Their change in slope with
KV O shows uniaxial magnetic anisotropy with an easy
6
11
axis of magnetization parallel to ͓001͔ at 5 K ͓Fig. 5͑a͔͒.
KV O behaves as a magnetically single domain with a co-
6
11
5
/2
3
respect to temperature is much milder than that of M ver-
ercive force of 1.8ϫ10 Oe at 5 K ͓Fig. 5͑b͔͒. The hysteresis
at zero field survives below 40 K but above 45 K. Figure 6
shows the initial magnetization curves of KV O with mag-
sus (H/M)3 plots. In any case, at least above T , success-
/4
C
ful plots are expected to be linear with a constant slope in-
6
11
dependent of temperature. As the M5/2 versus (H/M)3/4 plots
show the best linearity around TC , TC is determined by the
relationship of M5 intercept versus temperature. The TC
netic field parallel to ͓001͔. At 5 K, the magnetization satu-
rates at about 850 Oe, which may correspond to the demag-
netizing field. The demagnetizing field is not corrected
throughout this work. Even above saturation, the magnetiza-
tion increases gradually with increasing magnetic field. The
magnetization curves above saturation can be regarded as
linear lines below 50 K, but the curves are concave upward
/2
obtained is 66.8 K. The saturated magnetization M at each
s
temperature is analyzed by three methods: ͑1͒ from the mag-
netization curves above saturation, regarding as linear below
5
/2
50 K and parabolic at 55–62 K, ͑2͒ from the M intercepts
5
/2
3/4
above 55 K. The slopes of the linear lines, ␹ , are plotted
of the M versus (H/M) plots at 5–66 K, and ͑3͒ from
hf
4
4
against temperature in Fig. 7. ␹hf increases linearly with in-
the M intercepts of the M versus H/M plots at 5–64 K.
creasing temperature as follows:
The M values obtained by the three methods show insignifi-
s

PRB 60
3771
KV O : A MAGNETIC METAL SYNTHESIZED AT . . .
6
11
FIG. 6. Initial magnetization curves of KV O with a magnetic
6
11
field parallel to ͓001͔. 5–60 K: every 5 K. 62–70 K: every 1 K.
and 66.5 K as follows. The transition temperature 35.1 K
agrees well with corresponding 35.2 K in ␹ . In what fol-
hf
lows, 35.1 K will be adopted as the transition temperature:
␳Ќϭ1.869͑7͒ϫ10Ϫ7T2ϩ1.604͑4͒ϫ10Ϫ4 ͓⍀ cm͔
͑
at 5–35.1 K͒, ͑4͒
␳Ќϭ6.197͑18͒ϫ10Ϫ6Tϩ1.732͑9͒ϫ10Ϫ4 ͓⍀ cm͔
͑
at 35.1–66.5 K͒. ͑5͒
IV. DISCUSSION
A. Crystal structure
ϩ
Twelve-coordinated K ͑ionic radiusϭ1.64 Å͒ is much
FIG. 5. Hysteresis loops of KV O with external magnetic field
6
11
ϩ
2ϩ
larger than corresponding Na ͑1.39 Å͒, Sr ͑1.44 Å͒, and
parallel to the ͓001͔ direction ͑open shapes͒ and initial magnetiza-
tion curve of KV O with magnetic fields perpendicular to ͓001͔
2
ϩ
50
Pb ͑1.49 Å͒. However, the differences between the K-O
6
11
͑
͑
solid circle͒. ͑a͒ whole, 5 K and ͑b͒ magnified, 5 K ͑circle͒, 30 K
triangle͒, and 40 K ͑square͒.
distances in KV O and the corresponding A-O distances in
6
11
cant differences. In what follows, M values given by ͑2͒
s
will be adopted ͑Fig. 9͒. The M values of NaV O are
s
6
11
5
obtained by ͑1͒ below 53 K and by ͑2͒ above 55 K ͑Fig. 9͒.
By an extrapolation described later, the saturated magnetiza-
tion at 0 K, M (0 K), of KV O is determined to be
s
6
11
Ϫ1
Ϫ1
1
.5 ␮ f.u. . M (0 K) of NaV O ͑Ref. 5͒ is 1.7 ␮ f.u. .
B s 6 11 B
D. Resistivity
Resistivity of KV O is measured perpendicular to the
6
11
͓001͔ direction at 5–246.5 K ͑Fig. 10͒. Reproducible data are
not obtained above 246.5 K in this study. ␳ is of the order
Ќ
Ϫ4
of 10 ⍀ cm. ␳ shows anomalies at 190, 66.5, and 35.1 K
Ќ
which correspond to T , T , and the anomaly in ␹ , re-
t
C
hf
spectively. ץ␳ /ץT is positive below 66.5 K and above 190
Ќ
K, and is concave upward at 66.5–190 K, showing a broad
maximum at around 90 K. ␳ exhibits Fermi-liquid-type be-
Ќ
havior below 35.1 K, and ␳ versus T is linear between 35.1
FIG. 7. ␹hf vs temperature for KV O .
6 11
Ќ

3772
YASUSHI KANKE
PRB 60
FIG. 9. Ms vs temperature of KV O ͑circle͒ and NaV O
11
6
11
6
͑Ref. 5͒ ͑triangle͒. The fitting curves are on the basis of Eq. ͑7͒ ͑see
text͒.
ers. The pressure of 5.5–6.0 GPa appears to be effective to
ϩ
2Ϫ
shrink K with respect to O to form the hexagonal close-
packed layers.
The P6 mc phase of KV O shows twinning ͑Table I͒,
3
6
11
which suggests that corresponding twinning may occur in
NaV O and/or PbV O . However, the structural refine-
6
11
6
11
ments on the P6 mc forms of NaV O ͑Ref. 8͒ and
3
6
11
PbV O ͑Ref. 3͒ converged promptly with low enough R
6
11
factors, without applying twinning. This may be attributable
to small anomalous dispersion terms of Na in NaV O or
6
11
may suggest that the volume fraction ratio (x,y,z)/(x,y,
Ϫz) is far from 1.0 in PbV O and/or in NaV O . In the
6
11
6
11
P6 mc state of KV O , the differences in the atomic coor-
3
6
11
dinates are insignificant between the twin model and the
single-domain models. The twin P6 mc model should be
3
examined in both NaV O and PbV O , even though we
6
11
6
11
cannot expect so much improvement.
KV O shows a P6 /mmc-P6 mc second-order struc-
6
11
3
3
tural phase transition at a temperature between 154 and 295
FIG. 8. Isothermal ͑a͒ M vs H/M plots, ͑b͒ M5/2 vs (H/M)3/4
2
4
plots, and ͑c͒ M vs H/M plots for KV O .
6
11
AV O ͑AϭNa, Sr, Pb͒ are much smaller than those ex-
6
11
pected. The cation should be as large as four-coordinated
FIG. 10. Resistivity of KV O perpendicular to ͓001͔ as a func-
tion of temperature.
6
11
2
Ϫ
O
͑1.38 Å͒ ͑Ref. 50͒ to form hexagonal close-packed lay-

PRB 60
K ͑Tables I and II͒ as NaV O ͑Refs. 8 and 15͒ does. Both
3773
KV O : A MAGNETIC METAL SYNTHESIZED AT . . .
6
11
6
11
Ϫ1
␹
and ␳Ќ of KV O show anomalies at 190 K, without
6 11
Ϫ1
any other break point between 154 and 295 K (␹ ) or
between 154 and 246.5 K (␳ ) ͑Figs. 4 and 10͒. Considering
Ќ
4
,5,8,15
the case in NaV O ,
the structural transition in
6
11
KV O is expected to occur at 190 K. Though the transition
6
11
temperature should be confirmed, for example, by specific
heat, the discussion will be continued assuming that the
P6 /mmc-P6 mc transition accompanies the anomalies in
3
3
Ϫ1
both ␳Ќ and ␹ at T ϭ190 K.
t
The V͑1͒O and V͑2͒O octahedra in KV O are quite
6
6
6
11
7
,8
similar to the corresponding octahedra in NaV O , espe-
6
11
cially in the P6 /mmc state. The V͑3͒O trigonal bipyramid
3
5
in KV O shows, however, a small difference compared to
6
11
that in NaV O . The distance between V͑3͒ and axial O͑3͒
6
11
in KV O is longer than that in NaV O .
6
11
6
11
Among AV O compounds ͑AϭK, Na, Sr, Pb͒, T shows
6
11
t
5
6
drastic difference ͓K, 190 K; Na, 240 K; Sr, 320 K; Pb, 560
K ͑Ref. 28͔͒ but TC does not show so much difference ͓K,
6.8 K; Na, 64.2 K; Sr, 70 K; Pb, 90 K ͑Refs. 13 and 28͔͒.
5
6
6
In NaV O , the transition at Tt accompanies the
6
11
P6 /mmc-P6 mc transition, but the transition at T does
3
3
C
1
5
not accompany any structural transition. The magnetic
transition at T appears to be strongly correlated with the
t
P6 /mmc-P6 mc structural transition, namely, the V͑1͒
3
3
kagom e´ trimer formation, the V͑2͒ branching, or the distor-
tion of the V͑3͒O polyhedra from trigonal bipyramid toward
5
tetrahedron, whereas the magnetic ordering formation at TC
appears to be insensitive to the structural features.
The charge distribution among the V cations in KV O
6
11
may obey electrostatic stability, though KV O is funda-
6
11
mentally metallic ͑Fig. 10͒. Madelung energy calculations
suggest that the V͑1͒ sites prefer trivalent cations and the
V͑2͒ tetravalent cations in both P6 /mmc and P6 mc
3
3
7
7,27
forms of KV O ͑Table IV͒, NaV O , and SrV O .
6
11
6
11
6
11
The V͑3͒ sites prefer tetravalent cations in KV O and
6
11
7,27
7
FIG. 11. Schematic view of t2g orbitals of the V͑1͒ kagome´
lattice in ͑a͒ P6 /mmc form and ͑b͒ P6 mc form. Only in-plane
lobes are drawn. The solid and open lobes show occupied and un-
occupied orbitals, respectively.
NaV O , whereas the trivalent one in SrV O .
The
6
11
6
11
3
P6 mc form of PbV O shows a different preference prob-
3
3
3
6
11
ably due to large structural distortion caused by the steric
hindrance of the electron lone pair of Pb2 . The V͑1͒O6
octahedra of the AV O compounds ͑AϭK, Na, Sr, Pb͒
ϩ
6
11
ones. The V͑2͒ atoms branch into two types below T ; how-
forming a kagom e´ lattice show similar Jahn-Teller distortion:
apical V͑1͒-O͑3͒ distances are longer than basal V͑1͒-O͑1͒
t
ever, the V͑2͒-V͑2͒ distance is maintained almost constant,
independent of the transition at T . the V͑3͒ coordination
distances. The O͑3͒ atom caps the V͑3͒O͑2͒ triangle to form
t
3
a V͑3͒O͑2͒ O͑3͒ coordination trigonal bipyramid. The dis-
polyhedron shows distortion below Tt ; however, the V͑3͒
atoms is apparently distant from any adjacent V atom com-
pared to the V͑1͒ and V͑2͒ atoms. So the energy gap term of
3
2
tortion is observed in both P6 /mmc and P6 mc forms.
3
3
The t2g states of the V͑1͒ atom separate into two types,
higher (d ) and lower ͑d and d ͒, where the z direction
␹ below T may be attributable to the V͑1͒ atom. Then the
xy
xz
yz
t
corresponds to the apical axis. So d electrons in the V͑1͒
atom are considered to occupy the dxz and/or dyz orbitals
V͑2͒ and/or V͑3͒ atoms are responsible for the Curie-Weiss
term below T . Provided that that V͑2͒ and/or V͑3͒ atoms
t
͑Fig. 11͒. Similar orbital ordering has been discussed on
maintain their magnetic character above T also, the Curie-
t
NaV O ͑Refs. 8 and 12͒ and on the ordered rock salt-type
6
11
Weiss term above T should consist of two terms, the V͑1͒
t
5
1
insulator LiVO2. The trimer formation in ordered rocksalt
type results in a super structure formation, whereas the
trimer formation in the kagom e´ lattice does not ͑Fig. 11͒.
term and the V͑2͒ϩV͑3͒ term as follows:
5
1
␹ϭC /͑TϪ␪ ͒ϩC /͑TϪ␪2,3͒ϩ␹const
.
͑6͒
1
1
2,3
This is consistent with the P6 mc forms of NaV O ͑Ref.
3
6
11
C /(TϪ␪ ) corresponds to the V͑1͒ atom and C /(T
1
1
2,3
8
͒ and KV O .
6 11
Ϫ␪2,3) corresponds to the V͑2͒ and V͑3͒ atoms. Analyses
are carried out by fixing C2,3 , ␪2,3 , and ␹const to C, ␪, and
␹const below T ͑Fig. 4͒. The C and ␪ obtained ͑Table V͒
B. Paramagnetic states
t
1
1
1
. Spin gap V(1) model
appear to be reasonable.
The V͑1͒ atoms from a kagom e´ trimer below T and the
V͑1͒-V͑1͒ distance branches into the longer and the shorter
The model gives the following conclusions. The V͑1͒
atom shows Curie-Weiss character above Tt , whereas spin-
t

3
774
YASUSHI KANKE
PRB 60
gap character below T . The spin moment of the V͑1͒ atom
consistent with the fact that the cation of a face-sharing co-
ordination octahedron prefers lower valence to the cation of
an edge-sharing one. In the three compounds, d electrons of
the V͑1͒ atoms are considered to be band type and to exhibit
negligible spin. The V͑1͒ layer with band electrons and the
V͑2͒ and V͑3͒ layer with localized electrons stack alterna-
tively parallel to ͓001͔. This model, however, cannot explain
t
above T corresponds to Sϭ1 in NaV O and to slightly
t
6
11
smaller than Sϭ1 in both KV O and SrV O . The V͑2͒
6
11
6
11
and V͑3͒ atoms show Curie-Weiss character throughout the
paramagnetic state. Their Curie constant and Weiss tempera-
ture are unchanged by the transition at T . Provided that the
t
V͑2͒ and V͑3͒ atoms uniformly contribute to the Curie-
Weiss term, their spin moments correspond to almost S
ϭ1/2 in both KV O and NaV O and to slightly larger
why ␳ is much lower than ␳Ќ in NaV O .
ʈ
6 11
Mean V-O distance for the V͑1͒, V͑2͒, and V͑3͒ atoms
6
11
6
11
are almost constant between 295 K ͑above T ͒ and 154 K
t
than Sϭ1/2 in SrV O . Thus the given charge distributions
6
11
͑
below T ͒ in KV O . This is also observed in both
t 6 11
are consistent with electrostatic stability. The Weiss tem-
perature ␪1 and the gap temperature ⌬ of the V͑1͒ atom
show comparable absolute values in the three compounds,
7,27
NaV O ͑Refs. 7 and 8͒ and SrV O .
The transitions at
6
11
6
11
Tt probably do not cause charge transfer among the V atoms,
if any, to be negligible. At the transitions, the V͑1͒ atoms are
considered to maintain their valences and the band character
with negligible spin in the three compounds, whereas the
which would be reasonable. Positive ץ␳ /ץT above T and
Ќ
t
negative ץ␳ /ץT below T are consistent with this model.
Ќ
t
The V͑1͒-V͑1͒ distance in the P6 /mmc form is short
V͑2͒ and V͑3͒ atoms change their character below I . Pro-
3
t
enough to consider a t -t hybridization in the V͑1͒
vided that all of the V͑2͒ and V͑3͒ atoms uniformly contrib-
ute to the Curie-Weiss term below T as well, their p val-
2
g
2g
kagom e´ lattice ͑Table III͒. Combined with earlier discus-
sions, each dxz and dyz orbital of the V͑1͒ atom is expected
to contain nearly one electron ͑Fig. 11͒. The two orbitals dxz
and dyz are degenerate above T . Below T , the degeneracy
t
eff
ues almost correspond to Sϭ1/2 in the three compounds.
Remaining electron spins are considered to decrease with
decreasing temperature, obeying A exp(Ϫ⌬/T). So the V͑2͒
and V͑3͒ atoms include both Curie-Weiss type and spin-gap-
t
t
fails and the two orbitals branch into two types, bonding and
antibonding. This feature is consistent with spin-gap charac-
type spins below T , which would be questionable. In addi-
t
tion, this model cannot explain why ␳ does not show any
ʈ
ter below T . The gap temperature may be controlled by
t
anomaly at T in spite of the fact that ␳ shows an anomaly
competition between the energy gap of the bonding and an-
tibonding states and the Coulomb repulsion among the d
electrons.
t
Ќ
at T in NaV O .
t
6
11
C. Below TC
Arrot plots of both KV O and NaV O are not linear at
6
11
6
11
2
. Spin-free V(1) model
all ͓Fig. 8͑a͔͒, which suggests that well-known mean field
theory is not applicable to their magnetization. Their tem-
perature dependence of ␳Ќ resembles those of well-known
The above model is, however, in conflict with the NMR
study that the V͑1͒ atom of NaV O exhibits negligible spin
moment throughout the paramagnetic states. Two
NMR absorption peaks of NaV O are detected at 300 K.
One exhibits a small Knight shift of Ϫ0.1% and the shift is
almost independent of temperature. The Knight shift of the
other is Ϫ2% at 300 K, and the negative shift increases on
6
11
3
9
51
52
V
magnetic metals such as Fe. Ms(0 K) of neither KV6O11
6
nor NaV6O11 is integer ͑Fig. 9͒. Their Ms values at 5 K
6
11
4
increase with increasing H even above saturation. M versus
H/M plots show much better linearity than the Arrot plots in
KV O . These features suggest itinerant ferromagnetism.
6
11
2
4/3
2
2
cooling. The latter peak split into two in the P6 mc state.
Both plots, M versus T and M versus T ͑Fig. 12͒,
3
s
s
Recently, the former was assigned to the V͑1͒ atom and the
latter peaks to the V͑2͒ and V͑3͒ atoms.39 It means that the
V͑1͒ atom shows almost negligible spin moment throughout
the paramagnetic region and that the temperature dependence
of ␹ is almost exclusively caused by the V͑2͒ and V͑3͒ at-
oms. In what follows, the discussion will be continued, con-
sidering that the temperature-dependent terms of KV O
are not linear, which suggests that the origin of the magne-
47,49
tization is not spin fluctuations.
M versus temperature
s
of both KV O and NaV O can be analyzed by a hyper-
6
11
6
11
bolic function, like Curie-Weiss paramagnetism, as follows:
M ϭCЈ/͑TϪ␪Ј͒ϩM ͑7͒
.
const
s
6
11
and SrV O are also attributable exclusively to the V͑2͒
Though Eq. ͑7͒ has no theoretical background so far, it
6
11
and/or V͑3͒ atoms.
fits all of the data ͑Fig. 9͒. The parameters obtained are
Ϫ1
Effective Bohr magneton numbers peff are calculated as-
suming that one (nϭ1), two (nϭ2), or three (nϭ3) of the
V͑2͒ and V͑3͒ atoms per unit formula uniformly contribute
the Curie-Weiss term ͑Table V͒. In all of the compounds
CЈϭ8.8(4)␮ f.u. K,
␪Јϭ73.6(3) K,
for KV O
␪Јϭ72.1(4) K,
and Mconst
B
Ϫ1
ϭ1.572(9)␮ f.u.
and
and
CЈ
Mconst
B
6
11
Ϫ1
ϭ12.0(6)␮ f.u. K,
B
Ϫ1
ϭ1.854(15)␮ f.u. for NaV O . M at 0 K and T are
B
6
11
s
C
above T , both models with nϭ1 and 2 are excluded be-
given by extrapolating the plot to Tϭ0 K and Ms
t
Ϫ1
cause the peff values significantly exceed the theoretical
value for Sϭ1 (V3 ), 2.828. The peff values with nϭ3 are
consistent with Sϭ1, especially in SrV O . In the three
ϭ0␮ f.u. , respectively. Thus obtained parameters are
B
ϩ
Ϫ1
M (0 K)ϭ1.5␮ f.u.
M (0 K)ϭ1.7␮ f.u.
and T ϭ68 K for KV O and
s
B
C 6 11
Ϫ1
and T ϭ66 K for NaV O . The
C 6 11
6
11
s
B
compounds above T , consequently, both V͑2͒ and V͑3͒ at-
TC values are slightly higher than those obtained by the re-
lationship M intercept versus temperature described ear-
t
5
/2
oms are close to trivalent with Sϭ1. The V͑1͒ atoms are
close to 4ϩ in both KV O and NaV O and to 3.67ϩ in
lier; however, the M (0 K) values are reasonable.
6
11
6
11
s
SrV O . The charge distribution does not obey the electro-
KV O and NaV O show a similar temperature depen-
6
11
6
11
6
11
static stability mentioned earlier. However, the distribution is
dence of ␳ . Both compounds show three discontinuities in
Ќ

PRB 60
3775
KV O : A MAGNETIC METAL SYNTHESIZED AT . . .
6
11
the slope is continuous. The corresponding ␳Ќ versus T of
KV O is also linear down to 35.1 K. However, the relation-
6
11
ship changes into parabolic below 35.1 K, indicating Fermi
liquid character ͑Fig. 10͒.
V. CONCLUSION
An AV O -type magnetic metal KV O was discovered
6
11
6
11
by a high-pressure synthesis at 5.5–6.0 GPa. It crystallizes in
hexagonal P6 /mmc at 295 K, whereas in hexagonal
3
P6 mc at 154 K. KV O shows three magnetic transitions
3
6
11
at 190 K (ϭT ), 66.8 K (ϭT ), and 35.1 K. The paramag-
t
C
netic states were analyzed on the basis of the spin-gap V͑1͒
model and spin-free V͑1͒ model. ͑1͒ Spin-gap V͑1͒ model:
The V͑1͒ atom shows Curie-Weiss character with Sϭ1
above T , but exhibits spin-gap character below T . The
t
t
V͑2͒ and V͑3͒ atoms show Curie-Weiss character corre-
sponding to Sϭ1/2 throughout the paramagnetic states. ͑2͒
Spin-free V͑1͒ model: The V͑1͒ atom is almost tetravalent
and free from electron spin throughout the paramagnetic
states. The V͑2͒ and V͑3͒ atoms show Curie-Weiss character
with Sϭ1 above T , whereas below T , half of the spin
t
t
survives as Curie-Weiss type, but the remaining half exhibits
spin-gap character. Both models have several problems.
KV O shows uniaxial magnetic anisotropy with an easy
6
11
axis of magnetization parallel to the ͓001͔ direction below
TC . The saturated magnetization versus temperature cannot
be explained by the well-known mean field theory or spin
fluctuation mechanism, but exhibits a hyperbolic relation-
ship. KV O is essentially metallic. The resistivity normal to
6
11
Ϫ4
Ϫ1
͓
001͔, ␳ , is of the order of 10 ⍀ cm
.
␳Ќ versus T
Ќ
shows a positive slope above 190 K, a broad maximum at
around 90 K, a linear relationship with positive slope be-
tween 35.1 and 66.8 K, and Fermi-liquid-type behavior be-
low 35.1 K. Specific heat studies are required especially to
understand the Fermi liquid state below 35.1 K. Neutron and
NMR studies are required especially to reveal the origin of
the unusual paramagnetism below T and the magnetic struc-
ture ͑s͒ below TC .
t
2
4/3
2
s
2
FIG. 12. ͑a͒ M vs T plots and ͑b͒ M vs T plots for KV O
s
6
11
͑
circle͒ and NaV O ͑Ref. 5͒ ͑triangle͒.
6
11
ACKNOWLEDGMENTS
The author is grateful to M. Akaishi ͑NIRIM͒ and T. Ka-
washima ͑NIRIM͒ for significant support on high-pressure
experiments, E. Takayama-Muromachi ͑NIRIM͒ for encour-
aging high-pressure synthesis and valuable discussions of
magnetic susceptibility, K. Kato ͑NIRIM͒ for valuable ad-
vice on structural analysis, and H. Kato ͑Kyoto University͒
for kindly allowing the author to quote unpublished data on
PbV O . The author is indebted to H. Tsunetsugu ͑Univer-
sity of Tsukuba͒, M. Umehara ͑NIRIM͒, Y. Uchida
͑NIRIM͒, E. Kita ͑University of Tsukuba͒, M. Arai
͑NIRIM͒, and Y. Takahashi ͑Himeji Institute of Technology͒
for valuable discussions of magnetism. The author is grateful
to A. Sato ͑NIRIM͒ for help on the diffraction experiment
and K. Kosuda ͑NIRIM͒ for x-ray microanalysis. This work
was supported by the Science and Technology Agency of
Japan.
ץ␳ /ץT. Those at T and T are common, but the remaining
Ќ
C
t
one is different. NaV O ͑Ref. 5͒ shows the remaining one
6
11
͑
80 K͒ in the paramagnetic state between TC and T . The
t
discontinuity accompanies a structural transition, but no
anomaly in ␹, whereas in KV O , the remaining discontinu-
6
11
ity ͑35.1 K͒ is observed below T ͑Fig. 10͒. In addition, the
C
discontinuity accompanies an anomaly in ץ␹ /ץT ͑Fig. 7͒.
hf
6
11
In itinerant ferromagnetic system, ␹hf is sensitive to the band
structure and/or the difference between the density of states
for up spin and down spin. So the magnetic structure, the
band structure, and/or the difference in the density of states
of KV O may change at 35.1 K. A structural transition may
6
11
also occur at 35.1 K.
Below T , ␳Ќ versus T of NaV O is linear down to
C
6
11
about 30 K and becomes concave downward. The change in

3776
YASUSHI KANKE
PRB 60
1
26
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Y. Kanke, Y. Hata, E. Kita, and K. Kato ͑unpublished͒.
H. Kato, M. Kato, K. Yoshimura, and K. Kosuge ͑private com-
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2
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