MAGNETIC STRUCTURES AND PROPERTIES OF VI2.

Article abstract of DOI:10.1016/0038-1098(79)90661-6

Single-crystal measurements of the magnetic susceptibilities of VI//2 show an anomaly at a critical temperature of about 14 K. Neutron diffraction data show that this anomaly can be ascribed to a magnetic phase transition from a 120 degree structure to a collinear arrangement of the spins with a magnetic unit cell a//m//a//g//n equals a a square root of 3 , b//m//a//g//n equals 2a and c//m//a//g//n equals 2c.

Full text of DOI:10.1016/0038-1098(79)90661-6

Solid State Communications,VoL 30, pp. 403—408.
Pergainon Press Ltd. 1979. Printedin Great Britain.
MAGNETIC STRUCTURES AND PROPERTIES OF V !~
S.R. Kuindersma, C. Haas, J.P. Sanchez* and R. Al
Laboratory of Inorganic Chemistry, Materials Science Center of the University,
Nijenborgh 16,9747 AG Groningen, The Netherlands
(Received 19 Januwy 1979 byA.R. Miedema)
Single-crystal measurements of the magnetic susceptibilities of V!2 show an
anomaly at acritical temperature of about 14 K. Neutron diffraction data
show that this anomaly can be ascribed to a magnetic phase transition from
a 120°structure to a collinear arrangement of the spinswith amagnetic
unit cell a m ~
=
a’~/Lb m ,~ 2a and Cmagn = 2c.
=
1. INTRODUCTION
After afew weeks the reaction was complete, as
shown by the absence of free iodinein the vapourphase.
No sublimation or transport of V I~tookplace at 500°C.
V!2 IS A LAYERED COMPOUNDwhich crystallizes in
the well-known Cd(OH)2-structure, space groupD ~[1].
Then the tube was heated to 800°Cat one side and
700°Cat the other side. The sublimation of VI2 from
the hot to the cold side of the tube is a slowprocess and
The magnetic structure of V!2 has not been reported
previously,
According to the layer character of V12 one might
suspect it to behave like ametamagnetic system. A
proposition alongthese lines for the magnetic structure
of V!2 has been given by Friedt etaL on the basis of
data from 129j Mössbauer spectroscopy [21.These
authors concluded from the transferredhyperfme
field at the iodine nucleus that the spins on the three
vanadium atoms coordinated to an iodine atom are
parallel to one another,
the growth of single crystals may take several months.
3. MAGNETIC SUSCEF~IBILITIESOF V12
Measurements of the magnetic susceptibility and
magnetization of single crystals have been performed on
a Faraday-type system (Oxford Instruments) equipped
with a MettlerME 21 electronic vacuum microbalance,
described previously [5].
The susceptibilities fortwo directions of the mag-
netic field (8.61 kOe), H II c-axis and Hi. c-axis, are
shown in Fig. 1 for the temperature range from 5 to
Niel etaL [3,4] reportedthe magnetic powder
susceptibilities of the dthalides of vanadiumas a func-
tion of the temperature. These authors foundfor V12 a
critical temperature of 15 K, whereas the susceptibility
reaches its maximum at 25K. The difference between
both temperatures reflects the presence of short-range
order.
In this paperwe report magnetic susceptibilities of
single crystals of V!2. Neutron diffractogramsobtained
lOOK. Both curves are corrected for diamagnetism,
x ~
=
—
119 x l0~cm3mol1[61,and a temperature-
independent Van Vleck susceptibility. For the Van
Vleck term 8 k’N ~ 4 /~avalue of 210 x lO6cm3mol”
was calculated usingthe crystal-field splitting A
=
7870
cm1 [7] and assuming an orbital reduction factorof
at afew selected temperatures, reveal the presence of
two different magnetic structures.
=
0.8 [8,9].
The susceptibility data of Niel etaL [41agree very
well with ours. These authors founda Curie—Weiss type
behaviourat temperatures above 150K. Aparamagnetic
2. SYNTHESIS OF V!2
Synthesis of V12 was carried out at a temperature
of about 500°Cin a quartz tube starting from the el-
ements and usinga small excess of the metal, in order to
Curie temperature 0
calculated indicating=the presence of V24’(3d3) ions with
3/2 and agvalue of 2.02. The fact thatthe g value
—
143Kand lid! = 4-07PB were
S
=
avoid the formation of V13. To avoid the growth of a
mirror of silicates of vanadiumthe tube was filled with
argon witha pressure of 0.1 atm.
is larger than 2, and not smaller as in most V2’ corn-
pounds, can be explained by the contribution of the
spin-orbit coupling actingbetween at21 and an e,
orbital [101.
In the region of the critical temperature (14 K) and
*
Permanent address: Laboratoire de Chimie Nucléaire,
Centre de Recherches Nucléaires, 67037 Strasbourg,
Cedex, France.
of the temperatures where the susceptibilities are maxi-
mal, the susceptibilities show a very anisotropic
behaviour. Whereas the curve forH I c showsa broad
403

404
MAGNETIC STRUCTURES AND PROPERTIES OF V!2
Vol 30. No.6
175(X
Table 2. Observed andcalculatedintensitiesof the mag-
netic reflections of the 5.5Kdiffractogram (RM = 7.8%)
20
hkl
1obs
‘caic
595
011
15500
15100
784
1067
111
013
15150
15100
2000
I
I
1500
15500
—
1232
1359
113
211
2500
4600
2700
4600
0
E
- _ _ _ _
I
maximum(25K),themaximumfortheHllccurveis
I
quite sharp(14.4K).
From 14.4 to 12.5 K both susceptibilities sharply
again between 12.5 and 5K. This increase of the suscep-
tibility forH ~fccannot be attributed simply to a para-
decrease and onlythe H fl c susceptibility increases
magnetic impurity (d3 ) as onlythe H II c curve shows
the increment. Furthermore,the magnetization vs
applied field at 5.1 K forthe two directionsof the field
show straight lines up to 40kOe and a saturation as
13500
11500
expected for paramagnetic momentsis not observed.
The presence of a small amount of paramagnetic V~’
\
ions in V!2 mayaccount for the anisotropic behaviour
of the susceptibility atlow temperatures. The ground
state of V34(d2) in a cubic ligand field is 3T~,(t~,I)f.a
trigonal field and a relatively small spin—orbit inter-
action are included in the Hamiltonian,thisleads to
very anisotropicg values (g~~ 2,gj~’1.6 [111.
\
\
IIc
\
The anisotropy of the magnetic susceptibilityof
V!2 at hightemperatures is not large (smaller than 10%),
weighted only about 6mg.
‘S
and might be due to weighing errors. Our samples
4. MAGNETIC STRUCTURES
- ‘
Neutron-diffraction data were obtained from
7500
1
powder of V!2 at the high-fluxreactor of the E ~ at
I
I
50
Petten at temperatures of 300, 16.5, 14.4, 12.5, 7 and
T(K)
5.5 K,using neutronswith a wavelengthof X 2.5858 A.
=
At 300Kthe neutron diffractogram can be
Fig. 1. Magnetic susceptibilities of V!2 as a function of
the temperature inan applied field of 8.61 kOe. The
broken.curves have been calculatedwith the two-
dimensional model of Niel etal. (seetext).
described with the simple Cd(OH)2-structure, space
groupD ~[1].The hexagonal cell dimensions are: a
=
4.057Aand c
=
6.760A. The relative z-coordinates of
Table 1. Observed andcalculated intensitiesof the magnetic reflections of the 14.4K dlffractogram fortwoplanes
in which the spinspossibly rotate (X
=
2.5858 A)
ab
ab
20
hk~
‘obs
‘caic
RN (%)
‘caic
RN
748
1165
101
103
10200
2900
9100
3300
10000
2200
20.0
6.2
1438
201
2600
1600
2100
100 x ElJ~(obs)
-
1 J~(ca1c)I/EJ~(obs)w,here J ~ is the magnetic
coherent scattering cross section.

Vol. 30, No.6
MAGNETIC STRUCTURES AND PROPERTIES OF V!2
405
_10880
a
A
~
9200
7600
6000
Uz,
Iz-
-
1200200
10800
450
700
950
1200
1450
1700
2—THETA(OMC)
—
U,
~9200
B
z
A
z
7600
6000
~
200
450
700
950
1200
1450
1700
2—THETA IOIICI
Fig. 2. (a) Neutron dlffractogram of V!2 at 14.4 K. The dots indicate the measured counts. The full lineis calculated
with the 120°structure (sp~nsin ac plane). MandN denote magnetic and nuclear reflections. (b) Neutron diffracto-
gram of V!2 at 5.5K. The full lineis calculated withthe structure shown in Fig. 4.
the iodine ions have been refined to z =0.240. In the
16.5 K-dlffractogram a broad maximum is observed in
the region where a magnetic reflection peakis observed
in the 14.4 K-diffractogram, at about 20 =700 DMC
observedmagnetic reflections for the two structuresare
listed In Table 1 and Table 2.
The magnetic reflections at 14.4K can be indexed
on the basis of ahexagonal unit cell with~
=
a’J~
(1O~DMC 360°)(Fig.2).
and cm,., 2c. The magnetic contributions have been
=
Byloweringthe temperature to 12.5Kthe above-
mentioned magneticreflectiondisappeared and two
newreflections are dearly observed at about 590 and
830 DMC. In Fig. 2 the 5.5K.diffractogram is shown.
calculated withthe form factor for V ~ionsgiven by
Watson and Freeman [12].The observed intensitiesare
explained by the well-known 120°structurewith an
antitranslation of 1/2cm., (FIg. 3). it is possible to
The intensities of the magnetic reflections at 5.5K have determine the orientation of the spinsin the magnetic
increasedas compared to those at 7 and 12.5K. The structures from the observed intensities. In Table 1 a

406
MAGNETICSTRUCTURES AND PROPERTIES OF V!2
Vol. 30, No.6
Table3. Magneticparameters ofV!2 at various temperatures. M ~and M ~are the componentsalong the a and caxes
of the magnetic unit cell
T(K)
Structure
Mx(~B)
Mz(liB)
M(~8)
16.5
14.4
12.5
7.0
short range
120°(fig. 3)
coVlinear
structure
(fig. 4)
1.6
1.05
1.14
1.08
1.91
2.03
2.37
2.18
2.33
2.60
5.5
arrangement of the magnetic moments of V2~is shown
in Fig. 4. The orientationof the magnetic moments Is
not along one of the orthorhombic axes. The intensities
of the observed reflections arebest fitted withmagnetic
moments lying in theac-plane and making an angle of
________________________________
61°withthe a-axis. The observed and calculated
intensities are listed in Table 2.
The refmed magnetic parameters at varioustempera-
tures are listed in Table 3.
The magnetic reflections of the 120°structure are
(J’)
broader (by a factor of about 1.5) thanthe reflections of
the low temperature magnetic structure. We remark that
we have not been able to detect a transitiontemperature
between the 120°structure (with the fairly sharp mag-
netic reflections) and the paramagnetic state (with dif-
fuse magnetic reflections characteristic of short-range
Fig. 3. Arrangement of the spinsof V2~in the 120°
structure. The spins lie in a plane perpendicular to the
ab plane. The orientation of the spin in the origin of the transition were observed. Therefote, it is possible that
cellis arbitrary.
order correspondingto the 120°structure). Also in the
susceptibility no anomalies corresponding to such a
the reported 120°structure corresponds not to an
comparison is made with calculated intensitiesof two
structures with the magnetic moments lying in the ab-
plane and the ac-plane, respectively. The arrangement
with the spins in the ab-plane has been found, for
ordered magnetic phase, but to the paramagnetic phase
with a high degree of short.range orderjust above the
critical temperature.
5. DISCUSSION
instance, in L1CrS2 [13],the arrangement with the spins
in the ac-plane has been foundfor RbNiC13 and CsNiC13
The magnetic susceptibilities of V!2 at high tempera-
tures are well described by a two.dimensional model, as
[14]. The agreement between observed and calculated
intensities is better forthe structure withthe spins lying shown by Niel et aL [3, 4]. These authorsobtained from
in the ac-plane (smaller R-index), indicating that this is
the magnetic structure of V!2 at 14.4 K (Fig. 3). We
remark, however, thatthere area number of effects,
which may account for abad agreement between
a series expansion of the magnetic susceptibilityof atwo-
dimensionalHeisenberg antiferromagnet avalue of I/I
6K for the exchange interaction in the layers. With the
=
same series expansion we obtain from our.data slightly
observed and calculated intensities, One reason isthe use different values of 1.11 = 7.8 K from the susceptibilityfor
of the form factor of V2~w, hich decreases less rapidly as H I c and IJI
a function of sin0/A than that of ~+; due to covalency the susceptibility fails completely at temperatures near
=
6.6KforH II c. This series expansion of
the actual charge on vanadium is expected to be smaller thatw1iere the maximum of the susceptibility is reached.
than ina purely ionic description with V ~ions. Another From the value of Ill one calculates avalue o f ~45K
effect is the broadening of themagnetic reflections by
scattering near the critical point, as observed for instance T ~
in K2NiF4 [15—17].
The diffraction pattern at 12.5 K and lower tern-
peratures can be described by an orthorhombic magnetic lations which take into account only exchange inter-
for the Stanley—Kaplan transition temperaturc
~(z 1) [2S(S+ 1) 1] Ill/k, with z = 6and
S = 3/2 [4, 181. Thus, the observed critical temperature
T ~ismuch lower thanexpected on the basis of calcu-
=
—
—
cell witha m ~ = a’~/3~,
= 2a and cm ,.~= 2c. The actions between nearest neighbour magneticions.This

Vol. 30, No.6
MAGNETIC STRUCTURES AND PROPERTIES OF V!2
90°-superexchangeinteractioninvolving transferbe-
tween half-filled t,~and empty e ~orbitals of V ~ .
407
Cm
Because the single-ion anisotropy of V~(3d3i)ons
in an octahedral coordination is expected to be small,
the orientation of the spins will be determined by the
dipolar energy. With the aid of a computer progran~
called “DIPSUM” [8],we calculated the lattice sums
needed for the calculation of the dipolar energy of the
I
I
120°structure and the collinear structure of Fig. 4. The
magneticdipolar energies forthe 120°structure withthe
magneticmoments in the ab-plane and the ac-plane are
+ 3.82 x 106 and —1.91 x l06ergmol’, respectively.
The dipolar energy of the collinear structure of Fig. 4 is
Ethp = ~5.74 x lo6ergmoV1 at 12.5 K, if themagnetic
moments lie in theac-plane ofthe orthorhombic cell and
Fig. 4. Arrangement of the spins of V2~at 5.5 K. The
make an angle of 60°with the a-axis, as found experi-
spins lie In the ac-plane. The angle between the magnetic mentally. The dipolar energiesfor the same struc-
moment and the am axis decreases slightly from 5.5 to
12.5 K(see Table 3).
ture with the spins directed alongthe principal axes are
for the a, b and c axes —7.22 x 106, + 12.39 x 106 and
—
5.18 x l06ergmol~r,espectively. It is clear from
low value of T1, is due to the presence in V!2 of compet- these values that the magnetic momentspreferentially
ing antlferromagnetic interactions11 between nearest
neighbours and ferromagnetic interactions.12 between
next nearest neighbours.
lie in the ac-plane.
The transition from the collinear structure (Fig. 4)
to the 120°structure (Fig. 3) is probably due to the
The anisotropic behaviours of the susceptibilities at competition of several types of exchange interactions
high temperatures could be due to anisotropicg factors
and trigonal field effects, but these effects are small for
V2~(3d3)ions in a slightly-distorted octahedral coordi-
nation [10].
and dipolar energies in the vicinity of the critical tem-
perature.
Table 3 shows that the z-component of the mag-
netic moment increases about 24% from 12.5 to 5.5 K,
while the x-component remains approximately constant.
The maxima in the susceptibility curves for H II c
and H I chave a completely different character. Whereas A similar feature is observed In the susceptibility for
the maximum for H Ic is verybroad, the maximum for
H II c is very sharp. This isprobably a consequence of
the different dimensionality of the short.range ordering
in the two directions. The deviations due to neglecting
short-range order are more severe in a low.dimensional
system [19]. Thus, the H I c susceptibility reflects an
appreciable short-range order in the hexagonal plane
above the criticaltemperature.
H II c.
The proposed magnetic structure (Fig. 4) is in agree-
ment with the observation by 129J Mössbauer spectro-
scopy of a single magnetic iodine site [21;each iodine
being surrounded by two paralleland one antiparallel
nearest neighbours vanadium moments. The interpre-
tation of the transferred fleld (Ha, = 54 kOe, 0 = 54°)
at the iodine site obtained by a summation over the
three equivalent and independent V—I bonds [21gives
rise to two sets of solutions for the spin densityin the
From the stability diagrams for two-dimensional
magnetic structures [8] it is found that for zero aniso-
tropy the 120°structure is stable, if .J~is negative and .12
positive. J ~isthe exchange interaction between nearest
neighbour magnetic ions (distance a),J2 between next-
nearest neighbour magnetic ions (distance a..J~)in the
plane perpendicular to the c-axis. For a strong aniso-
tropy, favouring one particular orientation of the mag-
netic moments, the 120°structure is no longerstable and
it isfound that for the same values ofJ ~and .12 the
collinear structure of Fig. 4 is stable.
The sign of the exchange interactions J ~and .12 is in
accordance with the Goodenough—Kanamori rules [20,
21 ];J~is due to an antiferromagnetic direct exchange
between the V ~ ions, J2 is a ferromagnetic
5s(J) and Sp (fg —ft,) orbitals depending on the two
possible orientations of the spin direction with respect
to the bondingaxes:
f, =—0.4%, f0—f,,
f8 0.2%, fa f ~
=
=
—3.3%,
3.7%.
=
—
—
The second solution is favoured on the basis of a corn-
parison with determinationsin other systems [221.We
observe the expected large covalency for iodine as corn-
pared to fluorine data [22].The large value for
f8(— 0.2%) in V!2 as compared to CrI3(— 0.146%) [23]
can reflect an increasing of the 3d—4s splitting for
the Cr3~.

408
MAGNETICSTRUCFURES AND PROP~RTWSOF V!2
Vol. 30, No.6
Acknowledgments
—
The authors wishto express their
10. HJ.L Van der Valk, P. Meertens& C. Haas,Phys.
Status Solid! (b) 87, 135 (1978).
gratitude to Dr. R. Helmholdt and Mr. J. Strang of the
Energie Centrum Nederland for recordingthediffracto-
grams of V!2.
11. A. Abragam& B. Bleaney, Electron Paramagnetic
Resonance of Transition Ions, p. 428. Clarendon
Press, Oxford (1970).
12. R.E.Watson & A.J. Freeman,Acta Qyst. 14, 27
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