Effect of pressure on the magnetic properties of CrB₂
Magnetic susceptibility c of the itinerant antiferromagnet CrB₂ with TN ≃ 87K was studied as a function of the hydrostatic pressure up to 2 kbar at fixed temperatures 78 and 300 K. The pressure effect on c is found to be negative in sign and weakly dependent on the magnetic state of the compound. In...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Цитувати: | Effect of pressure on the magnetic properties of CrB₂ / G.E. Grechnev, A.S. Panfilov, A.V. Fedorchenko, V.B. Filippov, A.B. Lyashchenko, A.N. Vasiliev // Физика низких температур. — 2009. — Т. 35, № 7. — С. 677-682. — Бібліогр.: 26 назв. — англ. |
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Grechnev, G.E. Panfilov, A.S. Fedorchenko, A.V. Filippov, V.B. Lyashchenko, A.B. Vasiliev, A.N. 2017-05-21T16:45:38Z 2017-05-21T16:45:38Z 2009 Effect of pressure on the magnetic properties of CrB₂ / G.E. Grechnev, A.S. Panfilov, A.V. Fedorchenko, V.B. Filippov, A.B. Lyashchenko, A.N. Vasiliev // Физика низких температур. — 2009. — Т. 35, № 7. — С. 677-682. — Бібліогр.: 26 назв. — англ. 0132-6414 PACS: 75.50.Ee, 75.10.Lp, 75.80.+q https://nasplib.isofts.kiev.ua/handle/123456789/117258 Magnetic susceptibility c of the itinerant antiferromagnet CrB₂ with TN ≃ 87K was studied as a function of the hydrostatic pressure up to 2 kbar at fixed temperatures 78 and 300 K. The pressure effect on c is found to be negative in sign and weakly dependent on the magnetic state of the compound. In addition, the measured pressure dependence of the Néel temperature, dTN / dP = (0.1 ± 0.1) K/kbar, is roughly two orders of magnitude smaller than the corresponding value for the pure chromium. The main contributions to c and their volume dependence are calculated ab initio within the local spin density approximation, and appeared to be in close agreement with the experimental data. The authors thank Prof. I.V. Svechkarev and Dr. A. Grechnev for fruitful discussions and comments. This work has been supported by the Russian–Ukrainian RFBR-NASU project 8-2009. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Низкотемпеpатуpный магнетизм Effect of pressure on the magnetic properties of CrB₂ Article published earlier |
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Effect of pressure on the magnetic properties of CrB₂ |
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Effect of pressure on the magnetic properties of CrB₂ Grechnev, G.E. Panfilov, A.S. Fedorchenko, A.V. Filippov, V.B. Lyashchenko, A.B. Vasiliev, A.N. Низкотемпеpатуpный магнетизм |
| title_short |
Effect of pressure on the magnetic properties of CrB₂ |
| title_full |
Effect of pressure on the magnetic properties of CrB₂ |
| title_fullStr |
Effect of pressure on the magnetic properties of CrB₂ |
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Effect of pressure on the magnetic properties of CrB₂ |
| title_sort |
effect of pressure on the magnetic properties of crb₂ |
| author |
Grechnev, G.E. Panfilov, A.S. Fedorchenko, A.V. Filippov, V.B. Lyashchenko, A.B. Vasiliev, A.N. |
| author_facet |
Grechnev, G.E. Panfilov, A.S. Fedorchenko, A.V. Filippov, V.B. Lyashchenko, A.B. Vasiliev, A.N. |
| topic |
Низкотемпеpатуpный магнетизм |
| topic_facet |
Низкотемпеpатуpный магнетизм |
| publishDate |
2009 |
| language |
English |
| container_title |
Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
Magnetic susceptibility c of the itinerant antiferromagnet CrB₂ with TN ≃ 87K was studied as a function of the hydrostatic pressure up to 2 kbar at fixed temperatures 78 and 300 K. The pressure effect on c is found to be negative in sign and weakly dependent on the magnetic state of the compound. In addition, the measured pressure dependence of the Néel temperature, dTN / dP = (0.1 ± 0.1) K/kbar, is roughly two orders of magnitude smaller than the corresponding value for the pure chromium. The main contributions to c and their volume dependence are calculated ab initio within the local spin density approximation, and appeared to be in close agreement with the experimental data.
|
| issn |
0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/117258 |
| citation_txt |
Effect of pressure on the magnetic properties of CrB₂ / G.E. Grechnev, A.S. Panfilov, A.V. Fedorchenko, V.B. Filippov, A.B. Lyashchenko, A.N. Vasiliev // Физика низких температур. — 2009. — Т. 35, № 7. — С. 677-682. — Бібліогр.: 26 назв. — англ. |
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2025-11-26T01:39:29Z |
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2025-11-26T01:39:29Z |
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1850603087051358208 |
| fulltext |
Fizika Nizkikh Temperatur, 2009, v. 35, No. 7, p. 677–682
Effect of pressure on the magnetic properties of CrB2
G.E. Grechnev, A.S. Panfilov, and A.V. Fedorchenko
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine,
47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: panfilov@ilt.kharkov.ua
V.B. Filippov and A.B. Lyashchenko
I. Frantsevich Institute for Problems of Material Science, National Academy of Sciences,
3 Krzhyzhanovsky Str., Kiev 03680, Ukraine
A.N. Vasiliev
Department of Low Temperature Physics and Superconductivity, Physics Faculty,
M.V. Lomonosov Moscow State University, Moscow 119899, Russia
Received March 26, 2009
Magnetic susceptibility � of the itinerant antiferromagnet CrB2 with TN � 87 K was studied as a function
of the hydrostatic pressure up to 2 kbar at fixed temperatures 78 and 300 K. The pressure effect on � is found
to be negative in sign and weakly dependent on the magnetic state of the compound. In addition, the mea-
sured pressure dependence of the Néel temperature, dTN /dP = (0.1 � 0.1) K/kbar, is roughly two orders of
magnitude smaller than the corresponding value for the pure chromium. The main contributions to � and
their volume dependence are calculated ab initio within the local spin density approximation, and appeared
to be in close agreement with the experimental data.
PACS: 75.50.Ee Antiferromagnetics;
75.10.Lp Band and itinerant models;
75.80.+q Magnetomechanical and magnetoelectric effects, magnetostriction.
Keywords: CrB2, high pressure, magnetovolume effect, electronic structure.
1. Introduction
CrB2 is an itinerant-electron antiferromagnet with the
Néel temperature TN � 85–88 K [1–4], possessing a hexa-
gonal crystal structure of AlB2 type. As it follows from the
neutron diffraction study on a single crystal, CrB2 has a
complicated helicoidal magnetic structure, and the mag-
netic moment (of about 0.5 � B per Cr atom at T � 0) turns
in ac plane [5]. The electronic specific heat coefficient of
CrB2, � � 13.6 mJ/(K2�mol) [3], is abnormally high in com-
parison with those of the nonmagnetic 3d-metal diborides
such as ScB2, TiB2, VB2 (1–5 mJ/(K2�mol) [2,3,6]). The
electronic spin susceptibility of CrB2 is also an order of
magnitude higher than that of other diborides, demon-
strating a large exchange-enhancement effect. The band
structure calculations for CrB2 [7–10] have shown that its
Fermi level lies in a region of the high density of elec-
tronic states (DOS). Therefore the Stoner criterion is
nearly fulfilled in CrB2, and the susceptibility enhance-
ment factor, S � 9, was estimated [7,9]. In addition, the
spin density wave (SDW) along the hexagonal axis was
predicted in Ref. 7 to be due to the nesting of the 7th-band
Fermi surface. However, both the predicted SDW type of
magnetic structure and the estimated magnetization of
� � 0.01�B per Cr atom are inconsistent with the experi-
mental neutron data [5]. It should be noted that more rea-
sonable value of magnetization, � �� 0 3. B per Cr atom,
was obtained in the recent spin-polarized band structure
calculations for CrB2 [10].
Here we report results of our investigations of the
pressure effect on the magnetic susceptibility and Néel
temperature of CrB2 compound to clarify the nature of its
magnetic properties and details of the antiferromagnetic
(AFM) transition. The experimental data are supple-
mented by ab initio calculations of the volume dependent
band structure and magnetic susceptibility.
© G.E. Grechnev, A.S. Panfilov, A.V. Fedorchenko, V.B. Filippov, A.B. Lyashchenko, and A.N. Vasiliev, 2009
2. Experimental details and results
The polycrystalline sample of CrB2 compound was
initially prepared by arc-melting of the stoichiometric
amount of Cr and B elements of better than 99.8% purity
in a water cooled crucible under protective argon atmo-
sphere. The ingot was then crushed to powder and pres-
surized. The pressed sample was sintered at T � 1500 °C
followed by its melting in an inductance furnace and an-
nealing. The study of x-ray powder diffraction at room
temperature revealed that sample has the AlB2-type hex-
agonal crystal structure, and the obtained lattice parame-
ters agree closely with that published in literature [11].
Any other phases were not detected within the resolution
of the employed x-ray technique.
For additional examination of the sample quality, its
magnetic susceptibility was measured as a function of
temperature for the magnetic field H � 0.8 T using the
Faraday microbalance method. The data obtained show a
clear peak at T � 87 K (see Fig. 1), which corresponds to
magnetic ordering in the system. The observed �( )T be-
havior is in agreement with the known literature data for
the high quality CrB2 samples [4].
The pressure effect on the magnetic susceptibility was
measured under helium gas pressure up to 2 kbar at two
fixed temperatures, 78 and 300 K, using a pendulum-type
magnetometer placed into the nonmagnetic pressure cell
[12]. The relative errors of our measurements, performed
in the magnetic field H = 1.7 T, did not exceed 0.05%. The
experimental pressure dependencies of the magnetic sus-
ceptibility of CrB2 are shown in Fig. 2, which demon-
strate a magnitude of the pressure effect and its linear be-
havior. For each temperature the values of � at ambient
pressure and their pressure derivatives d /dPln � are listed
in Table 1. In order to transform the pressure derivative
into the volume one, we used the calculated bulk modulus
value (B = 2.3 Mbar, see Sec. 3.1).
Table 1. The magnetic susceptibility of CrB2 (in 10
–4
emu/mol)
and its pressure (in Mbar
–1
) and volume derivatives at different
temperatures
T, K
� d ln �/dP d ln �/d ln V
exp. theor.
a
exp. exp. theor.
a
0 7.3
b
7.5 – – 4.0
78 6.42 – –1.82 � 0.3 –4.2 � 0.7 –
300 5.11 – –1.65 � 0.2 –3.8 � 0.5 –
a
for paramagnetic state;
b
extrapolation of the experimental data
for paramagnetic state in Fig. 1.
With the aim of finding the pressure effect on the Néel
temperature, the �( )T dependence was studied in detail
around TN for two different pressures (see Fig. 3). The re-
sulting pressure derivative dT /dPN � (0.1 � 0.1) K/kbar
was estimated from a shift of the maximum in �( )T and
appears to show only weak tendency for an increase of TN
with pressure.
3. Computational method and results
3.1. Band structure calculations
The investigated diboride CrB2 possesses the hexago-
nal AlB2 (C32) crystal structure which is composed of
transition metal layers alternating with graphite-like bo-
ron layers stacked perpendicularly to the [ ]001 axis. Ab ini-
tio calculations of the electronic structure of CrB2 were
carried out by employing a modified FP-LMTO method
[13–15]. The exchange-correlation potential was treated
678 Fizika Nizkikh Temperatur, 2009, v. 35, No. 7
G.E. Grechnev, A.S. Panfilov, A.V. Fedorchenko, V.B. Filippov, A.B. Lyashchenko, and A.N. Vasiliev
6.5
6.0
5.5
5.0
0 50 100 150 200 250 300
T, K
T = 87 KN
�,
1
0
em
u
/m
o
l
–
4
Fig. 1. Temperature dependence of the magnetic susceptibility
for CrB2. The data obtained with pendulum magnetometer at
P � 0 are presented by filled squares.
1.000
0.999
0.998
0.997
0.996
0 0.5 1.0 1.5 2.0
P, kbar
�
�
(P
)/
(0
)
78 K
300 K
Fig. 2. Pressure dependence of the magnetic susceptibility for
CrB2 at T � 78 and 300 K normalized to its value at P � 0.
in the local density approximation (LDA) [16] of the den-
sity functional theory.
The calculated density of states N E( ) for the paramag-
netic (PM) phase of CrB2 is shown in Fig. 4, and it is in a
qualitative agreement with the results of KKR-ASA [7]
and LMTO-ASA [8–10] calculations. The calculated
DOS at the Fermi level N EF( ) � 31.7 Ry–1 is comparable
with the results of LMTO-ASA calculations, 33.7 [8] and
34.9 [10] Ry–1, but differs substantialy from the earlier
result of non-self-consistent calculations of Ref. 7,
N EF( ) � 20.9 Ry–1. As seen from Fig. 4, in CrB2 the
Fermi level is located at the steep slope of N E( ) peak
where DOS rapidly grows with energy. Among other
3d-diborides CrB2 possesses a comparatively large value
of N EF( ), resulting in a strongly enhanced spin paramag-
netism of the compound and transition to the magnetically
ordered state at T = 87 K.
In order to evaluate the bulk modulus value to be used
in the analysis of the pressure effects in CrB2, the band
structure calculations were performed for a number of lat-
tice parameters close to the experimental ones (the ratio
c/a was fixed at its experimental value 1.033). The equi-
librium unit cell volume V th and the corresponding theo-
retical bulk modulus BLDA were determined from the cal-
culated volume dependence of the total energy E V( ) by
using the well known Murnaghan equation [14], and ap-
pear to be V th � 21.79 �
3 and BLDA � 3.23 Mbar. The
Murnaghan equation is based on the assumption that the
pressure derivative �B of the bulk modulus B is constant.
By using the evaluated from the Murnaghan equation value
of � �B 3.9, we have estimated B � 2.3 Mbar, correspond-
ing to the experimental volume Vexp = 23.41 �
3 [17]. This
correction counterbalances the well known over-bonding
tendency of the LDA approach [14], and provides better
agreement with experimental values of bulk moduli, as it
comes from our previous calculations [13,15].
3.2. Magnetic susceptibility
The FP-LMTO calculations of the field-induced spin
and orbital (Van Vleck) magnetic moments were carried
out self-consistently within the procedure described in
Refs. 13, 15 by means of the Zeeman operator,
� ( �
�)H Z � � H s l2 , (1)
which was incorporated in the original FP-LMTO
Hamiltonian. Here H is the external magnetic field, �s and �l
are the spin and orbital angular momentum operators, re-
spectively. The field induced spin and orbital magnetic
moments were calculated in the external field of 10 T and
provided estimation of the related contributions to the
magnetic susceptibility, �spin and �orb . For the hexagonal
C32 crystal structure of CrB2, the components of these
contributions, � i || and � i
, were derived from the mag-
netic moments obtained in an external field, applied par-
allel and perpendicular to the c axis, respectively. The
averaged values of the calculated �spin and �orb compo-
nents, � � �i i i /�
( )|| 2 3, and the evaluated magnetic
anisotropy, which is determined by the orbital contribu-
tion, �� � �orb orb orb� �
|| , are listed in Table 2. For com-
pleteness, the table contains also an estimate of the
Langevin diamagnetism of filled shells �dia which ap-
pears to be close to a free-ionic diamagnetic susceptibility
[18,19].
In addition, the enhanced Pauli spin contribution to the
magnetic susceptibility was also calculated within the
Stoner model:
� � �ston �
� �S N E IN EP B F F
2 11( )[ ( )] , (2)
Effect of pressure on the magnetic properties of CrB2
Fizika Nizkikh Temperatur, 2009, v. 35, No. 7 679
P = 1.7 kbar
P = 0.1 kbar
dT /dP = 0.1 0.1 K/kbarN �
6.48
6.46
6.44
6.42
6.40
80 85 90 95
T, K
�,
1
0
em
u
/m
o
l
–
4
Fig. 3. Temperature dependence of the magnetic susceptibility
for CrB2 in the vicinity of TN at two fixed pressures.
0.8 1.0 1.2
Energy, Ry
0
20
40
60
N
(E
),
st
at
es
/R
y
CrB2
ScB2
VB2
MnB2
EF
TiB2
1.4
Fig. 4. Density of states for CrB2. The vertical lines indicate
the conduction band filling for the corresponding 3d diborides.
where � P = � B FN E2 ( ), S is the Stoner enhancement fac-
tor, and � B is the Bohr magneton. The Stoner integral I,
describing the exchange-correlation interaction of the
conduction electrons, can be expressed in terms of the
calculated parameters of the electronic structure [20,21]:
I
N E
N E J N E
F
ql
qll
F qll ql F�
�
� ��1
2( )
( ) ( ). (3)
Here N EF( ) is the total density of electronic states at the
Fermi level EF , N Eql F( ) is the partial density of states
for atom q in the unit cell, J qll� are the local exchange
integrals:
J g r r r drll l l� �� � �� ( ( )) ( ) ( )� 2 2 , (4)
where �l r( ) are the partial wave functions, and g r( ( ))� is a
function of the charge density [16]. The calculated value
of the enhanced Pauli susceptibility �ston is presented in
Table 2 and appears to be lower than the field-induced
spin susceptibility �spin , evaluated by using the full
Zeeman term (1). It should be noted, that the field-in-
duced and Pauli spin susceptibilities in Table 2 were cal-
culated for the equilibrium unit cell volume V th .
4. Discussion
In CrB2 the main contribution to N EF( ) comes from d
states of Cr, and the Stoner criterion is nearly fulfilled due
to the large value of N EF( ) (see Fig. 4). The calculated
susceptibility enhancement factor S IN EF� � �[ ( )]1 1 ap-
pears to be about 8, which is comparable with earlier esti-
mations (S � 9 [7]). In the PM phase of CrB2 the magnetic
susceptibility rises with decreasing temperature and
becomes �exp � 6.5�10–4 emu/mol at T � 90 K. The extra-
polated PM susceptibility �exp ( )T � 0 provides the es-
timation �exp ( )0 � 7.3�10–4 emu/mol, which is in agree-
ment with the calculated paramagnetic contributions �spin
and �orb from Table 2. The calculated small value of the
magnetic anisotropy in CrB2 (less than 1%) is also in line
with the experimental data of Ref. 4.
The total susceptibility of metallic systems in the ab-
sence of spontaneous magnetic moment can be expressed
as the sum ([15,19]):
� � � � �tot spin orb dia� L, (5)
which, along with the above mentioned contributions,
also includes the diamagnetism of conduction electrons
� L. A rigorous calculation of � L is rather difficult prob-
lem for a complicated band structure (see, e.g., [22]), and
the free-electron Landau limit is often used for estima-
tions, though for many systems this crude approximation
was found not to provide even the correct order of magni-
tude of the diamagnetic susceptibility. In fact, the agree-
ment of the contributions to the magnetic susceptibility
� � � �sum spin orb dia� calculated here (see Table 2)
with the experimental value of � (Table 1) gives evidence
that for CrB2 the diamagnetic contribution � L is presum-
ably negligible as compared with the dominating spin
contribution �spin .
In order to analyse the experimental data on pressure
effect in the magnetic susceptibility, the volume depend-
encies of the paramagnetic contributions to susceptibility
�spin and �orb are calculated ab initio within the field-in-
duced FP-LMTO technique. The evaluated volume deriva-
t i v e d /d Vln( ) ln .� �spin orb � 4 0 a p p e a r s t o b e i n
agreement with the experimental result for the PM phase
of CrB2, d /d Vln ln . .� � �3 8 0 5 (see Table 1). It should be
pointed out that the calculated value of the pressure effect
on � is predominately determined by the enhanced spin
contribution �spin .
The measured pressure derivative of the magnetic sus-
ceptibility d /dPln � can be used to derive the spontaneous
volume change in CrB2 due to the antiferromagnetic or-
dering �V/V m
� which relates to the squared local mag-
netic moment M T2( ) ([23]):
�m T
C
B
M T( ) ( )� 2 . (6)
Here B is the bulk modulus, C is the magnetoelastic cou-
pling constant. The latter can be determined within the
phenomenological relation [24]:
C
B V
d
dPm
� �
1
2�
�ln
, (7)
where � and Vm are the molar susceptibility and volume,
respectively. By using in Eq. (7) the experimental values
of � and d /dPln � from Table 1 and Vm � 14.1 cm3, one
estimates the magnetoelastic constant to be temperature
independent within experimental errors and equal to:
C/B /� � � � �( . . ) ( )1 07 0 15 10 10 2emu mol . The substitution
of the evaluated C/B value and the experimental mag-
netic moment M /B( ) .0 0 5� � Cr [5] in Eq. (6) yields
the volume change under the AFM transition to be
�m( ) ( . . )0 0 083 0 012� � %. This estimate agrees closely
with the experimental value �m( )0 � 0.085% [25].
680 Fizika Nizkikh Temperatur, 2009, v. 35, No. 7
G.E. Grechnev, A.S. Panfilov, A.V. Fedorchenko, V.B. Filippov, A.B. Lyashchenko, and A.N. Vasiliev
Table 2. Calculated bulk modulus B and contributions to the mag-
netic susceptibility of CrB2 in PM state (see text for details)
B, Mbar
�ston �spin �orb ��orb �dia �sum
a
10
–4
emu/mol
2.30 4.0 7.03 0.60 0.010 –0.10 7.53
�sum
a = �spin + �orb + �dia
The pressure dependence of the Néel temperature can
be examined in line with a phenomenological approach of
Ref. 26, which has been applied to the AFM chromium:
T /N � exp ( )�1 � , (8)
where kTB is of the order of the d-band width, and
� � IN EF( ). The volume dependence of the Stoner pro-
duct IN EF( ) can be obtained according to Eq. (2), which
gives
d
d V
d N E
d V
S
d IN E
d V
F Fln
ln
ln ( )
ln
( )
ln[ ( )]
ln
�
� �1 . (9)
By substituting the experimental data on d /d Vln ln� from
Table 1 into Eq. (9) together with our estimates
d N E /d VFln ( ) ln = 1.52 and S � 8, we obtain
d IN E
d V
Fln[ ( )]
ln
.� 0 3, (10)
which means a substantial cancellation of the volume ef-
fects on the density of states at the Fermi level and the ex-
change parameter in the Stoner product IN EF( ) of CrB2.
Therefore, according to Eq. (8), the effect of pressure on
TN is mainly determined by the band width behavior,
d T /dP d T /dPN Bln ln� , and appears to be rather small
and positive in sign. This is consistent with the measured
weak pressure dependence of the Néel temperature in
CrB2 (dT /dPN � �( . . )0 1 0 1 K/kbar). It should be noted,
that such behavior of TN differs essentially from that for
pure chromium, where the strong suppression of the AFM
state under pressure with dT /dPN � –5.1 K/kbar has been
reported [26]. Therefore we can presume, that a different
mechanism of the magnetic ordering takes place in CrB2
as compared to the AFM chromium.
To shed more light on the nature of the magnetic order-
ing in CrB2, the electronic structure calculations for its
low temperature helical magnetic structure are required.
Such calculations are extremely difficult to perform, and
in the present work the spin-polarized electronic structure
calculations are carried out for the ferromagnetic phase of
CrB2. These calculations provided the spontaneous mag-
netic moment of 0 8. � B , in a reasonable agreement with
the experiment [5].
5. Conclusions
For the first time the pressure effect on the magnetic
susceptibility of CrB2 is measured at temperatures both
above and below TN � 87 K, and it is found to be almost
independent on the magnetic state of the sample. Based
on the obtained pressure derivative of the magnetic sus-
ceptibility, we evaluated the magnetoelastic coupling
constant, which appears to describe correctly the reported
spontaneous volume change in CrB2 due to the anti-
ferromagnetic ordering. The measured pressure effect on
the Néel temperature is found to be considerably smaller
than that for the pure AFM chromium, and this indicates
that different mechanisms govern magnetic ordering in
CrB2 and Cr.
It is found that the Stoner approach underestimates
substantially the spin susceptibilty for the PM phase of
CrB2. This is presumably related to deficiency of the
Stoner approach, when both parameters involved in the
susceptibility enhancement, N EF( ) and I, are calculated
and averaged over the band states separately. It should be
noted that such response function as � is microscopically
not uniform in space, and induced magnetization density
varies considerably within the unit cell. On the other
hand, our ab initio calculations in an external magnetic
field provided the main contributions to the magnetic sus-
ceptibility of CrB2 and allowed to describe the large value
of � and the magneto-volume effect d /d Vln ln� in agree-
ment with the experiment.
The authors thank Prof. I.V. Svechkarev and Dr. A.
Grechnev for fruitful discussions and comments. This
work has been supported by the Russian–Ukrainian
RFBR-NASU project 8-2009.
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