Pressure effect on magnetic properties of gadolinium in paramagnetic state
In this report we are mostly focused on refinement of the experimental dependence of the magnetic transition temperature TC on pressure under pure hydrostatic (gaseous) conditions. Unlike previously used methods, we employed a new procedure, based on the measurement of pressure effect on the dc magn...
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Panfilov, A.S. Grechnev, G.E. Logosha, A.V. Zhuravleva, I.P. 2014-10-17T06:47:10Z 2014-10-17T06:47:10Z 2013 Pressure effect on magnetic properties of gadolinium in paramagnetic state / A.S. Panfilov, G.E. Grechnev, A.V. Logosha, I.P. Zhuravleva // Физика и техника высоких давлений. — 2013. — Т. 23, № 1. — С. 5-12. — Бібліогр.: 22 назв. — англ. 0868-5924 PACS: 71.20.Eh, 75.10.Lp, 75.30.Cr, 75.50.Cc, 75.80.+q https://nasplib.isofts.kiev.ua/handle/123456789/69601 In this report we are mostly focused on refinement of the experimental dependence of the magnetic transition temperature TC on pressure under pure hydrostatic (gaseous) conditions. Unlike previously used methods, we employed a new procedure, based on the measurement of pressure effect on the dc magnetic susceptibility of Gd in the paramagnetic state at temperatures above TC. The dc paramagnetic susceptibility of Gd was measured in the temperature range of 295−365 K and under hydrostatic pressure up to 0.16 GPa, yielding values of the paramagnetic Curie temperature Θ and its pressure derivative. Also we explored a possibility to describe pressure effects on magnetism of Gd within simple mean-field approaches, which are based on ab initio electronic structure calculations. Based on the results of electronic structure calculations within the density functional theory, the experimental behavior of Θ under pressure was described in the framework of mean-field like approach. Проведены измерения парамагнитной восприимчивости Gd в интервале температур 295−365 K в условиях гидростатического сжатия до 0.16 GPa, что позволило получить значения парамагнитной температуры Кюри Θ и ее производной по давлению. Основываясь на результатах расчетов электронной структуры с использованием теории функционала плотности, было исследовано поведение Θ под давлением в рамках теории среднего поля. С этой целью были вычислены эффективная восприимчивость зонных d-электронов и соответствующие обменные интегралы как функции параметров решетки. Було виміряно парамагнітну сприйнятливість Gd в інтервалі температур 295−365 K в умовах гідростатичного тиску до 0.16 GPa, що дозволило отримати значення парамагнітної температури Кюрі Θ та її похідної за тиском. На основі результатів розрахунків електронної структури з використанням теорії функціонала густини було досліджено поведінку Θ під тиском у рамках теорії середнього поля. З цією метою були обчислені ефективна сприйнятливість зонних d-станів і відповідні обмінні інтеграли як функції параметрів ґратки. en Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України Физика и техника высоких давлений Pressure effect on magnetic properties of gadolinium in paramagnetic state Article published earlier |
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Pressure effect on magnetic properties of gadolinium in paramagnetic state |
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Pressure effect on magnetic properties of gadolinium in paramagnetic state Panfilov, A.S. Grechnev, G.E. Logosha, A.V. Zhuravleva, I.P. |
| title_short |
Pressure effect on magnetic properties of gadolinium in paramagnetic state |
| title_full |
Pressure effect on magnetic properties of gadolinium in paramagnetic state |
| title_fullStr |
Pressure effect on magnetic properties of gadolinium in paramagnetic state |
| title_full_unstemmed |
Pressure effect on magnetic properties of gadolinium in paramagnetic state |
| title_sort |
pressure effect on magnetic properties of gadolinium in paramagnetic state |
| author |
Panfilov, A.S. Grechnev, G.E. Logosha, A.V. Zhuravleva, I.P. |
| author_facet |
Panfilov, A.S. Grechnev, G.E. Logosha, A.V. Zhuravleva, I.P. |
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2013 |
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Физика и техника высоких давлений |
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
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Article |
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In this report we are mostly focused on refinement of the experimental dependence of the magnetic transition temperature TC on pressure under pure hydrostatic (gaseous) conditions. Unlike previously used methods, we employed a new procedure, based on the measurement of pressure effect on the dc magnetic susceptibility of Gd in the paramagnetic state at temperatures above TC. The dc paramagnetic susceptibility of Gd was measured in the temperature range of 295−365 K and under hydrostatic pressure up to 0.16 GPa, yielding values of the paramagnetic Curie temperature Θ and its pressure derivative. Also we explored a possibility to describe pressure effects on magnetism of Gd within simple mean-field approaches, which are based on ab initio electronic structure calculations. Based on the results of electronic structure calculations within the density functional theory, the experimental behavior of Θ under pressure was described in the framework of mean-field like approach.
Проведены измерения парамагнитной восприимчивости Gd в интервале температур 295−365 K в условиях гидростатического сжатия до 0.16 GPa, что позволило получить значения парамагнитной температуры Кюри Θ и ее производной по давлению. Основываясь на результатах расчетов электронной структуры с использованием теории функционала плотности, было исследовано поведение Θ под давлением в рамках теории среднего поля. С этой целью были вычислены эффективная восприимчивость зонных d-электронов и соответствующие обменные интегралы как функции параметров решетки.
Було виміряно парамагнітну сприйнятливість Gd в інтервалі температур 295−365 K в умовах гідростатичного тиску до 0.16 GPa, що дозволило отримати значення парамагнітної температури Кюрі Θ та її похідної за тиском. На основі результатів розрахунків електронної структури з використанням теорії функціонала густини було досліджено поведінку Θ під тиском у рамках теорії середнього поля. З цією метою були обчислені ефективна сприйнятливість зонних d-станів і відповідні обмінні інтеграли як функції параметрів ґратки.
|
| issn |
0868-5924 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/69601 |
| citation_txt |
Pressure effect on magnetic properties of gadolinium in paramagnetic state / A.S. Panfilov, G.E. Grechnev, A.V. Logosha, I.P. Zhuravleva // Физика и техника высоких давлений. — 2013. — Т. 23, № 1. — С. 5-12. — Бібліогр.: 22 назв. — англ. |
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2025-11-25T22:31:35Z |
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2025-11-25T22:31:35Z |
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| fulltext |
Физика и техника высоких давлений 2013, том 23, № 1
© A.S. Panfilov, G.E. Grechnev, A.V. Logosha, I.P. Zhuravleva, 2013
PACS: 71.20.Eh, 75.10.Lp, 75.30.Cr, 75.50.Cc, 75.80.+q
A.S. Panfilov, G.E. Grechnev, A.V. Logosha, I.P. Zhuravleva
PRESSURE EFFECT ON MAGNETIC PROPERTIES OF GADOLINIUM
IN PARAMAGNETIC STATE
B. Verkin Institute for Low Temperature Physics and Engineering
47 Lenin Ave., Kharkov 61103, Ukraine
Received September 25, 2012
Проведены измерения парамагнитной восприимчивости Gd в интервале темпера-
тур 295−365 K в условиях гидростатического сжатия до 0.16 GPa, что позволило
получить значения парамагнитной температуры Кюри Θ и ее производной по дав-
лению. Основываясь на результатах расчетов электронной структуры с использо-
ванием теории функционала плотности, было исследовано поведение Θ под давле-
нием в рамках теории среднего поля. С этой целью были вычислены эффективная
восприимчивость зонных d-электронов и соответствующие обменные интегралы
как функции параметров решетки.
Ключевые слова: гадолиний, электронная структура, магнитная восприимчивость,
температура Кюри, высокое давление
Було виміряно парамагнітну сприйнятливість Gd в інтервалі температур 295−365 K в
умовах гідростатичного тиску до 0.16 GPa, що дозволило отримати значення па-
рамагнітної температури Кюрі Θ та її похідної за тиском. На основі результатів
розрахунків електронної структури з використанням теорії функціонала густини
було досліджено поведінку Θ під тиском у рамках теорії середнього поля. З цією
метою були обчислені ефективна сприйнятливість зонних d-станів і відповідні
обмінні інтеграли як функції параметрів ґратки.
Ключові слова: гадоліній, електронна структура, магнітна сприйнятливість, тем-
пература Кюрі, високий тиск
1. Introduction
Among the heavy rare earth metals, Gd is the only metal which undergoes a para-
magnetic−ferromagnetic transition at the highest magnetic ordering temperature TC ≈
≈ 293 K and remains ferromagnetic (FM) down to liquid helium temperature [1,2].
The half-filled 4f shell of Gd (S = 7/2, L = 0) provides a localized spin-only mag-
netic moment. Therefore gadolinium is often considered as a model system, where
the localized 4f spin moments are inserted in a sea of the itinerant electrons. It is
believed that 4f moments of Gd are ordered in a FM ground state by means of
Ruderman-Kittel−Kasuya−Yosida (RKKY)-type exchange interaction [1].
Физика и техника высоких давлений 2013, том 23, № 1
6
A number of experiments have been performed to study the pressure effect on the
Curie temperature of Gd (see, for example, [4] and references therein). With increas-
ing pressure, the crystal structure of Gd changes in the order HCP → Sm-type →
→ DHCP → FCC and the first HCP → Sm-type transition occurs at about 2.5 GPa [5].
For pressures below the structural transitions, the Curie temperature of Gd was
found to decrease monotonically with increasing pressure at the rate within the
range of dTC/dP = −(10.6−17.2) K/GPa [4]. In all cases the value of dTC/dP was
estimated from the pressure-induced shift of peculiarities in the temperature depen-
dences of various properties at the transition point (resistivity, magnetization, ac
susceptibility, etc.). The methods were of different accuracy, which caused the con-
siderable scatter of the experimental data. Another possible source of errors is a de-
viation from the hydrostatic conditions. The crucial role of stress homogeneity has
been revealed in studies of the uniaxial pressure effects on TC. These effects ap-
peared to be strongly anisotropic and more pronounced with the stress applied along
the c-axis [6,7]. This correlates with the anisotropic nature of the spontaneous mag-
netostriction resulted from the thermal expansion data for Gd in FM state [2].
In this report we are focused on refinement of the experimental dependence of
TC on pressure using pure hydrostatic (gaseous) conditions. Unlike previously
used methods, we employed a new procedure, based on the measurement of pres-
sure effect on the dc magnetic susceptibility of Gd in the paramagnetic (PM) state
at the temperatures above TC. Also we attempted to describe the pressure effects
on magnetism of Gd within a simple mean-field approach, which is based on ab
initio electronic structure calculations.
2. Experimental
In this study we used the polycrystalline Gd sample of 99.9% purity. The tem-
perature dependence of its magnetic susceptibility χ was measured by a Faraday
method between 295 and 365 K in magnetic field H = 0.1 T, and a Curie−Weiss
behavior
χ( ) CT
T
=
−Θ
(1)
has been revealed at T ≥ 320 K (solid line in Fig. 1). The corresponding values of
the paramagnetic Curie temperature and effective magnetic moment were evalu-
ated to be Θ ≃ 295 K and μeff = 8.18 ± 0.1μB in agreement with literature data.
The χ(P) measurements were performed under helium gas pressure P up to
0.16 GPa at fixed temperatures, T = 325.5, 333.5 and 352.1 K, by a levitation-type
magnetometer [8,9], using the spherical sample of about 1 mm in diameter. The
relative errors of magnetic measurements under pressure did not exceed 0.1% for
the employed magnetic fields close to H ~ 0.1 T. The field was produced by a
non-superconducting solenoid with geometrical parameters similar to those of the
superconducting coil used originally in Refs. [8,9]. The experimental χ(P) de-
pendencies are presented in Fig. 2 and found to be linear, yielding the pressure
derivatives dlnχ/dP, which are listed in Table 1.
Физика и техника высоких давлений 2013, том 23, № 1
7
Fig. 1. Temperature dependence of the reciprocal magnetic susceptibility for Gd, meas-
ured by the Faraday method (○). The data obtained with the levitation method at ambient
pressure are represented by black squares. The Curie−Weiss fit is indicated by the solid
line
Fig. 2. Pressure dependencies of the magnetic susceptibility of Gd normalized to its value
at P = 0 at different temperatures, K: ○ − 325.5, □ − 333.5, ◑ − 352.1
Table 1
Magnetic susceptibility χ and its pressure derivative dlnχ/dP for Gd at different
temperatures
T, K χ, 10−3 emu/mole dlnχ/dP, 10−2 GPa−1
325.5 269.1 −47.5 ± 1.5
333.5 215.7 −38.5 ± 1.5
352.1 145.5 −28.0 ± 1.5
Based on the Curie−Weiss behavior of χ(T), the dlnχ/dP is assumed to be pre-
dominantly governed by the pressure dependence of the paramagnetic Curie tem-
perature Θ:
( )
dlnχ dln 1 d χ d
d d d d
C
P P T P C P
Θ Θ
= + ≈
−Θ
(2)
where the Curie constant C is close to that of free Gd3+ ion value and expected to
be pressure independent. According to Eq. (2), the value of pressure derivative of
Θ was evaluated from a slope of the linear approximation of the dlnχ/dP vs χ de-
pendence in Fig. 3. The derivative was found to be dΘ/dP = −14.9 ± 0.3 K/GPa,
which is in excellent agreement with the most reliable data for polycrystalline
sample of Gd from Ref. [10], dTC/dP = −14.8 ± 0.2 K/GPa. Using the experi-
mental bulk modulus value B = 39 ± 1 GPa for Gd [11], one obtains the corre-
sponding volume derivative, dlnΘ/dlnV = 1.97 ± 0.08.
Физика и техника высоких давлений 2013, том 23, № 1
8
3. Computational details and results
In order to analyze the experimental data on the pressure effects, the volume-
dependent electronic structures and magnetic properties of Gd were calculated ab
initio. For these calculations we employed a full-potential relativistic linear muf-
fin-tin orbital method (FP-LMTO, code RSPt [12−14]), and also the LMTO
method in atomic sphere approximation (LMTO-ASA code, see Refs. [15,16].
The local spin density approximation (LSDA) of Ref. [17] was employed. In the
FP-LMTO calculations the basis set for Gd included 6s, 6p, 5d, and 5p orbitals,
with the 5p orbitals treated as pseudo-valence states. In both FP-LMTO and
LMTO-ASA approaches, the 4f states were treated fully relativistically as spin
polarized open core states, which contribute to the total spin density, but do not
hybridize with conduction electrons. The use of this approach was justified by
successful description of the FM ground state and the Fermi surface of HCP Gd
[18,19].
In the framework of a simple mean-field theory (see Refs. [15,16,20] and ref-
erences therein), the Curie temperature of the rare-earth metal can be described by
a functional relation of the form:
( ) ( )2ef 2
B C 4 5χ 1 1f
f d Jdk T J g J J∝ − + . (3)
Here effχd is the effective d-band spin susceptibility, gJ is the Lande factor, J4f5d is
the local 4f-5d exchange integral:
( ) 2 2
4 5 4 5( ) φ ( ) φ ( ) df d f dJ g p r r r r= ∫ , (4)
where ϕ4f(r) and ϕ5d(r) are the partial wave functions, and g(ρ(r)) is a functional
of the electronic density [17]. In this work we used Eq. (3) in order to determine
whether the simple mean-field theory is relevant to describe experimental data on
the pressure effects on TC in Gd. In order to evaluate the effective d-band suscep-
tibility entering Eq. (3), we carried on ab initio calculations of the exchange en-
hanced spin susceptibility for Gd in the PM state. Within a modified FP-LMTO
Fig. 3. Dependence of the pressure deriva-
tive dlnχ/dP for Gd on the corresponding
magnetic susceptibility at different tem-
peratures
Физика и техника высоких давлений 2013, том 23, № 1
9
method [13], the effect of external
magnetic field H was taken into ac-
count by means of the Zeeman opera-
tor ( )ˆˆ2 1H s + included in the FP-
LMTO Hamiltonian.
The self-consistent calculations of the
field-induced spin and orbital magnetic
moments were carried out in an external
magnetic field of 10 T. That allowed
determining of the corresponding contri-
butions χspin and χorb to the paramagnetic
susceptibility. These calculations were
performed for a number of lattice pa-
rameters a close to the experimental one.
This provided the behavior of χspin and
χorb in Gd for varying atomic volumes at
the fixed experimental HCP lattice pa-
rameters ratio, c/a = 1.59.
The results of calculations are shown in Fig. 4. It should be noted that the calcu-
lated total paramagnetic susceptibility of Gd, χ = χspin + χorb ≈ 142·10–6 emu/mole, cor-
responding to the experimental lattice parameters at ambient pressure, is consistent
with the experimental room temperature values of χ for related series of metallic Y,
La and Lu which amount (in the same units) to 190, 100 and 180, respectively [21].
Based on the calculated dependence χspin(V) for PM Gd, the pressure derivative
of χspin was evaluated and compiled in Table 2. In order to convert the calculated
volume derivative into the pressure one, we used the experimental bulk modulus
value for Gd (B = 39 GPa [11]).
For calculation of the pressure dependence of the local J4f5d exchange integral
(4) of Gd, we employed the atomic sphere approximation (LMTO-ASA) within
the open core approach for 4f states of Gd, in line with Refs. [15,16]. The calcu-
lated J4f5d is about 7·10–3 Ry, and its pressure derivative is also listed in Table 2.
Table 2
Pressure derivatives of magnetic parameters for Gd
Derivative, 10−2 GPa−1
Calculated
dlnχspin/dP = –7.3
dlnJ4f5d/dP = 1.3
dlnTC/dP = −4.7
Experimental
dlnΘ/dP = −5.05 ± 0.10 (present work)
dlnTC/dP = −4.78 ± 0.07 (single crystal) [10]
dlnTC/dP = −5.05 ± 0.07 (polycrystal) [10]
Note. Calculations are done for the PM state.
Fig. 4. Calculated dependencies of the
main contributions to the magnetic suscep-
tibility of Gd on the atomic volume. Arrow
marks the experimental value of volume at
ambient pressure
Физика и техника высоких давлений 2013, том 23, № 1
10
4. Discussion
According to Eq. (3), the pressure dependence of the Curie temperature of Gd
can be represented as:
4 5 spinC dln dlnχdln 2
d d d
f dJT
P P P
= + . (5)
By substituting in Eq. (3) the calculated pressure derivatives of J4f5d and χspin
from Table 2, we obtained theoretical estimations of dlnTC/dP, which are also
given in Table 2. The estimated value dlnTC/dP = −4.7·10−2 GPa−1 is in agreement
with the present experimental value dlnΘ/dP = −(5.05 ± 0.10)·10−2 GPa−1, as well
as with the literature data (see Table 2). This supports the validity of the func-
tional relation (3). The agreement also points to a predominant participation of the
itinerant 5d-electrons in the indirect exchange interaction for Gd. Therefore, the
magnetic ordering and peculiar magnetic properties of Gd can be hardly explained
within the simple RKKY coupling scheme.
The obtained pressure derivative for the paramagnetic Curie temperature of Gd
can be used for evaluation of a spontaneous volume change due to magnetic or-
dering, / ω ( )mV V TΔ ≡ , which is related to the squared molar magnetic moment
M2(T) (see Ref. [22] and references therein):
2ω ( ) ( )m
cT M T
B
= . (6)
Here B is the bulk modulus, and c is the magnetoelastic coupling constant. The
latter can be determined for PM Gd within the phenomenological relation [22]:
1 d nχ
2 χ d
c l
B V P
= − , (7)
where χ and V are the molar susceptibility and volume, respectively. From Eq. (2)
it follows:
1 dlnχ 1 d
χ d dP C P
Θ
= . (8)
By using the experimental values of dΘ/dP = −14.9 K/GPa, the Curie constant
C = 8.36 K·emu/mole and V = 19.9 cm3, one estimates c/B value to be equal
( ) ( ) 2121 d 4.4 0.3 10 emu/mole
2 d
c
B VC P
−−Θ
= − = ± ⋅ . (9)
The substitution of the evaluated c/B value and the experimental molar magnetic
moment of Gd at T → 0, M(0) ≈ 4.2·104 emu/mole (7.63μB per Gd atom [3]), in
Eq. (6) yields the volume change under magnetic transition to be ωm(0) ~ 0.8%.
This estimate reasonably agrees with the experimental value ωm(0) ~ 0.5%, which
resulted from the thermal expansion measurements for Gd [2]. It can be noted,
that our ab initio calculations of the difference between equilibrium atomic volu-
Физика и техника высоких давлений 2013, том 23, № 1
11
mes for FM and PM states of Gd ((VFM – VPM)/VFM ≈ 0.7%) also provided a
qualitative agreement with the experimental value of magnetovolume effect.
5. Summary
Measurements of the pressure effect on magnetic susceptibility of Gd in its PM
state provided a new experimental method to study the pressure dependence of the
Curie temperature. The ab initio calculated spin susceptibility and exchange inte-
gral were employed to analyze pressure dependence of magnetic properties of Gd
within the mean-field approach (3). By this way the reasonable description of the
observed uniform pressure effect on TC was obtained, indicating the decisive role
of 5d-electrons in the indirect exchange interaction.
However, the mean-field approach (3) leads to overestimated values of TC.
This disagreement is probably related to the assumption that only non-magnetic
spin-degenerate states are present above TC. Also spin fluctuations are obviously
of a substantial significance in determining the magnetic properties of heavy rare-
earth systems with ferromagnetic ordering.
The magnetovolume effect studies can be applied in future investigations as a
useful tool for identification in magnetic systems of the hierarchies of exchange
interactions and effects of the magnetic moments disorder. The recent theoretical
approaches, using a Monte Carlo simulation [19], seem promising, but require
further exploration to shed light on the nature of magnetism and its pressure de-
pendence in the rare-earth systems.
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A.S. Panfilov, G.E. Grechnev, A.V. Logosha, I.P. Zhuravleva
PRESSURE EFFECT ON MAGNETIC PROPERTIES OF GADOLINIUM
IN PARAMAGNETIC STATE
Gadolinium is usually considered as a model system, where the half-filled 4f shell
provides localized spin-only magnetic moments, which are widely believed to be ordered
by means of RKKY type exchange interaction. However, among the heavy rare earth
metals, Gd is the only metal which is ferromagnetic down to the liquid helium tempera-
ture, and this is not described by the RKKY theory. It is also surprising, that in HCP Gd
the easy axis of low temperature magnetization is directed at an angle about 20° from the
c-axis, exhibiting the preferred orientation of the magnetization. With increasing pressure,
the crystal structure of Gd changes in the order HCP-(Sm-type)-DHCP-FCC. Therefore,
further detailed experimental and theoretical studies of high pressure effects on magnetic
properties and phase transitions in gadolinium (and other rare earths) are required to shed
more light on mechanisms of magnetic ordering and electronic structure transformations,
the nature and extent of which are not clear.
In this report we are mostly focused on refinement of the experimental dependence of
the magnetic transition temperature TC on pressure under pure hydrostatic (gaseous) con-
ditions. Unlike previously used methods, we employed a new procedure, based on the
measurement of pressure effect on the dc magnetic susceptibility of Gd in the paramag-
netic state at temperatures above TC. The dc paramagnetic susceptibility of Gd was meas-
ured in the temperature range of 295−365 K and under hydrostatic pressure up to 0.16
GPa, yielding values of the paramagnetic Curie temperature Θ and its pressure derivative.
Also we explored a possibility to describe pressure effects on magnetism of Gd within
simple mean-field approaches, which are based on ab initio electronic structure calcula-
tions. Based on the results of electronic structure calculations within the density func-
tional theory, the experimental behavior of Θ under pressure was described in the frame-
work of mean-field like approach.
Keywords: gadolinium, electronic structure, magnetic susceptibility, Curie temperature,
high pressure
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