Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems
Effect of pressure on electronic structure and magnetic properties of GdMx (x = 1, 2, 3, 5) systems is studied experimentally and theoretically. By employing the ab initio electronic structure calculations, the magnetic susceptibilities, saturation moments, exchange parameters, magnetic ordering tem...
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| Cite this: | Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems / G.E. Grechnev, A.S. Panfilov, A.E. Baranovskiy, A.V. Logosha, I.V. Svechkarev // Физика и техника высоких давлений. — 2004. — Т. 14, № 4. — С. 68-75. — Бібліогр.: 19 назв. — англ. |
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irk-123456789-1681012020-04-22T01:25:56Z Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems Grechnev, G.E. Panfilov, A.S. Baranovskiy, A.E. Logosha, A.V. Svechkarev, I.V. Effect of pressure on electronic structure and magnetic properties of GdMx (x = 1, 2, 3, 5) systems is studied experimentally and theoretically. By employing the ab initio electronic structure calculations, the magnetic susceptibilities, saturation moments, exchange parameters, magnetic ordering temperature and their pressure derivatives are evaluated and appeared to be consistent with available experimental data. The obtained results are expected to promote further advance in the theory of magnetic ordering in rare-earth systems. 2004 Article Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems / G.E. Grechnev, A.S. Panfilov, A.E. Baranovskiy, A.V. Logosha, I.V. Svechkarev // Физика и техника высоких давлений. — 2004. — Т. 14, № 4. — С. 68-75. — Бібліогр.: 19 назв. — англ. 0868-5924 PACS: 71.20.Eh, 75.10.Lp, 75.30.Cr http://dspace.nbuv.gov.ua/handle/123456789/168101 en Физика и техника высоких давлений Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
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Effect of pressure on electronic structure and magnetic properties of GdMx (x = 1, 2, 3, 5) systems is studied experimentally and theoretically. By employing the ab initio electronic structure calculations, the magnetic susceptibilities, saturation moments, exchange parameters, magnetic ordering temperature and their pressure derivatives are evaluated and appeared to be consistent with available experimental data. The obtained results are expected to promote further advance in the theory of magnetic ordering in rare-earth systems. |
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Grechnev, G.E. Panfilov, A.S. Baranovskiy, A.E. Logosha, A.V. Svechkarev, I.V. |
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Grechnev, G.E. Panfilov, A.S. Baranovskiy, A.E. Logosha, A.V. Svechkarev, I.V. Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems Физика и техника высоких давлений |
| author_facet |
Grechnev, G.E. Panfilov, A.S. Baranovskiy, A.E. Logosha, A.V. Svechkarev, I.V. |
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Grechnev, G.E. |
| title |
Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems |
| title_short |
Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems |
| title_full |
Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems |
| title_fullStr |
Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems |
| title_full_unstemmed |
Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems |
| title_sort |
pressure effect on magnetic susceptibility and exchange interactions in gdmx (x = 1, 2, 3, 5) systems |
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
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2004 |
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http://dspace.nbuv.gov.ua/handle/123456789/168101 |
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Pressure effect on magnetic susceptibility and exchange interactions in GdMx (x = 1, 2, 3, 5) systems / G.E. Grechnev, A.S. Panfilov, A.E. Baranovskiy, A.V. Logosha, I.V. Svechkarev // Физика и техника высоких давлений. — 2004. — Т. 14, № 4. — С. 68-75. — Бібліогр.: 19 назв. — англ. |
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Физика и техника высоких давлений |
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AT grechnevge pressureeffectonmagneticsusceptibilityandexchangeinteractionsingdmxx1235systems AT panfilovas pressureeffectonmagneticsusceptibilityandexchangeinteractionsingdmxx1235systems AT baranovskiyae pressureeffectonmagneticsusceptibilityandexchangeinteractionsingdmxx1235systems AT logoshaav pressureeffectonmagneticsusceptibilityandexchangeinteractionsingdmxx1235systems AT svechkareviv pressureeffectonmagneticsusceptibilityandexchangeinteractionsingdmxx1235systems |
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Физика и техника высоких давлений 2004, том 14, № 4
68
PACS: 71.20.Eh, 75.10.Lp, 75.30.Cr
G.E. Grechnev, A.S. Panfilov, A.E. Baranovskiy, A.V. Logosha,
I.V. Svechkarev
PRESSURE EFFECT ON MAGNETIC SUSCEPTIBILITY
AND EXCHANGE INTERACTIONS IN GdMx (x = 1, 2, 3, 5) SYSTEMS
B. Verkin Institute for Low Temperature Physics and Engineering
47 Lenin Ave., 61103, Kharkov, Ukraine
Effect of pressure on electronic structure and magnetic properties of GdMx (x = 1, 2, 3, 5)
systems is studied experimentally and theoretically. By employing the ab initio electronic
structure calculations, the magnetic susceptibilities, saturation moments, exchange pa-
rameters, magnetic ordering temperature and their pressure derivatives are evaluated
and appeared to be consistent with available experimental data. The obtained results are
expected to promote further advance in the theory of magnetic ordering in rare-earth
systems.
Introduction
The rare-earth intermetallics and alloys RMx (M is sp- or d-metal) are of con-
siderable interest due to a large variety of magnetic properties. It is commonly be-
lieved, that peculiar magnetic properties of RMx are governed by different types of
interactions [1,2], involving the highly correlated and strongly localized 4f-states
of rare earth, the d-states of transition metal atoms, which are comparatively
weakly correlated and more delocalized, and also the valence states of R atoms,
which are expected to be the mediators of indirect exchange coupling. However,
many principal details of microscopic magnetic interactions in these materials are
still unclear. Some more or less successful approaches to the evaluation of mag-
netic ordering temperatures TC in rare earths [3−7] have been put forward re-
cently. These theories were applied only for selected systems, and they have not
been properly tested and validated because of the lack of adequate description of
the electronic structure.
The experimental study of the magnetic susceptibility in the paramagnetic state
provides an appropriate tool for evaluation of different contributions to the mag-
netic coupling in RMx compounds. Also, the pressure derivatives of the paramag-
netic Curie temperature, Θ, taken from these measurements, are of particular in-
terest owing to their assumed sensitivity to the nature of the exchange interaction.
Физика и техника высоких давлений 2004, том 14, № 4
69
The studies of pressure effects on the magnetic susceptibility can, therefore,
stimulate the development of new theoretical models for band structures, ex-
change interactions and crystal-field (CEF) parameters in rare-earth compounds.
In this connection, a study of pressure effects on the electronic structure and mag-
netic properties can shed more light on the nature of exchange interactions in RMx
compounds. Also, magnetization studies under pressure are useful tools to obtain
information on hybridization effects between electronic states. In this work, the
experimental studies of pressure effect on the magnetic susceptibility, χ, and the
paramagnetic Curie temperatures, Θ, were carried out for a number of GdMx (x =
= 1, 2, 3, 5) compounds and pseudo-binary alloys. In order to elucidate the origin
of the interactions and electronic states responsible for magnetic ordering, the ab
initio calculations of the volume-dependent electronic structures were also per-
formed for GdMx systems. The calculated magnetic moments, susceptibilities,
band and exchange parameters, and their volume (pressure) derivatives were em-
ployed to analyze available experimental data.
Experimental and theoretical details
The cubic single-crystalline samples of GdM (GdMg, GdZn, and GdCd, CsCl-
type structure) and GdM2 (GdMg2, GdAl2, GdCo2, and GdNi2, C15-type structure)
were made from the high-purity materials (the rare earths were at least 3N (99.9)),
as described in detail in Refs. [8] and [9], respectively, where some preliminary
measurements were carried out. The polycrystalline GdIn3−xSnx samples (the cubic
AuCu3-type structure, 0 < x < 3) were prepared in the Institute of Low Tempera-
tures and Structure Research (Wroclaw, Poland) by arc-melting of the constituent
elements under argon atmosphere, followed by annealing at 800°C for 7 days. The
single crystals of the hexagonal GdNi5 compound (CaCu5-type structure) were
analogous to the samples previously investigated in Ref. [10]. The magnetic sus-
ceptibilities of the GdMx systems were studied under helium gas pressure, P, up to
2 kbar in the temperature range 78(or TC)−330 K. The measurements were carried
out by the Faraday method, using a pendulum magnetometer placed into the pres-
sure cell [11]. The relative measurement errors did not exceed 0.05%. The χ(T) of
investigated Gd-based compounds obeys the Curie-Weiss law
Θ−
=χ
T
CT )( (1)
with the effective magnetic moment close to its value for the free Gd3+ ion, and the
corresponding paramagnetic Curie temperatures Θ are listed in Table 1. Within the
experimental accuracy, the linear change of magnetic susceptibility with pressure
was observed for all studied GdMx systems. According to Eq. (1), the corresponding
values of the pressure derivative dlnχ/dP are governed by the pressure dependence
of Θ, assuming the Curie constant C to be pressure independent:
PTP d
lnd
d
lnd Θ
Θ−
Θ
=
χ . (2)
Физика и техника высоких давлений 2004, том 14, № 4
70
Table 1
The magnetic parameters and their pressure/volume derivatives in GdMx compounds.
Calculated total Mt and experimental saturation MS magnetic moments (in µB/f.u.)
and calculated local Jfd and Jdd exchange integrals (in mRy) at Gd site, together with
their respective volume derivatives and the theoretical bulk moduli B (in kbar).
The experimental paramagnetic Curie temperatures Θ, the calculated TC, and their
pressure derivatives, dΘ/dP and dTC/dP in K/kbar. All data on Θ for GdMg, GdZn,
GdCd, GdAl2, GdNi2, GdIn3 and GdNi5 are obtained in the present work, whereas
the Curie temperatures for GdMg2 and GdCo2 are taken from Refs. [1,2,16]
Parameter GdMg GdZn GdCd GdMg2 GdAl2 GdCo2 GdNi2 GdIn3 GdNi5
MS 5.6−7.6 7.5 7.2 7.3 7.1 4.3−5.3 7.0−7.2 − 6.0−6.9
Mt 7.6 7.7 7.8 8.1 7.6 5.1 7.1 − 6.3
dlnMt/dlnV 0.12 0.04 0.03 −0.18 −0.05 −0.14 0.03 − −0.6
Jfd 7.3 7.1 7.3 6.45 6.1 6.1 6.35 7.7 7.9
dlnJfd/dlnV −0.3 −0.5 −0.45 −0.5 −1.3 −1.3 −1.3 −0.7 −0.6
Jdd 39.0 36.4 36.9 39.1 38.8 39.3 40.0 42.1 41.50
dlnJdd/dlnV −0.29 −0.25 −0.17 −0.27 −0.30 −0.26 −0.31 −0.33 −0.09
B 490 570 660 460 870 1110 1190 570 1700
Θ 116 270 265 81 167 400 75 −96 33
dΘ/dP −1.25 0.05 1.1 − 0.73 −1.1 −0.13 −0.38 0.013
TC 180 400 385 360 180 120 40 − 170
dTC/dP −1.0 0.3 0.6 0.1 0.6 −0.6 −0.3 − 0.1
The corresponding estimates for the dΘ/dP derivatives are given in Table 1. It
should be noted that for Gd-based systems the values of Θ are close to the ex-
perimental magnetic ordering temperatures, TC, and in the following consideration
no distinction is made between them.
Ab initio band structure calculations have been carried out for the paramagnetic
(PM) and ferromagnetic (FM) phases of GdMx compounds and alloys. The calcu-
lations were performed with the linear muffin-tin orbital (LMTO) method
[12−15]. The 4f-states of rare-earths were treated as spin polarized open core
states with the Hund’s rule restriction for the 4f spin, according to [12]. This ap-
proach is particularly suitable for Gd-based compounds, where 4f spin-up and
spin-down occupation numbers are +
fn = 7 and −
fn = 0. Also, the 4f electrons of Gd
form the S state, which is not affected by the CEF interactions. The exchange and
correlation potentials were calculated using the local spin density approximation
(LSDA). The atomic sphere approximation (LMTO−ASA) [12,13] was employed
together with the ab initio relativistic full-potential (FP−LMTO) method [14,15].
The spin polarized and paramagnetic band structure calculations were performed self-
consistently for a number of lattice parameters close to experimental ones. Also, the
band structures of the pseudo-binary alloys GdIn3−xSnx were calculated within the
virtual-crystal approximation. Namely, the true atom in the alloy was replaced by
an «average» atom which is interpolated in charge between the corresponding
pure atoms, and the band-filling effects are accounted properly. Other details of
the LMTO methods employed in the present work are given elsewhere [12−15].
Физика и техника высоких давлений 2004, том 14, № 4
71
Results and discussion
The main results of the calculations together with available experimental data
are presented in Table 1. As one can see, the calculated magnetic moments for the
ferromagnetic GdM and GdM2 compounds are in a fair agreement with the avail-
able experimental saturation moments. It should be taken into account that for
some GdMx systems the saturation of magnetic moments has not been achieved in
available fields. Also, in some cases, like e.g. GdMg [17], the canted ferromag-
netic structure is expected at low temperatures. Regarding the calculated local ex-
change integrals, the values of Jfd and Jdd at Gd site do not vary substantially over
the GdM, GdM2, GdM3, and GdM5 series. At the same time, the volume deriva-
tives of exchange integrals appeared to be rather large in some systems, in com-
parison to the typical values of dlnJ/dlnV ≈ −0.1 for transition metals and com-
pounds [15]. In particular, some calculated values of dlnJfd/dlnV (see Table 1) ap-
peared to be close to the volume derivative of the averaged exchange interaction
parameter, dlnJ/dlnV = −1.5, evaluated for the paramagnetic compound CeCo2
from the susceptibility measurements under pressure [15].
By using the results of the band structure calculations, the magnetic ordering
temperatures TC for GdM, GdM2 and GdNi5 can be estimated within the simplest
possible mean field theory [3,7] by:
( ) ( )11
2
1 22
fdCB +−χ= JJgJTk Jd (3)
where χd is the effective susceptibility, which is proportional to the partial density
of d-band states at the Fermi level EF, Jfd − is the exchange integral, gJ and
(gJ − 1)2J(J + 1) are the Lande and de Gennes factors, respectively. However, this ap-
proach, which is basically related to the assumption by Campbell [18] that 5d-electrons
at R play a dominant role in magnetic ordering, provided too high values of TC, and the
only good agreement obtained for GdCo2 [7] should be regarded as fortuitous.
The alternative molecular field approach for TC calculations has been proposed
for ferrimagnetic rare-earth intermetallics [5,12,19]:
( ) RMRMRR
J
J Cnn
g
gT '14 2
2
C χ+
−
= . (4)
In this approach the molecular-field coefficients nRR and nRM [2] can be related to
the exchange integrals and susceptibilities of conduction electrons at R and M
sites, which in turn can be evaluated ab initio in the framework of the LMTO cal-
culations described above (see Ref. [19] for details). The estimated by this way
values of TC and their derivatives are given in Table 1. As one can see, this ap-
proach yields a qualitative agreement with the experimental Θ and the corre-
sponding pressure derivatives, though a noticeable difference with the experiment
can be also noted in Table 1 for some GdMx compounds.
Физика и техника высоких давлений 2004, том 14, № 4
72
Actually, the calculated volume derivatives of TC are converted to the pressure
ones for comparison with the experimental data in Table 1, and the corresponding
bulk moduli, B, were calculated ab initio (see Ref. [14] for details) and also listed
in Table 1. One should take into account, however, the overbonding tendency of
LSDA calculations, which often provides overestimated bulk moduli (up to 10%).
This could contribute to discrepancies between the theoretical and experimental
pressure derivatives of magnetic ordering temperatures in Table 1.
The GdIn3−xSnx
alloys (0 < x < 3) order antiferromagnetically with the Neel
temperatures TN below 50 K, which show a complex W-shaped variation with
composition x. Their magnetic susceptibility is studied under hydrostatic pressure
at fixed temperatures (78 and 300 K) above TN. This study revealed well defined
peculiarities in the concentration dependences TN(x), the paramagnetic Curie tem-
perature Θ(x), as well as the pressure effect dlnχ(x)/dP (see Fig. 1). The values of
dlnχ(x)/dP and dlnΘ(x)/dP at 77.3 K, shown in Fig. 1, demonstrate a strong varia-
tion with x. The calculated volume derivative of the concentration dependence of the
partial density of s-states (DOS) at the Fermi level, dlnN(EF)/dlnV, is shown in
Fig. 1. The experimental estimates of the volume derivative dlnΘ(x)/dlnV and re-
sults of ab initio calculations of the volume-dependent electronic structure of the
alloys were used to analyze the nature of exchange interactions in GdIn3−xSnx.
The calculated bulk moduli for GdIn3 and GdSn3 appeared to be 570 and 610
kbar, and their average value B = 590 kbar was accepted for GdIn3−xSnx alloys.
a b
Fig. 1. (a) Experimental values of the pressure effects on magnetic susceptibility at 77.3 K
and the Curie temperature Θ in GdIn3−xSnx
alloys. (b) Volume derivatives for Θ and the
calculated partial DOS at the Fermi level for s-states at Gd (N(EF), solid line) versus
composition. Dashed lines are guides for the eye
Физика и техника высоких давлений 2004, том 14, № 4
73
The interaction between localized f-moments in rare-earth compounds can be
described within the RKKY model of indirect exchange via the conduction elec-
trons. In its simplest form [1,18] this model gives:
( )F
2 ENI∝Θ , (5)
where I is a strength of exchange interaction between f- and conduction electron
spins, and pressure independent factors are omitted. Thus one obtains:
V
EN
V
I
V lnd
)(lnd
lnd
lnd2
lnd
lnd F+=
Θ . (6)
In agreement with Eq. (6), a clear correlation between the concentration depen-
dences of dlnΘ(x)/dlnV and dlnN(EF)/dlnV derivatives is seen in Fig. 1(b). This
indicates the validity of the RKKY-type model of indirect interaction in the
GdIn3−xSnx system, presumably due to a substantial contribution of s- and p-states
to N(EF). By estimating a vertical shift which drops off dlnN(EF)/dlnV into ap-
proximate coincidence with dlnΘ(x)/dlnV dependence, we obtained average volume
derivative of I, dlnI/dlnV = −1.2, which is close to the corresponding value evalu-
ated in Ref. [15] for the effective exchange coupling between the d-band electrons.
The hexagonal RNi5 compounds, having relatively simple structure and uniax-
ial anisotropy, are especially suited for studies of both the exchange interactions
and the CEF effects [2]. Here we report experimental and theoretical results on the
pressure effects on the magnetic properties of GdNi5, which order ferromagneti-
cally at 33 K. The observed pressure derivative of the paramagnetic Curie tem-
perature appeared to be small (Table 1). According to our calculations, the itiner-
ant magnetism of GdNi5 is dominated by spin-polarized Gd 5d- and Ni 3d-states.
There is no charge transfer of the Gd outer electrons to the 3d-band, and the filling
of this band is not complete. The Fermi level is situated within the predominantly
Ni 3d-band at the local peak of the density of states N(E). As is seen in Fig. 2, at
Fig. 2. Fine structure of the den-
sity of states (DOS) of ferromag-
netic GdNi5 in the vicinity of the
Fermi level EF (marked with a
vertical dashed line). The solid
line corresponds to the ambient
atomic volume, whereas the dashed
and dotted lines represent DOS for
the lattice parameters reduced by
1 and 2%, respectively
Физика и техника высоких давлений 2004, том 14, № 4
74
high pressures (i.e. at reduced atomic volumes) the Fermi level is expected to pass
through the DOS peak, and this can affect substantially the magnetic state of
GdNi5. The volume dependence of the Curie temperature, calculated for GdNi5
within the approach (6), appeared to be weak in agreement with the experiment
(see Table 1).
Conclusions
It is demonstrated that the band theory within LSDA provides an adequate de-
scription of the electronic structure and peculiar magnetic properties of GdMx.
Our experimental magnetovolume data together with the results of first-principles
band structure calculations point to a predominant participation of d-electrons in
the indirect exchange interaction for GdM, GdM2, and GdNi5 compounds, where
ferromagnetic ordering can be hardly explained within the conventional RKKY
coupling scheme. The ferromagnetic instability in these compounds is apparently
induced by the local 4f−5d exchange interaction. It is shown that band structure
details, as well as a more general theory for the indirect exchange interactions are
required for an a priori description of the magnetic properties of these com-
pounds. The modified mean field approach, based on LSDA, gives a reasonable
description of TC and their behavior with pressure, indicating that the f−d ex-
change interaction can contribute substantially to magnetic ordering phenomena
in rare-earth systems. Also, one should expect a significance of spin fluctuations
in magnetic properties of R compounds with ferromagnetic ordering, and a suit-
able spin-fluctuation theory (e.g. [4]) can be applied to these systems. This might
provide a reduction of TC, and perhaps a better description of the experimental
dΘ/dP derivatives in ferromagnetic GdMx compounds. Most likely an interplay
between different kinds of magnetic interactions takes place in heavy rare-earth
compounds, and the magnetovolume effect can be applied in future investigations as
an efficient tool for identification of exchange interactions, as well as CEF effects.
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