Hall effect and magnetic ordering in RB₁₂
The concentration of carriers in LuB₁₂ is evaluated theoretically by applying ab initio FP-LMTO calculations. Theoretical results are found to be in agreement with high precision measurements of the Hall RH(T) coefficient which were carried out on single crystals of the rare earth dodecaborides RB₁₂...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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nasplib_isofts_kiev_ua-123456789-1172622025-06-03T16:26:43Z Hall effect and magnetic ordering in RB₁₂ Baranovskiy, A.E. Grechnev, G.E. Sluchanko, D.N. Glushkov, V.V. Demishev, S.V. Sluchanko, N.E. Shitsevalova, N.Yu. Электронные свойства проводящих систем The concentration of carriers in LuB₁₂ is evaluated theoretically by applying ab initio FP-LMTO calculations. Theoretical results are found to be in agreement with high precision measurements of the Hall RH(T) coefficient which were carried out on single crystals of the rare earth dodecaborides RB₁₂ (R = Ho, Er, Tm, Lu) at temperatures 1.8–300 K. A nature of the antiferromagnetic ordering in RB₁₂ is investigated within the RKKY-like model, which was supplemented by comprehensive electronic structure calculations for paramagnetic, ferromagnetic and antiferromagnetic phases. Support by the RAS Program «Strongly Correlated Electrons in Semiconductors, Metals, Superconductors and Magnetic materials» and the RFBR 07-02-90902 grant is acknowledged. 2009 Article Hall effect and magnetic ordering in RB₁₂ / A.E. Baranovskiy, G.E. Grechnev, N.Yu. Shitsevalova, D.N. Sluchanko, V.V. Glushkov, S.V. Demishev, N.E. Sluchanko // Физика низких температур. — 2009. — Т. 35, № 7. — С. 721-724. — Бібліогр.: 21 назв. — англ. 0132-6414 PACS: 71.20.Eh, 72.15.Qm, 75.30.–m https://nasplib.isofts.kiev.ua/handle/123456789/117262 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Электронные свойства проводящих систем Электронные свойства проводящих систем |
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Электронные свойства проводящих систем Электронные свойства проводящих систем Baranovskiy, A.E. Grechnev, G.E. Sluchanko, D.N. Glushkov, V.V. Demishev, S.V. Sluchanko, N.E. Shitsevalova, N.Yu. Hall effect and magnetic ordering in RB₁₂ Физика низких температур |
| description |
The concentration of carriers in LuB₁₂ is evaluated theoretically by applying ab initio FP-LMTO calculations. Theoretical results are found to be in agreement with high precision measurements of the Hall RH(T) coefficient which were carried out on single crystals of the rare earth dodecaborides RB₁₂ (R = Ho, Er, Tm, Lu) at temperatures 1.8–300 K. A nature of the antiferromagnetic ordering in RB₁₂ is investigated within the RKKY-like model, which was supplemented by comprehensive electronic structure calculations for paramagnetic, ferromagnetic and antiferromagnetic phases. |
| format |
Article |
| author |
Baranovskiy, A.E. Grechnev, G.E. Sluchanko, D.N. Glushkov, V.V. Demishev, S.V. Sluchanko, N.E. Shitsevalova, N.Yu. |
| author_facet |
Baranovskiy, A.E. Grechnev, G.E. Sluchanko, D.N. Glushkov, V.V. Demishev, S.V. Sluchanko, N.E. Shitsevalova, N.Yu. |
| author_sort |
Baranovskiy, A.E. |
| title |
Hall effect and magnetic ordering in RB₁₂ |
| title_short |
Hall effect and magnetic ordering in RB₁₂ |
| title_full |
Hall effect and magnetic ordering in RB₁₂ |
| title_fullStr |
Hall effect and magnetic ordering in RB₁₂ |
| title_full_unstemmed |
Hall effect and magnetic ordering in RB₁₂ |
| title_sort |
hall effect and magnetic ordering in rb₁₂ |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2009 |
| topic_facet |
Электронные свойства проводящих систем |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/117262 |
| citation_txt |
Hall effect and magnetic ordering in RB₁₂ / A.E. Baranovskiy, G.E. Grechnev, N.Yu. Shitsevalova, D.N. Sluchanko, V.V. Glushkov, S.V. Demishev, N.E. Sluchanko // Физика низких температур. — 2009. — Т. 35, № 7. — С. 721-724. — Бібліогр.: 21 назв. — англ. |
| series |
Физика низких температур |
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| fulltext |
Fizika Nizkikh Temperatur, 2009, v. 35, No. 7, p. 721–724
Hall effect and magnetic ordering in RB12
A.E. Baranovskiy and G.E. Grechnev
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: baranovskiy@ilt.kharkov.ua
N.Yu. Shitsevalova
Institute for Problems of Materials Science of NASU, Kiev 03680, Ukraine
D.N. Sluchanko, V.V. Glushkov, S.V. Demishev, and N.E. Sluchanko
A.M. Prokhorov General Physics Institute of RAS, 38 Vavilov Str., Moscow 119991, Russia
Received March 12, 2009, revised April 13, 2009
The concentration of carriers in LuB12 is evaluated theoretically by applying ab initio FP-LMTO calcu-
lations. Theoretical results are found to be in agreement with high precision measurements of the Hall RH(T)
coefficient which were carried out on single crystals of the rare earth dodecaborides RB12 (R = Ho, Er, Tm,
Lu) at temperatures 1.8–300 K. A nature of the antiferromagnetic ordering in RB12 is investigated within the
RKKY-like model, which was supplemented by comprehensive electronic structure calculations for para-
magnetic, ferromagnetic and antiferromagnetic phases.
PACS: 71.20.Eh Rare earth metals and alloys;
72.15.Qm Scattering mechanisms and Kondo effect;
75.30.–m Intrinsic properties of magnetically ordered materials.
Keywords: Hall effect, RKKY model, borides, electronic structure, magnetic ordering.
The MB12 dodecaborides (M is rare earth, early transi-
tion, or actinide metal) are of great scientific interest and
technological importance due to their extraordinary elec-
tronic, magnetic and structural properties such as peculiar
bonding [1], superconductivity (YB12 and ZrB12 [2,3]),
Kondo and valence fluctuation effects (YbB12 [4]). The
heavy rare earth (R) dodecaborides RB12, close to the fa-
mous Kondo insulator YbB12, are of particular interest
due to complicated scenario of magnetic ordering at low
temperatures and observed peculiar incommensurate
magnetic structures (TbB12–TmB12 [5]).
Though a number of experimental and theoretical in-
vestigations were carried out for RB12 [1,5–9], the mech-
anisms of microscopic magnetic interactions, as well as
fine details of the electronic structure in these com-
pounds, are still not clear.
In order to elucidate the origin of principal interac-
tions and electronic states responsible for magnetic order-
ing in RB12, the high precision measurements of the Hall
resistivity �H(�, T, H) were carried out for HoB12, ErB12,
TmB12 and LuB12 compounds within a wide temperature
range of 1.8–300 K in magnetic fields up to 80 kOe [6,7].
Based on the measured Hall coefficients of RB12 [6,7],
the corresponding values of normalized charge carrier
concentration n/n4f = (RHen4f)
–1 are evaluated and pre-
sented in Fig. 1. Here n and n4f are the numbers of carriers
and rare earth atoms per the primitive cell correspond-
ingly and RH is the Hall coefficient.
As can be seen in Fig. 1, the temperature dependences
of the charge carrier concentration are distinct from each
other for the nonmagnetic LuB12 and magnetic dode-
caborides. In particular, a pronounced anomaly of
n/n4f(T) is revealed in LuB12 at T* � 56 K, whereas mag-
netic compounds HoB12, ErB12 and TmB12 demonstrate a
weak enough variation of the carrier concentration n at in-
termediate temperatures. Indeed, on the average, the n/n4f
value is varied within about 10% through the paramag-
netic region of RB12 series, namely 2.0–2.2. It should be
stressed that this result contradicts to the assumption that
the conduction band in RB12 compounds is formed by
only one 5d electron of a rare earth element [10]. To shed
© A.E. Baranovskiy, G.E. Grechnev, N.Yu. Shitsevalova, D.N. Sluchanko, V.V. Glushkov, S.V. Demishev, and N.E. Sluchanko, 2009
light on the structure and filling of the conduction band in
RB12 compounds, the experimental study of Hall coeffi-
cients was supplemented by ab initio calculations of the
electronic structure for the paramagnetic (PM) and mag-
netically ordered (FM and AFM) phases of the RB12
dodecaborides. Based on the calculated band structure of
the reference LuB12 compound, which is supposed to rep-
resent a typical electronic configuration within RB12
series in the paramagnetic phase, manifestations of mag-
netic ordering are analyzed and discussed in the frame-
work of the RKKY model.
The stable B12 nanoclusters can be considered as basic
structural elements of the cubic dodecaborides. The cor-
responding UB12-type crystal structure is similar to the
simple rock-salt lattice, where U atoms and B12 cubo-
octahedrons occupy the Na- and Cl-sites, respectively.
The ab initio electronic structure calculations were car-
ried out for the paramagnetic, ferromagnetic and collinear
antiferromagnetic phases of RB12 (R = Ho, Er, Tm) by
using the relativistic full potential linear muffin-tin or-
bital (FP-LMTO) method [11,12] within the local density
approximation (LDA) [13] and the generalized gradient
approximation (GGA) [11]. With the present FP-LMTO
method, one can avoid extra shape approximations im-
posed on the charge density or potential. The localized 4f
states of rare earth ions were treated as spin-polarized
outer-core wave functions, contributing to the total spin
density. The spin occupation numbers were fixed by apply-
ing the Russel–Saunders coupling scheme to the 4f shell,
which was not allowed to hybridize with the conduction
band states. Other details of the FP-LMTO method em-
ployed in the present work are given in Refs. 11 and 12.
For each RB12 compound, the band structure was cal-
culated for a number of lattice parameters close to experi-
mental one. These calculations provided total energies for
a ground state and corresponding equations of states E(V)
with sufficient accuracy. By this way the magnetic stabil-
ity of AFM ordering in RB12 was confirmed by compre-
hensive total energy calculations for PM, FM and AFM
phases. Also, the detailed calculations of the band struc-
ture, Fermi surface, total and partial densities of elec-
tronic states (DOS) were carried out for the reference
LuB12 compound to reveal principal features of elec-
tronic spectra, which are common for the whole RB12 se-
ries. The corresponding band structure and total density
of electronic states of LuB12 in the close vicinity of the
Fermi level EF are presented in Figs. 2 and 3. According
to the present calculations, RB12 borides possess a rather
complicated Fermi surface (FS) consisting of three prin-
cipal parts. The first sheet of the FS is multiply connected
in the <111> directions (�L direction in the Brillouin
zone) and topologically similar to the FS of copper. The
second part of the FS forms «pancake»-like electron sur-
faces centred at X symmetry points. And the third Fermi
surface sheet consists of small electronic lenses centred at
K points of the Brillouin zone. These results are in agree-
ment with the recent FP-LAPW calculations [14],
whereas previous band structure calculations for the
heavy rare earth dodecaborides provided only two FS
sheets [8,15]. As it follows from our calculations, the
main features in the band structure of RB12 are governed
by hybridization of 5d states of rare-earth with 2p states
of boron. These hybridized bands exhibit a strong disper-
sion at the Fermi level (see Fig. 2), and the calculated ef-
fective masses of conduction electrons appeared to be
comparatively small (m* ~ m0 ), in agreement with re-
sults of the experimental studies of the de Haas–van
Alphen effect in LuB12 [9], HoB12, ErB12 and TmB12
compounds [16]. For LuB12 our evaluation of a volume
722 Fizika Nizkikh Temperatur, 2009, v. 35, No. 7
A.E. Baranovskiy, G.E. Grechnev, N.Yu. Shitsevalova, D.N. Sluchanko, V.V. Glushkov, S.V. Demishev, and N.E. Sluchanko
10 100
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
T, K
LuB12
TmB12
HoB12 ErB12
n
/n
4
f
Fig. 1. Temperature dependence of normalized charge carriers
concentration n/n4f = (RHen4f)
–1
of RB12.
3
2
1
0
–1
–2
–3
–4
–5
Ã Õ W L K XÃ
E
n
er
g
y,
eV
Fig. 2. Band structure for the reference LuB12 compound.
enclosed by the FS provides the estimated carrier density
about two conduction electrons per formula unit.
In order to elucidate a nature of magnetic ordering in
RB12 a qualitative analysis was carried out here within
the framework of the RKKY model [17],
� ~ Gn
2
J
2
/EFSF(n), (1)
where � is the paramagnetic Curie temperature, G is the
De Gennes factor, J is the effective exchange parameter,
and F(n) is the RKKY function. As is seen from the calcu-
lated dependence of the RKKY function versus carrier
concentration n in Fig. 4, for all investigated RB12 the
F(n) behavior in vicinity of n/n4f = 2 appeared to be con-
sistent with the AFM ordering in these borides. Also one
can see in Fig. 4, that in the range from n/ n4f = 2 to 2.2 the
RKKY function varies moderately, and relative changes of
F(n) do not exceed 30%. Therefore, the paramagnetic Cu-
rie temperatures behavior within the RB12 series is ex-
pected to be predominantly governed by the De Gennes
factor, which decreases monotonously for heavy rare-earth
ions R. The �(n) behavior is in a qualitative agreement
with the experimental relative values of the Néel tempera-
ture TN, which are equal to 7.4, 6.7 and 3.3 K for HoB12,
ErB12 and TmB12, respectively [5,6]. However, an attempt
to describe the relative values of TN more precisely within
Eq. (1) presumes that noticeable increase of the effective
exchange parameter J with the atomic number of rare earth
element should take place in the investigated RB12 series.
Indeed, the ratios JEr/JHo � 1.25 and JTm/JHo � 1.5 have to
be valid to satisfy the observed sequence of TN in the
framework of Eq. (1). On the other hand, such increase of
J with the atomic number of rare earth element contra-
dicts to the direct ab initio calculations for rare earth sys-
tems [18,19], which provide changes of the correspond-
ing exchange parameter not exceeding 5%. Therefore, the
deviations from De Gennes scaling for magnetic ordering
temperatures of RB12 occur that are probably due to a
mechanism not represented by the RKKY model.
As it follows from results of the recent studies of trans-
port properties in RB12 [6,7], an anomalous behavior of
transport parameters does not comply with the variation
of the De Gennes factor between HoB12 and LuB12, and
the decrease of charge carrier mobility with the 4f occupa-
tion number n is presumably related to the enhancement
of spin fluctuations (SF) within the HoB12 and TmB12 se-
ries. Accordingly we may also suggest, that the onsite
4f–5d spin fluctuations can also renormalize the values of
the magnetic ordering temperature of RB12, in addition to
the RKKY mechanism of Eq. (1) and in line with the sug-
gested SF mechanism of Refs. 20 and 21.
Thus, it is revealed, that 5d states of rare earth ions
which are hybridized with 2p states of boron are playing
an important role not only in formation of the electronic
structure and bulk properties, but also in the AFM order-
ing in RB12 via both the RKKY-like indirect exchange in-
teraction and the onsite 4f–5d spin fluctuations effects.
Support by the RAS Program «Strongly Correlated
Electrons in Semiconductors, Metals, Superconductors
and Magnetic materials» and the RFBR 07-02-90902
grant is acknowledged.
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Hall effect and magnetic ordering in RB12
Fizika Nizkikh Temperatur, 2009, v. 35, No. 7 723
–0.2 –0.1 0 0.1
0
10
20
30
40
50
60
Energy, Ry
N
(E
),
R
y
–
1
Fig. 3. Calculated total density of state for LuB12.
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n
�
F
(2
k
R
)
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Fig. 4. RKKY function vs normalized carrier concentration n
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724 Fizika Nizkikh Temperatur, 2009, v. 35, No. 7
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