Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application
The peculiarities of the exchange interaction between the carrier spin and localized spin moments of magnetic ions in the close vicinity of semimetal-semiconductor transition have been studied on the example of semimagnetic quaternary solid solution Hg₁₋x₋yCdxMnySe (x = 0.10, y = 0.02, Eg = 45 meV)...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
1999
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| Назва видання: | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Цитувати: | Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application / Yu.I. Mazur, G.G. Tarasov, E.V. Kuz'menko, A.E. Belyaev, W. Hoerstel, W. Kraak, W.T. Masselink // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 4. — С. 37-45. — Бібліогр.: 32 назв. — англ. |
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irk-123456789-1202542017-06-12T03:05:12Z Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application Mazur, Yu.I. Tarasov, G.G. Kuzmenko, E.V. Belyaev, A.E. Hoerstel, W. Kraak, W. Masselink, W.T. The peculiarities of the exchange interaction between the carrier spin and localized spin moments of magnetic ions in the close vicinity of semimetal-semiconductor transition have been studied on the example of semimagnetic quaternary solid solution Hg₁₋x₋yCdxMnySe (x = 0.10, y = 0.02, Eg = 45 meV) by means of Shubnikov-de Haas oscillations. It is shown that due to the s-p hybridization of electron wavefunctions the exchange constant α turns out in α complicated function of energy gap Eg and electron concentration which changes from positive αN₀ = 0.15 eV to negative αN₀ = -0.28 eV values which are typically accepted for wide gap semimagnetic semiconductors. 1999 Article Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application / Yu.I. Mazur, G.G. Tarasov, E.V. Kuz'menko, A.E. Belyaev, W. Hoerstel, W. Kraak, W.T. Masselink // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 4. — С. 37-45. — Бібліогр.: 32 назв. — англ. 1560-8034 PACS: 72.15.Gd, 72.20. My, 73.61.Ga. http://dspace.nbuv.gov.ua/handle/123456789/120254 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
The peculiarities of the exchange interaction between the carrier spin and localized spin moments of magnetic ions in the close vicinity of semimetal-semiconductor transition have been studied on the example of semimagnetic quaternary solid solution Hg₁₋x₋yCdxMnySe (x = 0.10, y = 0.02, Eg = 45 meV) by means of Shubnikov-de Haas oscillations. It is shown that due to the s-p hybridization of electron wavefunctions the exchange constant α turns out in α complicated function of energy gap Eg and electron concentration which changes from positive αN₀ = 0.15 eV to negative αN₀ = -0.28 eV values which are typically accepted for wide gap semimagnetic semiconductors. |
| format |
Article |
| author |
Mazur, Yu.I. Tarasov, G.G. Kuzmenko, E.V. Belyaev, A.E. Hoerstel, W. Kraak, W. Masselink, W.T. |
| spellingShingle |
Mazur, Yu.I. Tarasov, G.G. Kuzmenko, E.V. Belyaev, A.E. Hoerstel, W. Kraak, W. Masselink, W.T. Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Mazur, Yu.I. Tarasov, G.G. Kuzmenko, E.V. Belyaev, A.E. Hoerstel, W. Kraak, W. Masselink, W.T. |
| author_sort |
Mazur, Yu.I. |
| title |
Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application |
| title_short |
Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application |
| title_full |
Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application |
| title_fullStr |
Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application |
| title_full_unstemmed |
Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application |
| title_sort |
quaternary semimagnetic hg₁₋x₋ycdxmnyse crystals for optoelectronic application |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
1999 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120254 |
| citation_txt |
Quaternary semimagnetic Hg₁₋x₋yCdxMnySe crystals for optoelectronic application / Yu.I. Mazur, G.G. Tarasov, E.V. Kuz'menko, A.E. Belyaev, W. Hoerstel, W. Kraak, W.T. Masselink // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 4. — С. 37-45. — Бібліогр.: 32 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
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2025-07-08T17:32:51Z |
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2025-07-08T17:32:51Z |
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| fulltext |
3 7© 1999, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 1999. V. 2, N 4. P. 37-45.
1. Introduction
It has been demonstrated that «spin» doping of semicon-
ductors leads to a drastical changes in their optical and
transport properties [1, 2]. These changes originate from
the exchange interaction between the conduction electron
spin and the localized magnetic moments of magnetic ions,
typically, Mn ions. Exchange interaction modifies the
energy band structure and introduces a striking differ-
ences between the quantum transport phenomena observed
in diluted magnetic and nonmagnetic semiconductors [3,
4]. Usually in nonmagnetic semiconductors the ampli-
tude of a given magnetoresistance maximum decreases
monotonically with temperature increase, whereas the
oscillatory behavior of magnetoresistance can be observed
in semimagnetic materials.
The most suitable conditions for the Shubnikov-de Haas
(SdH) oscillations observation are met in narrow-gap mate-
rials due to a small value of a free carrier effective mass.
Mixed AIIBVI compounds Hg1-xMnxTe and Hg1-xMnxSe al-
low gradual transition from the zero-gap (semimetals HgTe,
HgSe) to the open-gap (semiconductor) state by increasing
the manganese content. However, when the semimetal-semi-
conductor transition has happened the manganese content
occurs high enough to generate a numerous magnetic clusters w
hich strongly affect the spin-dependent phenomena [5, 6]. In
order to avoid this obscuring influence the energy gap in
HgTe or HgSe can be preferably opened by adding the
cadmium with the subsequent introduction of magnetic ions
in mixed Hg1-xCdxTe or Hg1-xCdxSe crystals. Quaternary
compounds Hg1-x-yCdxMnyTe and Hg1-x-yCdxMnySe demo-
nstrate improved optical and transport characteristics
in comparison with those in ternary Hg1-xCdxTe and
Hg1-xCdxTe when their composition is matched properly [7−9].
In this paper the Hg1-x-yCdxMnySe single crystals with small
energy gap Eg, Eg ~ 50 meV, are studied. The manganese
concentration is kept to be a comparatively low (y ~ 0.02). In
this case the Brillouin function describes the crystal magne-
tization reasonably well.
The investigation is aimed to study the peculiarities of
exchange interaction in the close vicinity of semimetal-
semiconductor transition. This interaction is typically
described by two basic exchange constants, α and β, which
present s-d and p-d exchange integrals, respectively [10,
11]. The sign of parameter α, determined experimentally,
is negative, whereas β is of a positive value and differs
from α approximately by factor 2 in Hg1-xMnxTe [12].
For the wide gap diluted semimagnetics the values of α and
PACS: 72.15.Gd, 72.20. My, 73.61.Ga.
Quaternary semimagnetic Hg1-x-yCdxMnySe crystals
for optoelectronic application
Yu.I. Mazur, G.G. Tarasov, E.V. Kuz’menko, A.E. Belyaev, W. Hoerstel*,
W. Kraak*, W.T. Masselink
Institute of Semiconductor Physics, NAS of Ukraine,
45,prospect Nauki, 03650 Kyiv, Ukraine
*Humboldt-Universitat zu Berlin, Dept. of Physics, Invalidenstrasse
110, D-10115 Berlin, Germany
Abstract. The peculiarities of the exchange interaction between the carrier spin and localized spin
moments of magnetic ions in the close vicinity of semimetal-semiconductor transition have been
studied on the example of semimagnetic quaternary solid solution Hg1-x-yCdxMnySe (x = 0.10, y = 0.02,
Eg = 45 meV) by means of Shubnikov-de Haas oscillations. It is shown that due to the s-p hybridization
of electron wavefunctions the exchange constant α turns out in a complicated function ~α of energy
gap Eg and electron concentration which changes from positive ~αN 0 = 0.15 eV to negative
~αN 0 = -0.28 eV values which are typically accepted for wide gap semimagnetic semiconductors.
Keywords: semimagnetic semiconductor, constant of exchange interaction, semimetal-semiconductor
transition.
Paper received 13.10.99; revised manuscript received 14.12.99; accepted for publication 17.12.99.
Yu. I. Mazur et al.: Quaternary semimagnetic Hg1-x-yCdxMnySe crystals for...
38 SQO, 2(4), 1999
β are reproducible with a great accuracy, whereas for narrow-
gap semiconductors these values, determined by different
authors, e.g., for Hg1-xMnxSe, demonstrate a considerable
scattering [4, 13-15]. This latter mirrors the complicated nature
of the band structure in narrow-gap compounds, where both
spin and orbital quantization should be taken into account
simultaneously. Below we present the data which make it
questionable even the separate usage of α and β for the
description of the SdH oscillations behavior in narrow-gap
Hg1-x-yCdxMnySe, at least.
2. Experiment
The monocrystalline Hg1-x-yCdxMnySe samples were grown
by the modified Bridgman method. The composition of the
samples was determined by microprobe analysis. For the
SdH measurements were used the homogeneous samples
only. According to the results of microprobe analysis the
Mn distribution over the sample area differs by less than 0.1
at %.The measurements were performed on the samples
having the composition x = 0.10, y = 0.02. As-grown crystals
had the electron concentration n = (3–5)⋅1017 cm-3. In order
to change the free-carrier concentration the samples were
annealed in the vapor of the components. Due to heat treat-
ment the electron concentration was varied in the range (0.4–
20)⋅1017 cm-3. The magnetoresistance has been measured in
magnetic field up to 15T and temperature range 1.5–80 K.
The samples used for SdH measurements were sliced into a
rectangular Hall-bars with dimensions of 9×1.5×1.2 mm3.
Ohmic contacts were obtained by soldering with 10% tin-
indium. The Hall coefficient values did not depend
essentially on temperature due to degeneration of electron
gas. The value of electron mobility µn at T = 4.2 K approaches
the value 3⋅105 cm2V-1s-1 for n = 1.6⋅1017 cm-3, being to best
of our knowledge, the same order as that in the state-of-the
art Hg1-xCdxSe. The parameters of the samples used in our
measurements are given in Table 1.
Here the electron concentrations n were derived from
the period of SdH oscillations. They coincide within 2%
accuracy with those found from Hall measurements. The
Eg value was determined from the optical studies in nar-
row-gap Hg1-x-yCdxMnySe [9]. Parameters mn and me are
the electron mass at bottom of conduction band and the
mass of free electron, respectively. The effective mass mF
and the gyromagnetic factor g0 at Fermi energy were cal-
culated following [16] in the Kane approximation with
account of the contribution of higher energy bands. The
Luttinger parameters, the Kane momentum matrix ele-
ment P, and the spin-orbit splitting ∆ were those for
Hg1-xMnxSe [13]: g1 = 3.0, g2 = 0.5, g3 = -0.17,
k = -1.5, L = 0; P = 7.2⋅10-8 eV cm, and ∆ = 0.39 eV.
The composition used has been chosen due to follow-
ing experimental fact. It has been established [17] that in
Hg1-xCdxSe with x = 0.15 (semiconductor state) unusual
strong SdH oscillations develop and their positions in
transverse (ρxx) and longitudinal (ρzz) magnetoresistance
are not shifted by phase. The SdH patterns demonstrate
well resolved spin split structure. Following these find-
ings we take the composition x = 0.1 and y = 0.02, because
at zero magnetic field B the energy gap in Hg1-x-yCdxMnySe
is opened in the same manner as in Hg1-x’Cdx’Se with
effective concentration x’ = x + 2.52y (see Ref. [9]). With
such adjusted composition we believe to meet the most
favorable conditions for observation of exchange interaction
effect on the SdH spin-related structure in Hg1-x-yCdxMnySe.
3. Results and discussion
A. Experimental results
Fig. 1 depicts the SdH patterns for the ρxx and ρzz magne-
toresistance in sample 1 at different temperatures. Due to
low electron concentration the B0
− maximum for ρxx is
observed at B ≈ 6 T. Below it, the spin split maxima B0
± are
well resolved at low temperature (T = 1.5 K) with subsequent
smearing them at temperature increase. Comparison of this
dependence with that presented in Ref. [16] for non-magnetic
Hg1-xCdxSe of proper cadmium content shows a remarkable
similarity. The SdH dependence for ρzz reproduces all the
maxima of ρxx without a visible phase shift at low tempera-
ture. It is clearly seen also that BN
+ maxima (N ≥ 1) are
stronger than those of BN
− in the ρxx dependences, whereas
BN
− dominate BN
+ peaks in the ρzz dependences. With tem-
perature elevated the B0
− maximum shifts towards higher
magnetic field as shown in Fig.2. The spin splitting
δN, δN = BN
+ - BN
− , decreases for all Landau numbers N ≥ 1.
The linear dependences of the integer versus reciprocal
magnetic fields for the ρxx and ρzz spin split components,
shown in Fig. 3, allow to determine precisely the period of
SdH oscillations and to calculate the electron concentration
n (see Table 1).
Fig. 4 presents the temperature-induced evolution of
the SdH dependence for ρxx in the sample 2. In view of
higher electron concentration the B0
− maximum occurs
at B ≈ 12 T. The spin splitting is obviously seen for all
N ≤ 7 peaks at T = 1.5 K. With temperature increase δN
weakly reduces as shown by insert in Fig. 4. The tempera-
ture-induced shift of B0
− maximum is plotted in Fig. 5.
The peak motion toward higher magnetic field becomes
more energetic when temperature passes T ≈ 15 K.
Fig. 6 shows the modification of the ρxx dependence in
sample 4 with temperature growth. For the high electron
concentration the B0
− maximum is far beyond our experi-
mental facilities. We surely observe the magnetoresistance
peaks with N ≥ 6. These peaks being initially non-split at
low temperature reveal a well resolved spin structure at
higher temperature. The value of δN grows with tempera-
ture increasing, as shown by divergent dashed lines in
Fig. 7.
Fig. 8 summarizes our findings on the effective pa-
rameter ~α variation with the electron concentration n in
the vicinity of semimetal-semiconductor transition in the Hg1-
x-yCdxMnySe single crystals. This parameter is introduced
to describe the exchange interaction effect in semimagnetic
narrow-gap compounds.
Yu. I. Mazur et al.: Quaternary semimagnetic Hg1-x-yCdxMnySe crystals for...
39SQO, 2(4), 1999
Fig.1. SdH oscillations patterns for Hg1-x-yCdxMnySe single crys-
tal in transverse (ρxx) and longitudinal (ρzz) configurations. The
oscillation peaks are labeled by the Landau number N and the
sign for the spin state. Sample 1: x = 010, y = 0.02; n = 4.4⋅1016 cm-3
Fig.2. Temperature-induced shift of the spin split components
for the first SdH maxima of ρxx magnetoresistance (N = 0, 1, 2)
in sample 1.
0 2 4 6 8 10
2+
0-1+
1-
2+2-
1-
2-
1+
0-
x10
ρzz
ρxx
1.5
K
4.2 K
1.5 K
4.2 K
ρ xx
, ρ zz
B
( T)M agnetic field
(a
rb
. u
ni
t)
0 5 10 15 20 25
1.5
2.0
2.5
3.0
6.0
6.2
6.4
2-
2+
1-
1+
0-
B
(T
)
T
(K)
M
ag
ne
tic
fi
el
d
Temperature
B. Discussion
In order to start it should be mentioned that both the B0
−
speak position and the spin splitting of BN peaks of magne-
0.0 0.4 0.8 1.2 1.6
0
1
2
3
4
5
6
- ρxx+ - ρxx- -
ρzz+
-
ρzz
-
T=1.5
K
1
/
B
(T
-1)
0
1
2
3
4
5
6
L
an
da
u
in
te
ge
r
Fig.3. Plot of the Landau integer versus reciprocal magnetic fields:
triangles stand for the ρxx magnetoresistance, circles are for the ρxx
oscillations. Sample 1, T = 1.5 K
0 2 4 6 8 10 12 14
2- 2+ 1-
1+
0-
1.5
K
4.2
K
11
K
ρ xx
(ar
b. un
it
s)
0 10 20 30
3
4
5
6
2-
2+
1-
1+
B
N
±
-
Po
si
tio
n
(T
)
T (K)
M agnetic field B(T)
Fig.4. A temperature variation of the SdH patterns in ρxx configu-
ration for Hg1-x-yCdxMnySe, Sample 2. The peak shift caused by the
change of temperature for N = 1, 2 is plotted by insert. Sample 2:
x = 010, y = 0.02; n = 1.08⋅1017 cm-3
toresistance are defined to the great extent by the value of
gyromagnetic factor g0 at the Fermi level. Being negative at
B = 0, g0 decreases by module, as can be seen from Table 1,
with n increase following approximately the dependence
Yu. I. Mazur et al.: Quaternary semimagnetic Hg1-x-yCdxMnySe crystals for...
40 SQO, 2(4), 1999
g m
m E E
e
F F g
0 2 1 1
3 3 2
= + −
+ +
∆
∆ (1)
which has been derived from the Kane theory, when the
influence of remote energy bands was neglected [18]. In
magnetic field the g0-factor is contributed by exchange
interaction and becomes renormalized to [12]
g g N S Hy z B
* /= +0 α µ (2)
for the Г6 band and to
g g N S Hy z B
* /= +0 3β µ (3)
for the Г6 band in the semimagnetic semiconductors.
In equations (2) and (3) N y = yN0, where N0 is the
number of unit cells per unit volume, y is the Mn molar
ρ xx
(a
rb
.u
ni
ts
)
7 8 9 10 11 12 13 14
44
K
16.5 K
33 K
23 K
11
K
4.2
K
1.5
K
0 10 20 30 40
12.0
12.2
12.4
12.6
12.8
13.0
T (K)
0-
M agnetic field B(T)
Po
sit
io
n
(T
)
Fig.5. Plot of B0
− maximum motion in the ρxx dependence on tem-
perature in Sample 2. Nonmonotonic shift of B0
− is shown by insert.
ρ xx
(a
rb
.u
ni
ts
)
3 4 5 6 7
x
2
2.8
K
8
K
12
K
15
K
∆
M agnetic field B(T)
Fig.6. Temperature-induced transformation of the SdH pattern in
the ρxx configuration for Hg1-x-yCdxMnySe, Sample 4: x = 010, y =
0.02; n = 1.21⋅1018 cm-3 . The spin related structure develops at
higher temperatures.
3.5 4.0 4.5 5.0 5.5 6.0
0
5
10
15
20
25
9
- 9
+
8
-
8
+
7
-
7
+
6
- 6
+
M agnetic field B (T)
T
em
pe
ra
tu
re
T
(K
)
Fig.7. Thermally induced divergence of spin-splitted maxima in ρxx
configuration in Sample 4.
Fig.8. Plot of the ~αN 0 function on the electron concentration n.
Compilation of the data for Samples 1–4. Line is for eyeguidance.
10
17
10
18
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
~ α
N
0
(
eV
)
n
Electron concentration (cm )-3
Yu. I. Mazur et al.: Quaternary semimagnetic Hg1-x-yCdxMnySe crystals for...
41SQO, 2(4), 1999
fraction, and µB is the Bohr magneton. The thermal aver-
age Sz of the spin operator $S projection z is determined
by the Brillouin function [1]
( )S S Bz = − 0 ξ (4)
and
( )B S
S
S
S S S
ξ ξ ξ= + +
−
2 1
2
2 1
2
1
2
1
2
coth coth
( )ξ µ= +g SH k T TM n B B/ 0
Here gM n = 2 is the gyromagnetic factor of the Mn
ion, S = 5/2. Empirical parameters S0 and T0 take into
account the existence of magnetic clusters and the anti-
ferromagnetic interaction between the manganese ions,
respectively.
The sign of exchange parameter α is negative and its
contribution to g* (equation 2) is positive. Therefore the
exchange induced contribution to electron g-factor has
to reduce the latter by module in open-gap semiconduc-
tor (Г6 energy band). For zero-gap semimagnetics (Г8
band) the exchange contribution is of the same sign as the
g0-factor (β > 0) and, hence, g* has to be enhanced by
module. Following these arguments, one can expect in
open-gap materials that the exchange contribution, be-
ing a sizable fraction of the total spin splitting for the
conduction electrons, will favor a significant reduction
of the electron spin splitting at very low lattice tempera-
ture. With temperature increasing this contribution rap-
idly decay due to reduction of Sz (Eq. 4) and the total
spin splitting has to be increased. Contrary, in zero-gap
material the temperature increase produces a reduction
of the spin splitting by the same reason.
Let us go to discussion of temperature behavior of SdH
oscillations in sample 1. The position of B0
− maximum
can be determined from [19]
B
c
e
n
0
2 2
− =
h π
γ
4
1
3
, (5)
where γ =
m
m gF
e2 * . The peak position shift observed ex-
perimentally (Fig. 2) can be connected immediately with
the change of the parameter γ value since the electron
concentration is suggested to be constant at temperature
variation due to degeneration of electron gas. Hence, one
concludes from the experimental data that as far as B0
−
peak moves towards higher magnetic field with tempera-
ture increase the γ value has to decrease. For the multi-
plier ( )m mF e/ 2 definitely grows with the temperature
elevating the γ reduction can originate from the g*
reduction only. Because of the open-gap nature of the
Hg1-x-yCdxMnySe crystal under investigation here the g*
temperature behavior is governed by Eq. 2. The first term
in the right part of this equation, g0 , can be reduced by
module in principle with temperature increase due to en-
largement of Eg and EF (see Eq. 1). It was determined from the
earlier optical measurements (see Ref. [9]) that in the
Hg1-x-yCdxMnySe crystals of similar composition
dE dTg / equals to 0.54 meV/K. When this temperature-
induced «opening» the energy gap is taken into account
its contribution to the total B0
− peak shift gains approxi-
mately 12% of that observed experimentally only. There-
fore the contribution of exchange related term in equation
2 should be dominating. However, if the α sign is assumed
to be negative (the case of open-gap semimag-netics) one
meets a severe contradiction with experiment: either an
unreasonable high exchange contribution at y ≈ 0.02
should be admitted in order to make the sum g* positive
when α is negative, or the α sign is to be accepted positive.
In our earlier SdH experiment [20] with the
Hg1-x-yCdxMnySe crystals of similar composition it was
established that in order to agree the SdH data with theory,
operating with two independent α and β, the module of α
must be reduced by factor 1.5–2. Unfortunately, in those
experiments the B0
− maximum was not reached and the
conclusion was derived from the temperature dependence
of the spin splitting of the SdH maxima. This dependence
was found to be weak and did not allow the more definite
assignment. Nevertheless, it was supposed that such α re-
duction could arise from the admixture of p-like
wavefunctions to the s-like wave-functions of the conduc-
tion band electrons. In this case the exchange contribu-
tion has to be taken into account by substitution of
(F1α+F2β) instead of α into equation 2. The F1 and F2
functions depend on the Kane’s coefficients which include
the contribution of remote energy bands [21].
The SdH results presented here are much more indica-
tive, because the B0
− maximum is easily seen and it is
possible to trace its movement with temperature variation.
Using the data from Table 1 and the position of B0
− peak the
g* value has been derived and is found to be g* = 64,
whereas g0 = 47.5 (see Table 1). The number obtained
positively states that the exchange contribution to g * is
amplifying one, i.e., the exchange parameter α occurs positive
by sign even for the Г6 energy band. This crucial result
completely changes the physical picture and proves that in
the close vicinity of semimetal-semiconductor transition
(Eg > 0) the exchange contribution cannot be described
simply in terms of two independent exchange constants, as
it was done in the approximation of molecular field.
Nevertheless, this contribution stays to be proportional to
Sz and manganese concentration Ny. Therefore, we assume
that equation 2 holds its shape, but the physical meaning of
parameter α is different: α cannot be considered as a con-
stant but is the function of Eg in the range of small (positive)
Eg. Since we will imply further an effective parameter ~α
instead of α when appeal to equation 2. At low temperature
the Sz function tends its saturation value S0, which typi-
cally is less than 5/2 due to clustering effect. In this tempera-
ture range the g* value is to be the largest. When tempera-
ture is lifted up the Sz value reduces by module and the
rate of reduction is defined by effective temperature T0.
Following our experimental results the T0 value should be
Yu. I. Mazur et al.: Quaternary semimagnetic Hg1-x-yCdxMnySe crystals for...
42 SQO, 2(4), 1999
large enough, T0 ≈ 8 K, in the sample 1. Under these
conditions the B0
− peak motion with temperature increas-
ing towards higher magnetic field, seen in Fig. 2, becomes
well motivated.
Table 1
Hg1-x-yCdxMnySe single crystal
x = 010, y = 0.02, Eg = 45 meV, T = 4.2K
Sample
label 3
17
cm
,10
−
⋅n m
m
n
e
⋅103 m
m
F
e
⋅102 g0 meV
EF ,
1 0.44 4.7 1.48 -47 44
2 1.08 4.7 1.94 -36 68
3 2.33 4.7 2.46 -28 93
4 12.1 4.7 4.13 -15 183
The temperature variation of spin splitting for the SdH
maxima is shown in Fig. 2. The peak positions are deter-
mined by [19]
( )B
c
e n k kN
k
N
±
≥
= + ±
∑h
m
2 2
0
2
3
2
3
π γ
γ,
, N≥1 (6)
Here the thermal smearing of Fermi energy is not taken
into account and equation 6 is, strictly speaking, valid
only at very low temperature. If γ = 0 or γ << 1 the
SdH maxima can not be resolved practically. In the case
of sample 1 the γ value has been calculated from
the ratio B B1 1
+ −/ and occurs to be large enough, γ = 0.46,
resulting in a well resolved spin splitting at low tempera-
ture. The g * value determined from the spin splitting of
the N = 1 SdH peak is found to be equal g* = 62.3,
which reproduces the value derived from the B0
− position
within the 2.5 % accuracy. With the temperature increase
the γ value, found from the temperature variation of
δN , reduces and the spin splitting δN decreases as shown
in Fig. 2. Hence, the temperature behavior of the δN
value is also consistent with the general picture enlight-
ened above. It should be mentioned here that the spin split-
ting δN can be effectively reduced also due to thermally-
induced broadening of the SdH peaks, typically as in the
case of nonmagnetic semiconductors [17]. Therefore, the
smearing of spin split structure at higher temperature is
not so indicative as the motion of the B0
− peak. Indeed,
the consideration which takes carefully into account in-
complete degeneration of electron gas as well as the broad-
ening of Landau levels due to collisions (the Dingle
temperature), gives the corrections to γ facilitating the
motion of B0
− maximum towards the lower magnetic field, in
the direction upright opposite to that observed experimen-
tally.
The electron concentration n in sample 2 differs by
2.5 factor against that in sample 1. Fig. 4 reproduces the
SdH oscillations patterns in this sample at three different
temperatures. A well-pronounced spin splitting accompa-
nies each N-th SdH maximum at low temperature with subse-
quent smearing the spin structure at higher temperature (T ~
40 K). Basing on our findings for sample 1 we start the
analysis from the temperature behavior of B0
− maximum
located at B ~ 12 T. The non-monotonic shift of the B0
− peak
with temperature is mirrored by the insert in Fig. 5. Up to
temperature T ≈ 15 K the peak moves slightly towards lower
magnetic field, but then it changes the direction of motion
and goes quickly up to higher magnetic field. Using
the B0
− peak position, as well as, the spin splitting δ1 at T =
1.5 K (Fig. 4, insert) the g* value was derived. It occurs to
be a surprisingly close the g0 value in sample 2: g* = 37
against g0 = 36. According to equation 2 this indicates
either no contribution of the exchange interaction in sample
2 or a very small negative contri-bution to g* if the latter
exists. One could even suspect whether the manganese ions
present in this sample, but our earlier studies by means of
far-infrared phonon spectroscopy ( reflection, transmission
[9]) , as well as the data of microprobe analysis surely verify
the manganese presence of a proper concentration. Whence
we conclude that the exchange contribution in the range of
small Eg of semimagnetics becomes also strongly depen-
dent on electron concentration being nearly suppressed at
n ≈ 1⋅1017 cm-3. If this statement is true the low-temperature
behavior of the B0
− peak and the spin- splitting of the SdH
maxima can be reasonably explained. Indeed, due to thermal
smearing of the Fermi edge the B0
− peak position is deter-
mined by equation 5 with γ changed by ~γ :
~ /γ γ= +
−0.535 0k Tm c eBB F h
2
. (7)
As a result, the B0
− position is to be normally shifted to
the side of lower magnetic field with temperature increase.
This fact is mirrored by the lowering part of curve in Fig. 5
(insert). The similar corrections can be introduced in equa-
tion 6 also, but the thermal shift of BN
± maxima will be less
pronounced in comparison to that for the B0
− peak. The
spin splitting is also smeared with temperature growth:
besides diminishing the oscillations amplitudes, the
reconciliation of the spin split doublet components and their
broadening lead to complete disappearance of the spin related
structure of the SdH maxima. Hence, in the case of sample 2
we observed the behavior typical for nonmagnetic
semiconductors when temperature is below 15 K.
The further shift of the B0
− maximum towards higher
magnetic field after the temperature passes T = 15 K seems
to be of an activation nature. Indeed, when magnetic field
is strong enough (B ~ 12 T), the localization of electrons
at the fluctuations of potential is of high probability. At
the B strength which corresponds to the maxima of Hall
coefficient oscillations, the localization can be of a reso-
nant character [22] and the electrons which possess a low
kinetic energy ( slightly above the Landau sub-bands bot-
tom) become localized. The ratio of the localized elec-
trons number to their total quantity is not very small. The
resonant localization can be a reason of unusually large
amplitudes of the Hall oscillations and those for the ρxx.
In our case such sort of localization could develop at low
Yu. I. Mazur et al.: Quaternary semimagnetic Hg1-x-yCdxMnySe crystals for...
43SQO, 2(4), 1999
temperature (T ≤ 15 K). The temperature increased above
15 K releases the trapped electrons, effectively affecting
the electron concentration n. This latter results in the B0
−
peak shift towards higher magnetic field (see equation 5)
without a noticeable change of the γ value. Therefore, the
spin splitting of the SdH maxima does not react immediately
on the more energetic B0
− peak shift as shown in Fig. 4
(insert).
The further n increase by factor 2.2 does not change
basically the SdH oscillations behavior against that ob-
served in sample 2. In sample 3 the BN
± doublet was surely
detected at B ~ 9 T while the B0
− peak was beyond our
facilities. The g* value is derived to be g* = 26 from the
δ1 spin splitting , whereas g0 = 28 in sample 3. It shows
that the exchange interaction is not yet actual in the case.
Whenever the electron concentration was increased up to
1.21⋅1018 cm-3 the SdH oscillations behavior becomes dis-
tinctly different. Fig. 6 shows the ρxx variation versus
magnetic field up to B = 7 T, when the most prominent changes
of the SdH peaks develop with temperature increase. The
low temperature patterns do not reveal any spin splitting.
When temperature was elevated, the well resolved structure
of the BN peaks with N ≥ 6 was detected. The splitting grows
with temperature and is saturated when temperature reaches
15 K for the most of the SdH maxima (Fig. 7). Further tem-
perature increasing leads to a significant broadening of the
split components and the thermally induced structure
smearing. In terms of the g* factor the latter means that
g* ≈ 0 (δN is beyond the resolution for N ≥ 6) at low
temperature (T = 1.5 K) and reaches its maximal value g* =
18, derived from the δN splitting at T = 15 K. This latter is
found to be close to the g0 value in sample 4, g0 = 15.
Following the arguments presented above one can con-
clude that function ~α , which introduces the exchange
contribution in equation 2, takes now a negative value,
normally for open-gap semimagnetics. At low temperature
this contribution completely equalizes g0 and the g* value
turns out the zero leading to a disappearance of the SdH
peak spin splitting. With temperature increase the exchange
contribution decays due to effective Sz reduction and
one observe normally spin split maxima.
Taking into account our findings for all the samples
investigated the function ~α versus the electron concen-
tration n can be derived. Let us assume that the S0 and T0
parameters determining the Sz dependence are of the
same value for all samples. The T0 value derived from the
temperature dependence of δN is taken to be 8 K. The value
of clustering parameter S0 was calculated taking into ac-
count the probability of various magnetic clusters realization
when a stochastic distribution of magnetic ions over the crystal
lattice is assumed [5,6]. For y = 0.02 the S0 value is of 2.1.
Under these assumptions the ( )~α n dependence is that shown
in Fig. 8. Its magnitude varies from positive ( ~αN 0 = 0.15 eV)
to negative ( ~αN 0 = -0.28 eV) one when the electron concen-
tration n is within the range 4.4⋅1016 ≤ n ≤ 1.21⋅1018.
Until we deal with the peculiarities of exchange interaction
in narrow-gap semimagnetic semiconductor Hg1-x-yCdxMnySe
which reveal themselves in the tempera-turedependent
behavior of the SdH oscillations. These peculiarities are
connected with the complicated nature of the energy band
structure, when both spin and orbital quantization have to
be taken into account. New proofs of such hybridization
arise from the comparison of the ρxx and ρzz magnetoresis-
tances shown in Fig. 1. The SdH maxima coincide in the ρxx
and ρzz dependences within the experimental accuracy for all
Landau numbers N ≥ 0. Typically the spin split structure is
more distinct in the ρxx than in the ρzz dependence reflecting
the difference in the nature of transverse and longitudinal
magnetoresistances [23, 24]. It follows from the theory of
longitudinal magnetoresistance [24] that at T = 0 and without
damping to be taken into account both the BN
± peaks have
to be of equal strength. But, it was proved experimentally
that the BN
+ peaks are either of much smaller intensity if
observed or are absent completely [25–27]. Efros [28] has
shown that when inequality k T k T HB D B B〈〈 〈〈 µ takes place
(TD is the Dingle temperature, which determines the Landau
level broadening due to collisions), the maxima of the ρxx and
ρzz oscillations coincide. Nevertheless, when the spin-flip
transitions are of a negligible probability the B0
− maximum
in the ρzz dependence is forbidden. Suizu and Narita [29]
have found that if only a simple s-like wavefunctions are
considered for the conduction band both the BN
+ and B0
−
peaks are prohibited. However, if one takes into account the
p-like contribution of the conduction band wavefunction
these peaks should be allowed again. Besides, the direct
calculation of the non thermal broadening contribution to
the Landau levels also give the amplitudes of the BN
+ peaks
in the ρzz dependence much smaller, than those for the BN
−
[30]. Following our data we conclude that the clear
manifestation of the B0
− peak gives evidence for the spin-flip
transitions in the narrow-gap Hg1-x-yCdxMnySe. These tran-
sitions become very intensive when Eg → 0, and the elec-
tron wavefunction is hybridized from the s-like and p-like
states. This conclusion is in line also with our results for
quaternary Hg1-x-yCdxMnyTe with Eg ~ 120 meV where the
spin-flip stransitions where detected both in photolumines-
cence and in the SdH oscillations [31]. The well resolved
spin split structure in the ρzz oscillations and the absence of
a visible shift between the ρxx and ρzz maxima prove also a
good quality of the samples under investigation. Otherwise,
when TD is high enough, the spin related structure has to be
smeared.
Conclusions
The studies of the SdH oscillations behavior in narrow-gap
semimagnetic semiconductor Hg1-x-yCdxMnySe enlightened
novel aspects of the exchange interaction between the
conduction band electron spin and the localized spin moments
of magnetic ions which reveal themselves in the close vicinity
of the semimetal-semiconductor transition. It has been demo-
nstrated that the hybridization of the s-like and p-like elec-
tron wavefunctions strongly modifies the exchange interac-
tion related assignment of the electron states. As a result the
simple description in terms of two independent exchange
Yu. I. Mazur et al.: Quaternary semimagnetic Hg1-x-yCdxMnySe crystals for...
44 SQO, 2(4), 1999
constants α and β derived in the approximation of molecu-
lar field is not valid. The exchange parameter α transforms
into a function ~α which is strongly dependent on the energy
gap Eg and the electron concentration n. This function mag-
nitude varies within wide limits: from positive ~αN 0 = 0.15
eV to negative ~αN 0 = -0.28 eV values which are typically
accepted for wide gap semimagnetic semiconductors. How-
ever, it should be noticed that the normally negative value
the function ~α accepts at a sufficiently high electron con-
centrations, n ~ 1018 cm-3, when the renormalization of the
electron energy parameters is already of importance. The
findings of this study explains to some extent a consider-
able scattering the values of the exchange parameters ob-
served for the narrow-gap semimagnetic semiconductors
which is typically ascribed to an incomplete knowledge of
the crystal magnetization. Indeed, such parameters have to
be introduced for a particular crystal of a given composition
with account of a free carrier concentration. Besides novel
interesting aspects of semimag-netics physics our results
give also evidence for a high quality of a crystalline structure
of quaternary semiconductors under investigation. The well
resolved spin structure of the longitudinal and transverse
magnetoresistances without of a visible shift between their
SdH peaks proves, at least, a low TD originated due to
collisions. This finding is in line with the statement about
improved crystalline structure of spin doped semiconduc-
tors, derived earlier from our optical measurements in qua-
ternary semimagnetics [8, 9, 31]
Acknowledgevents
Authors are indebted to Dr. S.Yu. Paranchich for the high
quality crystals preparation. This work is supported by
the DFG grant No HO 1300/2-1 and 436UKR113/40/0.
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