Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions
The inhomogeneously broadened EPR lines of the solid solutions Hg₁₋x₋yCrxCdySe and Hg₁₋xCrxSe are rep-resented in the form of spin packets and their temperature evolution is analyzed upon the transition of the crystals to ferromagnetic ordering. In this case, the spin packets being introduced into t...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1761182021-02-04T01:29:36Z Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions Bekirov, B.E. Ivanchenko, I.V. Popenko, N.A. Низкотемпеpатуpный магнетизм The inhomogeneously broadened EPR lines of the solid solutions Hg₁₋x₋yCrxCdySe and Hg₁₋xCrxSe are rep-resented in the form of spin packets and their temperature evolution is analyzed upon the transition of the crystals to ferromagnetic ordering. In this case, the spin packets being introduced into the consideration are identified with allowed transitions of the localized electrons and with the delocalized electrons. It is established that a characteristic feature of the subsystem of delocalized electrons is the anomalous behavior of the g-factor in the vicinity of the transition to the ferromagnetic state. The introduced spin subsystems, which characterize the localized and delocalized electronic states, allow for explainig the differences in scenarios of the transition to magnetic ordering of crystals with different cluster structures. Just significantly lower concentration of clusters in the HgCrSe crystal leads to a slowing down of flip-flop processes that explains the longer relaxation times of spin packets in this diluted magnetic semiconductor in comparison with the relaxation times of spin packets in the HgCrCdSe crystal in the ferromagnetic temperature range. 2018 Article Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions / B.E. Bekirov, I.V. Ivanchenko, N.A. Popenko // Физика низких температур. — 2018. — Т. 44, № 5. — С. 561-567. — Бібліогр.: 16 назв. — англ. 0132-6414 PACS: 76.30.–v, 76.30.Da, 75.50.Pp http://dspace.nbuv.gov.ua/handle/123456789/176118 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм |
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Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм Bekirov, B.E. Ivanchenko, I.V. Popenko, N.A. Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions Физика низких температур |
| description |
The inhomogeneously broadened EPR lines of the solid solutions Hg₁₋x₋yCrxCdySe and Hg₁₋xCrxSe are rep-resented in the form of spin packets and their temperature evolution is analyzed upon the transition of the crystals to ferromagnetic ordering. In this case, the spin packets being introduced into the consideration are identified with allowed transitions of the localized electrons and with the delocalized electrons. It is established that a characteristic feature of the subsystem of delocalized electrons is the anomalous behavior of the g-factor in the vicinity of the transition to the ferromagnetic state. The introduced spin subsystems, which characterize the localized and delocalized electronic states, allow for explainig the differences in scenarios of the transition to magnetic ordering of crystals with different cluster structures. Just significantly lower concentration of clusters in the HgCrSe crystal leads to a slowing down of flip-flop processes that explains the longer relaxation times of spin packets in this diluted magnetic semiconductor in comparison with the relaxation times of spin packets in the HgCrCdSe crystal in the ferromagnetic temperature range. |
| format |
Article |
| author |
Bekirov, B.E. Ivanchenko, I.V. Popenko, N.A. |
| author_facet |
Bekirov, B.E. Ivanchenko, I.V. Popenko, N.A. |
| author_sort |
Bekirov, B.E. |
| title |
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions |
| title_short |
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions |
| title_full |
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions |
| title_fullStr |
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions |
| title_full_unstemmed |
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions |
| title_sort |
features of spin dynamics in hgcrcdse and hgcrse crystals in the vicinity of phase transitions |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2018 |
| topic_facet |
Низкотемпеpатуpный магнетизм |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/176118 |
| citation_txt |
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions / B.E. Bekirov, I.V. Ivanchenko, N.A. Popenko // Физика низких температур. — 2018. — Т. 44, № 5. — С. 561-567. — Бібліогр.: 16 назв. — англ. |
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Физика низких температур |
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2025-07-15T13:44:44Z |
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| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 5, pp. 561–567
Features of spin dynamics in HgCrCdSe and HgCrSe
crystals in the vicinity of phase transitions
B.E. Bekirov, I.V. Ivanchenko, and N.A. Popenko
O.Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12 Ac. Proskura str., Kharkov 61085, Ukraine
E-mail: ireburan@yahoo.com
Received September 29, 2017, revised December 5, 2017, published online March 27, 2018
The inhomogeneously broadened EPR lines of the solid solutions Hg1–x–yCrxCdySe and Hg1–xCrxSe are rep-
resented in the form of spin packets and their temperature evolution is analyzed upon the transition of the crys-
tals to ferromagnetic ordering. In this case, the spin packets being introduced into the consideration are identified
with allowed transitions of the localized electrons and with the delocalized electrons. It is established that a char-
acteristic feature of the subsystem of delocalized electrons is the anomalous behavior of the g-factor in the vi-
cinity of the transition to the ferromagnetic state. The introduced spin subsystems, which characterize the local-
ized and delocalized electronic states, allow for explainig the differences in scenarios of the transition to
magnetic ordering of crystals with different cluster structures. Just significantly lower concentration of clusters
in the HgCrSe crystal leads to a slowing down of flip-flop processes that explains the longer relaxation times of
spin packets in this diluted magnetic semiconductor in comparison with the relaxation times of spin packets in
the HgCrCdSe crystal in the ferromagnetic temperature range.
PACS: 76.30.–v Electron spin resonance and relaxation;
76.30.Da Ions and impurities: basic;
75.50.Pp Magnetic semiconductors.
Keywords: electron paramagnetic resonance, spin packet, relaxation.
1. Introduction
Taking into account that the diluted magnetic semi-
conductor (DMS) are classified as a class of magneto-
diluted spin systems with the dipole interaction due to the
randomness of the spatial distribution of the spins on a
crystal lattice, the speed of their “flip-flops” is much
slower than the speed of transverse (or spin-spin) relaxa-
tion of spins [1,2]. Therefore the inhomogeneous broad-
ening of the absorption lines is typical for the EPR spec-
tra of such systems.
It is known that the description of absorption lines like
that is based on the concept of Portis [3] on the representa-
tion of such lines in the form of a set of equivalent para-
magnetic centers (“spin packets”) with the same Larmor
frequencies and different g-factors, when each spin packet
separates a part of the inhomogeneously broadened ESR
line, which behaves homogeneously with respect to exter-
nal influences, such as a lattice or the electromagnetic ra-
diation. This approach has been proven to be used in the
theory and practice of magnetic resonance spectroscopy by
other authors [1,4–6].
In our research we apply the aforementioned concept
for the description of the experimental EPR spectra and use
the term “spin packet” as an individual line describing the
absorption signal from the set of spins with the same
Larmor frequency, without imposing additional conditions
on the infinite number of packets of the same physical
origin with a continuous spectral distribution. From our
point of view, this approach is expedient and promising for
the analysis of physical processes in DMS (in particular, in
the solid solutions Hg1–хCrхSe and Hg1–х–уCrхCdуSe) in
which a paramagnetic response is produced by both the
localized and delocalized electrons [7]. In doing so, we
take into account the fact that the difference in the g-factors
of spin packets can be due to the different position of the
paramagnetic center in the coordination complex of these
crystals [8]. Furthermore, the possible difference in the con-
centration of paramagnetic centers in the spin packets can
lead to different widths and integrated line intensities.
Then, under conditions of the weak SHF power, when
the balance in the spin system is not disturbed, the
knowledge of the temperature evolution of spin packet
© B.E. Bekirov, I.V. Ivanchenko, and N.A. Popenko, 2018
B.E. Bekirov, I.V. Ivanchenko, and N.A. Popenko
parameters can be very useful, in particular, for analyzing
the behavior of allowed transitions in the magnetically
diluted systems, especially in the vicinity of phase transi-
tions. In this paper, we use this approach to studying the
magnetoresonance properties of two aforementioned DMS
with the concentration of a paramagnetic impurity that
does not lead to splitting of the EPR line with the tempera-
ture decrease [7].
It was found earlier [8,9], that in both types of crystals
the transition to a ferromagnetic ordering phase occurs as a
result of s–d exchange interaction on the RKKY mecha-
nism [10]. The studies of magnetic moments were carried
out on the SQUID magnetometer MPMS-XL5 device. The
measured dependences point out the transition of the solid
solution Hg0.5Cd0.4Cr0.1Sе to the ferromagnetic ordered
phase occurs at the Curie temperature TC = (126 ± 1) K [9]
while the transition of the solid solution Hg0.97Cr0.03Se to
the ferromagnetic ordered phase occurs at TC = (106 ± 1) K
that is inherent to the HgCr2Se4 ferromagnetic spinel [11].
The main purpose of this research is studying the tem-
perature evolution of spin packets to reveal the features
and differences of the spin dynamics in the HgCrCdSe and
HgCrSe crystals at the transition of these DMS to the fer-
romagnetic ordering.
2. Samples and methods
In this research we focus on the investigations of
EPR spectra of the solid solutions Hg0.97Cr0.03Se and
Hg0.5Cd0.4Cr0.1Sе grown in the Chernivtsi National Uni-
versity by the solid state recrystallization method, which
in contrast to the Bridgman’s method allows obtaining a
more homogeneous distribution of the Hg, Cr, and Se
components.
The microanalysis of the samples was performed on the
scanning electron microscope ZEISS EVO 50XVP with a
combined system of the energy-dispersion analysis INCA
ENERGY 450 and structural HKL Channel 5 analysis. We
used the operational mode of the spectrometer so that the
analyzed surface area of the sample was less than 1 μm.
The Fig. 1 illustrates the typical electronic images of the
surface fragments of the samples [8,9].
The analysis of the percentage content of elements has
shown that the dark areas on the electron-diffraction pat-
tern of the HgCrSe sample correspond to the spinel phase
HgCr2Se4 [8] (Fig. 1(a)). At the same time the dark areas
on the electron-diffraction pattern of the HgCdCrSe sample
correspond to the four-component compound HgCdCrSe
while the light areas correspond to the nonmagnetic three-
component compound HgCdSe [9] (Fig. 1(b)). This gives
us reason to believe that just the presence of a four-
component compound HgCdCrSe in the nonmagnetic ma-
trix HgCdSe will determine the magnetic and magneto-
resonance properties of these samples.
Thus, two different compounds coexist in each of the
samples under test. It is worth noting that the chromium
content in such a four-component compound in percentage
(18.96%) is higher, than that in the spinel clusters
HgCr2Se4 (14%).
Thus, in the samples under test, an inhomogeneous
structure is formed during their growth, which consists
of both the nonmagnetic and magnetic phases. In the
three-component solid solution Hg1–хCrхSe two types of
paramagnetic inclusions are present, and two coordina-
tion complexes such as tetrahedral (HgCrSe) and
octohedral (HgCr2Se4) are considered in accordance with
[8]. At the same time, in the four-component solid solu-
tion Hg1–х–уCrхCdуSe only one type of paramagnetic in-
clusions such as HgCdCrSe occurs and, consequently, a
one tetrahedral coordination complex is considered.
The EPR spectra were measured on the X-band super-
heterodyne spectrometer operating in the temperature
range 1.7–300 K. The sensitivity of the spectrometer is
5⋅1014 spins/T. The accuracy of measuring the external
magnetic field is ± 10–4 T in the range 0–0.7 T that makes
it possible to determine the g-factor with an accuracy of
± 1⋅10–3. Spectrometer assures the accuracy of the meas-
urement and stabilization of the temperature ± 0.01 and
± 0.1 K, respectively.
Fig. 1. Electron-diffraction patterns of the HgCrSe (a) and
HgCdCrSe (b) crystals.
562 Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 5
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions
3. Electron spectra of Cr3+ ion
It was shown in [8] that the EPR signal observed in ex-
periments at temperatures above the nitrogen ones is origi-
nated by the Cr3+ ion. The calculations of the electron
spectrum for the high-spin state of the Cr3+ ion located in
both the cubic and tetrahedral environments have shown
that in the undistorted octahedral complex (CrSe6)9– and
tetrahedral complex (CrSe4)5–, the chromium ion is to be
trivalent and has an electron configuration of the valence
shell with the main term 4F. The crystal field splits this
basic electron term of the Cr3+ ion into the three crystal
terms depending on the ligand’s symmetry: in the case of
tetrahedral symmetry 4F = 4A1 + 4T2 + 4T1, while in the
case of cubic symmetry 4F = 4A2g + 4T2g + 4T1g. In this
case, the orbital triplet 4T1 in the tetrahedral case and the or-
bital singlet 4A2g in the cubic case are the basic ones [12].
Spin-orbit coupling does not result in the evident splitting of
the 4A2g term while the crystal triplet 4T2 splits into the two
spin quartets and two spin doublets in such a way that one of
the spin quartets is the lowest level. Thus, in both the un-
distorted tetrahedral and octahedral crystal fields the spin
quartet is the ground state. An external magnetic field splits
the aforementioned spin quartets in a different way (Fig. 2).
In the case of the octahedral crystal field, the arbitrarily
directed magnetic field splits the lowest 4A2g quartet into
the four spin singlets, which are equidistant, and the transi-
tions 1↔2, 2↔3 and 3↔4 are to be the allowed transitions
(Fig. 2(а)).
In the tetrahedral case, the lowest quartet splits into the
two quasi-doublets in such a way that the splitting between
quasi-doublets is much bigger than those located inside the
quasi-doublets. The transition 1↔2 has vanishingly small
intensity, i.e., it is forbidden, whereas the transitions 1↔3
and 1↔4 as well as 2↔3 and 2↔4 are to be the allowed
transitions (Fig. 2(b)). Thus, the EPR signal originates from
the transitions between two quasi-doublets and the 1↔4
transition is considered as the main representative [8].
4. Research results
Spin-packet concept we applied to the experimental
EPR spectra of HgCrSe and HgCdCrSe crystals published
in our previous papers [8,9].
When the EPR line was approximated, the resonance posi-
tion and the width of spin packets, as well as their number and
intensity varied. Calculations were carried out for both the
Lorentzian and the Gaussian forms of the spin packet. As it
follows from the results of investigations, the experimental
spectra for both crystals are good approximated by the ten
spin packets of the Gaussian shape. But only the first four spin
packets have the intensity exceeding the limits of the confi-
dence intervals of the detected EPR signals. These spin pack-
ets are located non-equidistantly, have different Larmour fre-
quencies, widths and integral intensity because they are
located in different conditions. The intensities of remaining
spin packets are negligible and are within the confines interval
of the detected EPR signal.
Taking into account a sensitivity of the radio spectrom-
eter used, we limited ourselves to the ratio of the levels of
the noise track and the detected EPR signal to no more
than 2%. As the result, the determination coefficients were
as follows: 0.9957 (T = 215 K) and 0.9894 (T = 87 K) for
the HgCdCrSe crystal; 0.9955 (T = 207 K) and 0.9877
(T = 85 K) for the HgCrSe crystal.
The examples of such approximation for two character-
istic temperatures, namely before and after the transition to
the ferromagnetic phase, show a good agreement with the
experimental data (Fig. 3).
A characteristic feature of DMS with an unfilled
3d-shell, to which the solid solutions Hg1–хCrхSe and
Hg1–х–уCrхCdуSe are related, is that they contain along
with the conduction electrons (delocalized spins) and 3d-
electrons localized on the appropriate atoms. To describe
the kinetics of the processes in such systems, the localized
and delocalized spins (which are the mediators between the
paramagnetic centers in the RKKY mechanism) are repre-
sented in the form of two subsystems “d” and “s”, in which
the interaction between them occurs with the appropriate
rates Vds and Vsd [13].
5. HgCrSe crystals
Following the temperature dependences of spin packet
parameters (Fig. 4) it can be stated that in the temperature
interval ranging from the room temperature to T = 128 K
the g-factor of spin packets remains virtually unchanged.
In the temperature range T = 128–110 K, foregoing to the
transition of the spinel to the ferromagnetic state (we call it
the transition region), their absolute values undergo differ-
ent changes, namely: for two spin packets described by
curves 1 and 2, the g-factors begin increase, while for the
other two spin packets the g-factors begin decrease with
some anomaly in the behavior of the g-factor, described
by the curve 3, near the temperature T ≈ 120 K. After the
transition of spinel clusters to the ferromagnetic ordering
(T < 106 K), the g-factors of the first pair of spin packets
(curves 1 and 2) continue to increase, reaching the values Fig. 2. The schemes of the Cr3+ ion level-splitting in the case of
octahedral (a) and tetrahedral (b) crystal fields.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 5 563
B.E. Bekirov, I.V. Ivanchenko, and N.A. Popenko
2.5 and 2.9 at T = 85 K, while the g-factors of the second pair
of spin packets (curves 3 and 4) tend to the value g ≈ 1.8.
The revealed behavior of the g-factors of spin packets
(Fig. 4(a)) can be explained by introducing the following
сonventional classification, namely: in the subsystem “d”
of localized electrons the spin packets described by the
curves 1, 2 and 4 may refer to the allowed transitions 1↔2,
2↔3 and 3↔4 in accordance with a scheme of the Cr3+
ion level-splitting in the octahedral crystal field (see
Fig. 2(a)), while the spin packet described by the curve 3
refers to the subsystem “s“ of delocalized electrons. In
accordance with [8], in this case the trigonal perturbations
of the crystal field are the most probable ones and the de-
velopment of those with the temperature decrese results in
the decrease of the octahedron cell volume and, hence, in
an increase of the crystal field strength that may be the
reason for the difference in the temperature dependences of
the g-factors of spin packets of the subsystem “d” of local-
ized electrons.
The widths of spin packets from the room temperature
to T = 128 K vary slightly (Fig. 4(b)) and begin to broaden
noticeably in the transition region in accordance with the
increase in the EPR line width when the temperature de-
creases, that is characteristic for the mixed-valence spinel
ferrites during the establishment of magnetic ordering in
the system [14]. In this case, the anomalous change in the
width of the spin packet at the temperature T ≈ 120 K (as
well as the g-factor described by the curve 3 in the Fig. 4(a)
confirms the legitimacy of the aforementioned classifica-
tion of spin packets, since in the vicinity of Т ≈ 120 K a
sharp change in the conductivity of the HgCr2Se4 crystal
occurs [15]. After the phase transition, the widths of spin
packets, described by the curves 2, 3, 4, increase sharply,
while the curve 1 slows down its growth.
With the temperature decrease, the integrated intensities
of spin packets described by the curves 1, 2 and 4 increase
monotonically, reaching the maximum values in the region
of the phase transition of the spinel to the ferromagnetic
state and decrease below the Curie point (T < TC = 106 K)
(Fig. 4(c)). At the same time, the integral intensity of the
spin packet described by the curve 3 increases monoton-
ically throughout the analyzed temperature range.
The values of T2 were determined from the well-known
equation for the single symmetric lines [16], which are the
spin packets obtained as a result of the approximation:
7 0
2 1.3131 10 / ,ppT g Н−= ⋅ ∆
where the values of the g-factor and the width ΔH of a sin-
gle symmetric line included in this equation were taken for
each spin packet and the values of T2 were calculated for
each temperature.
As follows from the Fig. 4(d), when the sample is cooled,
the spin-spin relaxation times T2 of spin packets decrease
Fig. 3. EPR spectra of HgCdCrSe and HgCrSe crystals: experiment (solid line), approximation (dotted line).
564 Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 5
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions
monotonically by a factor of 2 from T2 ≈ (8–9)⋅10–6 s at
T = 207 K to T2 ≈ (4–5)⋅10–6 s at T ≈ 128 K. In the transi-
tion region (T = 128–110 K), the relaxation times decrease
by more than 3 times, taking the values T2 ≈ (1.2–1.6)⋅10–6 s,
excepting the anomaly near the temperature T = 120 K for
the spin packet described by the curve 3. And after the
transition of the ferromagnetic spinel HgCr2Se4 to the fer-
romagnetic state (T < 100 K), the relaxation times of two
spin packets (curves 1 and 2) referring to the subsystem
“d” tend to the values T2 ≈ 9⋅10–7 s and 8⋅10–7 s, while the
relaxation times of third spin packet of the subsystem “d”
(curve 4) and the spin packet referring to the subsystem “d”
of delocalized electrons (curve 3) become equal (Vds ≈ Vsd).
6. HgCdCrSe crystals
As it shown by the results of microanalysis (see Fig. 1(b))
the solid solution Hg0.5Cd0.4Cr0.1Sе has a cluster structure
with the chaotic distribution of clasters in the bulk of the
DMS. Namely, in the nonmagnetic matrix formed by the
three-component compound HgCdSe, there are the clusters
HgCdCrSe with the magnetically active chromium ions,
which determine the magnetic and magnetoresonance proper-
ties of these crystals. It should be noted that the chromium
content in HgCdCrSe compounds is higher than that in clus-
ters of ferromagnetic spinel HgCr2Se4 in the solid solution
Hg0.97Cr0.03Se [9]. The substitution of Cr3+ ions in the host
tetrahedral matrix (see Fig. 2(b)) provides the additional de-
gree of freedom for the off-centered shifting of the chromium
ion as well as for the distortion of the ligand’s cell, which can
increases with the temperature decrease.
As can be seen from the Fig. 5(a), the g-factors of spin
packets (as in the case of HgCdSe) remain virtually un-
changed in the temperature interval ranging from the
room temperature to T = 157 K. In the transition region
(126 K < T < 160 K), for the two spin packets described by
the curves 1 and 2, the g-factors increase slightly and
sharply increase after the crystal transition to the ferro-
magnetic ordering, reaching the values 2.9 and 2.72 at
T = 87 K. It is quite clear that with the temperature de-
crease the chromium off-centering shift increases resulting
in the increase of the g-factor. Here, on the temperature
dependences of g-factors of two other spin packets de-
scribed by the curves 3 and 4 one can see the maxima in
the vicinity of the phase-transition temperature (T ≈ 126 K).
At the temperature T = 87 K the g-factors are 1.92 and
1.87, respectively. The aforementioned dependences of g-
factors allow one to introduce the following classification
of spin packets, namely: in accordance with a scheme of
the Cr3+ ion level-splitting in the tetrahedral crystal field
(see Fig. 2(b)) in the subsystem “d” of localized electrons,
the spin packets described by the curves 1 and 2 may refer
to the allowed transitions 1↔4 and 1↔3 as the main repre-
sentative [8], while the spin packets described by the
curves 3 and 4 can be attributed to the subsystem “s” of
delocalized electrons.
Fig. 4. Temperature dependences of g factor (a), width (b), integral intensity (c) and spin-spin relaxation time (d) of the spin packets
that approximate the EPR lines of the solid solution Hg0.97Cr0.03Se (the numbers 1–4 denote belonging to the appropriate spin packets).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 5 565
B.E. Bekirov, I.V. Ivanchenko, and N.A. Popenko
As for the widths of the spin packets, they remain virtu-
ally unchanged in the temperature interval ranging from
the room temperature to T = 157 K (Fig. 5(b)). In the tran-
sition region the packets begin to broaden. After the crystal
transition to ferromagnetic ordering (T < 126 K), the
widths of two spin packets continue to increase (curves 3
and 4), while the widths of other two spin packets (curves
1 and 2) start to decrease, illustrating the characteristic
extreme dependence and indicating a change in the domi-
nating mechanisms of the spin interaction after the phase
transition, namely, pointing out the increase of the ex-
change interaction on the RKKY mechanism.
With the temperature decrease, the integrated intensities
of spin packets described by the curves 1 and 2 increase
monotonically, reaching the maximum values in the region
of the phase transition, and do not undergo any visible
changes below the Curie point (T < TC = 126 K) (Fig. 5(c)).
At the same time, the integrated intensities of spin packets
described by the curves 3 and 4 increase throughout the
analyzed temperature range, as in the case of the curve 3 in
HgCrSe (see Fig. 4(c)).
As it follows from the Fig. 5(d), when the temperature
decreases (from the room temperatures to T ≈ 157 K), the
transverse relaxation times T2 of all spin packets remain
virtually unchanged, but they have some different absolute
values. For the spin packets of the subsystem “d” of local-
ized electrons (curves 1 and 2) referring to the allowed
transitions 1↔4 and 1↔3 (Fig. 2(b)), the time T2 ≈ 9⋅10–6 s,
while for the spin packets of the subsystem “s” of delocal-
ized electrons (curves 3 and 4), these times are equal to
T2 ≈ 5.5⋅10–6 s and T2 ≈ 3⋅10–6 s, respectively. Beginning
with T = 157 K and lower, the relaxation times of all spin
packets decrease sharply up to T ≈ 110 K, taking the values
T2 ≈ (6.5–8.0)⋅10–7 s. At T < 100 K the relaxation times of
spin packets (curves 1 and 2) referring to the subsystem
“d” of the localized electrons tend to the value T2 ≈ 6⋅10–7 s
while the relaxation times of spin packets (curves 3 and 4)
referring to the subsystem “s” of delocalized electrons be-
come equal T2 ≈ 4.8⋅10–7 s. It should be noted that the er-
ror in determining the spin-spin relaxation times does not
exceed 2⋅10–8 s.
7. Conclusions
For the first time the concept of spin packets for the de-
scription of inhomogeneously broadened EPR lines with
respect to the DMS has been applied. It is shown that the
inhomogeneously broadened EPR lines of the solid solu-
tions Hg1–х–уCrхCdуSe and Hg1–хCrхSe are well approxi-
mated by the four spin packets. The analysis of tempera-
ture dependences of the g-factors of spin packets and the
comparison of the obtained data with the results of calcula-
tions of the electron spectra of the Cr3+ ion located in the
cubic (HgCr2Se4) and tetrahedral (HgCrSe and HgCdCrSe)
environment [8] pointed out that for the HgCrSe crystal
three spin-packets can be correlated with the allowed tran-
Fig. 5. Temperature dependences of g factor (a), width (b), integral intensities (c) and spin-spin relaxation time (d) of the spin
packets that approximate the EPR lines of the solid solution Hg0.5Cd0.4Cr0.1Sе (the numbers 1–4 denote belonging to the appro-
priate spin packets).
566 Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 5
Features of spin dynamics in HgCrCdSe and HgCrSe crystals in the vicinity of phase transitions
sitions in the subsystem “d” of localized electrons and a
one spin-packet — with the subsystem “s” of delocalized
electrons. Unlike the HgCrSe crystal, in the HgCdCrSe
crystal two spin-packets refer to the allowed transitions in
the subsystem “d” of localized electrons and two spin-
packets — to the subsystem “s” of delocalized electrons.
The features of spin dynamics in HgCrCdSe and
HgCrSe crystals in the vicinity of phase transitions have
been revealed, namely: (i) the temperature interval of the
transition of the HgCrCdSe crystal exceeds twice that of
the HgCrSe crystal; (ii) unlike the HgCrSe crystal the dif-
ference in the g-factors, widths, and spin-spin relaxation
times of both spin packets related to the delocalized elec-
trons of the HgCrCdSe crystal are diminished at T < 100 K;
(iii) in the ferromagnetic temperature region the relaxation
times of spin packets for the HgCrSe crystal (subsystem
“d”↔T2 ≈ 9⋅10–7 s and 8⋅10–7 s; subsystem “s”↔ T2 ≈
≈ 6⋅10–7 s) are longer than for the HgCrCdSe crystal (sub-
system “d”↔T2 ≈ 6⋅10–7 s; subsystem “s”↔T2 ≈ 4.8⋅10–7 s);
(iv) unlike the HgCdCrSe crystal, the presence of two dif-
ferent phase states in the HgCrSe crystal (HgCrSe and
HgCr2Se4) leads to the flip-flop slowing.
_______
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1. Introduction
2. Samples and methods
3. Electron spectra of Cr3+ ion
4. Research results
5. HgCrSe crystals
6. HgCdCrSe crystals
7. Conclusions
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