- Email: [email protected]
Specific heat in diluted magnetic semiconductor quantum ring
Accepted Manuscript Spesific heat in diluted magnetic semiconductor quantum ring A.M. Babanlı, B.G. Ibragimov
PII:
S0749-6036(17)31325-3
DOI:
10.1016/j.spmi.2017.07.012
Reference:
YSPMI 5122
To appear in:
Superlattices and Microstructures
Received Date: 31 May 2017 Accepted Date: 5 July 2017
Please cite this article as: A.M. Babanlı, B.G. Ibragimov, Spesific heat in diluted magnetic semiconductor quantum ring, Superlattices and Microstructures (2017), doi: 10.1016/j.spmi.2017.07.012. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
ACCEPTED MANUSCRIPT SPESIFIC HEAT IN DILUTED MAGNETIC SEMICONDUCTOR QUANTUM RING A. M. Babanlı1, 2, B.G.Ibragimov3 Department of Physics, University of Süleyman Demirel, 32260 Isparta, Turkey
2
RI PT
1
Institute of Physics, Azerbaijan National Academy of Sciences, 370143 Baku,
Baku State University Baku Az1148, Azerbaijan
M AN U
3
SC
Azerbaijan
AC C
EP
TE D
Corresponding author e-mail address: [email protected]
2
ACCEPTED MANUSCRIPT Abstract In the present paper, we have calculated the specific heat and magnetization of a quantum ring of a diluted magnetic semiconductor (DMS) material in the presence of magnetic field. We take into account the effect of Rashba spin-orbital interaction, the
RI PT
exchange interaction and the Zeeman term on the specific heat. We have calculated the energy spectrum of the electrons in diluted magnetic semiconductor quantum ring. Moreover we have calculated the specific heat dependency on the magnetic
SC
field and Mn concentration at finite temperature of a diluted magnetic semiconductor
M AN U
quantum ring. PACS: 73.23.-b
Keywords: Rashba effect, specific heat, diluted magnetic semiconductor
TE D
1.Introduction
In the last decade enormous attention has been devoted toward control and engineering of spin degree of freedom at mesoscopic scale, usually referred to as
EP
spintronics [1]. Important class of materials for spintronics forms diluted magnetic
AC C
semiconductors (DMS). They are A2B6 or A3B5 solutions with high density of magnetic impurities (usually, Mn). DMS is one of the best candidates to combine semiconductor electronics with magnetism. DMS provides us with an interesting possibility for tailoring the spin splitting and the spin polarization due to the strong s –d exchange interaction between the carriers and the local magnetic ions [2,3]. Nanostructures geometry of the ring is of much interest because they offer unique opportunities for the study of quantum interference effects, such as persistent current and the Aharonov-Bohm effect [4]. The effect of the spin-orbit interaction on the
3
ACCEPTED MANUSCRIPT properties of one-dimensional quantum rings has attracted much attention [5]. The effect of the magnetic field, the Rashba SO interaction, the s-d exchange interaction, and the finite temperature on the conductance of a DMS hollow cylindrical wire have been studied in Ref. [6]. The heat capacity and entropy effect in GaAs quantum dot
RI PT
with Gaussian confinement was calculated in the presence of a magnetic field and its interaction with the electron spin using the canonical ensemble approach [7].
In the paper [8] was studied the thermal and magnetic properties of a cylindrical
SC
quantum dot with asymmetric confinement in the presence of external electric and magnetic field. The thermodynamic properties of an InSb quantum dot have been
field [9]. 2.Computational details
M AN U
investigated in the presence of Rashba spin-orbit interaction and a static magnetic
In the present paper we take into account the effects of the Zeeman and exchange
TE D
terms on the specific heat of DMS quantum ring, the electron is assumed to be
EP
moving in a parabolic potential of the Fock-Darwin type given by 10: =
, ≤ .
(1)
AC C
Where −defines the depth of this potential and is the distance of electron from the centre of the DMS quantum ring. In this paper, we consider the influence of the Rashba spin-orbit interaction and the exchange interaction in the specific heat DMS ring. The quantum ring is subjected to =(0,0,H) normal to the quantum ring plane. We assume a uniform magnetic field that the spin-orbit interaction is described by the Rashba Hamiltonians, which for the case of quantum ring reads [11]:
4
ACCEPTED MANUSCRIPT =
−!
" #
#$
+
&' (
)
(2)
where −is the Pauli z matrix, -is the Rashba spin-orbital coupling parameter. The total Hamiltonian of the system is given by: "
= + * +, + + &
RI PT
(3)
where "
./
& 0 + 1) +
(4)
SC
=
M AN U
In the mean field approximation the exchange Hamiltonian term can be written as [6]:
"
&- = < 3 > 5 678 = 31
(5)
where 78 is a constant which describes the exchange interaction, 5 -is the density
TE D
of the unit cells. The thermodynamic average < 3 > of the z component of the
EP
localized Mn spin is determined by the expression
where ;<=
CB D
AC C
>?@/ AB '
< 3 >= −3 ;<=
>?@/ AB ' CB D
)
(6)
) is the Brilloin functions, *EF = 2 is the g factor of Mn ions,
S=5/2 and kB is the Boltzmann constant.
For uniform magnetic field, H directed along z-axis, the vector potentials in cylindrical polar coordinates have the components 1$ = equation in lateral cylindrical coordinates is
,
, 1 = 0 and Schrödinger
5
ACCEPTED MANUSCRIPT (
−
#
./ #
+
" #
#
+
" #
#$
+
#
&'
)Ψ + I
−!
#$
+
&'
(
./
(
(
"
) + 31 + * +, +
"
) − ! (J
#
#$
K Ψ = EΨ (7)
We seek solution in the form [12]: "
√N
O!PQ
RI PT
Ψ= with radial part that satisfies R
"
where we have used notations: ΩVX = YJ + &'
Z [
S ./ T
(
+ Π) FRV = 0
M AN U
+ − −
SC
+
VX \Z (
, J = Y.
/
(8)
(9)
, = ,
(10)
/
Π=
TE D
J = . -is the cyclotron frequency and ./ (
\
"
"
] − * +, − 31 − P + P(ω )
(11)
EP
The energy levels given by [12]:
"
"
\
AC C
]FRV = (ΩV 2_ + |P| + 1 + P(ω + * +, + 31 + P
(12)
The partition function for the Boltzmann statistics is given by a = ∑F,R,V O
8
c/,d,T eB f
where ]FRV -is the energy spectrum of considered system.
(13)
6
ACCEPTED MANUSCRIPT The Rashba spin-orbital interaction lifts spin degeneracy of energy states and partition function branches out into two parts giving spin up and spin-down contributions
+
h ij klmn B eB f " & h t (s g (p uv oI ↓ K8or eB f eB f
RI PT
a=
h ijB klmn g eB f " & h t (s l (p uv oI ↑ K8or eB f eB f
(14)
The partition function can be used to obtain the heat capacity as |DRF ↑ } ↓ ~ D
M AN U
and the average magnetization as
= z, {
3.Results and Discussions
SC
xy = z, {
|RF ↑ } ↓ ~ '
(15)
(16)
TE D
Here, we present our numerical results on the energy dispersions of the electrons and the specific heat for Hg1-xMnxTe DMS quantum ring. We use the following set of parameters: F =0.047m0, where m0 is the free electron mass, R=14.8nm and
EP
(J = 7.5O. Other parameters used in our calculations, N0 Jsd=0.4eV, and ge =-
AC C
20 are taken from the literature [6]. In Fig.1 and we show the specific heat of the DMS quantum ring in the presence of Rashba spin-orbital interaction, exchange interaction and Zeeman term as function of temperature and Mn concentration at fixed H=0.5Tl and Rashba spin-orbit coupling constant α=160 meV.nm. In Fig. 2, the same graphics plot for H = 1Tl. According to this figure as the temperature is increased the specific heat suddenly increases and then decreases giving a peak-like structure. In Fig.3 we plot the heat capacity in DMS quantum ring versus magnetic field and
7
ACCEPTED MANUSCRIPT Mn concentration at fixed T=5K and Rashba spin-orbit coupling constant α=160 meV.nm in the presence of the exchange interaction. As shown from the Fig.3 specific heat initially raises with the increase in magnetic field, come to maximum value and then decreases to zero. In Fig. 4 show the average magnetization of DMS
RI PT
quantum ring as a function of magnetic with Rashba spin-orbit coupling constant α=160 meV.nm at fixed Mn concentration x=0.05 and T=10K.The magnetization
magnetization starts to decrease.
M AN U
4. Conclusions
SC
changes abruptly with a small increase in H and the peak is observed after which the
In this paper the effect of the magnetic field, the exchange interaction and the Rashba spin-orbital interaction on the specific heat and magnetization of a DMS quantum ring have been studied. The energy spectrum of electrons is calculated for quantum
TE D
ring with parabolic potentials. According to the results obtained from the present work at low magnetic field, the dependence of specific heat with temperature gives a peak-like structure.
EP
References
AC C
[1]. S.A.Wolf, et al., Spintronics: A Spin-Based Electronics Vision for the Future Science 294, ( 2001) 1488. [2]. P.A. Wolff, Semiconductors and Semimetals, in: J.K. Furdyna, J. Kossut (Eds.),
Diluted Magnetic Semiconductors, Academic, New York, 1988. [3]. H. Xin, P.D. Wang, A. Yin, C. Kim, M. Dobrowolska, Merz, J.K. Furdyna, Formation of self‐assembling CdSe quantum dots on ZnSe by molecular beam epitaxy, Appl.Phys. Lett. 69,(1996) 3884.
8
ACCEPTED MANUSCRIPT [4].V.A. Margulis, V.A. Mironov, Magnetic moment of an one-dimensional ring with spin-orbit interaction, Physica E 43, (2011), 905-908 [6]. B. H. Mehdiyev, A. M. Babayev, S. Cakmak, E. Artunc, Rashba spin_orbit
RI PT
coupling effect on a diluted magnetic semiconductor cylinder surface and ballistic transport, Superlattice. Microst. 46, (2009) 4
[7]. B. Boyacıoglu and A. Chatterjee, Journal of Applied Physics 112,083514 (2012), Heat capacity and entropy effect in GaAs quantum dot with Gaussian confinement
Kumar Jha Can.J.Phys.93: 1-5, 2015
SC
8. Sukirti Gumber, Manoj Kumar, Monica Gamblur, Man Mohan, and Pradip
B vol.25, No.5 (2016), 056502
M AN U
9. Sukirti Gumber, Manoj Kumar, Pradip Kumar Jha, and Man Mohan, Chin. Phys. 10. C.G. Darwin Proc. Cambridge Philos. Soc. 27 86
TE D
11. O. Voskoboynikov, C.P. Lee, and O. Tretyak, Spin-orbit splitting in semiconductor quantum dots with a parabolic confinement potential, Phys. Rev B 63, 165306
EP
12. L D Landau and L M Lifshitz 2001 Quantum Mechanics: Non-Relativistic
AC C
Theory vol 3 3rd edn (Amsterdam: Elsevier)
ACCEPTED MANUSCRIPT
SC
RI PT
x 𝐶! 𝑘 ! T Fig.1 The specific heat of the DMS quantum ring as function of temperature and Mn
M AN U
AC C
EP
TE D
concentration at fixed H=0.5Tl and Rashba spin-orbit coupling constant α=160 meV.nm. x 𝐶! 𝑘!
T
Fig. 2. The same graphics plot for H = 1Tl
1
ACCEPTED MANUSCRIPT
x
M AN U
SC
RI PT
𝐶! 𝑘!
H
Fig.3 The heat capacity in DMS quantum ring versus magnetic field and Mn concentration at fixed T=5K and Rashba spin-orbit coupling constant α=160 meV.nm.
EP
AC C
TE D
ACCEPTED MANUSCRIPT
M AN U
SC
RI PT
EP
AC C
𝑀 𝑚𝑒𝑉 ∙ 𝑇 !
TE D
H
ACCEPTED MANUSCRIPT Fig. 4 The average magnetization of DMS quantum ring as a function of magnetic
M AN U
SC
RI PT
with Rashba spin-orbit coupling constant α=160 meV.nm at fixed Mn concentration x=0.05 and T=10K.
EP
AC C
TE D
ACCEPTED MANUSCRIPT •
We calculate the specific heat of electron gas in diluted magnetic semiconductor quantum ring. The specific heat dependence of the magnetic field was studied.
•
We study influence of Rashba spin-orbital interaction on the specific heat.
AC C
EP
TE D
M AN U
SC
RI PT
•
PII:
S0749-6036(17)31325-3
DOI:
10.1016/j.spmi.2017.07.012
Reference:
YSPMI 5122
To appear in:
Superlattices and Microstructures
Received Date: 31 May 2017 Accepted Date: 5 July 2017
Please cite this article as: A.M. Babanlı, B.G. Ibragimov, Spesific heat in diluted magnetic semiconductor quantum ring, Superlattices and Microstructures (2017), doi: 10.1016/j.spmi.2017.07.012. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
ACCEPTED MANUSCRIPT SPESIFIC HEAT IN DILUTED MAGNETIC SEMICONDUCTOR QUANTUM RING A. M. Babanlı1, 2, B.G.Ibragimov3 Department of Physics, University of Süleyman Demirel, 32260 Isparta, Turkey
2
RI PT
1
Institute of Physics, Azerbaijan National Academy of Sciences, 370143 Baku,
Baku State University Baku Az1148, Azerbaijan
M AN U
3
SC
Azerbaijan
AC C
EP
TE D
Corresponding author e-mail address: [email protected]
2
ACCEPTED MANUSCRIPT Abstract In the present paper, we have calculated the specific heat and magnetization of a quantum ring of a diluted magnetic semiconductor (DMS) material in the presence of magnetic field. We take into account the effect of Rashba spin-orbital interaction, the
RI PT
exchange interaction and the Zeeman term on the specific heat. We have calculated the energy spectrum of the electrons in diluted magnetic semiconductor quantum ring. Moreover we have calculated the specific heat dependency on the magnetic
SC
field and Mn concentration at finite temperature of a diluted magnetic semiconductor
M AN U
quantum ring. PACS: 73.23.-b
Keywords: Rashba effect, specific heat, diluted magnetic semiconductor
TE D
1.Introduction
In the last decade enormous attention has been devoted toward control and engineering of spin degree of freedom at mesoscopic scale, usually referred to as
EP
spintronics [1]. Important class of materials for spintronics forms diluted magnetic
AC C
semiconductors (DMS). They are A2B6 or A3B5 solutions with high density of magnetic impurities (usually, Mn). DMS is one of the best candidates to combine semiconductor electronics with magnetism. DMS provides us with an interesting possibility for tailoring the spin splitting and the spin polarization due to the strong s –d exchange interaction between the carriers and the local magnetic ions [2,3]. Nanostructures geometry of the ring is of much interest because they offer unique opportunities for the study of quantum interference effects, such as persistent current and the Aharonov-Bohm effect [4]. The effect of the spin-orbit interaction on the
3
ACCEPTED MANUSCRIPT properties of one-dimensional quantum rings has attracted much attention [5]. The effect of the magnetic field, the Rashba SO interaction, the s-d exchange interaction, and the finite temperature on the conductance of a DMS hollow cylindrical wire have been studied in Ref. [6]. The heat capacity and entropy effect in GaAs quantum dot
RI PT
with Gaussian confinement was calculated in the presence of a magnetic field and its interaction with the electron spin using the canonical ensemble approach [7].
In the paper [8] was studied the thermal and magnetic properties of a cylindrical
SC
quantum dot with asymmetric confinement in the presence of external electric and magnetic field. The thermodynamic properties of an InSb quantum dot have been
field [9]. 2.Computational details
M AN U
investigated in the presence of Rashba spin-orbit interaction and a static magnetic
In the present paper we take into account the effects of the Zeeman and exchange
TE D
terms on the specific heat of DMS quantum ring, the electron is assumed to be
EP
moving in a parabolic potential of the Fock-Darwin type given by 10: =
, ≤ .
(1)
AC C
Where −defines the depth of this potential and is the distance of electron from the centre of the DMS quantum ring. In this paper, we consider the influence of the Rashba spin-orbit interaction and the exchange interaction in the specific heat DMS ring. The quantum ring is subjected to =(0,0,H) normal to the quantum ring plane. We assume a uniform magnetic field that the spin-orbit interaction is described by the Rashba Hamiltonians, which for the case of quantum ring reads [11]:
4
ACCEPTED MANUSCRIPT =
−!
" #
#$
+
&' (
)
(2)
where −is the Pauli z matrix, -is the Rashba spin-orbital coupling parameter. The total Hamiltonian of the system is given by: "
= + * +, + + &
RI PT
(3)
where "
./
& 0 + 1) +
(4)
SC
=
M AN U
In the mean field approximation the exchange Hamiltonian term can be written as [6]:
"
&- = < 3 > 5 678 = 31
(5)
where 78 is a constant which describes the exchange interaction, 5 -is the density
TE D
of the unit cells. The thermodynamic average < 3 > of the z component of the
EP
localized Mn spin is determined by the expression
where ;<=
CB D
AC C
>?@/ AB '
< 3 >= −3 ;<=
>?@/ AB ' CB D
)
(6)
) is the Brilloin functions, *EF = 2 is the g factor of Mn ions,
S=5/2 and kB is the Boltzmann constant.
For uniform magnetic field, H directed along z-axis, the vector potentials in cylindrical polar coordinates have the components 1$ = equation in lateral cylindrical coordinates is
,
, 1 = 0 and Schrödinger
5
ACCEPTED MANUSCRIPT (
−
#
./ #
+
" #
#
+
" #
#$
+
#
&'
)Ψ + I
−!
#$
+
&'
(
./
(
(
"
) + 31 + * +, +
"
) − ! (J
#
#$
K Ψ = EΨ (7)
We seek solution in the form [12]: "
√N
O!PQ
RI PT
Ψ= with radial part that satisfies R
"
where we have used notations: ΩVX = YJ + &'
Z [
S ./ T
(
+ Π) FRV = 0
M AN U
+ − −
SC
+
VX \Z (
, J = Y.
/
(8)
(9)
, = ,
(10)
/
Π=
TE D
J = . -is the cyclotron frequency and ./ (
\
"
"
] − * +, − 31 − P + P(ω )
(11)
EP
The energy levels given by [12]:
"
"
\
AC C
]FRV = (ΩV 2_ + |P| + 1 + P(ω + * +, + 31 + P
(12)
The partition function for the Boltzmann statistics is given by a = ∑F,R,V O
8
c/,d,T eB f
where ]FRV -is the energy spectrum of considered system.
(13)
6
ACCEPTED MANUSCRIPT The Rashba spin-orbital interaction lifts spin degeneracy of energy states and partition function branches out into two parts giving spin up and spin-down contributions
+
h ij klmn B eB f " & h t (s g (p uv oI ↓ K8or eB f eB f
RI PT
a=
h ijB klmn g eB f " & h t (s l (p uv oI ↑ K8or eB f eB f
(14)
The partition function can be used to obtain the heat capacity as |DRF ↑ } ↓ ~ D
M AN U
and the average magnetization as
= z, {
3.Results and Discussions
SC
xy = z, {
|RF ↑ } ↓ ~ '
(15)
(16)
TE D
Here, we present our numerical results on the energy dispersions of the electrons and the specific heat for Hg1-xMnxTe DMS quantum ring. We use the following set of parameters: F =0.047m0, where m0 is the free electron mass, R=14.8nm and
EP
(J = 7.5O. Other parameters used in our calculations, N0 Jsd=0.4eV, and ge =-
AC C
20 are taken from the literature [6]. In Fig.1 and we show the specific heat of the DMS quantum ring in the presence of Rashba spin-orbital interaction, exchange interaction and Zeeman term as function of temperature and Mn concentration at fixed H=0.5Tl and Rashba spin-orbit coupling constant α=160 meV.nm. In Fig. 2, the same graphics plot for H = 1Tl. According to this figure as the temperature is increased the specific heat suddenly increases and then decreases giving a peak-like structure. In Fig.3 we plot the heat capacity in DMS quantum ring versus magnetic field and
7
ACCEPTED MANUSCRIPT Mn concentration at fixed T=5K and Rashba spin-orbit coupling constant α=160 meV.nm in the presence of the exchange interaction. As shown from the Fig.3 specific heat initially raises with the increase in magnetic field, come to maximum value and then decreases to zero. In Fig. 4 show the average magnetization of DMS
RI PT
quantum ring as a function of magnetic with Rashba spin-orbit coupling constant α=160 meV.nm at fixed Mn concentration x=0.05 and T=10K.The magnetization
magnetization starts to decrease.
M AN U
4. Conclusions
SC
changes abruptly with a small increase in H and the peak is observed after which the
In this paper the effect of the magnetic field, the exchange interaction and the Rashba spin-orbital interaction on the specific heat and magnetization of a DMS quantum ring have been studied. The energy spectrum of electrons is calculated for quantum
TE D
ring with parabolic potentials. According to the results obtained from the present work at low magnetic field, the dependence of specific heat with temperature gives a peak-like structure.
EP
References
AC C
[1]. S.A.Wolf, et al., Spintronics: A Spin-Based Electronics Vision for the Future Science 294, ( 2001) 1488. [2]. P.A. Wolff, Semiconductors and Semimetals, in: J.K. Furdyna, J. Kossut (Eds.),
Diluted Magnetic Semiconductors, Academic, New York, 1988. [3]. H. Xin, P.D. Wang, A. Yin, C. Kim, M. Dobrowolska, Merz, J.K. Furdyna, Formation of self‐assembling CdSe quantum dots on ZnSe by molecular beam epitaxy, Appl.Phys. Lett. 69,(1996) 3884.
8
ACCEPTED MANUSCRIPT [4].V.A. Margulis, V.A. Mironov, Magnetic moment of an one-dimensional ring with spin-orbit interaction, Physica E 43, (2011), 905-908 [6]. B. H. Mehdiyev, A. M. Babayev, S. Cakmak, E. Artunc, Rashba spin_orbit
RI PT
coupling effect on a diluted magnetic semiconductor cylinder surface and ballistic transport, Superlattice. Microst. 46, (2009) 4
[7]. B. Boyacıoglu and A. Chatterjee, Journal of Applied Physics 112,083514 (2012), Heat capacity and entropy effect in GaAs quantum dot with Gaussian confinement
Kumar Jha Can.J.Phys.93: 1-5, 2015
SC
8. Sukirti Gumber, Manoj Kumar, Monica Gamblur, Man Mohan, and Pradip
B vol.25, No.5 (2016), 056502
M AN U
9. Sukirti Gumber, Manoj Kumar, Pradip Kumar Jha, and Man Mohan, Chin. Phys. 10. C.G. Darwin Proc. Cambridge Philos. Soc. 27 86
TE D
11. O. Voskoboynikov, C.P. Lee, and O. Tretyak, Spin-orbit splitting in semiconductor quantum dots with a parabolic confinement potential, Phys. Rev B 63, 165306
EP
12. L D Landau and L M Lifshitz 2001 Quantum Mechanics: Non-Relativistic
AC C
Theory vol 3 3rd edn (Amsterdam: Elsevier)
ACCEPTED MANUSCRIPT
SC
RI PT
x 𝐶! 𝑘 ! T Fig.1 The specific heat of the DMS quantum ring as function of temperature and Mn
M AN U
AC C
EP
TE D
concentration at fixed H=0.5Tl and Rashba spin-orbit coupling constant α=160 meV.nm. x 𝐶! 𝑘!
T
Fig. 2. The same graphics plot for H = 1Tl
1
ACCEPTED MANUSCRIPT
x
M AN U
SC
RI PT
𝐶! 𝑘!
H
Fig.3 The heat capacity in DMS quantum ring versus magnetic field and Mn concentration at fixed T=5K and Rashba spin-orbit coupling constant α=160 meV.nm.
EP
AC C
TE D
ACCEPTED MANUSCRIPT
M AN U
SC
RI PT
EP
AC C
𝑀 𝑚𝑒𝑉 ∙ 𝑇 !
TE D
H
ACCEPTED MANUSCRIPT Fig. 4 The average magnetization of DMS quantum ring as a function of magnetic
M AN U
SC
RI PT
with Rashba spin-orbit coupling constant α=160 meV.nm at fixed Mn concentration x=0.05 and T=10K.
EP
AC C
TE D
ACCEPTED MANUSCRIPT •
We calculate the specific heat of electron gas in diluted magnetic semiconductor quantum ring. The specific heat dependence of the magnetic field was studied.
•
We study influence of Rashba spin-orbital interaction on the specific heat.
AC C
EP
TE D
M AN U
SC
RI PT
•