In the present investigation binding energy of the laser dressed hydrogenic donor in a Semi magnetic Quantum Wire like Cd1 – xMnx2Te/Cd1 – x1Mnx1Te/Cd1 – x2Mnx2Te and spin polaronic shift has been computed for various magnetic and laser fields within the effective mass approximation in the finite barrier model using variational method. The results are presented and discussed.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2790

Jayakumar, K.

Mohan, C. Raja

English

SocioEconomic Challenges Journal (Sumy State University)

 
 
 
J. Nano- Electron. Phys. 
3 (2011) No1, P. 1005-1009 
 2011 SumDU 
(Sumy State University) 
 
 
1005 
PACS numbers: 42.55. – f, 71.38. – k, 73.21. – Hb, 75.50.Pp 
 
EFFECT OF LASER ON THE BOUND MAGNETIC POLARON IN A 
SEMIMAGNETIC QUANTUM WIRE 
 
C. Raja Mohan1, K. Jayakumar2  
 
1 Department of Physics, Gandhigram Rural University, 
 Gandhigram 624302, Tamilnadu, India 
2 Department of Physics, Gandhigram Rural University, 
 Gandhigram-624302, Tamilnadu, India 
 E-mail: kjkumar_gri@rediffmail.com 
 
In the present investigation binding energy of the laser dressed hydrogenic donor in a 
Semi magnetic Quantum Wire like Cd1 – xMnx2Te/Cd1 – x1Mnx1Te/Cd1 – x2Mnx2Te 
and spin polaronic shift has been computed for various magnetic and laser fields 
within the effective mass approximation in the finite barrier model using variational 
method. The results are presented and discussed.  
 
Keywords: LASER, MAGNETIC SEMICONDUCTOR QUANTUM WIRE, SPIN 
POLARON, MAGNETICFEILD, DONOR BINDING ENERGY. 
 
(Received 04 February 2011) 
 
1. INTRODUCTION 
 
When a magnetic impurity is doped in a semiconductor, there is a strong sp-
d spin dependent interaction between the localized magnetic moment of the 
magnetic impurity in a doped semiconductor with the (i) bound charge carrier 
gives rise to Bound Magnetic Polaron (BMP) [1] (ii) free charge carrier leads 
to Free Magnetic Polaron (FMP) [2] (iii) exciton gives rise to Excitonic 
Magnetic Polaron (EMP) [3]. All these polaronic effect in Semimagnetic 
Semiconductors (SMSC) such as Cd1 – xMnxTe/CdTe show novel and poten-
tially important phenomena such as Giant negative magneto resistance, Spin 
glass transition, anti ferromagnetic cluster, large Faraday rotations etc., 
Bound magnetic polaron has been observed both experimentally and 
theoretically in modulation doped SMSC material [4]. There are reports on 
fractional dimensional approach to BMP in Quantum Well(QW), Quantum 
Well Wire (QWW) [5], effect of magnetic field on exciton level [6] and effect 
of intense laser field [7, 8] in a QWW are available in the literature. In the 
present work the effect of laser and magnetic field on the Spin Polaron in a 
magnetic QW Cd1 – x1Mnx1Te surrounded by magnetic barrier Cd1 – x2Mnx2Te 
has been investigated in the effective mass approximation using variational 
method. We have considered mean field theory with modified Brillouin 
function in the above calculations. 
 
2. THEORY 
 
The Hamiltonian of the laser dressed hydrogenic donor in the presence of 
applied magnetic field along the growth axis in a Cd1 – x2Mnx2Te/Cd1 –
 
 
 
1006 C. RAJA MOHAN, K. JAYAKUMAR   
 x1Mnx1Te /Cd1 – x2Mnx2Te quantum wire of fintie barrier in the effective 
mass approximation is given by [9], 
 
 
( )
2 2
*
0
1
( )2
B
eA e
H P V z
c r am e
æ ö= + - +ç ÷ +è ø
r
 
(1) 
 
where 2 2 2r x y z= + +  “a”  is  the  amplitude  of  electron  oscillation  in  the  
radiation field ( )a eA mcw= r , which is proportional to I1/2w–2, I being the 
intensity of laser radiation. The potential barrier height of Cd1 – x2Mnx2Te 
Quantum Wire is given by, 
 ( ) ( ) 0
0 2
,
, 2
B
z L
V z a
V z a V z L
ì £ï= í
ïî >
 (2) 
 
            
 
with the laser dressed donor potential [10], 
 
 ( )201( , ) 2 EWV z a V z L= Q -  (3)  
where Θ(z) is the step function, LEW = LW/2 is the effective well width for a 
laser-dressed donor. 0 70%
B
gV E= D ;  L  is  the  width  of  the  potential  well,  
B
gED  is the band gap difference with magnetic field and 0gED  is without 
magnetic field and they can be related by (4), 
 
 0
1
1
B
g gE E
eVgh
h
é ù-D = D ê ú-ë û
, (4) 
 
  
(4) 
 
where 0eVgh =  is chosen with z as  a  parameter(  = 0.5) and g0 as the critical 
magnetic field which depends upon the value of the composition ‘x’ ( = x2 – x1). 
The critical magnetic field for different composition is given in Tesla as 
B0 = Aenx with A = 0.734 and n = 19.082 which gives the best fit to the 
extrapolated experimentally available critical fields [11]. The band gap of 
Cd1 – xMnxTe is given to be 1606 + 1587x (meV). The variational ansatz for 
the donor in a finite Quantum Wire is chosen as, 
 
 
( )
cos cos 2,
2,
r
x y r
x y e z L
N
z LB e e
l
b l
a a
y
-
- + -
ì £
ï= í
ï >î
 
(5) 
where N is the normalisation constant and l is the variational parameter and, 
 
 
( )0.5 0.52 202 2  and   2 2m E m V Ea bé ù é ù= × = × -ë û ë ûh h  
 
(6) 
 
 
 
 
 EFFECT OF LASER ON THE BOUND MAGNETIC POLARON… 1007 
The dimensionless form of Eq. (1) can be written as, 
 
 
( )
2
2 2 2 *2( ) , .
4z B
H L x y V z a R
r a
gg= -Ñ + + + - +
+  
(7) 
 
The dimensionless quantity of magnetic field parameter is defined as, 
 
 
*2
eB
m cR
g æ ö= ç ÷×è ø
r
h
 
(8) 
 
where R* is the effective Rydberg which is R* = e2/2e0aB* and the effective 
Bohr radius is aB* = ħ2e0/m*e2, with m* and e0 are the effective mass of 
electron and static dielectric constant for the CdTe respectively. The donor 
binding energy of a Quantum Wire in the presence of magnetic field is given 
by [9], 
 
 
( )BE E H Sg= + -
 
(9) 
 
where E is  the  subband  energy  which  can  be  obtained  by  solving  the  
transcendental equation, 
 
 
( )tan 0.5 La a b× =
 
(10) 
 
2.1 Spin Polaronic effect 
 
The exchange interaction between the carrier and Mn2+ ion in the presence 
of an external magnetic field B
r
 can be calculated using modified Brillouin 
function [12]. The spin polaronic shift is given by, 
 
 
{ ( ) ( ) }0 1 1 1 1 2 2 2 212sp s sE SN x B y x B yb y y y y= +  (11)  
where Bs(y) is the modified Brillouin function and it is given by, 
 
 
( ) 2 1 2 1 1coth coth
2 2 2 2
j
s j j
yS S
B y y
S S S S
+ += -
 
(12) 
 
 
2
2
j B
j
S g S
y
KT KT
b y m b= +
 
(13) 
 
where β - exchange coupling parameter, S is  the spin of  Mn2+ ( = 5/2 ), and 
xN0 is the Mn ion concentration with N0 = 2.94 ´ 1022 cm–3 and bN0 = 220 meV 
for CdTe12. Also gMn » 2, K is the Boltzmann constant. 
 
3. RESULTS AND DISCUSSIONS 
 
Fig. 1 gives the variation of barrier height with magnetic field for laser 
amplitudes a = 0 Å (i.e. without laser) and a = 150 Å. It shows that the 
application of laser field also reduces the barrier height in addition to the 
magnetic field.  
 
 
 
 
1008 C. RAJA MOHAN, K. JAYAKUMAR   
0 0.05 0.1 0.15 0.2 0.25
0
20
40
60
80
100
120
Po
te
nt
ia
l b
ar
rie
r h
ei
gh
t (
m
eV
)
g
 a = 0 Å
 a = 150 Å
 
 
Fig. 1 –Variation of potential barrier height with magnetic field 
 
 Fig. 2 gives the variation of binding energy with well width for two laser 
fields a = 0 Å and a = 150 Å with three different magnetic fields of γ = 0, 
γ = 0.1 and γ = 0.25 for the Mn composition x = 0.1. It is observed that the 
binding energy decreases with increase of well width and the application of 
magnetic field. This is due to the reduction of potential barrier height with 
γ which in turn reduces the confinement of the carrier. The application of 
laser field also reduces the binding of the donor which is due to reduction in 
the well width and also due to dressed donor potential. At higher well 
widths the variation of binding energy due to magnetic field is not 
appreciable and the same trend is observed for higher laser intensity. 
 
0
1 0
2 0
3 0
4 0
5 0
6 0
0 1 0 0 2 0 0 3 0 0
W e ll W id th(Å )
B
in
di
ng
 E
ne
rg
y(
m
eV
)
g = 0
g= 0 . 1
g= 0 . 25
g= 0
g= 0 . 1
g= 0 . 25
a = 0 Å
a = 1 5 0  Å
 
 
Fig. 2 - Variation of Binding Energy with Well width 
  
 The variation of magnetic polaronic shift of the donor for a = 0 Å and 
a = 150 Å and for x = 0, x = 0.1 and x = 0.25 is given in Fig. 3 for x = 0.1. 
It is noticed that there is a competition between laser field and magnetic 
 
 
 
 EFFECT OF LASER ON THE BOUND MAGNETIC POLARON… 1009 
field on the bound magnetic polaron, since application of magnetic field 
increases the polaronic shift in contrast to laser field which decreases the 
binding of spin polaron. It is also noticed that there is a drastic variation of 
magnetic polaronic shift with well width and also with magnetic field. When 
the magnetic field is increased, spin polaron effect is increased. This is due 
to the reduction in barrier height which in turn increases the interaction 
between the carrier ion and the magnetic ions due to smaller confinement. 
 
- 0 .5
0 .5
1 .5
2 .5
3 .5
4 .5
5 .5
6 .5
7 .5
0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0
W e ll W id th(Å )
Sp
in
 P
ol
ar
on
ic
 sh
ift
(m
eV
)
g = 0.25
g = 0.1
g = 0
- - - - - - - -    a  =1 5 0 Å
              a =0 Å
 
 
Fig. 3 - Variation of Spin Polaronic Shift with Well width 
 
The effect of laser decreases the magnetic polaronic shift. The same trend is 
observed for all the magnetic fields. To conclude, the effect of laser and 
magnetic field in SMSC like CdMnTe system plays a vital role in the spin 
related phenomena. We hope the present investigation may through some 
light on spintronics applications and optoelectronic devices. More 
experimental results should come to prove these facts. 
 
One of the authors K. Jayakumar thanks the University Grants Commission, 
New Delhi, India for the financial support under Major Research Project.  
 
REFERENCES 
1. J.K. Furdyna, J. Appl. Phys. 64, R29 (1988).  
2. C.B. Guillaume, phys. stat. solidi b 175, 369 (1993). 
3. Z.H Chen, H. Sakurai, K. Seo, K. Kayanuma, T. Tomita, A. Murayama, Y. Oka, 
Physica B 340, 890 (2003). 
4. A.C. Drust, R.N. Bhatt, P.A. Wolff, Phys. Rev. B 65, 235205 (2002). 
5. T.M. Rusin, J. Kossut, Phys. Re.v B. 56(8), 4687 (1997). 
6. V. Sugakov, A.V. Vertsimakha, phys. stat. solidi b 217, 841 (2000). 
7. E. Kasapoglu, H. Sari, U. Yesilgul, I. Sokmen, J. Phys.: Condens. Matter. 18, 
6263 (2006).  
8. E.C. Niculescu, A. Radu, Curr. Appl. Phys. 10, 1359 (2010). 
9. S.G. Jayam, K.N. Krishnan, Int. J. Mod. Phys. B 16, 3737 (2002).  
10. P. Nithiananthi, C. Rajamohan, K. Jayakumar. J. Nanosci. Nanotechnol. 9, 5669 
(2009). 
11. H. Yokoi, S.W. Tozer, Y. Kim, D. Rickel, Y. Kakudate, S. Usuba, S. Fugiwara, 
S. Takeyama, G. Karczewski, T. Wojitowicz, J. Appl. Phys. 85, 5935, (1999). 
12. J.A. Gaj, R. Planel, G. Fishman, Solid State Commun. 29, 435 (1979). 


Effect of laser on the bound magnetic polaron in a semimagnetic quantum wire

Electronic Sumy State University Institutional Repository

   J. Nano- Electron. Phys. 3 (2011) No1, P. 1005-1009  2011 SumDU (Sumy State University)   1005 PACS numbers: 42.55. – f, 71.38. – k, 73.21. – Hb, 75.50.Pp  EFFECT OF LASER ON THE BOUND MAGNETIC POLARON IN A SEMIMAGNETIC QUANTUM WIRE  C. Raja Mohan1, K. Jayakumar2   1 Department of Physics, Gandhigram Rural University,   Gandhigram 624302, Tamilnadu, India 2 Department of Physics, Gandhigram Rural University,   Gandhigram-624302, Tamilnadu, India   E-mail: kjkumar_gri@rediffmail.com  In the present investigation binding energy of the laser dressed hydrogenic donor in a Semi  magnetic  Quantum  Wire  like  Cd1 – xMnx2Te/Cd1 – x1Mnx1Te/Cd1 – x2Mnx2Te and  spin  polaronic  shift  has  been  computed  for  various  magnetic  and  laser  fields within the effective mass approximation in the finite barrier model using variational method. The results are presented and discussed.   Keywords:  LASER,  MAGNETIC  SEMICONDUCTOR  QUANTUM  WIRE,  SPIN POLARON, MAGNETICFEILD, DONOR BINDING ENERGY.  (Received 04 February 2011)  1.  INTRODUCTION  When a magnetic impurity is doped in a semiconductor, there is a strong sp-d spin dependent interaction between the localized magnetic moment of the magnetic impurity in a doped semiconductor with the (i) bound charge carrier gives rise to Bound Magnetic Polaron (BMP) [1] (ii) free charge carrier leads to  Free  Magnetic  Polaron  (FMP) [2]  (iii)  exciton  gives  rise  to  Excitonic Magnetic  Polaron  (EMP)  [3].  All  these  polaronic  effect  in  Semimagnetic Semiconductors  (SMSC)  such  as  Cd1 – xMnxTe/CdTe  show  novel  and  poten-tially important phenomena such as Giant negative magneto resistance, Spin glass  transition,  anti  ferromagnetic  cluster,  large  Faraday  rotations  etc., Bound  magnetic  polaron  has  been  observed  both  experimentally  and theoretically  in  modulation  doped  SMSC  material  [4].  There  are  reports  on fractional  dimensional  approach  to  BMP  in  Quantum  Well(QW),  Quantum Well Wire (QWW) [5], effect of magnetic field on exciton level [6] and effect of intense laser field [7, 8] in a QWW are available in the literature. In the present work the effect of laser and magnetic field on the Spin Polaron in a magnetic QW Cd1 – x1Mnx1Te surrounded by magnetic barrier Cd1 – x2Mnx2Te has been investigated in the effective mass approximation using variational method.  We  have  considered  mean  field  theory  with  modified  Brillouin function in the above calculations.  2.  THEORY  The Hamiltonian of the laser dressed hydrogenic donor in the presence of applied  magnetic  field  along  the  growth  axis  in  a  Cd1 – x2Mnx2Te/Cd1 –   1006  C. RAJA MOHAN, K. JAYAKUMAR     x1Mnx1Te /Cd1 – x2Mnx2Te quantum wire of fintie barrier in the effective mass approximation is given by [9],   ()2 2*01() 2Be AeH P Vzc ra m eæö= + -+ ç÷ + èør (1)  where  222 r xyz = ++ “ a ” i s t h e  a m p l i t u d e  o f  e l e c t r o n  o s c i l l a t i o n  i n  t h e radiation field ( ) a eA mc w =r, which is proportional to I1/2w–2, I being the intensity of laser radiation. The potential barrier height of Cd1 – x2Mnx2Te Quantum Wire is given by,   ()() 002,,2BzLV zaV z a V zLì £ ï =íï î >  (2)               with the laser dressed donor potential [10],    ( )201(,)2EW V z a VzL = Q-   (3)   where Θ(z) is the step function, LEW = LW/2 is the effective well width for a laser-dressed donor.  0 70%Bg VE =D ; L i s t h e  w i d t h  o f t h e  p o t e n t i a l w e l l , Bg E D  is the band gap difference with magnetic field and 0g E D  is without magnetic field and they can be related by (4),   0 11Bgg EE eVg hhéù -D =D êú - ëû,  (4)     (4)  where  0 eVg h =  is chosen with z as a parameter(  = 0.5) and g0 as the critical magnetic field which depends upon the value of the composition ‘x’ ( = x2 – x1). The critical magnetic field for different composition is given in Tesla as B0 = Aenx with A = 0.734 and n = 19.082 which gives the best fit to the extrapolated experimentally available critical fields [11]. The band gap of Cd1 – xMnxTe is given to be 1606 + 1587x (meV). The variational ansatz for the donor in a finite Quantum Wire is chosen as,   ()cos cos 2,2,rx yrx y e zLNzL B eelblaay-- +-ì £ï=íï > î (5)  where N is the normalisation constant and l is the variational parameter and,   ( )0.5 0.5 220 2 2   and    2 2 m E m VE ab é ù éù =× =× - ëû ëû hh   (6)       EFFECT  OF  LASER  ON  THE  BOUND  MAGNETIC  POLARON… 1007 The dimensionless form of Eq. (1) can be written as,   ()22 2 2* 2( ) ,.4zB H L x y V zaRragg = - Ñ + + + -++  (7)  The dimensionless quantity of magnetic field parameter is defined as,   * 2eBmc Rgæö= ç÷× èørh (8)  where R* is the effective Rydberg which is R* = e2/2e0aB* and the effective Bohr radius is aB* = ħ2e0/m*e2, with m*  and  e0 are the effective mass of electron and static dielectric constant for the CdTe respectively. The donor binding energy of a Quantum Wire in the presence of magnetic field is given by [9],    ( ) B E E HS g = +- (9)  where  E i s  t h e  s u b b a n d  e n e r g y  w h i c h  c a n  b e  o b t a i n e d  b y  s o l v i n g  t h e transcendental equation,   ( ) tan 0.5 L a ab ×= (10)  2.1  S    P                 The exchange interaction between the carrier and Mn2+ ion in the presence of an external magnetic field  Br can be calculated using modified Brillouin function [12]. The spin polaronic shift is given by,    { () () } 0 1 1 11 2 2 2212s p ss E S N x By x By b yy yy =+ (11)  where Bs(y) is the modified Brillouin function and it is given by,   ()21 21 1coth coth2 2 22js jjy SSB yyS S SS++=- (12)   22j BjS gSyKT KTby mb=+ (13)  where β - exchange coupling parameter, S is the spin of Mn 2+ ( = 5/2 ), and xN0 is the Mn ion concentration with N0 = 2.94 ´ 1022 cm–3 and bN0 = 220 meV for CdTe12. Also gMn » 2, K is the Boltzmann constant.  3.  RESULTS AND DISCUSSIONS  Fig. 1 gives the variation of barrier height with magnetic field for laser amplitudes a = 0 ￅ (i.e. without laser) and a = 150 ￅ. It shows that the application of laser field also reduces the barrier height in addition to the magnetic field.      1008  C. RAJA MOHAN, K. JAYAKUMAR    0 0.05 0.1 0.15 0.2 0.25020406080100120Potential barrier height (meV)g a = 0 ￅ a = 150 ￅ  F  . 1 –Variation of potential barrier height with magnetic field    Fig. 2 gives the variation of binding energy with well width for two laser fields a = 0 ￅ and a = 150 ￅ with three different magnetic fields of γ = 0, γ = 0.1 and γ = 0.25 for the Mn composition x = 0.1. It is observed that the binding energy decreases with increase of well width and the application of magnetic field. This is due to the reduction of potential barrier height with γ which in turn reduces the confinement of the carrier. The application of laser field also reduces the binding of the donor which is due to reduction in the well width and also due to dressed donor potential. At higher well widths the variation of binding energy due to magnetic field is not appreciable and the same trend is observed for higher laser intensity.  01020304050600 100 200 300W ell W idth(ￅ)Binding Energy(meV) g=0g=0.1g=0.25g=0g=0.1g=0.25a=0ￅa=150 ￅ  F  . 2 - Variation of Binding Energy with Well width      The variation of magnetic polaronic shift of the donor for a = 0 ￅ and a = 150 ￅ and for x = 0, x = 0.1 and x = 0.25 is given in Fig. 3 for x = 0.1. It is noticed that there is a competition between laser field and magnetic      EFFECT  OF  LASER  ON  THE  BOUND  MAGNETIC  POLARON… 1009 field on the bound magnetic polaron, since application of magnetic field increases the polaronic shift in contrast to laser field which decreases the binding of spin polaron. It is also noticed that there is a drastic variation of magnetic polaronic shift with well width and also with magnetic field. When the magnetic field is increased, spin polaron effect is increased. This is due to the reduction in barrier height which in turn increases the interaction between the carrier ion and the magnetic ions due to smaller confinement.  -0.50.51.52.53.54.55.56.57.50 50 100 150 200 250 300 350W ell W idth(ￅ )Spin Polaronic shift(meV)g =0.25g =0.1g=0--------   a =150ￅ              a=0ￅ  F  . 3 - Variation of Spin Polaronic Shift with Well width  The effect of laser decreases the magnetic polaronic shift. The same trend is observed for all the magnetic fields. To conclude, the effect of laser and magnetic field in SMSC like CdMnTe system plays a vital role in the spin related phenomena. We hope the present investigation may through some light on spintronics applications and optoelectronic devices. More experimental results should come to prove these facts.  One of the authors K. Jayakumar thanks the University Grants Commission, New Delhi, India for the financial support under Major Research Project.   REFERENCES 1.  J.K. Furdyna, J. Appl. Phys. 64, R29 (1988).  2.  C.B. Guillaume, phys. stat. solidi b 175, 369 (1993). 3.  Z.H Chen, H. Sakurai, K. Seo, K. Kayanuma, T. Tomita, A. Murayama, Y. Oka, Physica B 340, 890 (2003). 4.  A.C. Drust, R.N. Bhatt, P.A. Wolff, Phys. Rev. B 65, 235205 (2002). 5.  T.M. Rusin, J. Kossut, Phys. Re.v B. 56(8), 4687 (1997). 6.  V. Sugakov, A.V. Vertsimakha, phys. stat. solidi b 217, 841 (2000). 7.  E. Kasapoglu,  H. Sari,  U.  Yesilgul,  I. Sokmen,  J. Phys.: Condens. Matter.  18, 6263 (2006).  8.  E.C. Niculescu, A. Radu, Curr. Appl. Phys. 10, 1359 (2010). 9.  S.G. Jayam, K.N. Krishnan, Int. J. Mod. Phys. B 16, 3737 (2002).  10. P. Nithiananthi, C. Rajamohan, K. Jayakumar. J. Nanosci. Nanotechnol. 9, 5669 (2009). 11. H. Yokoi,  S.W. Tozer, Y. Kim, D. Rickel, Y. Kakudate,  S. Usuba,  S. Fugiwara, S. Takeyama, G. Karczewski, T. Wojitowicz, J. Appl. Phys. 85, 5935, (1999). 12. J.A. Gaj, R. Planel, G. Fishman, Solid State Commun. 29, 435 (1979). 

phys. stat. solidi b 175,

phys. stat. solidi b 217,

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Effect of laser on the bound magnetic polaron in a semimagnetic quantum wire

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