We consider a possibility of generation of the stationary spin current in (110) –
oriented GaAs-basedsymmetric quantum well due to the nonlinear response to externalperiodic
electric field. The model includes the Dresselhaus spin-orbit interaction and
the random Rashbaspin-orbit coupling.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2055

Barnas, J.

Dugaev, V.K.

Ivanov, V.I.

Sherman, E.Y.

Electronic Sumy State University Institutional Repository

Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   7  SPIN CURRENT IN (110)-ORIENTED GaAs  QUANTUM WELLS Volodymyr I. Ivanov1*, Vitalii K. Dugaev2,3, Eugene Ya. Sherman4,5, Józef BarnaĞ6,7  1 Institute for Problems of Materials Science (Chernivtsi Branch), Ukrainian Academy of Scienc-es, Vilde 5, 58001 Chernivtsi, Ukraine 2 Department of Physics, Rzeszów University of Technology, al. PowstaĔców Warszawy 6, 35-959 Rzeszów, Poland 3 Department of Physics and CFIF, Instituto Superior Técnico, TU Lisbon,Av. Rovisco País 1049-001 Lisbon, Portugal 4 Department of Physical Chemistry, Universidad del Pais Vasco, Bilbao,Spain 5 IKERBASQUE Basque Foundation for Science, 48011, Bilbao, Spain 6 Adam Mickiewicz University, ul.Umultowska 85, 61-614 PoznaĔ, Poland 7 Institute of Molecular Physics, Polish Academy of Sciences, ul. Smoáuchowskiego 17, 60-179 PoznaĔ, Poland  ABSTRACT We consider a possibility of generation of the stationary spin current in  (110) – oriented GaAs-basedsymmetric quantum well due to the nonlinear response to exter-nalperiodic electric field. The model includes the Dresselhaus spin-orbit interaction and the random Rashbaspin-orbit coupling.   Key words: spin current, spin-orbit coupling, GaAs, quantum well  INTRODUCTION Recently, symmetric GaAs (110) quantum wells (QWs) became the sub-ject of extensive studies [1-3]. Spin orbit (SO) interaction in these systems, described by the Dresselhaus term [4], conserves the electron spin along the axis normal to the QW plane for any electron momentum k. As a result, the random motion of an electron does not lead to spin relaxation. In reality, this spin  component  relaxes  very  slowly,  and  its  analysis  provides  a  test  for  the  rapidly developing spin-noise spectroscopy [2]. In the case of perfect z to -z symmetry (the axis z is perpendicular to the QW plane), the Rashba SO interac-tion is zero. But in real structures, however, the Rashba coupling still exists in the form of a spatially fluctuating SO field (though being zero on average) [5-7]. This interaction induces spin-flip processes leading to the spin relaxation [3], and can be also responsible for generation of non-equilibrium spin density due to the absorption of external electromagnetic field [7].  In this work we propose a new possibility of exciting a steadypure spin current, thus extending the abilities of spinmanipulation in real situations. In                                                * e-mail: volodya_iv@mail.ru; tel: (+30)322525155 8                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I             contrast to the conventionalspin Hall effect, which is linear in external electric field, theproposed spin current is quadratic in periodic field.The effect is a result of the interplay of constant Dresselhausand spatially non-uniform Rash-bainteractions. The exact mechanism of this effect does not involve real spin-flip transitions of electronsbetween the spin-split subbands in (110)-GaAs QW, but relies onvirtual spin-flip processes renormalizing the wave functionsof electrons in non-equilibrium state. This makes such anonlinear responsethe physically new phenomenon, which appears ifone takes into account more realistic cases than those describedby the conventional Rashba and Dresselhaus models. MODEL AND GENERAL APPROACH Hamiltonian of a two-dimensional electron gas with a constantDressel-haus term and spatially fluctuating Rashbaspin-orbit interaction, subjected to externalelectromagnetic field described by the vector potential A(r, t) takes the form (we use units with= = 1)   212xz xieAieH im c cDV § ·§ ·     ¨ ¸ ¨ ¸© ¹ © ¹A ^ ` ^ `, ( ) / 2 , ( ) / 2x y y xi i VV O V O    r r , (1)  Where Į is the Dresselhaus coupling constant,{ ,} denoting the anticom-mutator and Ȝ(r) is the random Rashba SO interaction. The term Vdescribes coupling of the electron spin to theexternal field A(r,t) via the Rashba field. Due to the assumed symmetry with respect to z-inversion, thespatially av-eraged Rashba interaction vanishes, 0)(  O r .We assume that the random-Rashba field can be described by the some correlation function relatedto fluctu-ating density of impurities near the QW [5, 7]. SPIN CURRENT A nonzero pure spin currentcan be generated by anexternal field in the presence of random Rashba coupling. In the following we consider the z-component of spin current flowing along the x axis. The macroscopic spin current densityis then given by  2z zx x kkdj iTr j G HHS ¦ ³ (2)  Where Ƶzx =  kxız/m + Į is spin current tensor component, Gkİ is  the  Green's functionof thesystem.  Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   9    Fig. 1 – Dependence of the light-induced spin current on thefrequency Ȧ for  different values of the correlation length R   The stationary spin currentis excited by the external electromagneticfield described byA(t)=2A0cos Ȧt. We point out that only Rashba SO interaction can generate the spincurrent since the field-induced perturbation in Dresselhaus term commuteswith ız and thus does not lead to spin dynamics. After expand-ing Green's functionup to the first order inĮ and secondorder in A(t) we obtain the following form of the spin current   2qcq0Fk02zx ||2qdq4kdk)(Cj OSSZ ³³     ¸¸¹·¨¨©§EEEEEEEu 2/5211221222122/522222)1(kq9qq2k2k4)1(k2k4q3k  (3)  Whereqc = – k/2 + (k2/4 + 2mȦ)1/2, ȕ1,2 = 2mȦ/kq r q/k.  RESULTS AND DISCUSSION Numerical results on jzx are shown in Fig. 1 for different values of the pa-rameter  R.  We  used  the  parameters  typical  for  GaAs:  m  =  0.067  m0,  kF = 1.8•106 cm-1 and ȝ = 18.5 meV. We emphasize here that the calculated spin current is a stationary nonline-ar effect proportional to the intensity of incident light, in contrast to the spin 10                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I             current generated by pulse excitations, where the result is proportional to the total influence in the pulse [6]. In the flux-dependent processes the pulse changes the real occupation of the spin-up and spin-down states. The calculated current is also not related to the linear response at frequency Ȧ. CONCLUSIONS We have proposed a new effect which consists in thenonlinear generation of a steady pure spin currents in GaAs (110) quantum wells by electromagnetic wave. The spin current isproportional to the intensity of the external mono-chromaticradiation. Physical mechanism of the effect is related to thevirtual spin reorientation of electrons filling the spin subband(split by Dresselhaus interaction) in the presence of a non-uniformRashba coupling. As a result, a 'spin hole' virtually appears inthe subband, leading to the light-induced spin current.  Acknowledgements This work is partly supported byFCT Grant PTDC/FIS/70843/2006 in Portugal and by PolishMinistry of Science and Higher Education as a research project in years 2011-2013. The work of EYS was supported by theUniversity of Basque Country UPV/EHU grant GIU07/40, MCI of Spaingrant FIS2009-12773-C02-01, and "GruposConsolidados UPV/EHU delGobierno Vasco" Grant IT-472-10. REFERENCES [1] Y. Ohno, R. Terauchi, T. Adachi et al. Phys. Rev. Lett., 1999, Vol. 83, No20, P. 4196-4199. [2] G.M. Muller, M. Oestreich, M.L. Romer, J. Hubner, Physica E, 2010, Vol. 43, No2, P. 569-687. [3] Y. Zhou, M.W. Wu, EPL, 2010, Vol. 89, No5, P. 57001. [4] R. Winkler, Spin-Orbit Coupling Effects in Two-dimensional Electron and Hole Systems, Springer, New York, 2003. [5] E.Ya. Sherman, Phys. Rev. B, 2003, Vol. 67, No16, P. 161303(R). [6] E.Ya. Sherman, A. Najmaie, J.E. Sipe, Appl. Phys. Lett., 2005, Vol. 86, No12, P. 122103. [7] M.M. Glazov, E.Ya. Sherman, V.K. Dugaev, Physica E, 2010, Vol. 42, No9, P. 2157-2177. [8] V.K. Dugaev, E.Ya. Sherman, V.I. Ivanov, J. BarnaĞ, Phys. Rev. B, 2009, Vol. 80, No8, P. 081301(R).    

Spin current in (110)-oriented GaAs quantum wells

SocioEconomic Challenges Journal (Sumy State University)

Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   7 
 
SPIN CURRENT IN (110)-ORIENTED GaAs  
QUANTUM WELLS 
Volodymyr I. Ivanov1*, Vitalii K. Dugaev2,3, Eugene Ya. Sherman4,5, Józef BarnaĞ6,7 
 
1 Institute for Problems of Materials Science (Chernivtsi Branch), Ukrainian Academy of Scienc-
es, Vilde 5, 58001 Chernivtsi, Ukraine 
2 Department of Physics, Rzeszów University of Technology, al. PowstaĔców Warszawy 6, 35-
959 Rzeszów, Poland 
3 Department of Physics and CFIF, Instituto Superior Técnico, TU Lisbon,Av. Rovisco País 1049-
001 Lisbon, Portugal 
4 Department of Physical Chemistry, Universidad del Pais Vasco, Bilbao,Spain 
5 IKERBASQUE Basque Foundation for Science, 48011, Bilbao, Spain 
6 Adam Mickiewicz University, ul.Umultowska 85, 61-614 PoznaĔ, Poland 
7 Institute of Molecular Physics, Polish Academy of Sciences, ul. Smoáuchowskiego 17, 60-179 
PoznaĔ, Poland 
 
ABSTRACT 
We consider a possibility of generation of the stationary spin current in  (110) – 
oriented GaAs-basedsymmetric quantum well due to the nonlinear response to exter-
nalperiodic electric field. The model includes the Dresselhaus spin-orbit interaction and 
the random Rashbaspin-orbit coupling.  
 
Key words: spin current, spin-orbit coupling, GaAs, quantum well 
 
INTRODUCTION 
Recently, symmetric GaAs (110) quantum wells (QWs) became the sub-
ject of extensive studies [1-3]. Spin orbit (SO) interaction in these systems, 
described by the Dresselhaus term [4], conserves the electron spin along the 
axis normal to the QW plane for any electron momentum k. As a result, the 
random motion of an electron does not lead to spin relaxation. In reality, this 
spin  component  relaxes  very  slowly,  and  its  analysis  provides  a  test  for  the  
rapidly developing spin-noise spectroscopy [2]. In the case of perfect z to -z 
symmetry (the axis z is perpendicular to the QW plane), the Rashba SO interac-
tion is zero. But in real structures, however, the Rashba coupling still exists in 
the form of a spatially fluctuating SO field (though being zero on average) [5-
7]. This interaction induces spin-flip processes leading to the spin relaxation 
[3], and can be also responsible for generation of non-equilibrium spin density 
due to the absorption of external electromagnetic field [7].  
In this work we propose a new possibility of exciting a steadypure spin 
current, thus extending the abilities of spinmanipulation in real situations. In 
                                               
* e-mail: volodya_iv@mail.ru; tel: (+30)322525155 
8                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I            
 
contrast to the conventionalspin Hall effect, which is linear in external electric 
field, theproposed spin current is quadratic in periodic field.The effect is a 
result of the interplay of constant Dresselhausand spatially non-uniform Rash-
bainteractions. The exact mechanism of this effect does not involve real spin-
flip transitions of electronsbetween the spin-split subbands in (110)-GaAs QW, 
but relies onvirtual spin-flip processes renormalizing the wave functionsof 
electrons in non-equilibrium state. This makes such anonlinear responsethe 
physically new phenomenon, which appears ifone takes into account more 
realistic cases than those describedby the conventional Rashba and Dresselhaus 
models. 
MODEL AND GENERAL APPROACH 
Hamiltonian of a two-dimensional electron gas with a constantDressel-
haus term and spatially fluctuating Rashbaspin-orbit interaction, subjected to 
externalelectromagnetic field described by the vector potential A(r, t) takes the 
form (we use units with= = 1) 
 
 
21
2
x
z x
ieAieH i
m c c
DV § ·§ ·     ¨ ¸ ¨ ¸© ¹ © ¹
A
 ^ ` ^ `, ( ) / 2 , ( ) / 2x y y xi i VV O V O    r r , (1) 
 
Where Į is the Dresselhaus coupling constant,{ ,} denoting the anticom-
mutator and Ȝ(r) is the random Rashba SO interaction. The term Vdescribes 
coupling of the electron spin to theexternal field A(r,t) via the Rashba field. 
Due to the assumed symmetry with respect to z-inversion, thespatially av-
eraged Rashba interaction vanishes, 0)(  O r .We assume that the random-
Rashba field can be described by the some correlation function relatedto fluctu-
ating density of impurities near the QW [5, 7]. 
SPIN CURRENT 
A nonzero pure spin currentcan be generated by anexternal field in the 
presence of random Rashba coupling. In the following we consider the z-
component of spin current flowing along the x axis. The macroscopic spin 
current densityis then given by 
 
2
z z
x x k
k
dj iTr j G H
H
S ¦ ³

 (2) 
 
Where Ƶzx =  kxız/m + Į is spin current tensor component, Gkİ is  the  
Green's functionof thesystem. 
 
Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   9 
 
 
 
Fig. 1 – Dependence of the light-induced spin current on thefrequency Ȧ for  
different values of the correlation length R 
  
The stationary spin currentis excited by the external electromagneticfield 
described byA(t)=2A0cos Ȧt. We point out that only Rashba SO interaction can 
generate the spincurrent since the field-induced perturbation in Dresselhaus 
term commuteswith ız and thus does not lead to spin dynamics. After expand-
ing Green's functionup to the first order inĮ and secondorder in A(t) we obtain 
the following form of the spin current 
 
 2q
cq
0
Fk
0
2
z
x ||2
qdq
4
kdk)(Cj OSS
Z ³³   
 
 ¸¸¹
·
¨¨©
§
E
EEE
E
EEu 2/52
1
1
22
1
222
1
2
2/52
2
2
22
)1(
kq9qq2k2k4
)1(
k2k4q3k  (3) 
 
Whereqc = – k/2 + (k2/4 + 2mȦ)1/2, ȕ1,2 = 2mȦ/kq r q/k. 
 
RESULTS AND DISCUSSION 
Numerical results on jzx are shown in Fig. 1 for different values of the pa-
rameter  R.  We  used  the  parameters  typical  for  GaAs:  m  =  0.067  m0,  kF = 
1.8•106 cm-1 and ȝ = 18.5 meV. 
We emphasize here that the calculated spin current is a stationary nonline-
ar effect proportional to the intensity of incident light, in contrast to the spin 
10                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I            
 
current generated by pulse excitations, where the result is proportional to the 
total influence in the pulse [6]. In the flux-dependent processes the pulse 
changes the real occupation of the spin-up and spin-down states. The calculated 
current is also not related to the linear response at frequency Ȧ. 
CONCLUSIONS 
We have proposed a new effect which consists in thenonlinear generation 
of a steady pure spin currents in GaAs (110) quantum wells by electromagnetic 
wave. The spin current isproportional to the intensity of the external mono-
chromaticradiation. Physical mechanism of the effect is related to thevirtual 
spin reorientation of electrons filling the spin subband(split by Dresselhaus 
interaction) in the presence of a non-uniformRashba coupling. As a result, a 
'spin hole' virtually appears inthe subband, leading to the light-induced spin 
current. 
 
Acknowledgements 
This work is partly supported byFCT Grant PTDC/FIS/70843/2006 in 
Portugal and by PolishMinistry of Science and Higher Education as a research 
project in years 2011-2013. The work of EYS was supported by theUniversity 
of Basque Country UPV/EHU grant GIU07/40, MCI of Spaingrant FIS2009-
12773-C02-01, and "GruposConsolidados UPV/EHU delGobierno Vasco" 
Grant IT-472-10. 
REFERENCES 
[1] Y. Ohno, R. Terauchi, T. Adachi et al. Phys. Rev. Lett., 1999, Vol. 83, No20, 
P. 4196-4199. 
[2] G.M. Muller, M. Oestreich, M.L. Romer, J. Hubner, Physica E, 2010, Vol. 43, No2, 
P. 569-687. 
[3] Y. Zhou, M.W. Wu, EPL, 2010, Vol. 89, No5, P. 57001. 
[4] R. Winkler, Spin-Orbit Coupling Effects in Two-dimensional Electron and Hole 
Systems, Springer, New York, 2003. 
[5] E.Ya. Sherman, Phys. Rev. B, 2003, Vol. 67, No16, P. 161303(R). 
[6] E.Ya. Sherman, A. Najmaie, J.E. Sipe, Appl. Phys. Lett., 2005, Vol. 86, No12, 
P. 122103. 
[7] M.M. Glazov, E.Ya. Sherman, V.K. Dugaev, Physica E, 2010, Vol. 42, No9, 
P. 2157-2177. 
[8] V.K. Dugaev, E.Ya. Sherman, V.I. Ivanov, J. BarnaĞ, Phys. Rev. B, 2009, Vol. 80, 
No8, P. 081301(R). 
 
  


https://essuir.sumdu.edu.ua/bitstream/123456789/20556/1/1.pdf

Spin current in (110)-oriented GaAs quantum wells

Abstract

Similar works

Full text

Available Versions

Electronic Sumy State University Institutional Repository

SocioEconomic Challenges Journal (Sumy State University)