Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires
We study the role of electron-electron collisions in the formation of spin-polarized current states in a "spin guide" which is a system consisting of a non-magnetic conducting channel wrapped in the grounded nanoscale magnetic shell. It is shown that under certain conditions the spin guide...
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| Zitieren: | Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires / R.N. Gurzhi, A.N. Kalinenko, A.I. Kopeliovich, A.V. Yanovsky, E.N. Bogachek Uzi Landman // Физика низких температур. — 2003. — Т. 29, № 7. — С. 809-811. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-1288782018-01-15T03:03:15Z Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires Gurzhi, R.N. Kalinenko, A.N. Kopeliovich, A.I. Yanovsky, A.V. Bogachek, E.N. Landman, Uzi Низкоразмерные и неупорядоченные системы We study the role of electron-electron collisions in the formation of spin-polarized current states in a "spin guide" which is a system consisting of a non-magnetic conducting channel wrapped in the grounded nanoscale magnetic shell. It is shown that under certain conditions the spin guide may generate and transport over long distances the non-equilibrium electron density with a high level of spin polarization, even though the frequent electron-electron scattering leads to a common drift of non-equilibrium electrons. We also propose some ways to convert the spin-polarized electron density into a spin-polarized electric current. 2003 Article Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires / R.N. Gurzhi, A.N. Kalinenko, A.I. Kopeliovich, A.V. Yanovsky, E.N. Bogachek Uzi Landman // Физика низких температур. — 2003. — Т. 29, № 7. — С. 809-811. — Бібліогр.: 8 назв. — англ. 0132-6414 PACS: 72.25.Hg, 72.25Mk, 73.40.Sx, 73.61.Ga http://dspace.nbuv.gov.ua/handle/123456789/128878 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Низкоразмерные и неупорядоченные системы Низкоразмерные и неупорядоченные системы |
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Низкоразмерные и неупорядоченные системы Низкоразмерные и неупорядоченные системы Gurzhi, R.N. Kalinenko, A.N. Kopeliovich, A.I. Yanovsky, A.V. Bogachek, E.N. Landman, Uzi Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires Физика низких температур |
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We study the role of electron-electron collisions in the formation of spin-polarized current states in a "spin guide" which is a system consisting of a non-magnetic conducting channel wrapped in the grounded nanoscale magnetic shell. It is shown that under certain conditions the spin guide may generate and transport over long distances the non-equilibrium electron density with a high level of spin polarization, even though the frequent electron-electron scattering leads to a common drift of non-equilibrium electrons. We also propose some ways to convert the spin-polarized electron density into a spin-polarized electric current. |
| format |
Article |
| author |
Gurzhi, R.N. Kalinenko, A.N. Kopeliovich, A.I. Yanovsky, A.V. Bogachek, E.N. Landman, Uzi |
| author_facet |
Gurzhi, R.N. Kalinenko, A.N. Kopeliovich, A.I. Yanovsky, A.V. Bogachek, E.N. Landman, Uzi |
| author_sort |
Gurzhi, R.N. |
| title |
Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires |
| title_short |
Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires |
| title_full |
Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires |
| title_fullStr |
Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires |
| title_full_unstemmed |
Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires |
| title_sort |
influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2003 |
| topic_facet |
Низкоразмерные и неупорядоченные системы |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/128878 |
| citation_txt |
Influence of electron-electron scattering on spin-polarized current states in magnetic wrapped nanowires / R.N. Gurzhi, A.N. Kalinenko, A.I. Kopeliovich, A.V. Yanovsky, E.N. Bogachek Uzi Landman // Физика низких температур. — 2003. — Т. 29, № 7. — С. 809-811. — Бібліогр.: 8 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT gurzhirn influenceofelectronelectronscatteringonspinpolarizedcurrentstatesinmagneticwrappednanowires AT kalinenkoan influenceofelectronelectronscatteringonspinpolarizedcurrentstatesinmagneticwrappednanowires AT kopeliovichai influenceofelectronelectronscatteringonspinpolarizedcurrentstatesinmagneticwrappednanowires AT yanovskyav influenceofelectronelectronscatteringonspinpolarizedcurrentstatesinmagneticwrappednanowires AT bogacheken influenceofelectronelectronscatteringonspinpolarizedcurrentstatesinmagneticwrappednanowires AT landmanuzi influenceofelectronelectronscatteringonspinpolarizedcurrentstatesinmagneticwrappednanowires |
| first_indexed |
2025-07-09T10:09:06Z |
| last_indexed |
2025-07-09T10:09:06Z |
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1837163611260190720 |
| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, No. 7, p. 809–811
Influence of electron–electron scattering on spin-polarized
current states in magnetic wrapped nanowires*
R.N. Gurzhi, A.N. Kalinenko, A.I. Kopeliovich, and A.V. Yanovsky
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Science
of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: gurzhi@ilt.kharkov.ua
E.N. Bogachek and Uzi Landman
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
Received November 29, 2002
We study the role of electron–electron collisions in the formation of spin-polarized current
states in a «spin guide» which is a system consisting of a non-magnetic conducting channel
wrapped in the grounded nanoscale magnetic shell. It is shown that under certain conditions the
spin guide may generate and transport over long distances the non-equilibrium electron density
with a high level of spin polarization, even though the frequent electron–electron scattering leads
to a common drift of non-equilibrium electrons. We also propose some ways to convert the spin-po-
larized electron density into a spin-polarized electric current.
PACS: 72.25.Hg, 72.25Mk, 73.40.Sx, 73.61.Ga
Spin-guide idea
Spintronic devices based on a spin degree of free-
dom in addition to charge may lead to new possibili-
ties in the information processing and storage. Effi-
cient spin injection into a semiconductor and
long-distance propagation of the spin signal are main
requirements for the development of spintronic de-
vices. The basis for the most methods of stationary
spin polarization generation is the idea of spin injec-
tion through the interface «magnetic conductor
(M)–non-magnetic matter (N)», we’ll refer it by a
«spin-filter» scheme, see, for example, [1–3]. Re-
cently, we have proposed a new method of generation
and transportation of high-level spin-polarized cur-
rents, namely a «spin-guide» scheme [4]. Spin-guide
scheme was proposed as a non-magnetic conducting
channel which is wrapped by a magnetic shell whose
external boundaries are grounded, see Fig. 1. (Note,
there is no need to wrap around the non-magnetic con-
ductor by the magnetic shell, it is enough to contact it
with the grounded magnetic material.) Unlike the
spin-filter scheme, current flows here along to the
M–N interface. The main principle of the spin-guide
scheme is based on the removal of the one spin polar-
ization, in contrast with the spin-filter scheme, when
spin polarization in a non-magnetic conductor is cre-
ated by electrons injected from the magnetic material.
In the spin-guide scheme those non-equilibrium elec-
© R.N. Gurzhi, A.N. Kalinenko, A.I. Kopeliovich, A.V. Yanovsky, E.N. Bogachek, and Uzi Landman, 2003
Fig. 1. The spin-guide scheme. Here d is the distance be-
tween grounded contacts.
* The report was submitted at the 3rd International Workshop on Low Temperature Microgravity Physics (CWS-2002).
trons of one of the polarizations (spin-down, for exam-
ple) which penetrate to M easier then another one, do
not return back into the channel due to grounding of
outside boundaries of the magnetic shell. So, the po-
larization of the electric current increases as we get
further away from the channel entrance due to
spin-down carrier depletion. Note, the spin-guide
scheme exploits the withdrawal of the one spin com-
ponent, so to increase the spin polarization one should
decrease the thickens of magnetic region (in contrast
to the spin-filter scheme). That is why nanoscale
shells are preferable for the spin-guide scheme. As we
have shown [4,5] spin guide allows one to alleviate
some intrinsic limitations associated with spin-filter
schemes: i) the spin polarization of the current in a
spin guide can exceed significantly the degree of spin
polarization in the magnetic material that is never pos-
sible in the spin-filter scheme; ii) the spin polarization
of the current may be propagated over arbitrarily long
distances, in contrast to the spin-filter scheme where
the transport length-scale is of order of the diffusion
spin-flip length. In the spin-guide scheme the negative
role of spin-flip processes is falls off as to compare
with the spin-filter scheme both in the magnetic shell
[5] and in the non-magnetic channel too [4]; iii) spin
guides allow easy detection and control of the spin po-
larization and they may form the basis for creating fast
spin-polarization switches which do not require mag-
netization inversion of the magnetic material; iv) one
can use one-dimensional wire as non-magnetic channel
for the spin guide. As it is known, no-backscattering
1D spin-filter is not possible, if magnetic material is
not fully polarized; v) finally, there are a number of
spin guide specific effects, some of them allow one di-
rect observation of the spin polarization of the current
flowing in a spin guide.
In this paper, we show that, to a large extent, ad-
vantageous of spin guides as to compare with spin-fil-
ters remain valid even through normal electron–elec-
tron (e–e) collisions are the most frequent scattering
process.
The role of the electron–electron scattering
in spin guides
Normal electron–electron collisions play an essen-
tial role in the spin-guide scheme. This is because the
e–e interaction leads to a momentum exchange be-
tween spin-up and spin-down electron subsystems
and, thus, to the establishing of a common drift of the
current carriers in the non-magnetic channel. As a re-
sult, e–e collisions lead to the depolarization of the
current in a spin guide. (There is no the effect in com-
pensated conductors due to the absence of the electric
charge transfer at the common drift of carriers.) How-
ever, the spin polarization of the non-equilibrium den-
sity of carriers is not affected by the e–e scattering
(this is in accordance with the conservation of the to-
tal spin at these collisions). So, hand in hand with the
common drift of the non-equilibrium carriers there is
the spin polarization of the density in a spin guide. Ac-
cordingly, aforementioned advantageous of the spin-
guide scheme are substantially conserved. Below we
show that the spin-polarized density may be converted
into the spin-polarized current. Therefore, the spin-
guide scheme could be rather effective at the tempera-
ture increase. Note, under certain conditions normal
e–e scattering dominates in a two-dimensional degen-
erated electron gas in high mobility hetorostructures,
see, e.g. [6].
We use macroscopic transport equations, which
were derived by Flensberg et al. [7] with taking into
account the e–e scattering. We consider the case of the
rare spin-flip scattering, i.e. �sf > �ee (�sf is the spin-
flip scattering time, �ee is the electron–electron scat-
tering time). We rewrite Eqs. (1,a) and (1,b) of
Ref. 7 in the following form:
div j� � � � � �� �
�
�
�
�
�
�
�
e
sf
�0
�
( ), (1)
� � � � ��
� � � � � � � �
�
� �
�
� � � �
�
� �e An n ni
1 1 1 1
� j j j( ) .
(2)
Here j� � are the densities of the currents carried by
electrons with spin-up and spin-down, respectively,
� � are electrochemical potentials for the spin-up
and spin-down electrons, � i��
are the resistivities, e is
the electron charge, n
��
are the electron densities,
A e m nee m� �2 � is the e–e spin drag coefficient [7],
� �ee ee T� ��1 2 is e–e collision frequency and nm is
the minor of two spin component electron densities;
value �0 defined by � � �0
1 1 1�
�
�
�
�� � , where �� �
are densities of states at the Fermi surface. The sec-
ond term in the right-hand side of Eq. (2) describes
the mutual friction of the two spin subsystems, which
leads to the common drift of electron system. In the
sake of simplicity we ignore the small term, which is
related to the anisotropic spin-flip scattering [7].
We consider the simple spin-guide model, i.e. a
two-dimensional geometry where the interface is
formed by a non-magnetic plate which is surrounded
by the magnetic layers with grounded outside bound-
aries, see Fig. 1. As we concentrate our efforts on the
e–e scattering role, we will neglect here by the
spin-flip scattering and we consider here fully polar-
ized magnetic layers only (for example, diluted mag-
netic semiconductors with giant Zeeman splitting or
fully polarized half-metals, see [3,8]). Let the x-axis
810 Fizika Nizkikh Temperatur, 2003, v. 29, No. 7
R.N. Gurzhi, A.N. Kalinenko, A.I. Kopeliovich, A.V. Yanovsky, E.N. Bogachek, and Uzi Landman
be directed along the channel and lie in it’s middle,
and take the z-axis to be perpendicular to the interfa-
cial planes, with the origin of the coordinate system
located in the center of the entrance into the channel
(see Fig. 1). The grounding of the outside boundaries
is equivalent to the condition � �
� � � � �z d/2 0. For
definiteness, let us assume that the magnetic shell is
transparent for «spin-down» electrons. For distances
from the entrance long enough, so x >> d, we have
the established solution of Eqs. (1) and (2) given by
� � �a bx,
� � 0, (3)
where a, b are arbitrary constants (the relation be-
tween a and b is determined by the boundary condi-
tions at the channel entrance). Writing corresponding
currents from the Eq. (2) we see that e–e collisions
suppress radically the spin polarization of the current:
�
�
�
�
�
�
�
� �
�
�
�
�
�
�
� �
�
�
��
��
� �
� �
� �j j
j j
A
ni
E E
i
1 1
2
1 1
– , (4)
where �i is electron–impurity collision frequency.
Thus, as aforementioned above, the spin polarization
of the electric current tends to the unity when the
electron–impurity scattering dominates over the elec-
tron–electron scattering, i.e. � �ee i/ � 0. And vice
versa, � tends to zero (spin currents will tend to be
equalized) at increasing spin drag coefficient which is
proportional to the e–e collision frequency. On the
other hand, the relative spin polarization of the elec-
tron density does not depend on the e–e frequency
at all:
�
� �
�
�
�
�� � � �n n
eU eU�
. (5)
Here eU� is the maximal possible change of electron
density in the potential difference between the ends
of the spin guideU, � is the electron density of states
at the Fermi level in the non-magnetic conductor.
Here we should note, that the spin polarization of
the electron density may be converted into the practi-
cally one-hundred percent spin polarization of the
electric current. It may be done in different ways.
Firstly, one may use extra local concentration of im-
purities near the exit from the spin guide, so the
electron–impurity scattering dominates over the elec-
tron–electron scattering in this region. A compara-
tively short dirty region, the width of which is of or-
der of the d, will be enough for this purpose. The
other way is using of electrostatic constrictions or
atomic wires at the exits of the non-magnetic channel;
the transport mean free-path in the constriction have
to be less then electron–electron mean free path. In
the case of atomic wires (one-dimensional quantum
point contact) the spin polarization of the current at
exit of the spin guide is determined by the ratio be-
tween the electrochemical potentials
� � before the
constriction and the electrochemical potential out of
channel
� . If
� �� then the spin polarization of
the current will be 100%.
Note, that if the resistance of the constriction in the
end of a spin guide is much higher than the channel re-
sistance, then the spin polarization of the density in
the channel � will be constant and it reaches its maxi-
mum value: � � 1, i.e. the non-equilibrium density is
fully polarized.
The research described in this publication was
made possible in part by Award No.UP2-2430-KH-02
of the U.S. Civilian Research & Development Foun-
dation for the Independent States of the Former So-
viet Union (CRDF). The research of E.N.B. and U.L.
was also supported by the US Department of Energy,
Grant No.FG05-86ER-45234.
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Influence of electron–electron scattering on spin-polarized current states
Fizika Nizkikh Temperatur, 2003, v. 29, No. 7 811
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