Spin-Guide: A New Source of High Spin-Polarized Current

8 Pages·0.22 MB·English

by  R. N. Gurzhi

Spin-Guide: A New Source of High Spin-Polarized Current
R.N.Gurzhi,1 A.N.Kalinenko,1 A.I.Kopeliovich,1 A.V.Yanovsky,1 E.N.Bogachek,2 and Uzi Landman2
1B.Verkin Institute for Low Temperature Physics & Engineering of the National
Academy of Science of the Ukraine, 47 Lenin Ave, Kharkov, 61103, Ukraine
2School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
3
(Dated: January 8, 2003)
0
0 We propose a “spin-guide” source for generation of electric currents with a high degree of spin
2 polarization, allowing long-distance transmission of the spin-polarization. Inthespin-guidescheme
n proposed here, a non-magnetic conducting channel is wrapped by a magnetic shell which prefer-
a entially transmits electrons with a particular spin polarization. It is shown that this method is
J significantlymoreeffectivethenthespin-filter-likeschemewherethecurrentflowsperpendicularto
2 theinterface between aferromagnetic metal toa non-magneticconductingmaterial. Undercertain
2 conditions a spin-guide may generate an almost perfectly spin-polarized current, even when the
magnetic material used is not fully polarized. The spin-guide is predicted to allow the transport

] of spin polarization over long distances which may exceed significantly the spin-flip length in the
ll channel. Inaddition,itreadilypermitsdetectionandcontrolofthespin-polarizationofthecurrent.
a The spin-guide may be employed for spin-flow manipulations in semiconductors used in spintronic
h
devices.
-
s
e PACSnumbers: 72.25.Hg,72.25Mk,73.40.Sx,73.61.Ga
m
.
t I. INTRODUCTION high frequency of spin-flip processes the probability to
a
lose the spin is high in the magnetic material. Further-
m
more, due to the aforementioned conductivity mismatch
- Recently there has been a growing interest in “spin- between the ferromagnetic and nonmagnetic materials,
d tronic” devices1,2, where the spin degree of freedom is
n the electrons will spend most of the time in the ferro-
utilizedfordatamanipulations,ratherthenjusttheelec-
o magnetic material, and this will increase the probability
tronicchargeasincustomarydevices. This is due to the
c to lose the excess spin orientation. Consequently, the
[ obvious advantages of integrating a magnetic data stor-
spin polarization of the current in the semiconductor is
3 age device with an electronic readout, as well as due to expected to be extremely low.
thepromisingprospectsforapplicationsofspin-polarized
v
currents in quantum computing. The main technical There are number of additional essential limitations
2
requirements for the development of spintronic devices, inherent to the spin-filter scheme. First, the spin po-
4
1 pertain to: (i) high efficiency spin injection into a semi- larizationofthe injected currentcannotexceedthe spin
1 conductor,and(ii) long-distancepropagationofthe spin polarizationofthecurrentinthemagneticmaterial(serv-
0 signal. Currently, some of the major issues concern- ing as an injector). Secondly, the distance over which a
3 ing the fabrication of spintronic devices center on the significantdegreeofspinpolarizationmaybemaintained
0 generation of stationary spin-polarized currents in non- in a non-magnetic material, can not exceed the diffusion
/
t magnetic semiconductors. spin-fliplengthinit. Inaddition,wenotethatitisprac-
a
tically impossible to vary the spin polarizationof the in-
m Some of the methods for the generation of station-
jected current, and additional methods are required in
aryspinpolarizationarebasedonspininjectionthrough
-
order to detect and /or measure the degree of spin po-
d the interface between a ferromagnetic metal to a non-
n magnetic conducting material; we will refer to this idea larization (such as the use of a light emitting diode10 or
o as the “spin-filter” scheme3. In the diffusive transport the oblique Hanle effect technique7).
c
regime, the spin-filter scheme has been shown initially Recently, the spin-injection efficiency has been
:
v to be associated with a very small degree of spin po- markedly increased11,12; indeed, by replacing the fer-
Xi larization (of the order of a few percent4,5,6,7). There romagnetic metal by a diluted magnetic semiconductor
are two main reasons for this inefficiency8,9: (i) the spin (DMS), Be Mn Zn Se, a record degree of polariza-
r x y 1−x−y
a relaxation time is much smaller in a ferromagnetic ma- tion (up to 90%) has been achieved11. This remarkable
terial than in a non-magnetic one, and (ii) the conduc- result originates from specific properties of the DMS. In
tivity of the ferromagnetic metal injector is much higher particular,becauseoftheverylargesplitofthespinsub-
than the conductivity of the semiconductors which are bands in a magnetic field, these compounds may have
usually used as non-magnetic materials. In effect, the a sufficiently high degree of spin polarization. Conse-
nonequilibrium electrons that are injected from the fer- quently,if the Fermilevelinthe DMS appearsbelow the
romagnet, undergo a Brownian motion. Consequently, bottomofoneofthespinsubbands,thespin-polarization
prior to reaching the detector (collector) these electrons may reach 100%. However, the use of a DMS instead
returnbackintotheferromagnetrepeatedly(ortheyun- of a ferromagnetic metal, as well as a number of other
dergo a spin-flip in the semiconductor). Because of the wayssuggestedrecently7,13,14, overcomesonly one ofthe
2
For the sake of specificity, let us consider a flat con-
figuration where the interface is a planar plate; the ex-
tension to the three-dimensional case (cylindrical wire)
is straightforward. We will consider the diffusive trans-
port regime, where the diffusion length l (where l
↑,↓ ↑,↓
are the electron-impurity mean-free paths for the spin-
upandspin-downelectrons,correspondingly)aresignifi-
cantly shorterthanany characteristiclengthof the spin-
guide. In this paper the effects of electron-electron colli-
sionsare neglected- this is a fortiori validatsufficiently
low temperatures (i.e., several degrees Kelvin).
Let µ denote the electrochemical potentials for the
↑,↓
spin-up and spin-down electrons, respectively. The elec-
tric currentdensities J arerelatedto the electrochem-
FIG. 1: Cross-sectional view of the spin-guide scheme. w ↑,↓
is the width of the non-magnetic channel (N), and d is the ical potentials via Ohm’s law
distance between thegrounded magnetic (M) contacts.
σ
↑,↓
J =− ∇µ , (1)
↑,↓ ↑,↓
e
above mentioned limitations, i.e., they address only the
enhancementofthespin-polarizationofthe injectedcur- where σ↑,↓ are the corresponding conductivities. The
rent. spin transport, within the diffusive regime approxima-
In this paper we propose a new method for genera- tion, is described by Mott’s equations:
tion and transport of high spin-polarized currents. We
term the proposed method a “spin-guide” scheme. The
spin-guide is based on a new interface configuration15 div(σ↑,↓∇µ↑,↓)= Πτ0sef2(µ↑,↓−µ↓,↑),
which allows one to alleviate the aforementioned intrin- (2)
siclimitationsassociatedwithspin-filterschemes. Under Π−1 =Π−1+Π−1.
0 ↓ ↑
certain conditions a spin-guide may generate an almost
perfect (100%) spin-polarized current even when a mag- Here Π↑,↓ are the densities of states at the Fermi
net with a relatively low degree of spin polarization is level of the up and down spins, and τsf is the spin-
used. Moreover, in the spin-guide scheme spin polariza- flip scattering time. Eqs.(2) hold under the assump-
tionmaybetransmittedoverlargedistancesthatexceeds tion that the spin-flip mean free-paths lsf↑,↓= vF↑,↓τsf
significantly the spin-flip length in non-magneticmateri- (where vF↑,↓ are the Fermi velocities of the spin-up and
als. Finally,spin-guidesalloweasydetectionandcontrol spin-down electrons) exceed significantly the diffusion
ofthespinpolarizationand,asdiscussedbelow,theymay lengths l , i.e. lsf >> l ; otherwise, the problem
↑,↓ ↑,↓ ↑,↓
formthebasisforcreatingfastspin-polarizationswitches. should be studied within the kinetic equation approach.
A typical lengthscale on which the equilibrium between
the spin subsystems is established is the diffusive length
II. BASIC IDEA AND APPROACH λ=(σ τ /e2Π )1/2, where σ−1 = σ−1+σ−1.
0 sf 0 0 ↑ ↓
Note that we can find the currents in the spin-guide
without separation of the electrochemical potential into
A ”spin-guide” is a system consisting of a non-
the chemical (η) and electrical (ϕ) potential contribu-
magnetic conducting channel (wire or strip) wrapped
tions,i.e., µ =η +eϕ. These potentials canbe easy
around by a grounded magnetic shell (see Fig. 1). Un- ↑,↓ ↑,↓
obtained from the solution for µ when the screening
like the spin-filter, electric current flows here along the ↑,↓
radius is much shorter than the size of the spin-guide
interface,insteadofbeingnormalto it. Themainideais
(which is the case in reality). Then, from the condition
that nonequilibrium electrons with a particular spin po-
of electric neutrality, Π η +Π η =0, we have
larization (e.g., which coincides with the magnetization ↑ ↑ ↓ ↓
axis)leavepreferentiallythenon-magneticchanneltothe
magneticmaterial. Thereturnoftheseelectronsintothe
η =Π (µ −µ )/Π,
channel is prohibited because the outside magnetic shell ↑,↓ ↓,↑ ↑,↓ ↓,↑
boundaries are grounded. Consequently, a permanent
outflow of nonequilibrium electrons with a definite spin
eϕ=(Π µ +Π µ )/Π,
↑ ↑ ↓ ↓
polarizationisobtained,andanexcessofnonequilibrium
electrons of the other spin polarization appears in the
channel. Note, that the spin polarization of the current Π=Π +Π .
↑ ↓
in the channel is opposite to the spin polarization of the
currentflowinginthesurroundingmagneticshell,incon- The above equations should be supplemented by the
trast to the spin-filter geometry. imposedboundaryconditions. Letthex-axisbedirected
3
along the channel and lie in it’s middle, and take the z- to consider only the solution with the smallest value of
axistobeperpendiculartotheinterfacialplanes,withthe k. Thephysicalmeaningofk−1 isquiteobvious: itisthe
origin of the coordinate system located in the center of distanceinthex-directionwhichanelectronwilltraverse
theentranceintothechannel(seeFig.1). Thegrounding diffusively before it will reach the grounded contact.
of the outside boundaries is equivalent to the condition IngeneralthesolutionsgivenbyEqs.(3)arenotappli-
µ = 0. Taking into account the condition of electric cable at distances from the channel ends which are less
↑,↓
neutrality, we obtain η =ϕ=0. It would appear rea- than k−1. But, under the assumption that L >> k−1,
↑,↓
sonable to take the same potentials at the channel exit. and to the accuracy of our analysis, we may use these
(An excess of exit potential over the grounded bound- solutions even near the channel exit. As shown below
ariesisequivalenttoaninefficientremovalofenergyinto this amounts to a neglect of a preexponential factor in
the ground.) the expression for the current spin polarization.
Let an unpolarized current I be driven through the Beforeclosingthissection,letusconsideranothertype
channel entrance. We find that the spin-up and spin- ofsolution whichis validfor distances fromthe entrance
down current densities may be expressed as J = where spin-flip processes have not yet occurred. In the
↑,↓
−e−1σ ∂µ /∂x = I/2w. As we show below, at the absence of spin-flip Eqs.(2) for µ and µ become in-
N ↑,↓ ↑ ↓
level of accuracy to which we restrict ourselves in this dependent and a separation of variables can be accom-
paper, the result is insensitive to the type of boundary plished separately for each potential. Thus, we have
conditions that are imposed atthe end faces ofthe mag-
netic shell (grounding, or absence of current). We also µ↑,↓ =e−k↑,↓xf↑,↓, (5a)
assume that the conductivity in the non-magnetic chan-
nel σ is spin independent, and that the conductivity in with
N
each region is constant.
For the spin-guide model described above, the diffu- f =A cos(k z) at |z|<w/2,
↑,↓ ↑,↓ ↑,↓
sion equation can be solved exactly. Instead of quot-
(5b)
ing here the general solution (which is rather compli-
f =B sin(k (d/2−z)) at |z|>w/2.
cated) it is sufficient for our purpose to focus attention ↑,↓ ↑,↓ ↑,↓
on the solutions that hold far way from the ends of the
Fromthematchingconditionsatz =±w/2thefollow-
spin-guide. We also assume that the length of the non-
ing transcendental equations are obtained for the damp-
magnetic channel, L, is much larger then the width of
ing factors
the spin-guide, i.e. L ≫ d, and solve Eqs.(2) through a
separationofvariables,byintroducingthe newfunctions
µ =(σ µ +σ µ )/(σ +σ ) and µ =µ −µ .
+ ↑ ↑ ↓ ↓ ↑ ↓ − ↑ ↓ tan(k w/2)tan(k (d−w)/2))=σ /σ . (6)
↑,↓ ↑,↓ M↑,↓ N
Due to the symmetry of the system and the boundary
conditions at z =±d/2,we obtain the following solution
In the next section we use the above solutions Eqs.
(3) -(6) in the analysis of several limiting situations for
µ =e−kxf (z), (3)
± ± different spin-guide parameters.
where the functions f± are given by:
III. RESULTS
C cos(κ z), |z|<w/2,
f = N
− (cid:26)D sin(κM(d/2−z)), |z|>w/2, A. A fully polarized magnetic region
(4)
A cos(kz), |z|<w/2, A most effective implementation of the spin-guide in-
f =
+ (cid:26)B sin(k(d/2−z)), |z|>w/2, volves the use of a DMS with a very large Zeeman split-
tingasthemagneticenvironment,sothattheelectronsin
the magnetic material are fully spin-polarized. Clearly,
and spin-flip process in the magnetic region are precluded in
this case. For definiteness, let us assume that the mag-
κM,N = k2−λ−M2,N , netic shell is not transparentfor ”spin-up” electrons, i.e.
q
σ =0.
M↑
where λ is the diffusion length in the magnetic (M) Weconsiderthecasewhenthe spinpolarizationofthe
M,N
and non-magnetic (N) regions, respectively. Matching current in the channel is high enough, i.e. the width
the functions µ and the current (i.e. the derivatives of the non-magnetic channel w is less than the spin-flip
↑,↓
σ ∂µ /∂z)atz =±w/2,wecandetermine the values length λ . This situation is quite real; in particular,
↑,↓ ↑,↓ N
of the coefficients A,B,C and D (in terms of the value of we note that since the spin-flip process is of relativistic
one of them), as well as find the possible values of the origins it is characterized by a large spin-flip length in
dampingfactork. Toexponentialaccuracy,itissufficient non-magnetic semiconductors, i.e. up to 100 µm16,17.
4
For distances from the entrance short enough so that no scheme. For simplicity, we will neglect in the following
spin-flip processes have occurred, the current I will be spin-flip processes in the non-magnetic channel.
↑
conservedinside the channel(that is, it does not depend We consider first the case where we may neglect the
on x). On the other hand, the current of electrons with spin-flipprocessesinthemagneticshellneartheentrance
theoppositespindirection,I willdecreaseexponentially to the spin-guide. Then, according to Eq.(5), the spin
↓
with distance from the entrance into the channel, i.e. polarizationofthe currentinthe channelwilltendexpo-
I ∝exp(−k x). nentially to the unity,
↑ ↓
According to Eq.(6) we have k = 0, and k will de-
↑ ↓
pend on the ratio σ /σ . Accordingly, for σ = σ α≈1−e−(k↓−k↑)x. (11)
M↓ N M↓ N
the damping factor k = π/d. If the conductivity of
↓
Moreover, from Eqs. (10) and (6) we have k > k .
the magnetic shell is much higher than that of the non- ↓ ↑
magnetic channel, i.e. when σM↓ >> σN, the damping As shown in the previous section, k↓−1 6 d, and for
factortakesthevaluek↓ =min{π/w,π/(d−w)}. Conse- σM↑ ≪ σN thespin-upcurrentdecaysonalength-scale
quently, the spin polarizationofthe currentat the chan- which is large compare to d, i.e.
nel exit tends exponentially to unity with increasing L,
that is
σ
M↑
k =2 . (12)
α= I↑−I↓ ≈1−e−k↓L. (7) ↑ rσNw(d−w)
I +I
↑ ↓
Now we consider the role of spin-flip processes in the
Note that the difference between α and unity, which magnetic shell. As discussed above, the exponential de-
decreases for larger distances, is determined here only crease of the currents J (as a function of distance
↑,↓
within a pre-exponential factor. awayfrom the channel entrance) occurringwith the cor-
We turn now to analysis of the role of spin-flip pro- responding damping factors k , will be changed due to
↑,↓
cesses in the non-magnetic channel. Using Eqs.(3) and the spin-flip processes in such a way that both the up
(4) we obtain and down components of the current will decrease with
the same damping factor k. Assuming that the diffusion
k−1 =λN (8) of the electrons to the grounded boundaries occurs with
a faster rate than the spin-flip processes, i.e. that the
and
condition λ ≫(d−w) is fulfilled, we obtain (to a first
M
w(3d−2w) wd approximation) that the damping factor k is the same
1−α= ≤ ≪1. (9)
12λ2 λ2 as k↑ determined from the Eq.(6). The reason is that
N N
the overalldamping rate is governedby that component
Thus, the exponentialdecreaseof1−α (recallEq.(7)) whichtakesmoretimetoreachthegroundedboundaries.
is bounded below by the value given in Eq.(9). Conse- The spinpolarizationαwhicharisesatsuchlength-scale
quently, the spin polarization remains constant and suf- (measured from the channel entrance) can be found by
ficiently high for all distances away from the entrance. matching the solutions of Eq.(4) and expanding them in
However, both the spin-up and spin-down currents J terms of the small parameter. Thus, we obtain:
↑,↓
willdecayexponentiallywiththesamedampingfactork.
Thetotalcurrentwilldecayasthespin-upelectronssuc-
γ k(d−w)
ceedinleavingthenon-magneticchannelduetospin-flip 1−α= · −1 . (13)
processes. 2(1−γ2)(kλM)2 (cid:18)sink(d−w) (cid:19)
In conjunction with Eq.(6) for k =k , Eq. (13) deter-
↑
mines a high enough degree of the spin polarization:
B. A non-ideal magnetic region
1−α ≈ γ(d−w)2/λ2 (1−γ2)<<1.
M
Inthissection,wediscussthesituationwhenthemag-
neticshellwhichsurroundstheconductingnon-magnetic We remark that this inequality will be violated if γ is
channel is not fully polarized - in this case both spin-up too close to the unity, i.e. in this case our expansion is
and spin-down currents flow through the shell and spin- inapplicable.
flip processes are possible. The coefficient of selective In conclusion, we obtained that in the spin-guide
transparency of the magnetic shell is determined by the schemethe spinpolarizationofthecurrentmaybeprop-
relation agated over arbitrarily long distances, in contrast to the
spin-filter scheme where the transport length-scale is of
σ the order of the diffusion spin-flip length λ. There are
M↑
γ = <1. (10)
additionalessentialdifferencesbetweenthe twoschemes.
σ
M↓
Unlike the spin-filter scheme, the spin polarization α in
This parameter determines the upper bound value of the spin-guide does not depend on the ratio σ /σ .
M↑ N
thespinpolarizationα=(1−γ)/(1+γ)inthespin-filter Moreover, as may be seen from Eqs.(11) and (13) the
5
degree of spin polarization in the non-magnetic channel
canexceedsignificantlythedegreeofspinpolarizationin
the magnetic material.
In the case that λ ≫ d, a sufficiently high degree
M
of spin polarizationmay be achievedwhen the condition
γ(d−w)<<λ is fulfilled, i.e.
M
tan k (d−w) d−w
1−α=γ ≈γ <<1. (14)
2kλ λ
M M
If the magnetic shell is too thick, i.e. when γ(d −
w)/λ ≫ 1, then the spin polarization of the current
M
will be low.
As aforementioned, to increase the spin polarization
one should decrease the width of magnetic region. To
this end, the ballistic regime when (d−w)≪l , lsf
M↑ ↑,↓ FIG. 2: The spin-drag scheme. The semiconducting non-
is most favorable. A calculation which goes beyond the
frameworkofthediffusionapproachyieldsintheballistic magnetic (N) channels 1 and 2 are of widths w1 and w2,
respectively. respectively. The width of the magnetic (M)
limit the following result:
interlayeris dM.
l (d−w) l
M↓ M↓
1−α≈γ ln . (15)
λ2 (d−w)(l2 λ−2+1) The polarizations of the currents in channels 1 and 2
M M↓ M
are opposite to each other, and the total current in the
The logarithmic factor in this formula reflects an en- two channels is non-polarized. It is of interest to note
hancement of the spin-flip probability for electrons graz- that if channel 2 is sufficiently wide such that w ≪w ,
1 2
ing along a magnetic layer. thepolarizedcurrentswillbeequallydividedbetweenthe
channels,i.e. anentirelypolarizedcurrentJ =J /2will
↑ 0
appear in channel 1, with an equal value and opposite
IV. SPECIFIC EFFECTS AND POSSIBLE polarization to that in channel 2. In the derivation of
EXPERIMENTAL REALIZATIONS
Eq.(16) we have assumed that the potential applied at
the exit of channel 2 is the same as that applied at the
Inthis sectionwe considersomepossible experimental exitofchannel1(thelatterisdeterminedinourmodelby
schemes aiming at realization of the proposed transport thevalueofthecurrentJ ). Varyingthepotentialatthe
0
phenomena, and at direct observation of the spin polar- exitofchannel2,onecancontrolthecurrentpolarization
ization of the current flowing in a spin-guide. in the channels.
In case that the magnetic interlayer is not fully
polarized, but γ ≪ 1, the spin polarization deter-
A. Spin drag
mined by Eq.(16) is conserved at distances L < R,
where R = min{(rwσ /σ )1/2, λ } and
N M↑ N
We begin with a discussion of an alternative scheme r = min{d ,λ ,l }. Here we take into account
M M M↑
to the one discussed above, for obtaining the spin-guide the possibility that the propagation of the electrons in
effect onthe polarizationofthe electric current. This al- the magnetic interlayer is either diffusive or ballistic. If
ternative scheme is based on a new spin-drag effect that the magnetic interlayer is wider than the non-magnetic
canberealizedinageometryoftwosemiconductorchan- channels, i.e. d > w , w , then the Sharvin resis-
M 1 2
nels separated by a magnetic interlayer (see Fig. 2). tances of the exit constrictions of the system should be
Letanon-polarizedcurrententerintothenonmagnetic used in the expressions for α .
1,2
(semiconductor) channel 1. In the case of a fully polar- The above considerations lead us to suggest the cre-
izedmagneticinterlayerafullypolarizedcurrentwillap- ation of a fast switch of the spin polarized current,
pearinthesemiconductorchannel2duetothespin-filter achievedbycombiningthespindragschemewithelectro-
effect, i.e. |α2|=1. At the same time, a polarization α1 static gates at the exits of the channels one may switch
will appear in the first channel due to the spin-guide ef- thespinpolarizationofthecurrentatafastratewithout
fect,andit’smagnitudewilldependontherelativewidth switchingthemagnetizationofthemagneticmaterial. In
of the channels. If the thickness of the magnetic inter- the spin-filter scheme fast switching of the current spin
layer is taken to be less than the values of w1, w2 and polarization is unachievable even under the best condi-
L≫w1, w2 (where L is the channel length), we have tions,i.e. whenusingDMSstructures. Thisisbecauseof
the required applied high magnetic fields, and the com-
w2 paratively long relaxation times of the atomic magnetic
α = . (16)
1 w +2w moments. On the other hand, as mentioned above the
2 1
6
direction of the spin polarizationin the spin-guide is op-
positetothatappearinginthe spin-filterschemeatthe
samepolarizationofthemagneticmaterial. Therefore,it
maybepossibletocreateanalternativeswitchingscheme
thatcombinesthespin-filterandthespin-guideschemes
with controllable electrostatic gates.
B. Giant magnetoresistance and direct
measurement of the current spin polarization
Inthissectionwediscusscertainphysicaleffectswhich
could be utilized for the detection and measurement of
the current spin polarization.
Aspin-guideconsistingofaDMSmagneticshellshould
exhibit a giant magnetoresistance effect. The effect
is associated with the decrease of the conductance in FIG. 3: Schemeof theexperiment with a locking of thenon-
magnetic channel in a spin guide. G is an electrostatic lock-
the channel (to an essentially vanishing value) upon
switching-off of the magnetizing field; the reverse hap- ing gate, dM and w are the widths of the magnetic (M) and
non-magnetic(N)materials,thedoublehatchingindicatesthe
pens when the magnetizing field is switched-on, i.e. a
dielectric regions.
current appears in the channel. This is caused by the
factthatthedisappearanceofallthenonequilibriumelec-
trons at the grounded boundaries is faster then the rate
In this case the relative change of the current δI/I at
of their arrival to the channel exit. This effect may re-
locking of the channel is in direct proportion to the spin
sult in a most significant change of the resistance of the
polarization, α, and to the ratio w/d , where d is the
M M
devicewithamagnetizingfield,perhapsevenlargerthen
width of a magnetic layer (M).
the the giant magnetoresistance effect measured in the
spin-filter scheme12,18.
Iftheferromagneticmaterialwhichsurroundsthenon-
V. DISCUSSION
magnetic channel in a spin- guide is not fully polarized,
a giantmagnetoresistanceeffect maybe observedforthe
The main operational principle of a spin-guide is the
case of mutually opposite magnetizations of the upper
removalofoneofthecomponentsofthespincurrentfrom
andlowermagneticlayers(seeFig.1))toavoidtheresid-
the channel due to the selective transparency (with re-
ual magnetization. If the upper and lower magnetic lay-
spectto thespindirection)ofamagneticshell. Thespin
ers have the same magnetization then there is a current
polarization of the current increases with distance from
atthechannelexit,butiftheirmagnetizationsareoppo-
the channel entrance until spin-flip processes become
site then the current will essentially vanish. Therefore,
effective. Thus, in contrast to the spin-filter scheme,
by changing the applied magnetic field we may change
the spin polarization in a spin-guide can exceed signif-
the resistance of the device.
icantly the spin polarization of the current in the mag-
Another spin guide effect with may be observed by
netic material which surrounds the non-magnetic chan-
locking a non-magnetic channel far from the entry and
nel. In general, a spin-guide may generate an almost
exit by an electrostatic gate, as shown schematically in
fully (100%) spin-polarized current even if the magnetic
Fig. 3. In this case,the essentialvariationof the current
material which is used is not fully polarized. Even a
indicates on the effectiveness of the spin guide.
smalldifference betweenthe spin-up andspin-downcon-
At last, in spin-guide with blocked channel and fully
ductivities in the magnetic material (σ /σ < 1 in
polarized magnetic shell one can measure the spin- M↑ M↓
our case) would lead to a depletion of the current states
polarization α directly:
in the non-magnetic channel, with spin-down electrons
being affected over shorter distances from the channel
I(B 6=0) entrance than the spin-up electrons. In this case, the
α =1−
I(B =0) spin polarization will be determined by the difference of
the quantities in the exponent of Eq.( 11); consequently,
here I(B 6=0), I(B = 0) are currents at exit of spin- thespinpolarizationofthecurrentwilltendtoapproach
guide at switched-on and switched-off magnetized mag- the limiting value (i.e. 100%) further into the channel.
netic field correspondingly,both in case of locked gate. Atthisstage,certainissuespertainingtotheoperation
The spin polarization of the current in a spin-guide oftheproposedspin-guideschemewarrantcomment. We
with a DMS shell can be measured directly by locking begin by noting that though the spin polarization is ex-
a non-magnetic channel far from the entry and exit by pected to remain high even when a non-ideal magnetic
an electrostatic gate, as shown schematically in Fig. 3. materialis used, the total currentin the channelwillde-
7
crease with increasing channel length (see Eqs.(1), ( 3) an additional applied voltage to the tunnel barrier, then
and(5)). Thisoccursbecauseboththespin-upandspin- thebarriersactasadditionalfilters. Thoseelectronsthat
down electrons can leave the channel and thus reach the crossedthebarriersandunderwentaninelasticscattering
groundedcontact. Inthis contextwe note thatthere are in the magnetic shell are not capable to return backinto
ways to reduce significantly the loss of current, thus al- the non-magnetic channel. Consequently, the spin-flip
lowing its at transmission over a large distance. To this processes in the magnetic region will affect the current
end one may wish to use an alternation of the grounded spin polarization in the channel to a lesser extent.
and ungrounded sections of the magnetic shell along the Thus, there is a physical difference in the role of spin-
spin-guide. Alternatively, one may reduce the loss of to- flip between the two schemes. Spin-flip scattering in
talcurrentinthe channelby creatingtunnelbarriersbe- the magnetic shell of spin-guide leads mainly to a re-
tween the non-magnetic channel and the magnetic shell; duction of the total current, while the spin polarization
such barriers, however, will retard the exit of both elec- may change only by a small amount. The reverse situ-
tron polarizations to the grounded boundaries. ation occurs in the spin-filter scheme, i.e. the spin-flip
The polarizing ability of a spin-guide is limited only processes maintain the total current as a constant but
by the spin-flip processes. Here we should note, that the cause a significant reduction in the spin-polarization, as
role of spin-flip processes both in a non-magnetic chan- discussed in Section I.
nel and in the magnetic region of the spin-guide, differs Asevidentfromtheabove,thespinpolarizationofthe
in an essential way from the role of spin-flip processes currentin a spin-guide depends significantly both onit’s
in a spin-filter. First, let us consider spin-flip processes length and on the widths of the channel and the mag-
in the non-magnetic semiconductor only. In contrast neticshell. Hence,byvaryingtheseparametersitshould
to the spin-filter scheme, while spin-flip limits the spin- be possible to readily change and control the degree of
polarizationin the spin-guide, it can not destroy it fully. currentpolarizationatthe channelexit. In the following
Moreover, the spin polarization remains a constant and we provide some quantitative estimates concerning the
highenough,asfollowsfromEq.(9),forarbitrarilylarge degree of spin polarization that may be achieved in the
distance from the entrance. spin-guide scheme.
Next we consider the role of spin-flip in the magnetic Among the most promising candidates for the mag-
shellofaspin-guide. Generallyspeaking,theexitofelec- netic shell materialin a spin-guide are II-VI-DMSc com-
tronswithaspin“parallel”tothatinthemagneticregion pounds(likeaBexMnyZn1−x−ySe)orhalfmetalswhere
(spin-down in our case), from the non-magnetic channel one of the spin subbands can be fully pinned. Assuming
intothemagneticsurroundings(asaresultoftheirBrow- anon-magneticchannelwithλN =1.5µm(acasethatis
nian motion) is a harmless useful process. It is obvious farfrombeingoptimal),=0.3µmandd=0.4µm,weob-
that spin-flip scattering of these electrons will not re- tain according to the Eq.(9) a current spin polarization
duce the spin polarization in the non-magnetic channel. in the channel α = 100% (within a 1% accuracy) for an
However, spin polarization will be reduced due to the arbitrary distance from the entrance; the current ampli-
exit from the channel of spin-up electrons. They could tude will decay with λN, according to Eq.(9). Even for
change the spin polarization due to spin-flip scattering DMScompoundswhicharenotfullypolarized,employed
in the magnetic region and, subsequently, they could re- asthemagneticregion,wecanachieveahighspinpolar-
turn back in the non-magnetic channel. The spin-flip ization. For example, taking Zn0.97Be0.03Se as a NMS
probability could be decreased by reducing the width of (non-magnetic semiconductor) channel material, in con-
themagneticregion;thismethodofbringingaboutade- tact with a 45% polarized Zn0.89Be0.05Mn0.06Se as a
crease in the spin-flip probability is not possible for the DMS shell with a spin-flip length λ ≈ 20nm, yields
spin-filter scheme. In fact if the magnetic shell width is according to Eqs.(13) and (14) a 95% spin polarization
less than λ the sources of nonequilibrium spin concen- for a width of the magnetic shell (d−w) 6 10nm; for
M
trationat the entrance andthe exit of the currentin the (d−w)≈50nm we obtain a spin polarization α≈17%.
magneticregionwillmutuallycanceleachother,andthe Finally, a very high degree of spin polarization of the
polarizing ability of the magnetic filter will decrease sig- current may be achieved even if a ferromagnetic metal
nificantly,asobservedexperimentally11,12. Furthermore, shell (e.g., Ni , Fe or Py) is used in the spin-guide. Here
the high conductivity of the magnetic material in the oneshouldemploythinferromagneticfilms witha thick-
spin-guide scheme does not increase the spin-flip proba- ness that is less than the diffusion spin-flip length λM;
bility because it speeds up the transport of electrons to this is feasible even when λM is about several tens of
the ground contact. Unlike the spin-filter scheme, spin nanometers. Thus, when the ballistic regime is reached
polarizationinthespin-guide,α,doesnotdependonthe in the magnetic region, f.e. λM ≈ 20nm21,22, with
ratio σM↑/σN↑. We recall that the large ratio σM↑/σN↑ γ ≈ 0.6, d − w ≈ 8nm and λN ≈ 1.5µm, one ob-
, characteristic of the spin-filter “ferromagnetic metal- tains from Eq.(15) that α ≈ 100%, within the accu-
semiconductor”interface4,5,6,7,isoneofthemainreasons racy of the model. For rather thick film, such that the
forthe lowdegreeofspinpolarizationinthis scheme8. If diffusion regime is reached, with d = 60nm, w = 0.7d,
the spin-guide is used with tunnel barriers between the λM =20nm, we obtain from Eq.(13) α≈0.97%.
non-magnetic channel and the magnetic shell and with From the above we conclude that the spin-guide
8
scheme works most effectively if both the widths of the in a non-magnetic channel of a spin-guide may exceed
non-magnetic channel and the magnetic shell are taken significantly the spin-flip length in the material.
to be much less than the corresponding spin-flip length. (iii) Spin-flip processes in the magnetic shell restrict
Inviewofrealisticspin-fliplengthscales,wesuggestthat thepeakvalueofthespinpolarizationofthecurrentina
nano-scalestructureswouldbe mostappropriateforfab- spin-guide to a much lesser degree than in the spin-filter
rication of spin-guide devices; for example through the scheme.
use of nanowires and layers of nano-widths dimensions. (iv) Through the use of the spin-drag scheme (or by
combining the spin-guide and spin-filter schemes) with
electrostatic gates on the channel exits, it may be pos-
VI. SUMMARY
sible to control the spin polarization of the current and
to switch it easily and promptly, without magnetization
In this paper a spin-guide has been proposedas a new reversalof the magnetic shell.
type of source and a long-distance transmission medium (v) A very large magneto-resistanceeffect is predicted
of electric currents with a high degree of spin polariza- tooccur,whichshouldallowdirectsensingandmeasure-
tion. We have shown that spin-guide enhances signifi- ment of presence and degree of spin polarization.
cantlythecapabilitiesforgenerationandmanipulationof
spin-polarized currents. The main features of the spin-
guide scheme which make it a most promising tool for
VII. ACKNOWLEDGEMENTS
creationandtransportof spin-polarizedcurrents in non-
magneticsemiconductors,maybesummarizedasfollows:
(i) In a spin-guide, a permanent withdrawal of elec- The research described in this publication was made
trons of one spin polarization leads to an increase in the possible in part by Award No.UP2-2430-KH-02 of the
other spin polarization, thus allowing to achieve a high U.S. Civilian Research & Development Foundation for
degree of spin-polarization of the current, considerably the Independent States of the Former Soviet Union
exceeding the degree polarization in the magnetic shell. (CRDF), and by the US Department of Energy Grant
(ii)Thepropagationlengthofaspin-polarizedcurrent FG05-86ER-45234.
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