Giant dynamical Zeeman split in inverse spin valves

0.09 MB·English

by  X. R. Wang

Giant dynamical Zeeman split in inverse spin valves
X. R. Wang
Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
(Dated: February 2, 2008)
The inversion of a spin valvedevice is proposed. Opposite to a conventionalspin valveof a non-
magneticspacersandwichedbetweentwoferromagneticmetals,aninversespinvalveisaferromagnet
sandwiched between two non-magnetic metals. It is predicted that, under a bias, the chemical
potentials of spin-up and spin-down electrons in the metals split at metal-ferromagnet interfaces,
8
a dynamical Zeeman effect. This split is of the order of an applied bias. Thus, there should be
0
no problem of generating an eV split that is not possible to be realized on the earth by the usual
0
Zeeman effect.
2
n PACSnumbers:
a
J
Spintronicsbecomesanemergentsubfieldincondensed SUandSDelectronsforahalf-metalisillustratedbythe
1
1 matterphysicssincethe discoveryofgiantmagnetoresis- middlediagramofFig. 1b. UnderabiasV,SUelectrons
tance in 1988 by Fert[1] and Grunberg[2]. Spintronics in M1 flow into the empty SU electron states in M2 via

] is about the control and manipulation of both electron the empty SU electron states in the half-metal, shown
l
l charge and electron spin. Many interesting phenomena pictorially by the curved arrows in Fig. 1b. The flow of
a
h arerelatedtothe interplaybetweenelectronspinandits the electrons creates chemical potential differences (∆µi
- charge degrees of freedom. For example, electron trans- in Fig. 1b) between SU and SD electrons in both M1
s portcanbemanipulatedbythemagnetizationconfigura- and M2 near the metal-ferromagnetinterfaces.
e
m tions. Thisisthebasisofgiantmagnetoresistance[1,2,3]
and tunneling magnetoresistance[4, 5] phenomena and V
.
t devices. Its inverse effect, known as spin-transfer torque
a (STT)[6,7,8],wasalsodiscovered. TheSTTopensanew M1 HM M2
m
way to manipulate magnetizationother than a magnetic (a)
- E E
d field[9], which has been much of recent focus in the field
n due to its potential applications in information storage ∆µ1 E ∆V
o industry. ∆µ
2
c
[ In this letter, an inverse spin valve structure of a fer- DOS
romagnet sandwiched between two non-magnetic metals M1 HM DOS
1 is studied when a bias is applied to the device. Due to (b) M2
v
the spin-dependent electron transport of the structure,
5
the chemical potentials of spin-up (SU) and spin-down
7
FIG.1: Schematicillustrationoftheinversespinvalve(a)and
7 (SD) electrons at the metal-ferromagnet interfaces split
relative chemical potentials of spin-up and spin-down elec-
1 by the magnitude of an applied bias. We term this split
trons in nonmagnetic metals and half-metal (b). The curved
. dynamical Zeeman effect. This split can be of the order
1 arrows indicate the electron flow. ∆µ1 and the ∆µ2 are the
ofeV ifpropermaterialsareused. Tointroduceasimilar
0 chemicalpotentialsplitsbetweenspin-upandspin-downelec-
8 splitbythe usualZeemaneffect, amagneticfieldunreal- trons at the left and right metal-ferromagnet interfaces. ∆V
0 izable on the earth is required. Thus, a giant dynamical is theeffective bias on thehalf-metal.
: Zeeman effect is predicted.
v
i A conventional spin valve is a layered structure of a In order to understand why the chemical potentials of
X
non-magnetic spacer sandwiched between two ferromag- SU and SD electrons at the M1−HM and M2−HM
r
a netic metals. The spinvalve is calleda giantmagnetore- interfaces split under a bias, let us consider an extreme
sistance device if the spacer is a normal metal while it case in which spin relaxation time in both M1 and M2
is a tunneling magnetoresistance device for an insulator is infinite long (no spin relaxation so that SU and SD
spacer. Theelectrontransportofaspinvalvedependson electrons are isolated from each other). Since electron
therelativepolaritiesofthetwomagnets. Aninversespin transport in a nanostructure depends on how a bias is
valveisalsoalayeredstructurewithaferromagnetsand- applied[10], we assume, to be precise and without losing
wiched between two non-magnetic metals as illustrated generality, that the electron chemical potential in M1
in Fig. 1a. M1 and M2 are two normal metals with is initially moved up by eV while that of M2 is kept
identical SU and SD electron density of states (DOS) as unchanged. Initially, SU electrons flow into the empty
depicted schematically in the left and right diagrams of SU electronstates in M2 because the half-metal prevent
Fig. 1b. To simplify our analysis, a half-metal (HM) SD electrons from flowing. The same amount electrons
spacer is considered first so that only electrons of one will be pumped back from M2 to M1 by a battery to
typeofspins(spin-up)canpassthroughit. TheDOSsof keep the electron neutrality in M1 and M2. However, a
2
batterydoesnotdistinguishelectronspin,andasaresult (I+I’)/2 Reservoir of I Reservoir of (I+I’)/2
it will pump equal amount of SU and SD electrons. In SU electrons SU electrons
other words, SU electrons flow out of M1 and into M2
I I
via the half-metallic spacer. In the meanwhile, an equal 1 2
amount of electrons with half of them being in the SU Reservoir of I’ Reservoir of
(I+I’)/2 SD electrons SD electrons
state andthe otherhalfin the SD state aredrawnoutof (I+I’)/2
M1 M2
M2andaresuppliedintoM1bythebattery. Asaresult,
M1accumulatesmoreSDelectrons,andM2accumulates
more SU electrons. Thus, the chemical potential of the I+I’ I+I’
Battery
SD electrons will be higher than that of SU electrons
in M1. Vice versa, the chemical potential of the SU
electronswillbe higherthanthatofSDelectronsinM2.
The chemical potential splits keep increasing until the FIG. 2: Schematic illustration of current flow from and into
spin-up and spin-down states in M1 and M2. At the steady
chemical potential of SU electrons in M1 equals that in
state, current flowing into any reservoir should be equal to
M2. At this point, the steady state with no current in
those flowing out.
thecircuitisreachedandchemicalpotentialsplitsinM1
and M2 are established with ∆µ1+∆µ2 =eV.
Thespinrelaxation[11]alwaysexistsinamaterial,and and converting themselves into SU electrons. Let τ1 and
the magnitude ofthe chemicalpotentialsplit for SU and τ2 be the spin flipping time (spin-relaxationtime T1[11])
SD electrons depends sensitively on the spin relaxation. in M1 and M2, corresponding to the flipping rate of
This sensitivity can be seen from another extreme case 1/τ1 and 1/τ2, respectively. Due to the conversionof SD
thatthe spinflipping issofastthatSUandSDelectrons electronstoSUelectronsthatistheproductoftheexcess
can be converted into each other any time at no cost SD electrons n1∆µ1ξ1A and the single electron flipping
(meaning SU and SD electrons are at equilibrium with rate,thecurrentfromSDreservoirtoSUreservoirinM1
respecttoeachothersatalltimesinM1andM2). Thus, is
itisimpossibletocreateanychemicalpotentialdifference
for SU and SD electrons in M1 and M2. The reality, of I1 = n1∆µ1eξ1A, (2)
course,issomewhereinbetween(thetwoextremecases). τ1
The spin relaxation time of a real material is finite, and
wheren1 isthedensityofstatesofSDelectronsinM1at
it depends on the strength of spin-orbital coupling, hy-
the Fermi level. A is the cross section of M1. Similarly,
perfineinteractionandotherinteractionsthatcausespin
the current due to the conversion of SU electrons to SD
flipping. In order to include the spin relaxation time
electrons in M2 is
quantitatively, consider an ideal model at zero tempera-
ture. Assumethespinflipoccursonlyneartheinterfaces n2∆µ2eξ2A
I2 = . (3)
withinawidthofspindiffusionlengthξ1 inM1andξ2 in τ2
M2. This is justified because both SU and SD electrons
At the steady state, there is no net electron build up
intherestpartsofthecircuit(otherthanthehalf-metal)
anywhere in the circuit. Since the current through the
should have same chemical potential. Thus number of
battery is unpolarized, spin-up electrons will be mixed
electrons flipped from up-spin state to down-spin state
up with spin-down electrons and be pumped by the bat-
is the same as that from down-spin to up-spin. Further-
tery fromM2 into M1. Thus, the SU electrons make up
more, let us assume the resistance of the half-metal is R
half of the current while other half is made up from the
(forSUelectrons,the resistanceforSDelectronsisinfin-
SD electrons, and the balancing conditions and external
ity due to the half-metallic nature of the middle spacer).
constraint require
The equations of the motion of the device can be ob-
I1 =I/2,
tained by considering electron flow diagram of Fig. 2.
There are two reservoirsin M1 and M2 each. One is for I2 =I/2, (4)
SU electrons, and the other is for SD electrons (denoted ∆µ1/e+∆µ2/e+∆V =V.
by rectangular boxes). SU electrons in M1 can flow into
SolvingEqs. (1),(2),(3),and(4),thedynamicalZeeman
SU electron reservoir of M2. The current I depends on
resistance R and chemical potential difference ∆V (Fig. split ∆µ1 and ∆µ2 are
1b) of SU electrons in M1 and M2, (eV)τ1/(n1e2ξ1A)
∆V ∆µ1 = 2R+τ1/(n1e2ξ1A)+τ2/(n2e2ξ2A),
I = R . (1) (eV)τ2/(n2e2ξ2A)
∆µ2 = 2R+τ1/(n1e2ξ1A)+τ2/(n2e2ξ2A). (5)
If one neglects the direct tunneling of SD electron from
′
M1 to M2 throughthe half-metal (I =0 in Fig. 2), SD ItisinterestingtoseethatthelargestdynamicalZeeman
electrons can only go to M2 by first flipping their spins split occur at R = 0, a short circuit for spin-up (SU)
3
electrons! In this particular case, one, of course, needs It is interesting to notice that a large spin-dependent
to use metals with propermaterialparameterssuchthat chemical potential difference means a large dynamical
currentdensityisnottoolargetocausethemetalbreak- magnet. For ∆µi = 1eV and a typical electron den-
ing down by heating. Further discussions on this issue sity of states of 1022eV−1cm−3 for a metal, the dynami-
are given soon. cal magnetizationis about 105A/m which is comparable
The half-metal may be replaced by a usual ferromag- withmanymagnets. ThusonecanuseMOKE(magneto-
netic metal. In this case, SD electrons in M1 can also opticalKerreffect)to‘see’thedynamicalmagnetization.
′
flow directly into M2, contributing an extra current I Uponverificationofthisdynamicalmagnetism,itshould
to the circuit be interesting to explore the potential applications of
this electric-field controlled magnet. Another possible
V
I′ = , (6) applicationofthepredictedphenomenaispolarizedelec-
R′ tron/lightsource[12]. Sinceelectronsofonetypeofspins
′ occupy higher energy levels than those of the opposite
where R is the resistance of ferromagnet for SD elec-
spin,the predictedeffectcanbe usedas apolarizedelec-
trons. Without losinggenerality,the minority carriersof
tron source, or light source when the electrons flip their
theferromagnetareassumedtobetheSDelectrons,and
′ spins and emitted well-defined polarized photons. Thus,
R isalsoassumedtobelargerthanR. Thechemicalpo-
thephenomenoncanbeusedtomaketunablelightemit-
tential difference of SD electrons in M1 and M2 equals
ting diode or laser in very wide frequency range. The
V as it is shown in Fig. 1b. Eq. (4) should be modified
large chemical potential difference may also be used to
accordingly as
enhance electron magnetic resonance signal. The elec-
I1 =(I −I′)/2, tron magnetic resonance is useful in probing material
I2 =(I −I′)/2, (7) propertiesinvarioustechnologieswithwideapplications,
including imaging in information processing.
∆µ1/e+∆µ2/e+∆V =V.
It should be pointed out that we have not considered
′
Thissetofequationswithnon-zeroI canbe solved,and
the spatial distribution of the chemical potential split.
thedynamicalZeemansplit∆µ1and∆µ2,incomparison Ourresultsmaybemodifiedquantitatively,butnotqual-
with that of half-metal case, are reduced by a factor of
itatively, when the detailed distribution is taken into ac-
(1−R/R′)
count. This is because a factor characterized the dis-
eV(1−R/R′)τ1/(n1e2ξ1A) tribution should be added to equations (3) and (4). It
∆µ1 = 2R+τ1/(n1e2ξ1A)+τ2/(n2e2ξ2A), sshpoliutlrdepaolsrotebdehneroeteids dtihffaetretnhtefrgoiamntthdeysnpalmiticinalthZeeeDmOaSn
eV(1−R/R′)τ2/(n2e2ξ2A) of a ferromagnet. In the usual ferromagnets, electron
∆µ2 = 2R+τ1/(n1e2ξ1A)+τ2/(n2e2ξ2A). (8) DOS is spin dependent, but the chemical potential of
both SU and SD electrons are the same at the equilib-
One should not be surprised about this reduction from rium. However, the dynamical Zeeman split predicted
our early explanations of the origin of this split. Ob- here occurs inside a non-magnetic metal where the elec-
viously, previous results Eq. (5) are recovered when tronDOSis spin-independent, butthe spin-upandspin-
R′ = ∞. Also, there are no chemical potential splits in down electrons fill their DOSs to different levels, leading
′
M1 and M2 when the spacer is non-magnetic (R=R). to a chemical potential difference.
Therefore,agoodhalf-metal(goodconductorforthema-
jority carriers and good insulator for the minority carri- In conclusion, we propose an inverse spin valve struc-
ers)shouldbeusedifonewantstomaximizethesplit. In ture consisting of a ferromagnet sandwiched between
the following discussion, R′ =∞ case is considered only. two normal metals. Under a bias, we predicted a gi-
Theconventionalwayofintroducinganenergysplitfor ant dynamical Zeeman split of the chemical potential
SU and SD electrons is through the Zeeman effect. Due for spin-up electrons and spin-down electrons at metal-
tothesmallvalueofBohrmagneton,anorderof10T field ferromagnet interfaces. This prediction is yet to be con-
can only induce about 1meV energy split. However, the firmed by experiments.
dynamicalZeemansplitpredictedherecouldeasilybeof
the order of 1eV, a truly giant Zeeman effect. Compare The author would like to thank Prof. Yongli Gao and
with the static Zeeman effect, this split is equivalent to Prof. John Xiao for the useful discussions. This work
a field in the order of 104T,an impossible magnetic field issupportedbyUGC, HongKong,throughCERGgrant
on the earth! (# 603007 and SBI07/08.SC09).
[1] M.N. Baibich, J.M. Broto, A. Fert, F.N. Van Dau, F. Chazelas, Phys. Rev.Lett. 61, 2427 (1988).
Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. [2] G. Binach, P. Grunberg, F. Saurenbach, and W. Zinn,
4
Phys.Rev.B 39, 4828 (1989). [9] Z.Z. Sun, and X.R. Wang, Phys. Rev. Lett. 97, 077205
[3] R.F.C.Farrow,C.H.Lee,andS.S.P.Parkin,IBMJ.Res. (2006); Phys.Rev.B 71, 174430 (2005); ibid73, 092416
Dev.bf 34, 903 (1990). (2006);ibid73,(2007);T.Moriyama,R.Cao,J.Q.Xiao,
[4] T.MiyazakiandN.Tezuka,J.Magn.Magn.Mater.139, J.Lu,X.R.Wang,Q.Wen,andH.W.Zhang,Appl.Phys.
L231 (1995). Lett. 90, 152503 (2007).
[5] J.S. Moodera et al., Phys. Rev.Lett. 74, 3273 (1995). [10] S.D.Wang,Z.Z.Sun,N.Cue,H.Q.Xu,andX.R.Wang,
[6] J.C. Slonczewski, J. Magn. Magn. Mater. 159, L1-L7 Phys. Rev.B 65, 125307 (2002).
(1996). [11] X.R. Wang, Y.S. Zheng, and S. Yin, Phys. Rev. B 72,
[7] L. Berger, Phys.Rev.B 54, 9353 (1996). R121303 (2005).
[8] X.R. Wang, and Z.Z. Sun, Phys. Rev. Lett. 98, 077201 [12] X.R. Wang, unpublished.
(2007).