“orthospintronics” electronics with charge replaced by...
TRANSCRIPT
“Orthospintronics” ― Electronics with charge replaced by spin
Chia-Ren Hu (胡家仁)Texas A&M UniversityDepartment of Physics
Condensed matter physics seminar September 29, 2003
I. Introduction• “Spintronics” refers to all electronic applica-
tions and devices where the spin degrees of freedom of electrons are non-trivially utilized.
• A narrower definition, for which I coined the new term “orthospintronics”, is electronics with the electron charge replaced by the electron spin.
• All other spintronic applications and devices may then be called “paraspintronics”.
• Spintronics then refers to their combination.
In orthospintronics,
• A charge current I is replaced by a spincurrent Is ― meaning that spin-up and spin-down electrons are moving in opposite directions. Thus
I/A = n↑v↑ + n↓v↓ , Is/A = n↑v↑- n↓v↓ .• Also, electromotive force E (emf ) is replaced
by spinomotive force Es (smf ) ― meaning that spin-up and spin-down electrons receive forces in opposite directions, but of the same magnitude.
• One can define spinoresistance as:Rs = Vs /Is = Vs /(n↑v↑- n↓v↓)A,
or spinoconductance:Gs = Is /Vs = (n↑v↑- n↓v↓)A/Vs .
• And if Vs and Is are ac, we can even definespinocapacitance, via Is = Cs dVs/dt , or Qs = CsVs, where Qs = ÚIs dt = Q↑-Q↓.A conducting plate receiving Qs will become spin polarized, unless it has very strong spin relaxation, since Qs means spin injection.
• And spinoinductance, via Vs = Ls dIs/dt .
• For ac spin currents, one can also define: • A spinotransformer, which can cause step-
up or step-down of spinovoltage.• A spinorectifier, which can remove every
other half cycle of an ac spin current.• A spinotransistor, which is a three-terminal
device, containing a spin-current emitter, a spin-current collector, and a spin-current base, so that the emitter spin current can control the collector spin current, just like a usual transistor.
• etc., etc., etc.!
• The big challenge is to realize each of these components.
• By far the most important one to invent first is a source for (dc or ac) smf, which is the source of power for a spin circuit, since there will be dissipation for spin current in a conductor just like a charge current.
• Recently, there is a proposal for a semicon-ductor optical device to generate a dc smf.
[Q.-F. Sun, H. Guo, and J, Wang, Phys. Rev. Lett. 90, 258301 (2003).]
• In electronics, by far the most convenient and useful emf source is through induction ― via Faraday’s law .
• Also, induction can generate an ac emf, which is much more versatile than a dc emf.
• To generate an smf inductively, we need the magnetic analog of Faraday’s law, namely, the Ampére-Maxwell law:
,
where the Je term is not important here.
II. Inductive generation of ac or pseudo-dc smf. [C.-R. Hu, cond-mat/0308027]
• However, in order for an applied E(t) to reach every electron in a conductor, it is necessary to suppress screening. This can be done by fabricating a heterostructure:
• It is made of many conducting sheets (facing the y direction), each thinner than the screen-ing length.
• The conducting sheets should be separated by thick insulating sheets to prevent tunneling.
• External E(t) should be applied ^ to the con-ducting sheets (the y direction). To generate pseudo-dc smf, E(t) should vary with t as:
• Then the generated smf will vary in time as:
• This is what I mean by pseudo-dc.
• To generate an ac smf, let , then the induced ac smf in the x directionwill vary with time as: .
• (In general, we have .)• Why? Look at all spin-up electrons in just
one conducting sheet:• It is equivalent to a line of nega-
tive magnetic charge at the upper edge, and a lineof positive magneticcharge at the loweredge.
x
z y
• A positive will induce a magnetic field in the +xdirection on the upper edge, and in the -xdirection in the lower edge.
• Thus both lines of magnetic charges will receive a force in the –x direction.
• The total force on all magnetic charges is proportional to the total number of electrons. So it is actually a force acting on each elec-tron, and is in the –x direction.
H
y
x
H
z
• The spin-down electrons will receive a force in the opposite direction.
• Thus what has been induced is an smf. Its magnitude is simply the force per electron divided by e (to get the smf in volt), and then multiplied by Lx.
• Magnitude of this ac smf : Using the value of the Bohr magneton,
we find that if Lx = 10 cm, E0 = 106 V/m, and ω = 1012 Hz, then Es = 6.44× 10-5 V.
,
• Subtlety about the SI unit of magnetic dipole moment:
Dipole moment appears in such formulas as and , but magnetic
charge appears in the formula . So the Bohr magneton must still be multiplied by µ0, before it has the unit of magnetic charge times length.Only then should it be used in our formulas!
[J. D. Jackson, Classical Electrodynamics]
• Since ω = 1012 Hz already corresponds to a wavelength of about 2 mm, the film width along z should be less than 1mm, so that all electrons can see E in phase. So the applied E(t) should be a standing wave with its wave vector in the z direc-tion.
• There is no limitation to the width of the film along x, so it can be 10 cm or larger. Note than the induced smf is proportion-al to this length.
III. Electromagnetic detection of spin current (dc or ac).
• Spin currents along xin many parallel films corrospond to mag-netic charge currentalong +x in all lower film edges and along–x in all upper film edges.Together they generateE along +y.
Is
E
xy
z
Jm
Jm
E
• Magnitude (Sensitivity):The electric field is that generated by two op-posite magnetic current sheets at z = ±Lz / 2.
• For e(n↑v↑ - n↓v↓) =107 A/m2, d = 10t, the front factor is found to be 7.274×10-5 V/m.
• This is a weak field, but clearly detectible.• 107 A/m2 is a very large spin current, probably
not possible to generate with the induction method, but it can be generated. (See below).
• ∆V = Ú-∞∞ Ey(t) =
= 7.274×10-6 V, if Ly = 10 cm, t/d = 0.1.(Here t is thickness of each conducting sheet, and d is thickness of each insulating sheet.)
• Here ∆V can be dc or ac (at the same fre-quency as the input spin current).
• When it is ac, it may be possible to use a resonance technique to increase the sensiti-vity of its detection.
• Detecting this induced electric field or voltage is a sure confirmation of a spin current.
IV. The lead problem• At high frequencies,
one can probably just add two end conduct-ing sheets, and attachleads to them.
• At low frequencies, one needs to insert in-ductors between the conducting sheets and the leads, so that no charge can flow from one sheet to the next to achieve screening.
Is
E
xy
z
V. Spin Hall effect.• Definition: Transverse smf induced by a longi-
tudinal charge current.[J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999).][S. Zhang, Phys. Rev. Lett. 85, 393 (2000).][Sinova et al., cond-mat/0307663.] [D. Culcer et al., UT preprint.][S. Murakami et al., cond-mat/0308167. Science.]
• Replacing ∂D/∂t by Je in our previous discus-sion leads to a new source for spin Hall effect.
• All other sources proposed so far needs spin-orbit interaction, but not this one! Thus one can work with conductors with few spin-orbit scatterers, and not worry about spin diffusion.
Je
smf
• Remark 1:References
[Sinova et al., cond-mat/0307663.][D. Culcer et al., UT preprint.][S. Murakami et al., cond-mat/0308167. Science.]
also do not need spin-orbit scatterers, but they still need spin-orbit interaction, so the spin-Hall effect predicted by them occur in the hole bands of semiconductors, but the spin Hall effect predicted here exists also in the electron band of semiconductors, and also in all conductors!
• Remark 2:The spin Hall effect predicted here is a universal effect. It predicts a universal spin Hall conductivity with magnitude σs = e/µ0µB .
(The factor µ0 is needed if µB is given in J/T, and the factor e is needed if σs is measured in units of (Ω◊m)-1.)
• Magnitude of the present mechanism for spin Hall effect:With Je = 8.854×106 A/m2 along y, I obtainEs = 6.44×10-5 V along –x.
• No applied magnetic field is needed, unlike the usual Hall effect.
• Why no Es along z or -z? What broke the symmetry between x and z?Answer: Geometry. Need Lx >> Lz, then Es is in the –x direction.
x
Je
y
zJs
• Since no external electric field is involved, no screening problem needs to be solved.Thus to observe this spin Hall effect, one can use a bulk conductor of size Lx×Ly×Lz,with all dimensions macroscopic, as long as Lx>>Lz. One also needs Ly to be long, so
• Geometry really needed:
This is so that the generated H is along x.
Je
x
y
zJs or
smf
• We have emphasized that this new source for the spin Hall effect actually predicts a Universal spin Hall conductivity
σs = e/µ0µB = 1.3748×1010 (Ω◊m)-1,
or, equivalently, a Universal spin Hall resistivity
ρs = µ0µB/e = 7.2739×10-11 Ω◊m .
(The factor µ0 is needed here only because µB is given in units of J/T.)
VI. A controversy• So far, my calculations are classical and
macroscopic. This is a simple view. But the same results can also be obtained by doing the calculations microscopically, (but still classical,) by looking at one electron at a time.
• All one needs to realize is (a) the force formula F = (µ◊—)H on each magnetic dipole, and (b) a moving magnetic dipole field generates an electric field, which is a consequence of special relativity.
• So far, no controversy. But many recent works on spin Hall effect are based on quantum me-chanical linear-response calculations. They concluded that without spin-orbit scattering or interaction, there can be no spin Hall effect!
• The mechanism for spin Hall effect presented here does not need any spin-orbit interaction!
• Partial resolution: The quantum mechanical linear-response calculations must begin with a Hamiltonian, not a force formula. So they used the Zeeman energy plus the spin-orbit energyas the starting Hamiltonian.
• Lorentz force formula on a charge q:F = q (E + v×B) .
• Magnetic analog on a magnetic charge qm: Fm = qm (H − v×D) .
• A magnetic dipole µ is qm and -qm separated by d, with the limit qm d → µ taken.
• So the force formula for a magnetic dipole is:Fµ = (µ◊—)(H − v×D) + D×(ω×µ) ,
where the last term has often been given as D×(∂µ/∂t). [O. Costa de Beauregard, Phys. Lett. 24A, 177 (1967);
S. Coleman and J. H. van Vleck, Phys. Rev., 171, 1370 (1968); W. Shockley and R. P. James, Phys. Rev. Lett. 18, 876 (1967); A. S. Gold-haber, Phys. Rev. Lett. 62, 482 (1989), which gives also the first term.]
• How does this force formula for a magnetic dipole related to Zeeman + spin-orbit terms in the Hamiltonian?
• If the dipole is neither moving nor rotating, the only surviving term in Fµ is (µ◊—)H . Using the vector identity µ×(—×H) = —(µ◊H) − (µ◊—)H , one finds Fµ = —(µ◊H)− µ×(Je+∂D/∂t) .
• The first term is just the force due to the Zeeman energy. The second term gives the new source for spin Hall effect, and the third term gives the inductive generation of smf.
• They are not related to spin-orbit interaction!
VII. Miscellaneous Remarks• A simple way to obtain spinocapacitor,
spinoinductor, spinorectifier, etc., that have two terminals, is to use 100% spin-polarized conductors to separate the spin-up current and the spin-down current, and then insert usual capacitors, inductors, rectifiers, etc., in the two branches.
↑
↓Js
• Spinotransformer is a four-terminal device, but it can be similarly designed.
• Spinotransistor is a three-terminal device, but it can also be similarly designed.
spinoemitter
spinobasespinocollector
spinoprimaryspinoprimary
spinosecondary spinosecondary
• There is also another simple way to design a device for generating a high-frequency acsmf, and it is no longer limited to weak mag-nitude:
L
spin-polarized conducting wire
spin-unpolarized conductor
C
E
large inductor
large capacitor
high frequency ac emf
spin-unpolarizedconducting wire
How it works:1. The high-frequency ac emf E generates I↑ and I↓
in the spin-polarized wires connected to it. 2. We expect I↑ = n↑ev and I↓ = n↓ev. Thus as
long as n↑ ≠ n↓, we have Is ≠ 0, since I = (I↑+ I↓), and Is = (I↑− I↓).
3. The charge current I will take the path of the large capacitance C, since it gives practically no impedance. It cannot flow through the inductor.
4. The spin current Is will take the path of the induc-tance L, since it gives practically no spinoimpe-dance. It cannot flow through the capacitor.
5. Thus an ac smf is generated inside the unpolar-ized conductor!
VIII. Summary• We showed that there are (a) an inductive way
to generate an smf, (b) an elecromagnetic way to detect a spin current, (c) a new source for a universal spin Hall effect. They are all weak effects, but large enough for some purposes, and the predicted universal spin Hall effect is comparable to other sources of this effect.
• Much more work is needed to generate prac-tically useful devices from these ideas, but it surely is fun to think about this “charge circuit – spin circuit” parallelism!