Hot electrons in magnetic point contacts as a photon source

0.18 MB·English

by  A. M. Kadigrobov

Hot electrons in magnetic point contacts as a photon source
A. M. Kadigrobov,1,2 R. I. Shekhter,1 S. I. Kulinich,1,3 M. Jonson,1,4,5 O. P. Balkashin,3
V. V. Fisun,3 Yu. G. Naidyuk,3 I. K. Yanson,3 S. Andersson,6 and V. Korenivski6
1Department of Physics, University of Gothenburg, SE-412 96 G¨oteborg, Sweden
2Theoretische Physik III, Ruhr-Universit¨at Bochum, D-44801 Bochum, Germany
3B. I. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Avenue, 61103 Kharkov, Ukraine
4School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK
5 Division of Quantum Phases and Devices, School of Physics, Konkuk University, Seoul 143-701, Korea
1 6Nanostructure Physics, Royal Institute of Technology, SE-106 91 Stockholm, Sweden
1
(Dated: January 17, 2011)
0
2 We propose to use a point contact between a ferromagnetic and a normal metal in the presence
of a magnetic field for creating a large inverted spin-population of hot electrons in the contact
n
core. The key point of the proposal is that when these hot electrons relax by flipping their spin,
a
J microwave photons are emitted, with a frequency tunable by the applied magnetic field. While
point contacts is an established technology their use as a photon source is a new and potentially
4
very useful application. We show that this photon emission process can be detected by means of
1
transport spectroscopy and demonstrate stimulated emission of radiation in the 10-100 GHz range

] for a model point contact system using a minority-spin ferromagnetic injector. These results can
l potentially lead to new typesof lasers based on spin injection in metals.
l
a
h PACSnumbers: 42.55.Ah,42.55Rz,73.63.Rt
-
s
e
m Introduction — Point contact spectroscopy detects re- means of anexternalmagnetic field throughthe Zeeman
laxationofhotelectronsinasmallregionofalargesam- splitting of the spin-up and spin-down energy subbands
.
t ple and is a well known method for studying elementary on the normal metal side of the contact. We show ad-
a
m excitations in metals.15 By using this method the spec- ditionally that for realistic magnetic point contacts the
tral properties of, e.g., phonons and magnons can be ex- spin-flipradiationproducedcanbedetectedbymeansof
-
d tracted from the bias-voltage dependence of the current conventionalpoint contact spectroscopy.
n flowing through the point contact and, in particular, its We will first present our model and start with the
o component due to the inelastic backscattering of elec- formalism used for analyzing the transport through the
c trons in collisions involving large momentum transfers. modelpoint contactshownin Fig. 1. The relative weak-
[
Whether the point contact geometry can be used to ness of the electron-photon interaction allows us to pro-

1 makeametalbasedlaser2 is aninterestingquestionthat ceed in two steps. In the first step we calculate the spin
v we explore in this Letter. For this to be possible it is populationsfortheelectronsinthecontactregion,toze-
2 necessaryto show that photons canbe emitted as a con- rothorderintheelectron-photoninteractionstrength. In
6
tinuous flow of hot electrons relax in the contact region the secondstep we find the photocurrentin the presence
8
2 and, specifically, that stimulated photon emission leads of radiation as well as the resulting change in the point
. to a greatly enhanced radiation intensity. This is what contact resistance, to first order in the electron-photon
1
we will do in what follows. interaction.
0
Formalism — In order to calculate the electrical cur-
1 Point contact spectroscopy can not be applied to
rent and the spin accumulation one needs to find the
1 studying of electron-photon interactions directly, since
v: themomentumofphotonsisverysmall. However,byus- electron distribution function fσ(sp) on either side of the
i ing a point contactbetween a ferromagnetand a normal contact,i.e., inthe ferromagnet(s=1)andinthe normal
X metal (or between two ferromagnets) the electron spin metal (s=2), for both spin projections σ/2 (σ = ±1) as
r comesintoplaythroughspin-polarizedinjection3–9. The a function of position r and electron momentum p. In
a
spin-splitenergybands ofthe injected electronscanlead eachof the metals these functions satisfy the Boltzmann
to the emmision of photons when the electrons undergo equation
spin-fliprelaxation,essentiallywithnochangeinthemo-
mentum. Since the resistance of spin-up and spin-down v(s)∂fσ(sp) −e∂Φ(s)∂fσ(sp) + fσ(sp)−hfσ(sp)i
channels in magnetic point contacts is different, both σ ∂r ∂r ∂p τ(s)
σ
emission and absorption of photons caused by spin-flip
=σw(s){f(s),f(s)}; s=1,2. (1)
inter-channeltransitionsaffectsthetotalcurrentthrough ph ↑p ↓p
the contact and, therefore, is detectable by transport
spectroscopy. Here v(σs) is the electron velocity in each metal, which is
given by a momentum derivative of the electron energy
Belowweshowthatavoltage-biasedpointcontactbe-
tweena ferromagnetand a normalmetalcanbe usedfor as v(σs) = ∂Eσ(s)(p)/∂p, where Eσ(1)(p) = ε(1)(p)−σJ1
generatingphotonswithafrequencythatcanbetunedby and E(2)(p) = ε(2)(p)+σµ H both contain a spin in-
σ B
2
between metals 1 and 2 can be written in the form
.. . .. . . . . .. . hw.. .. .. fσ(1p) =(1−Dσ)fσ(1p)R +Dσfσ(2p)T
1.. M. . . .. .. . . . .H. ..2 . where Dσ f=σ(2p)D=σD(pσ,fpσ(T1p))T +is(t1h−e Dspσi)nf-σd(2pe)Rpendent tran(3s)-
. parency of the interface; p = (p , p ) and p =
k z R
(p , −p ) (here p = (p ,p )) are the momenta of the
k z k x y
incidentandreflectedelectrons,respectively;themomen-
FIG.1: Diffusivepointcontactunderirradiation(notshown) tum of the transmitted electronp is determined by the
T
in the presence of a static magnetic field H. A voltage bias conditionoftheenergyconservationE1,2(p)=E2,1(p ).
V injectsaspinpolarizedcurrentfromaferromagneticmetal σ σ T
Awayfromthecontactregionthecurrentspreadsover
(1) with magnetic moment M into a normal metal (2). An
a large volume so that its density decreases and the
electron with its magnetic moment up (spin-down) is shown
electron system is essentially in equilibrium at distances
to move along a diffusive trajectory from metal 1 to metal
2 (red line) where it resonantly interacts with the irradia- |r|≫d. In oursimplified geometrywe willthereforeuse
tion field, which results in a spin flip and the emission of a the additional boundary conditions f(1,2)(z =±L/2) =
σp
photon. The electron continues along its diffusive path with n (E(1,2)(p)) where n is the Fermi distribution func-
the magnetic moment down (blue line) thereby changing the F σ F
tion and the z-axis is directed along the point contact.
spin-dependentcontact resistance.
Wewillnowsolvetheelectron-photonscatteringprob-
lem formulated above in the weak scattering limit char-
dependent kinetic energy term ε(s)(p). For convenience acterized by d/lph ≪1, where lph is the electron-photon
of notation, σ = +1 and σ = −1 here and below corre- scatteringlength. This allows us to solve the Boltzmann
spondtothe directionsofthe electronmagneticmoment equations (1) by perturbation theory, where w(s), f(s),
ph σp
parallel and antiparallel to the magnetization direction and Φ(s) are expanded in powers of the small parameter
inthe ferromagnet(s=1),respectively(that is the elec-
d/l . We will first solve the problem to zeroth order in
ph
tron magnetic moment projections in the ferromagnet
d/l ,whichallowsustofindthedensityofhotelectrons
ph
are m(σ1) = µBσ/2). The spin dependence of the energy with an inverse spin population in the contact region,
in the normal metal (s=2) is due to a static external andthensolveforthephotocurrenttofirst(linear)order
magnetic field H and the associated Zeeman energy gap in d/l .
ph
2µBH (here and below we assume the electron g-factor Spin accumulation — In order to solve the kinetic
g = 2), while the much stronger spin-dependence in the equations (1) to zeroth order in d/l we generalize the
ph
ferromagneticmetal(s=1)isduetothe exchangeenergy proceduredevelopedinRefs.10–12toallowforspindepen-
J1 (the Zeeman energy can be neglected here). Further- dentelectrondynamics. Tozerothorder,thedistribution
more τσ(s) =l0/|v(σs)| is the elastic relaxation time and l0 functions fσ(sp) can be written as
is the elastic mean free path of the electrons in the dif-
fusive transport regime considered in this paper, Φ(s) is f(s) =α(s)n E(s)(p)+eφ (r)−eV/2
the electric potential in the respective metal and the no- σp σp F σ 0
(cid:16) (cid:17)
tation h...i implies an averageof the bracketed quantity +(1−α(s))n E(s)(p)+eφ (r)+eV/2 , (4)
σp F σ 0
over the Fermi surface. (cid:16) (cid:17)
The amplitude of the electromagnetic field irradiating
the point contact is assumed to be large enough to al- whereα(σsp)(r)istheprobabilitythatanelectronemanat-
low the electron-photon interaction to be treated semi- ing from far inside the ferromagnet (z = −∞) diffuses
classically,sothatthecollisionintegralinEq. (1)canbe elasticallytoreachpointr inmetalswithmomentump;
written as the concrete form of the electrical potential φ0(r) inside
the pointcontactisnotimportantinthe limiteV ≪ε .
2π F
wp(sh){f↑(ps),f↓(ps)}= ~ |µBhac|2 f↓(ps)−q −f↑(ps) × The distribution functions fσ(2p) are sketched in Fig. 2.
h i
To linear order in the parameter l /d ≪ 1, it fol-
δ E↑(s)(p)−E↓(s)(p−q)−~ω (2) lows from Eqs. (1) and (3) that this0 probability can
(cid:16) (cid:17)
beexpressedasα(s) =hα(s)i−l (v /|v|)dhα(s)i/dz. The
Here h is the magnetic amplitude of the electromag- σp σp 0 z σp
netic waacve of frequency ω and momentum |q| = ~ω/c isotropic part of α(σsp) satisfies the diffusion equation
thatirradiatesthepointcontact;cisthevelocityoflight.
To facilitate explicit calculations we will consider a d2 hα(s)i=0, (5)
simplified contact geometry, approximating the point dz2 σp
contact by a cylindrical channel of length L and diam-
eter d, with L ≫ d ≫ l0. The boundary conditions for with the boundary conditions hα(σ1p)(z =−L/2)i=1 and
the electron distribution functions f(s) at the interface hα(2)(z =L/2)i=0; in the vicinity of the F/N interface
σp σp
3
f (2) Using Eqs. (4), (7), and (8) this expression can be eval-
(a) p
1 eV uated to give
H
(c) f ap(2) e e(2) δnσ = βσ2(2) n0Ω(P2C) eεV , (9)
p p (cid:16) (cid:17) F
2mH
B f f (2) wheren istheconductionelectrondensityinthenormal
p p 0
1 metal.
(b) eV Fromthe result(9)we concludethatthe totalnumber
a(2)
ofhotelectronsinjectedintothenormal-metalsideofthe
p
e e(2) contact is
p
(2) (2)
eV β +β
FIG. 2: Zero-temperature energy distributions for (a) δn=γ n Ω(2) ; γ = ↑ ↓ (10)
magnetic moment-up (spin-down), fp↑, and (b) magnetic tr(cid:16) 0 PC(cid:17)εF tr 2
moment-down (spin-up) electrons, fp↓, at point r on the
normal-metal side of the point contact. The inset (c) shows and the induced magnetic moment corresponding to the
theZeemanenergysplittingandthedirectionofthemagnetic net spin density accumulated in the same region is
fieldH. Allstatesareoccupied uptoε↑ =εf −eV/2−µBH
and ε↓ = εf −eV/2+µBH, respectively (blue rectangles), δM =µ Sδn=µ β n Ω(2) eV . (11)
butin theintervals(ε↑,ε↑+eV)and (ε↓,ε↓+eV) thestates B B tr(cid:16) 0 PC(cid:17)2εF
are only partly occupied (red rectangles) and to an extent
that is determined by the probabilities α↑p(r) and α↓p(r) Here S, the effective spin of an injected electron, is
for “hot” electrons in the ferromagnet to reach r. Clearly,
(2) (2)
thedifferencebetweenthedensitiesofspin-downandspin-up 1δn −δn 1β −β 1
electrons,n↑(r)−n↓(r)∝[(α(↑2)−α(↓2))eV −2µBH],depends S = 2 ↑δn ↓ = 2β↑(2)+β↓(2) ≡ 2βtr (12)
on the bias voltage V. It follows that the spin population ↑ ↓
can beinverted,so that n↑(r)>n↓(r), for large enough V if
and β is a measure of the spin polarization of the hot
α(2) >α(2). tr
↑ ↓ electronsinjected into the contactregion. Ifthe size dof
the contact is a few times 10 nm and β ∼ 0.3, which
tr
correspondstoanearlyballisticpointcontactwithd∼l
the effective boundary conditions are11 0
and a spin polarization of 30% at the F/N interface, the
injected number of hot electrons and the induced mag-
hα(2)i−hα(1)i = l0 dhα(σ1p)i; netic moment in the contact region is δn ∼ 106eV/εF
σp σp hDσi dz and δM ∼106µBeV/εF, respectively.
dhα(1)i dhα(2)i Photocurrent—Thepreviouscalculationscanread-
σp σp
= ; (6) ily be extended to findthe photocurrentflowingthrough
dz dz
the point contact under irradiation. Since the electron-
ifthetransparencyoftheinterfaceisassumedtobesmall, photoninteractionhardlyaffectstheelectronmomentum
hD i≪ 1. Solving the diffusion equation (5) with these at all, the main cause of the photocurrentis the photon-
σ
boundary conditions one finds inducedelectronspin-fliptransitionsinconjunctionwith
the spin-dependence of the contact resistance. The spin
hα(1)i=1−β(1)(1+ 2z); hα(2)i=β(2)(1− 2z), (7) flipschangetheelectronspindensitiesinthecontactand
σ σ L σ σ L the spin-dependent contact resistance is connected with
the different densities of states for the two spin projec-
where
tions.
κ(s) L In order to find the photocurrent we first solve the
β(s) = σ ; κ(s) =hD i . (8) Boltzmann equation (1) for the photon-induced change
σ 1+κ(σ1)+κ(σ2) σ σ 2l0 f(s) (r) in the electron distribution function. We do so
σp,1
to lowest(linear)orderinthe smallparameterd/l and
If electrons are injected from the ferromagnet (1) into ph
the normal metal (2) (i.e., if eV > 0) the number of withtheboundaryconditionsfσ(1p,,21)(z =∓L/2)=0. The
“hot” electronswith spin up ↑ anddown↓ that accumu- matchingconditionsattheF/NinterfacearegivenbyEq.
lateinthe effective volumeΩ(2) ∼d3 ofnormalmetalin (3) with the change f(s) → f(s) . Using these solutions
PC σp σp,1
the point contact (PC) is one finds the photocurrent as
d3p dp
δnσ =ZΩ(P2C) d3rZ (2π~)3 × Iph = esX=1,2ZΩ(PsC) drZ (2π~)3 × (13)
f(2)(r)−n E(2)(p)+eφ (r)+eV/2 . α(s) (r)−α(s) (r) w(s){f(s),f(s)}.
pσ F σ 0 ↑,−p ↓,−p ph ↑p0 ↓p0
h (cid:16) (cid:17)i (cid:16) (cid:17)
4
UsingEqs. (13),(7)and(8)oneobtainsthetotalcurrent Comparing Eq. (14) and Eq. (19) one finds that
I(V) in a diffusive point contact under irradiation as
3V −V∗
V |~ω−2µBH| c jph(V)= 4 V∗2 P0, (20)
I(V) = +θ 1− j (V);
R (cid:18) ~ω v (cid:19) ph
F
which makes it possible to find the power P absorbed
∆R 0
jph(V) = R2 (V −V∗) (14) (frsoeme Etqh.e(e1l4ec))traofmteargfinresttichfiaevlidngbydemteeramsuinriendgVdj∗phfr(oVm)/tdhVe
HereRisthe“dark”contactresistanceduemainlytothe condition jph(V∗) = 0. Furthermore, the net emitted
impurities,while the relativechangeofthe pointcontact powerP(V)canbedeterminedbymeasuringjph(V)with
resistance caused by the irradiation is the help of Eq. (20) and Eq. (18).
So far, we have shown theoretically that an inverted
∆R (2πβ¯tr)2 c |µBhac|2 (2) 2e2 spin population is accumulated in a voltagebiased point
= (n Ω ) R , (15)
R 6 v ε ~ω 0 PC h contact between a ferromagnet (F) and a normal metal
F F (cid:16) (cid:17)
(N). Fora contactoflineardimensiond∼10 nm, biased
where β¯tr =βtrγtr and eV∗ =(3/4)~ω/β¯tr. As one sees byavoltageV,andwithaspinpolarizationof30%atthe
fromEq. (14)thedependenceofthephotocurrentonthe F/N interface (β ∼ 0.3) we find that the correspond-
tr
magnetic field has a peak corresponding to the resonant ing magnetic moment injected into the contact region is
interaction of the electron spin and the electromagnetic δM ∼ 106µ eV/ε . We have furthermore shown that
B F
field. if the point contact is irradiated by an electromagnetic
A comparisonbetween Eq. (13) andthe rate equation field, photon-induced electron spin-flip scattering gives
for photons generated by electronic spin-flip transitions rise to a peak in the relative change of the point contact
induced by the electromagnetic field (see7), resistance, ∆R/R as a function of the irradiation fre-
quency. Thepeakappearswhenthefrequencyisresonant
dn(psh) =− w(s){f(s),f(s)} d3p , (16) with the Zeemansplitting in the normal-metalspectrum
dt Z ph ↑p ↓p (2π~)3 of conduction electrons, which for an external magnetic
field of 1 T occurs at 30 GHz. The net power, P(V),
where nph is the photon density, shows that the pho- generated by the stimulated emission of photons in the
tocurrent may be re-written in the form electronspin-fliprelaxationprocesscanbedeterminedby
measuringthephotoncurrentj (V)definedinEq.(14).
dn(s) ph
I =−e dr hα(s)i−hα(s)i ph , (17) Intheexperimentdiscussedbelowwithtypically 10mW,
ph sX=1,2ZΩs (cid:16) ↑,p ↓,p (cid:17) dt 10-100GHzmicrowavesirradiatingthepointcontactpro-
duces a magnetic amplitude (h )of the electromagnetic
ac
which makes it clear that its magnitude depends on the fieldinsidethepointcontactofapproximately30mT.For
net rate of photon absorption/emission in combination such a field we find that ∆R/R ∼ 0.01–0.10% and that
with the spin dependence of the effective transparency P(V) is given by Eq. (18) with P(0) ∼ 1–10 pW; P(0)
of the point contact. From Eq. (14) one notes that the being the power absorbedfrom the electromagnetic field
microwave-induced current changes sign at V = V∗, i.e. due to photon absorption in the contact region. These
when the rate of photon emission by “hot” electrons be- estimates show that an experimental implementation of
gins to exceed the rate of photon absorption. the proposedspin-laser effect in magnetic point contacts
The close association between the electron transport is feasible, and is demonstrated below. Two comments
and photon radiation processes allows us to express the are in order. The neglect of spin-flip scattering in the
photocurrent in terms of the power of emission and ab- normal metal due to magnetic impurities or spin-orbit
sorption of photons by electrons in the point contact. interactionis welljustified since the pointcontactsizeof
Using Eqs. (2), (4), and (7) one finds that the net emit- 10 nm is one to two orders of magnitude smaller than
ted power due to resonant(~ω =2µ H) absorptionand the spin-diffusion length in a typical normal metal such
B
emission of photons in the irradiated point contact, de- as Cu. Another possible imperfection is spin perturba-
fined as P(V)=~ω drdn /dt, can be expressed as tions that can occur in nano-constrictions, especially in
ph
R external fields applied opposite to the magnetization in
3 V the ferromagnetic electrode (needed for spin-population
P(V)=P −1+ . (18)
0(cid:18) 2V∗(cid:19) inversion). One would need a veryhard ferromagnetun-
affected even at the interface by a reversing field field
Here
of 1 T, such as transition metal-rare earth alloy. There
π c |µ h |2 is another, rather interesting solution employing a spin-
P0 = 2v n0Ω(P2C) Bε ac ω (19) minority injector, where possible spin perturbations are
F(cid:16) (cid:17) F
actually fully suppressed by the high Zeeman field. This
is the absorbed power due to photon absorption, while latter configuration is illustrated experimentally below.
the second term in Eq.(18) is the emitted power due to Stimulated photon emission in FeCr/Cu point
photon emission from the point contact. contacts — In this section we provide experimental ev-
5
idence for the effect described above. The system is a (a)
point contact of tip-surface type, between a ferromag-
netic film andanonmagnetictip made ofCu. The ferro-
magnetic materialchosenfor this experiment is a known
minority-carrierFe70Cr30alloy13, in which the majority
oftheconductionelectronshavetheirmagneticmoments j>1 MA/cm2
opposite to the local magnetization and therefore spins FeCr Cu
parallelto the local magnetization(conduction electrons
with magnetic moments parallel to the local magneti-
zation are a minority). This inverse spin polarization 3
is approximately 30% for the chosen alloy composition.
(b)
The use of a minority-spin injector offers a rather spe-
0
cialconfigurationfor creating a strongZeemansplitting, 0 2
0
which is desirable in detecting the laser effect discussed 1
x
above. An external magnetic field applied parallel to 0
=
the magnetizationof the minorityinjector automatically RP 1
R/
is anti-parallel to the net injected magnetic moment in D
Cu. Thisproducesthedesiredspin-populationinversion,
0
withthehigh-energylevelmorepopulatedbytheinjected 0 1 2 3 4
20
polarized electrons then the low-energy level. Since the
field is parallel to the injector’s magnetization, its mag-
(c)
nitude can be increased arbitrarily high and the spin-
population inversioncondition would only improve. The )10
V
field of a few Tesla yields a Zeeman splitting of the or- m
(
derof100GHz, welloutside the 1-10GHz range,typical Vdet
for spin-torque dynamics. (We note also that the bias
0
current of order of 10 µ A used below is two orders of
magnitude lower than that typically required for induc-
ing spin-torque effects – see, e.g., our recent results14 0 1 2 3 4
B(T)
for details). This allows to effectively separate the spin-
photoniceffectsdiscussedhereinfromthespin-torqueef-
fects in the system. Furthermore, a high field in excess
FIG. 3: (a) Schematic illustration of spin-flip photon emis-
of2 T leads to anessentiallyperfect magnetic alignment
sion in F/N point contact, with the ferromagnetic electrode
in the ferromagnet, including the interfacial spins in the
of spin-minority type. The injected electrons are spin-split
nano-constriction, which greatly simplifies the interpre-
by the external field applied parallel to the magnetization
tationofthe experiment. This minority-injectorconfigu-
of the injector, and the spin-up and spin-down levels are
rationofstimulatedspin-flipphoto-emissionisillustrated inversely populated. (b) Resistance of a point contact un-
in Fig. 3a. irradiated(greycurve)andirradiated(blackcurve),∆R/R :
0
Cu100/Fe70Cr3050/Cu3-Cu,f=64GHz,P =10mW,T=4.2
The experimental arrangement in terms of producing K, V =-0.16 mV, R = R(P = 0,V → 0)=10.6 Ω corre-
bias 0
point contacts and microwaveirradiating them were dis- spondingtothepointcontactdiameterof∼10nm. (c)Detec-
cussed in detail in our recent publications14,15. Here torvoltagelocked-intothechoppingfrequency(2kHz)ofthe
we concentrate on the region in the phase space of the irradiatingmicrowavefield(64GHz),directlyproportionalto
system, in terms of the bias current and irradiation fre- the change in the point contact resistance under irradiation:
quency, where previously reported effects of spin-torque T=4.2K,Vbias=-0.16mV,R0 =20ΩcorrespondingtodPC ∼
dynamics are absent. The irradiation frequency is 64 5 nm. (b) and (c) are for two different point contacts.
GHz,correspondingtotheZeemanfieldofapproximately
2.3 T for a free electron (appropriate for Cu). The re-
sistance with the microwave power off is essentially flat provethe signalto noise ratio,the microwavepower was
within the noise floor of the measurement, in the entire chopped at 2 kHz and the resistance measured using a
field range of 4 T. This background is subtracted from lock-in amplifier referenced to the chopping frequency.
the resistance measured with the microwave power on. The lock-in signal is then directly proportional to the
The difference is then normalized and shown in Fig. 3b difference in resistancewith and without the irradiation.
asafunctionoffield. Theresistancebecomesbell-shaped The resulting detector voltage measured for a FeCr/Cu
under irradiation, centered around 2.5 T, corresponding point contact (different from that in b) is shown in Fig.
well to the expected Zeeman splitting at 64 GHz. The 3c. A pronounced peak in the vicinity of the expected
magnitudeofthemeasured∆R/Risoftheorderof0.1%, Zeemansplittingisevidenceforarelaxationprocessstim-
which also agrees well with the above theoretical predic- ulated by the microwave field. This process has a reso-
tions for this point contact geometry. In order to im- nant character in terms of its field-frequency condition,
6
coinciding with that for stimulated photon emission by example to semiconductor lasers7.
spin-flip relaxation.
In conclusion, we have shown that a suitably imple- Acknowledgements. Financial support from the
mented spin injection can be used to achieve a tunable European Commission (FP7-ICT-FET proj no 225955
photon emission by a metal. This effect has a great po- STELE), the Swedish VR, and the Korean WCU pro-
tential for new types of spin-based lasers, which are ex- gram funded by MEST/NFR (R31-2008-000-10057-0)is
pected to have extremely highoptical gaincomparedfor gratefully acknowledged.
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