ARTICLES

Zero-field optical manipulation of magneticions in semiconductorsR. C. MYERS1, M. H. MIKKELSEN1, J.-M. TANG2*, A. C. GOSSARD1, M. E. FLATTE2AND D. D. AWSCHALOM1†

1Center for Spintronics and Quantum Computation, University of California, Santa Barbara, California 93106, USA2Optical Science and Technology Center and Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA*Present address: Department of Physics, University of New Hampshire, Durham, New Hampshire 03824, USA†e-mail: awsch@physics.ucsb.edu

Published online: 17 February 2008; doi:10.1038/nmat2123

Controlling and monitoring individual spins is desirable for building spin-based devices, as well as implementing quantuminformation processing schemes. As with trapped ions in cold gases, magnetic ions trapped on a semiconductor lattice have uniformproperties and relatively long spin lifetimes. Furthermore, diluted magnetic moments in semiconductors can be strongly coupledto the surrounding host, permitting optical or electrical spin manipulation. Here we describe the zero-field optical manipulationof a few hundred manganese ions in a single gallium arsenide quantum well. Optically created mobile electron spins dynamicallygenerate an energy splitting of the ion spins and enable magnetic moment orientation solely by changing either photon helicity orenergy. These polarized manganese spins precess in a transverse field, enabling measurements of the spin lifetimes. As the magneticion concentration is reduced and the manganese spin lifetime increases, coherent optical control and readout of single manganesespins in gallium arsenide should be possible.

The detection and manipulation of single spins in semiconductorsmay constitute the basis of quantum information processingdevices1,2. Single spins in non-magnetic semiconductors mayalready be coherently controlled, as in coupled quantum dots(QDs) defined by depleting a two-dimensional electron gas3. Analternative approach is to reduce the size of the QD to the sizeof a single, isolated impurity atom in the host semiconductor4–6.Although addressing single impurities is di!cult, inhomogeneitiesbetween QDs are eliminated because each atom is identical. Whenmagnetic ions are trapped on a semiconductor lattice, the spin–spin interactions between the magnetic ion and electrons in thesemiconductor are electrically and structurally controllable bybandgap engineering7. Such techniques are scalable to the single-ion limit, as in II–VI magnetic QDs, in which single Mn ion spinshave been optically detected and electrically manipulated8,9. Todetect single Mn ions, they must be located at specific locationswithin a single QD, which is di!cult considering the randomposition of both QDs and Mn ions. Coherent precession ofMn ion spins can be optically detected by Faraday rotation inquantum wells (QWs) of II–VI semiconductors, typically at highMn doping levels10. In these II–VI semiconductors, the Mn ionsare isoelectronic dopants, and their polarization is inferred fromthe exciton spins exchange coupled to them11. For III–V materialssuch as GaAs, however, Mn contributes an acceptor state withinthe bandgap12,13, into which conduction-band electrons can fall.This transition provides a path for direct optical readout andcontrol of single Mn spins. Furthermore, the mixing of the Mnion and valence-band states opens the possibility for electricalmanipulation of a single magnetic ion even in a bulk crystal14.

Here we describe measurements of the optical emission fromMn ions in single GaAs QWs, enabling the detection of a few

hundred Mn ion spins. At zero magnetic field, optical spin injectioninto the QW results in a polarization and a splitting of the Mnion spin states. In contrast to what occurs in II–VI magneticsemiconductors10,15, this optically established non-equilibrium Mnpolarization cannot be explained by the sp–d carrier exchangeinteractions. Rather, this dynamic exchange splitting (DES) ispossible because optically generated mobile spins partially orientthe Mn spins, analogously to the dynamic nuclear polarization,which can be generated by the mutual spin-flip of non-equilibriumelectron spins and nuclei coupled by the hyperfine interaction16.Once the Mn ions are partially oriented, Mn–Mn interactionsbecome the dominant factor in determining the size of the exchangesplitting and the decoherence times of the polarized Mn ions, overthe range of densities we have measured. These interactions areenhanced owing to the extended wavefunction of the hole boundto each Mn ion. Spin precession is measured by the Hanle e"ect,enabling measurements of Mn ion spin lifetimes. The polarizedMn spins further split the valence-band spin states, resultingin a measurable DES of the QW excitons. Experimental resultsare compared with a tight-binding model for the Mn acceptorelectronic structure and optical properties, which has successfullypredicted the Mn acceptor electronic structure17,18 and interactionbetween pairs of Mn ions19.

The samples consist of 10-nm-thick Mn:GaAs single QWswith Al0.2Ga0.8As barriers grown by molecular beam epitaxy20,21

on (001) semi-insulating GaAs wafers, with doping density (Mn)varied from !1019 to 1016 cm"3, corresponding to 57,000–550 Mnions within a 1-µm-diameter spot. The band-edge diagram alongthe growth direction is schematically shown in Fig. 1a togetherwith the Mn acceptor level and optical transitions. For theseMn doping densities, the neutral Mn acceptor (A0

Mn = A"Mn + h+)

nature materials VOL 7 MARCH 2008 www.nature.com/naturematerials 203

© 2008 Nature Publishing Group

ARTICLES

!M

n (µeV)P Mn

(%)

Excitation helicity"

B = 0 TT = 10 K

ECB

EVB

+1

–1

–1/2

2!Mn

+1/2

+3/2

–3/2

e1

hh1

!Ee

!Eh

(X)

PL (a

rb. u

nits

)

E (eV)

(X)

T = 5 K

~107 meV P Mn

(%)

Bz (T)

E (eV)

PL (a

rb. u

nits

)

B = 0 TT = 10 K

"–

T = 5 K

0

Apparent Mn transitions

B = 0 T PMn< 0

1.451.42 1.43 1.44E (eV)

PL (a

rb. u

nits

)

!EMn

X +

1.40 1.48 1.561.521.44102

104

106

80

60

40

20

–20

–40

–60

–80

0

0 2 4 6 8–2–4–6–8

30

20

10

0

–10

–20

–30

0

1

2

3

4

5

1.451.42 1.43 1.44

50

25

0

–25

–50

0

1

2

3

4

5a

b

c d

e fPump

(e, A0Mn)

(e, A0Mn)

A0Mn

# X –# M –# M –# M –#M +#

M +# M +#

#

–# +#

+#

Figure 1 Optical spectra of magnetic ions in the QW and DES. a, Schematic band edge diagram along the growth direction and the optical selection rules. When Mn spinsare dynamically polarized (PMn < 0) the electron and hole spin states are exchange split as shown. Mn acceptor photoluminescence (PL) arises owing to transitions ofelectrons in the QW into the Mn state. An apparent spectroscopic splitting of Mn acceptor PL (!Mn) occurs during DES (see the Supplementary Information). b, Full PLemission energy (E ) spectrum of a 10-nm-thick Mn:GaAs single QW with Al0.1Ga0.9As barriers; similar spectra are seen for the other samples with higher barriers.c, Polarization-resolved Mn acceptor PL using a pump laser that is "+ polarized and resonant at the (X) transition; d, the same spectrum as modelled in the text. Solid linesin c are fits to the data (black points). e, Polarization of the Mn acceptor emission (PMn) in a longitudinal field (Bz ) for three different excitation helicities. Red lines aresimulations as described in the text. f, Zero-field polarization of the Mn acceptor versus the excitation helicity. The dynamic exchange splitting (!Mn) is shown on the rightvertical axis. Mn= 7.3#1018 cm"3.

is formed, consisting of a quasi-bound heavy hole (h+) withspin S = 3/2 antiferromagnetically coupled to a core Mn2+ 3d5

ion with S = 5/2. The neutral Mn acceptor has a total angularmomentum state J = 1 and a g-factor gA0

Mn= 2.77, as confirmed

by electron paramagnetic resonance and superconducting quantuminterference device magnetometry22,23.

PL spectroscopy provides optical access to the QWs and Mnions within them (Fig. 1b). Electrons that recombine with holesbound to Mn ions within the wells emit PL (e, A0

Mn), which canbe identified from its characteristic lineshape and spectral positionred-shifted by !107 meV from the QW exciton (X) line. In bulk,the A0

Mn state lies !110 meV above the valence band edge. In ourQWs, the confinement does not significantly alter the ionizationenergy of the Mn acceptor, which becomes large in wells narrowerthan 7 nm (ref. 24). Also present in the spectrum are bulk emissionpeaks (1.46–1.52 eV) from the GaAs bu"er layer and Mn acceptoremission at !1.40 eV occurring owing to donor bound electronsrelaxing into unintentionally incorporated Mn acceptors in thebulk (D0, A0

Mn)25,26. The phonon replica of this transition is seen asa broader peak at slightly lower energy than the Mn acceptor peakin both the QW and bulk.

Our calculations show that the polarization of the Mn acceptoremission is sensitive to the spin state of the Mn ions. Opticaltransitions of a single Mn ion have the form of a Fano resonance,

owing to the overlap of optical transitions to the localized statewith those to a continuum of states in the band tail. Analysis ofthe Clebsch–Gordan coe!cients27 indicates that recombination ofunpolarized electrons with the hole of a neutral Mn acceptor inthe mJ = "1 state yields circularly polarized light of polarization5/7, where mJ is the quantum number of total angular momentumalong the magnetic field. Recombination of spin-down electronswith unpolarized Mn acceptors yields circularly polarized light ofpolarization 1/2. Thus the circular polarization of the (e, A0

Mn)emission indicates a spin polarization of the Mn ions or theelectrons. Measurements of this type have tracked the polarizationof the Mn acceptor from the (D0, A0

Mn) PL in bulk28,29, and from thehot-carrier PL in multiple QWs30. The shape of the theoretical PLspectrum (Fig. 1d) is well fitted by the Fano form31, and reproducesthe experimental lineshape (Fig. 1c). Such PL spectra are fitted bytwo gaussians (solid lines) to extract the peak position (M!±) andintensity (I!±

M ).To demonstrate optical readout of the Mn ion spin state, we

show the Bz dependence of the polarization of the Mn acceptoremission (PMn = (I!+

M " I!"M )/(I!+

M + I!"M )) (Fig. 1e). Following

from the QW selection rules, a spin-polarized electron (spin downfor !+ and spin up for !") recombines with a hole boundto a Mn acceptor in thermodynamic equilibrium with Bz . Forrecombination of a spin-down electron with the mJ = "1 state,

204 nature materials VOL 7 MARCH 2008 www.nature.com/naturematerials

© 2008 Nature Publishing Group

ARTICLES

PL (a

rb. u

nits

)

P X (%

)

Bz (T)

!E X

(µeV

)

1.560 1.564E (eV)

Pump

B = 0 TT = 5 K

Detect+

1

2

3

4

80

60

40

20

–20

–40

–60

0

–80

Bz (T)

1,500

1,000

500

0

–500

–1,000

–1,500–8 8–2–4–6 2 4 60–8 8–2–4–6 2 4 60

+

"

a b c

#–# #

–#

Figure 2 DES of exciton spins in the QW. a, Exchange splitting of the QW exciton PL at zero magnetic field due to DES. Spectra are shown for "+ (filled) and "" (open)polarized excitation set to 1.65 eV. Detection helicity is colour coded. b, Exciton PL polarization (PX = (I "+

X " I ""X )/ (I "+

X + I ""X )), and c, splitting in a longitudinal magnetic field

(Bz ), for different excitation helicities. !EX = X"+ " X"". Mn= 7.3#1018 cm"3. Exciton emission energy (X"±) and intensity (I "±X ) are determined from gaussian fits to the

PL spectra.

the polarization of the light emission should be 9/11, close towhat is seen for large negative field in Fig. 1e. Recombination ofa spin-down electron with the mJ = +1 state yields a polarizationof "1/3, corresponding to large positive field in Fig. 1e. For Bz = 0,where all mJ states are occupied, the polarization would be 1/2.These numbers are in good agreement with the trends shown inFig. 1e. Also shown in Fig. 1e are theoretical curves incorporatingthese e"ects and the thermal occupation of the Mn ion states. In thecase of optical spin injection using a !±-polarized pump, PMn(Bz)does not show odd symmetry and shows faster saturation in onefield direction than the other. The same trend is seen for the excitonpolarization (Fig. 2), which suggests an optically driven splitting ofthe mJ states, described below.

Optical spin injection, even at zero magnetic field, generatesa non-equilibrium polarization of the Mn ions. This is observedas a splitting of the (e, A0

Mn) emission (!Mn = M!+ " M!") thattracks the helicity of the excitation (Fig. 1f). Simulations show thatthe apparent spectroscopic splitting of the Mn emission (!Mn) isproportional to the energy splitting of the Mn states (!EMn), seeSupplementary Information. The finite polarization of Mn, in turn,generates a clearly observable splitting of the QW exciton PL atzero field (Fig. 2a). This arises from the exchange splitting of theQW conduction and valence subbands (Fig. 1a), !Ee and !Eh,respectively. !Ee = xN0"$JMn% and !Eh = xN0#$JMn%, where x isthe Mn concentration, N0 is the cation density, " and # are the s–dand p–d exchange parameters, respectively, and $JMn% is the averageangular momentum (out of a maximum of unity) of the neutral Mnacceptor ensemble. In our samples we measured N0" = "0.06 eVand N0# = "1.5 eV (ref. 32), thus the valence subband exchangedominates the exciton splitting. The splittings shown in Fig. 1a aregenerated by $JMn% < 0, permitting the orientation of the Mn ionsto be clearly identified.

Because the Zeeman splitting is zero at zero field, the Mnspin splitting along the optical axis contains only the exchangecontributions from the electron and hole spins, and the non-equilibrium polarization of the neighbouring Mn,

!EMn = n"$Se%+p#$Sh%+l$JMn%, (1)

where n and p are the optically excited electron and hole densities,$Se% and $Sh% are the electron- and hole-spin average values,respectively, and l is an e"ective mean-field coupling parameterto the neighbouring Mn (the Weiss molecular field). We estimatethe contributions to !EMn in equation (1) from the photoexcitedpolarized electrons and holes for the sample in Fig. 1f withx = 0.033% and assuming n = p = 4 # 1017 cm"3. Electron spinsremain spin polarized over long times (as shown below), leadingto !EMn = 1 µeV, whereas the hole spins have too short a spinlifetime to substantially contribute33. The observed !Mn ! 50 µeVis too large to be explained by the s–d exchange coupling betweenelectron and Mn spins alone.

DES decreases with Mn doping and is not observed forthe lowest-Mn-doped sample, suggesting that the dominantcontribution to !EMn comes from interactions with neighbouringpolarized Mn. Optically injected carriers partially polarize theMn acceptors through a dynamical process, and once they arepartially polarized the energies of Mn acceptors will di"er on thebasis of their alignment with the non-equilibrium magnetizationdirection. The value of l, the Weiss molecular field, is the sum ofall the interactions with neighbouring Mn spins. For a Heisenberghamiltonian H =!

i<j J(Ri "Rj)Ji ·Jj , where i and j label all the Mnspins in the solid at position R, J = !

i J(Ri) and l = J$JMn%.Using methods developed previously17,19, we calculate the averageinteraction energy between two Mn spins at the average separationfor a given density by using an e"ective Bohr radius of 13 A. Weestimate J from the interaction energy of a Mn ion with its (six)neighbours at the average separation for the given Mn dopingdensity, and obtain, for the three densities shown in Fig. 5 below,0.01 µeV, 6 µeV and 400 µeV, respectively.

To test the hypothesis that DES is initiated by the scattering ofQW spins with Mn spins, given above, we study the dependence ofDES on the energy of the incident photons. In this PL excitationspectroscopy measurement, the excitation energy is swept frombelow the QW ground-state heavy-hole exciton absorption edge(hh1) to above the light-hole (lh1) absorption edge, whilemonitoring the polarization-resolved PL of the neutral Mn acceptorwithin the QW. Figure 3a, b plots the PL excitation spectra of the

nature materials VOL 7 MARCH 2008 www.nature.com/naturematerials 205

© 2008 Nature Publishing Group

ARTICLES

Excitation energy (eV)

PL (arb. units)

!M

n (µeV)

hh1 lh1

1.43

1.44

1.451.43

1.44

1.45

1.550 1.555 1.560 1.56525

0

–50

–75

–25

+

2

30

20

10

0

–10

Detect +

012

Emis

sion

en

ergy

(eV)

Emis

sion

en

ergy

(eV)

1.545

P Mn

(%)

1

3

0

PL (a

rb. u

nits

)

a

b

c

d

"

"

–"

Detect –"

PL (arb. units)

Pump + T = 10 K B = 0 G"

Figure 3 Laser-energy dependence of the DES. Choosing the excitation energyenables control of the orientation of Mn spins at zero field. The PL intensity of theMn acceptor emission in the QW (colour intensity) is plotted as a function of bothemission energy (E ) and excitation energy for "+ and "" detection helicities in aand b, respectively. The inset shows a linecut at a particular excitation energy,revealing PL spectra fitted to two gaussians. Results of these fits yield PL intensity(c) and polarization (PMn) and DES (!Mn) (d) as functions of excitation energy.Detection helicity is labelled in the figure. Dotted lines indicate the excitonabsorption lines in the QW. Mn= 2.2#1018 cm"3.

(e, A0Mn) emission for the two detection helicities. About 17,000

Mn ions are detected in Fig. 3 and similar trends are observed atthe other Mn densities. Mn emission is observed only when theexcitation is equal to or above the ground-state (X) absorptionenergy of the QW, and the PL intensity is maximum on resonancewith the exciton transitions (Fig. 3c). This exemplifies the localcharacter of the Mn acceptor state, in which the PL is driven byphotoexcitation into the delocalized QW subbands and subsequentrelaxation into the local Mn acceptor levels. The Mn polarizationand DES track a similar excitation-energy dependence (Fig. 3d),where the maximum is observed near the hh1 absorption edge.Interestingly, a sign change in Mn polarization and DES occurswhen the excitation is tuned resonantly with the lh1 absorption.

The PL excitation measurements provide insight into themechanism of DES. !+ excitation at the hh1 resonance creates100% spin-down electrons and spin-up heavy holes, whereas onthe lh1 resonance it creates 100% spin-up electrons and spin-uplight holes, but only one-third as many. Mechanisms of DES couldinclude dynamic scattering of spin-polarized electrons or holesfrom the neutral Mn spins, leading to preferential alignment, orcapture of the spin-polarized holes by temporarily ionized Mn.Captured spin-up heavy holes will lead to population of the Mnstates mJ =1,0,"1 in the ratio 1:4:10, or a maximum $JMn%="0.6,whereas captured spin-up light holes will lead to the ratio 1:2:2,or a maximum $JMn% =" 0.2. Thus scattering of hole spins fromMn ions will not produce the correct sign of the Mn polarization,whereas the sign of the electron spin switches between the hh andlh transitions for a given photon helicity. This indicates that DES

Bx (G) Bx (G)

(X)

T 2* (

ns)

Mn (!1018 cm–3)

Mn2+

e–

T = 5 K

P Mn

(%)

5505,00017,00057,000

Mn ions detected

–10K 10K5K0–5K –400 0 400–200 2000

5

10

0

5P X (%

)

15

10

0.10

1.00

10.00

0.010 8642

a b

c

(e, A0Mn)

Figure 4 Spin dynamics of Mn ions in GaAs QWs. Time-averaged spin precessionis observed by monitoring the transverse magnetic field (Bx ) dependence of thepolarization of the QW emission of the ground-state exciton (X) (a) and the Mnacceptor emission for samples with different doping densities (Mn) indicated bydifferent colours (b). Error bars represent the experimental standard deviation. Linesare fits to equation (2). c, Spin lifetime (T &

2 ) of the Mn acceptor state (circles) and theconduction-band electrons (red triangles) as a function of Mn. Lines guide the eye.The blue curve is calculated with zero fit parameters, assuming that Mn–Mn spinscattering dominates T &

2 . Error bars indicate the standard error from least-squaresfits to equation (2).

is generated by the scattering of non-equilibrium electrons fromthe neutral Mn acceptors, in a fashion similar to dynamic nuclearpolarization. A related mechanism (for electron interaction with aMn d-state spin rather than electron interaction with a Mn–holecomplex) was suggested in the case of optically induced magnetismin II–VI compounds, but was found not to apply34.

Having established a method for optically polarizing Mnspins, we now apply a transverse field (Bx) to induce coherentspin precession. The average spin polarization, and thereforethe PL polarization, decays with magnetic field because spinsprecess further away from the optical axis and relax. In thisHanle measurement, the PL polarization tracks a lorentzian fielddependence with a width proportional to 1/gT&

2 ,

P(Bx) = P(0)"

gµB Bx T&2

h

#2

+1, (2)

and 1/T&2 = 1/$r + 1/$s, where T&

2 is the e"ective transverse-spinlifetime of the spin ensemble, µB is the Bohr magneton, $r is therecombination lifetime and $s is the spin relaxation time35.

We begin by examining the e"ect of electron spin precessionin the QW (Fig. 4a). The polarization of the (X) emission tracksa Hanle curve as a function of Bx , representing time-averagedelectron spin precession in the QW. Heavy-hole spins do not precessowing to their small in-plane g-factors36. The electron g-factorfor this sample, ge = "0.218, measured by time-resolved Kerrrotation32, enables the spin lifetime (T&

2 ) to be extracted, and itis plotted as a function of Mn (solid triangles) in Fig. 4c. Thesedata match the T&

2 extracted from time-resolved Kerr rotationmeasurements (open triangles), indicating that the Hanle spinlifetimes are not recombination limited.

206 nature materials VOL 7 MARCH 2008 www.nature.com/naturematerials

© 2008 Nature Publishing Group

ARTICLES

Mn spin precession is observed from Hanle measurements ofthe Mn acceptor emission (Fig. 4b). The pump energy is tunedresonantly with the hh1 absorption to maximize the PL intensityand PMn (Fig. 3d). The field widths of these Hanle curves areorders of magnitude narrower than those of the electron-spinHanle curves, demonstrating that for the (e, A0

Mn) PL the Hanlee"ect occurs owing to spin precession of the Mn acceptor state,and not owing to electron spins. T&

2 values of the Mn acceptorsare extracted from these Hanle curves assuming a gA0

Mn= 2.77

(ref. 22), and plotted as a function of Mn in Fig. 4c. As the Mnions remain in the neutral acceptor configuration over the rangeof densities studied, their g-factors will remain constant. As Mnis reduced below 2 # 1018 cm"3 the Mn spin lifetime increasesexponentially. These e"ective spin lifetimes are not recombinationlimited because $r = 1.5 µs for the Mn acceptor in GaAs (ref. 26).The dependence of the Mn spin lifetime on the doping density isconsistent with inhomogeneous Mn–Mn interactions dominatingT&

2 . The precession rate of a Mn in a field is modified if aneighbouring Mn spin switches from parallel to antiparallel to thefield, which contributes to the dephasing rate T&"1

2 . The presence ofsmall numbers of Mn interstitials that may also contribute to thedephasing cannot be ruled out, although their density is smallerthan the density of substitutional Mn for the growth conditionsused here21. As the Mn interstitial acts as a donor, however, andthe strength of the spin-dependent interaction between an electronbound to the donor and a hole bound to an acceptor should beweaker than the spin-dependent interaction between two holesbound to two acceptors, interstitials are unlikely to play a majorrole in Mn spin dephasing unless the interstitial concentrationgreatly exceeds that of substitutional Mn. Assuming the values of Jcalculated above, T&

2 is plotted as a function of Mn in Fig. 4c as theblue curve, which follows the trend seen in the experiment. NearbyMn ions clearly limit the observed spin lifetimes.

As a final examination of DES, we study the pump powerand temperature dependence of the Mn acceptor PL intensity,polarization and spin lifetime for three di"erent samples (Fig. 5).At high pump power, the (e, A0

Mn) PL should saturate once thenumber of photocarriers exceeds the Mn density. This is clearlyobserved in the lowest-doped sample (Fig. 5a). The DES tracksa similar power dependence as the PL (Fig. 5b), whereas fromequation (1) we would expect a linear power dependence of !EMn

(and !Mn) as p increases. In all samples we observe a decrease inspin lifetime with power, with the strongest dependence occurringfor the lowest-doped sample at pump powers below saturation(Fig. 5c). The temperature dependences of P(0) and T&

2 (Fig. 5d,e)are measured using a constant pump power at which !Mn cannotbe detected within the experimental precision. As temperatureincreases (e, A0

Mn) PL broadens and red-shifts, and the excitationenergy is adjusted to ensure excitation at the (X) absorptionproviding the maximum (e, A0

Mn) PL intensity. For all samples,a decrease in the spin lifetime with temperature is seen with astronger dependence at lower Mn densities.

Our results constitute a new mechanism for optically addressingand controlling small numbers of magnetic ions in semiconductorswithout magnetic fields or magnetic materials. Furthermore,Mn ion spin lifetimes in GaAs reach promising timescales inthe low-doping limit, demonstrating that individual magneticspins in a solid are useful systems for coherent manipulation ofspin information. In contrast to what occurs in II–VI magneticsemiconductors, our method involves an optically establishednon-equilibrium polarization that is not explained by sp–d carrierexchange interactions, nor can it be attributed to magnetic polaronsconsisting of one hole interacting with multiple Mn spins; Mnspin-trap centres in GaAs consist of one hole bound to one Mnion. Instead, a dynamic process of magnetic ion polarization is

PL (a

rb. u

nits

)!M

n (µ

eV)

T 2*M

n (p

s)

T 2*M

n (p

s)

0

P Mn(

0) (%

)

Incident power (kW cm–2)T (K)

1.7 kW cm–2

6"1017 cm–3

2"1018 cm–3

7"1018 cm–3

2

4

6

8

0

0

–25

–50

–75

600

400

200

01000 1 10

Incident power (kW cm–2)

1000 1 10

Incident power (kW cm–2)

1000 1 10

30

20

10

400

200

020 400

T (K)20 400

a

b

c

d

e

T = 10 KB = 0 G

Figure 5 Power and temperature dependence of DES and lifetime of Mn ionspins. a–c, Incident-power dependence of the Mn acceptor PL intensity (a), thedynamic exchange splitting (!Mn) (b) and the Mn acceptor spin lifetime (c) forMn:GaAs QWs with three different Mn concentrations. d,e, Temperature dependenceof the zero-field polarization (d) and spin lifetime (e). Data points in c–e are from fitsto equation (2) of data obtained by Hanle-effect measurements, as in Fig. 4. Linesguide the eye. Large data points in b are also from Hanle measurements. Error barsindicate the standard error from least-squares fits to equation (2).

revealed that is more akin to dynamic nuclear polarization. Weexpect this process to be driven by an s–p spin-flip interactionbetween electrons and Mn spins owing to the extended p-likecharacter of the hole bound to the Mn. Such an interaction isnot relevant in II–VI semiconductors because p-like hole spins canflip independently of the Mn spins. Theoretical analysis indicatesthat long coherence times of Mn ion spins will be retained insingle-ion situations, but a practical signal–noise limit preventsthese measurements in our current structures. Given the versatilityof bandgap and photonic engineering in III–Vs, several routes toamplify the Mn emission signal are possible, and may also a"ect thedynamic exchange mechanism, such as confinement engineeringin di"erent wells, or photonic cavity coupling of the acceptortransition in vertical Fabry–Perot cavities or microdisc structures.

METHODS

Samples of !1 µm thickness are grown at a substrate temperature of !400 'Con semi-insulating GaAs(001) substrates by molecular beam epitaxy. The QWis located 100 nm below the surface between Al0.4Ga0.6As barriers20,21. Mndoping densities within the QWs are Mn = 7.3#1018, 2.2#1018, 6.4#1017

and 7.0#1016 cm"3 as measured by secondary ion mass spectroscopy. PLis measured with a wavelength-tunable, continuous-wave Ti–sapphire laserfocused by a microscope objective to a !1 µm spot in a liquid-He flow cryostatcentred in the bore of an electromagnet capable of a transverse field (Bx) upto 0.15 T, or with a mode-locked Ti–sapphire laser with a 76 MHz repetitionrate of !100-fs-wide pulses, focused to a !50 µm spot in a liquid-He cryostatwith a superconducting magnet capable of fields up to 8 T. Helicity is controlledusing variable wave plates. Magnetic field is measured in situ by a Hall sensormounted next to the sample. PL is dispersed in a 1.0 m spectrometer and

nature materials VOL 7 MARCH 2008 www.nature.com/naturematerials 207

© 2008 Nature Publishing Group

ARTICLES

detected by either a liquid-nitrogen-cooled CCD (charge-coupled device) or acooled photomultiplier tube. The data are analysed by fitting each PL spectrumto two gaussians, as in Fig. 1c, to determine the PL intensity (I!+

M + I!"M ),

!Mn and PMn. Pump power is varied using a motorized filter wheel. Hanlemeasurements carried out at various pump powers and temperatures arefitted to equation (2) to obtain T&

2 and P(0). Longitudinal field (Bz ) andtime-resolved Kerr rotation measurements are made using mode-lockedexcitation with PL detected by CCD.

CALCULATIONSThe properties of Mn acceptors in GaAs are calculated using a 16-band sp3

tight-binding model for the GaAs host with spin–orbit interaction17. TheMn atoms are modelled with an e"ective potential consisting of an on-siteCoulomb term of 1 eV and a spin-polarized term, non-zero for only the p statesat the first-nearest-neighbour As sites, of 3.634 eV to describe the hybridizationbetween the Mn d orbitals and As p orbitals. The e"ective interaction of thed orbitals and the As s orbitals is set to zero. These values produce the correctacceptor-state binding energy in bulk GaAs. The spin of the Mn 3d electrons isassumed to be aligned along a given axis. When two Mn acceptors so modelledare considered near to each other in the GaAs host their magnetic interactioncan be determined theoretically17,19.

The optical properties of the Mn-doped GaAs are calculated within areal-space formalism designed for inhomogeneous systems (J.-M.T. and M.E.F.,manuscript in preparation). Instead of describing the electronic structure withe"ective bands and imposing momentum conservation for optical transitions,our approach assumes that the coherence length for the carrier momentum inboth the valence and conduction bands is of the order of the lattice constant.We maintain in this theory, however, the short-range spatial correlationsbetween valence-band and conduction-band electronic structure, which areoften discarded in calculations of optical transitions, and can be expected to belarge for transitions from a bound state to a continuum.

Received 9 October 2007; accepted 17 January 2008; published 17 February 2008.

References1. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57,

120–126 (1998).2. Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).3. Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in

few-electron quantum dots. Rev. Mod. Phys. 79, 1217 (2007).4. Jelezko, F. et al. Observation of coherent oscillation of a single nuclear spin and realization of a

two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501 (2004).5. Hanson, R., Gywat, O. & Awschalom, D. D. Room-temperature manipulation and decoherence of a

single spin in diamond. Phys. Rev. B 74, 161203 (2006).6. Childress, L. et al. Coherent dynamics of coupled electron and nuclear spin qubits in diamond.

Science 314, 281–285 (2006).7. Awschalom, D. D. & Samarth, N. Spin dynamics and quantum transport in magnetic semiconductor

quantum structures. J. Magn. Magn. Mater. 200, 130–147 (1999).8. Besombes, L. et al. Probing the spin state of a single magnetic ion in an individual quantum dot. Phys.

Rev. Lett. 93, 207403 (2004).9. Leger, Y., Besombes, L., Fernandez-Rossier, J., Maingault, L. & Mariette, H. Electrical control of a

single Mn atom in a quantum dot. Phys. Rev. Lett. 97, 107401 (2006).

10. Crooker, S. A., Awschalom, D. D., Baumberg, J. J., Flack, F. & Samarth, N. Optical spin resonance andtransverse spin relaxation in magnetic semiconductor quantum wells. Phys. Rev. B 56,7574–7588 (1997).

11. Furdyna, J. K. Diluted magnetic semiconductors. J. Appl. Phys. 64, R29–R64 (1988).12. Chapman, R. A. & Hutchinson, W. G. Photoexcitation and photoionization of neutral manganese

acceptors in gallium arsenide. Phys. Rev. Lett. 18, 443–445 (1967).13. Schairer, W. & Schmidt, M. Strongly quenched deformation potentials of the Mn acceptor in GaAs.

Phys. Rev. B 10, 2501–2506 (1974).14. Tang, J.-M., Levy, J. & Flatte, M. E. All-electrical control of single ion spins in a semiconductor. Phys.

Rev. Lett. 97, 106803 (2006).15. Krenn, H., Zawadzki, W. & Bauer, G. Optically induced magnetization in a dilute magnetic

semiconductor: Hg1"x Mnx Te. Phys. Rev. Lett. 55, 1510–1513 (1985).16. Lampel, G. Nuclear dynamic polarization by optical electronic saturation and optical pumping in

semiconductors. Phys. Rev. Lett. 20, 491–493 (1968).17. Tang, J.-M. & Flatte, M. E. Multiband tight-binding model of local magnetism in Ga1"x Mnx As. Phys.

Rev. Lett. 92, 047201 (2004).18. Yakunin, A. M. et al. Spatial structure of an individual Mn acceptor in GaAs. Phys. Rev. Lett. 92,

216806 (2004).19. Kitchen, D., Richardella, A., Tang, J.-M., Flatte, M. E. & Yazdani, A. Atom-by-atom substitution of

Mn in GaAs and visualization of their hole-mediated interactions. Nature 442, 436–439 (2006).20. Myers, R. C., Poggio, M., Stern, N. P., Gossard, A. C. & Awschalom, D. D. Antiferromagnetic s–d

exchange coupling in GaMnAs. Phys. Rev. Lett. 95, 017204 (2005).21. Poggio, M., Myers, R. C., Stern, N. P., Gossard, A. C. & Awschalom, D. D. Structural, electrical, and

magneto-optical characterization of paramagnetic GaMnAs quantum wells. Phys. Rev. B 72,235313 (2005).

22. Schneider, J., Kaufmann, U., Wilkening, W., Baeumler, M. & Kohl, F. Electronic structure of theneutral manganese acceptor in gallium arsenide. Phys. Rev. Lett. 59, 240–243 (1987).

23. Frey, T., Maier, M., Schneider, J. & Gehrke, M. Paramagnetism of the manganese acceptor in galliumarsenide. J. Phys. C 21, 5539–5545 (1988).

24. Plot, B., Deveaud, B., Lambert, B., Chomette, A. & Regreny, A. Manganese luminescence inGaAs/GaAlAs superlattices. J. Phys. C 19, 4279–4289 (1986).

25. Yu, P. W. & Park, Y. S. Photoluminescence in Mn-implanted GaAs—an explanation on the !1.40-eVemission. J. Appl. Phys. 50, 1097–1103 (1979).

26. Bantien, F. & Weber, J. Properties of the optical transitions within the Mn acceptor in Alx Ga1"x As.Phys. Rev. B 37, 10111–10117 (1988).

27. Averkiev, N. S., Gutkin, A. A., Osipov, E. B. & Reshchikov, M. A. E"ect of the exchange interaction ofa hole with 3d electrons on the properties of a deep Mn acceptor in gallium arsenide. Sov. Phys. SolidState 30, 438 (1988).

28. Karlik, I. Y. et al. Magnetization of holes at acceptors and the polarization of the hotphotoluminescence in GaAs:Mn crystals. Sov. Phys. Solid State 24, 2022 (1982).

29. Kim, Y., Shon, Y., Takamasu, T. & Yokoi, H. Deep-level optical transitions of (Ga,Mn)As in highmagnetic fields. Phys. Rev. B 71, 073308 (2005).

30. Sapega, V. F. et al. Hole spin polarization in GaAs:Mn/AlAs multiple quantum wells. Phys. Rev. B 75,113310 (2007).

31. Fano, U. E"ects of configuration interaction on intensities and phase shifts. Phys. Rev. 124,1866–1878 (1961).

32. Stern, N. P., Myers, R. C., Poggio, M., Gossard, A. C. & Awschalom, D. D. Confinement engineeringof s–d exchange interactions in Ga1"x Mnx As/Aly Ga1"y As quantum wells. Phys. Rev. B 75,045329 (2007).

33. Damen, T. C., Via, L., Cunningham, J. E., Shah, J. & Sham, L. J. Subpicosecond spin relaxationdynamics of excitons and free carriers in GaAs quantum wells. Phys. Rev. Lett. 67, 3432–3435 (1991).

34. Krenn, H., Kaltenegger, K., Dietl, T., Spa!ek, J. & Bauer, G. Photoinduced magnetization in dilutemagnetic (semimagnetic) semiconductors. Phys. Rev. B 39, 10918–10934 (1989).

35. Meier, F. & Zakharchenya, B. P. (eds) Optical Orientation (Elsevier, Amsterdam, 1984).36. Marie, X. et al. Hole spin quantum beats in quantum-well structures. Phys. Rev. B 60,

5811–5817 (1999).

AcknowledgementsThis work was supported by the ONR, the AFOSR and the NSF.Correspondence and requests for materials should be addressed to D.D.A.Supplementary Information accompanies this paper on www.nature.com/naturematerials.

Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/

208 nature materials VOL 7 MARCH 2008 www.nature.com/naturematerials

© 2008 Nature Publishing Group

ERRATUM

Zero-field optical manipulation of magnetic ions in semiconductors

R. C. MYERS, M. H. MIKKELSEN, J.-M. TANG, A. C. GOSSARD, M. E. FLATTÉ AND D. D. AWSCHALOM

Nature Materials 7, 203–208 (2008).

Owing to a printing error, the character denoting exchange interaction appeared incorrectly, it should have appeared as !. !e corrected text is below:

Page 3, second column, second paragraph: For a Heisenberg hamiltonian H = "i<j ! (Ri"Rj)Ji#Jj , where i and j label all the Mn spins in the solid at position R, ! = "i !(Ri) and $ = !〈JMn〉. Using methods developed previously17,19, we calculate the average interaction energy between two Mn spins at the average separation for a given density by using an e#ective Bohr radius of 13 Å. We estimate ! from the interaction energy…

Page 5, second column, $rst line:Assuming the values of ! calculated above…

nature materials | ADVANCE ONLINE PUBLICATION | www.nature.com/naturematerials 1© 2008 Nature Publishing Group

Supplementary Material Origin of the peak splitting in the optical spectrum The J=1 ground-state spin state of the Mn-hole complex is split into energetically nondegenerate m=1, 0, and -1 states by the nonequilibrium spin polarization and the interaction with neighboring spin-polarized Mn ions. An optical transition involving a spin-down electron is possible with each of those bound hole states, and can produce a σ + or σ- photon. The same is true for optical transitions involving spin-up electrons. The amplitudes of those transitions, however, differ for spin-up and spin-down electrons, and for σ+ and σ− photons. If the optical linewidth is smaller than the state splitting, then these three peaks would be visible, with different heights for recombination with spin-up and spin-down electrons, and different probabilities for σ+ and σ− photons, due to the Clebsch-Gordan coefficients. If the optical linewidth is larger than the state splitting, as in our samples, the different transition strengths for σ+ and σ− photons for the three different states appears as two peaks of different heights and peak positions for σ+ and σ−. The relative intensities from the relevant Clebsch-Gordan coefficients are: e spin-up

m=1 e spin-up

m=0 e spin-up

m=-1 e spin-down

m=1 e spin-down

m=0 e spin-down

m=-1 σ+ 1 2 2 1 4 10 σ− 10 4 1 2 2 1 Shown in Supplementary Figure 1 is the predicted optical spectrum when the optical linewidth is smaller than the state splitting (A, D) and is larger (B, E). The peak heights are normalized for the larger linewidth in (C, F).

Figure S1: Optical spectrum for differing optical linewidths based on recombination of spin-polarized electrons with the Mn-hole complex. The splitting of the m=1 and m=0 states, and of the m=0 and m=-1 states, is 0.5 meV. Red curves correspond to σ+ emission and blue corresponds to σ− emission. A-C. 100% spin-down electron

polarization, 50% Mn polarization. A. Full-width half-maximum (FWHM) of optical transition = 0.2 meV, B. FWHM 2meV, C. FWHM 2meV, peaks normalized. D-F. 0% electron spin polarization, 50% Mn polarization. D. FWHM 0.2meV, E. FWHM 2meV, F. FWHM 2meV, peaks normalized. When the linewidth is larger than the state splitting (ΔEMn), the splitting of the two apparent peaks (ΔMn) depends on the Mn spin polarization and the electron spin polarization. Shown in supplementary figure 2 is the apparent splitting (labeled ΔMn in the text) of the two peaks in the optical spectrum for several values of the Mn spin polarization and electron spin polarization.

Figure S2: Dependence of peak splitting of the PL emission (ΔMn) on the energy splitting of the Mn states (ΔEMn). (Blue) electron spin polarization 0%, Mn spin polarization 0%, (red) electron spin polarization 50%, Mn spin polarization 0%, (yellow) electron spin polarization 100%, Mn spin polarization 0%, (purple) electron spin polarization 0%, Mn spin polarization 50%, (green) electron spin polarization 50%, Mn spin polarization 50%, (black) electron spin polarization 100%, Mn spin polarization 99%.