GaN:Gd: A superdilute ferromagnetic semiconductor with a Curie temperature above 300 K

0.18 MB·English

by  S. Dhar

GaN:Gd: Asuperdilute ferromagnetic semiconductor witha Curie temperature above300K
S. Dhar,∗ O. Brandt, M. Ramsteiner, V. F. Sapega,† and K. H. Ploog
Paul-Drude-Institut fu¨rFestko¨rperelektronik, Hausvogteiplatz 5–7, D-10117 Berlin, Germany
Weinvestigatethemagneticandmagneto-opticpropertiesofepitaxialGaN:Gdlayersasafunctionoftheex-
5 ternalmagneticfieldandtemperature.Anunprecedentedmagneticmomentisobservedinthisdilutedmagnetic
0 semiconductor. TheaveragevalueofthemomentperGdatomisfoundtobeashighas4000m B ascompared
0 toitsatomicmomentof8m B.Thelong-rangespin-polarizationoftheGaNmatrixbyGdisalsoreflectedinthe
2 circularpolarization of magneto-photoluminescence measurements. Moreover, thematerialssystemisfound
tobeferromagneticaboveroomtemperatureintheentireconcentrationrangeunderinvestigation(7×1015 to
n
2×1019cm−3).Weproposeaphenomenologicalmodeltounderstandthemacroscopicmagneticbehaviorofthe
a
J system. Ourstudyrevealsacloseconnectionbetweentheobservedferromagnetismandthecolossalmagnetic
momentofGd.
9
1
PACSnumbers:75.50.Pp,76.30.Kg,75.50.Dd,71.35.Ji

]
i
c Efficientspininjectionintosemiconductorstructuresisone beam epitaxy (RMBE). The RMBE system (base pressure:
s
- ofthemostimportantrequirementstorealizefuturespintronic 2×10−10 Torr) is equipped with conventional effusion cells
l
r devices. A ferromagneticmaterialcompatiblewith semicon- forGa (purity: 7N)andGd(purity: 4N)[5] andanunheated
mt ductorgrowthwhichthuscouldeasilybeintegratedintosemi- NH3 (purity: 7N) gas injector. A substrate temperature of
conductordeviceswouldbethebestchoice.Sincethediscov- 810◦C (ourstandardgrowth temperaturefor GaN) was used.
.
t eryofaCurietemperatureT ashighas110Kin(Ga,Mn)As The Gd/Ga flux ratio was changed in order to adjust the Gd
a C
m [1],III-Vdilutemagneticsemiconductors(DMS)havegained concentrationinthelayers. Nucleationandgrowthwasmon-
alotofattention. GaN-basedDMShavethepotentialforex- itored in situ by reflection high-energy electron diffraction
-
d hibiting high temperature ferromagnetism which is essential (RHEED). A spotty (1×1) pattern, reflecting a purely three-
n fordevelopingfuturespintronicdevices[2]. Severaltransition dimensionalgrowthmode,wasobservedduringnucleationof
o
metal(TM)dopedGaNDMShavebeeninvestigated. Room- thelayers.Thepatternquicklybecamestreaky,reflectingtwo-
c
temperatureferromagnetisminthesematerials,however,isof- dimensionalgrowth.
[
ten found to result from the formation of precipitates rather TheGdconcentrationofthelayerswasdeterminedbysec-
2
than from a homogeneousalloy [3]. The rare-earth (RE) el- ondaryionmassspectrometryusingaCAMECAIMS4fsys-
v
4 ements could be an interesting alternative to transition met- tem, employing 0+2 primary ions with an impact energy of
6 als. REatomshavepartiallyfilled f orbitalswhichcarrymag- 7 keV. Mass interferencedueto parasitic molecularionswas
5 netic moments and may take part in magnetic coupling like avoidedbyselectingpreciselythemassesoftwoGdisotopes
2 in the case of TM with partially filled d orbitals. While it is (155.922and157.924). Theresultingionrateswereidentical
1
expected that the magnetic coupling strength of f orbitals is to within 1%. Measurements at different locations, each of
4
0 muchweakerthanthatofd orbitalsduetothestrongerlocal- whichinvolvedan area of 50×50 m m2, deviatedby nomore
/ ization of the f electrons, Gd is the only RE element which than5%. Theconcentrationwascalculatedaccordingtomea-
t
a hasbothpartiallyfilled4f and5d orbitals. Togethertheseor- surementsofanion-implantedstandard(sampleI),whichwas
m bitalscantakepartina newcouplingmechanismproceeding implantedwith a Gd dose of1015 cm−2. The detectionlimit
- viaintra-ion4f-5dexchangeinteractionfollowedbyinter-ion wasfoundtobe2×1015cm−3.
d
5d-5dcouplingmediatedbychargecarriers[4].
Magnetization measurements up to 360 K were done in a
n
o Here,weperformasystematicstudyofthemagneticprop- Quantum Design superconducting quantum interference de-
c erties of the DMS GaN:Gd. The magnetization measure- vice (SQUID) magnetometerwith the sample held in a plas-
v: ments reveal an unprecedented magnetic moment of up to tic straw providedby Quantum Design. The response of the
Xi 4000 m B per Gd atom. This colossal magnetic moment can magnetometerwascalibratedwithepitaxialFeandMnAslay-
beexplainedintermsofalong-rangespin-polarizationofthe ersonGaAsforwhichthemagnetizationisaccuratelyknown.
r
a GaN matrix by Gd. This conclusion is independently con- The magnetization of undoped GaN layers was found to be
firmedbythepronouncedchangesofthecircularpolarization indistinguishablefromthatofbareSiCsubstrates.Magnetiza-
inmagneto-photoluminescencemeasurementsuponlightGd- tionloopswererecordedatvarioustemperaturesformagnetic
doping. Moreover,allsamplesarefoundtobeferromagnetic fieldsbetween±50kOe. Themagneticfieldwasappliedpar-
above room temperature. A phenomenologicalmodel is de- allel to the sample surface, i. e., perpendicular to the c-axis,
velopedtoexplainthemacroscopicmagneticbehaviorof the forallmeasurements. Alldatapresentedherewerecorrected
system, suggesting a close connection between the observed forthediamagneticbackgroundofthesubstrate.
ferromagnetismandthecolossalmagneticmomentofGd. For magneto-PL, the sample was excited by a He-Cd ion
The 400–700 nm thick GaN layers with a Gd concentra- laser at a wavelength of 325 nm. The laser power densities
tion ranging from 7×1015 to 2×1019 cm−3 were grown di- focused on the sample were in the range between 200 and
rectly on 6H-SiC(0001) substrates using reactive molecular- 250 Wcm−2. The experiments were carried out in the tem-
2
samples. Figure 2 (b) and (c) show the temperature depen-
F
1019 G denceofthe magnetizationundera magneticfield of100Oe
forsamplesAandC,respectively.Priortomeasuringthetem-
E
-3m) 1018 D SIMS profile : sample C pcoeroalteudrefrodmeperonodmentceemopfetrhaetumreatgon2etKizaetiitohne,rtuhnedsearmapslaetuirsafitirosnt
(cd1017 C -3m) 1017 fieldof20kOe(Field cooled: FC) oratzerofield (zerofield
NG1016 A B (cNGd1015 cZoFoClecdu:rvZeFsCar)e. IqtuiaslictaletiavrelfyrosmimtihlaersfeorfibgoutrhessatmhaptlethsefeFaCturainndg
10130 300 600 adoublesteplikestructurebelow100KintheFCcurves. In
Depth (nm)
1015 thecaseofsampleC,thetwocurvesremainseparatedthrough-
10-6 10-5 10-4 10-3 10-2 outthe entire temperaturerange (2–360K), while they coin-
Flux ratio J /J
Gd Ga cide at around 360 K for sample A. The separation between
theFCandZFCcurvesindicatesahystereticbehaviorwhich
FIG. 1: Gd concentration as measured by SIMS as a function of
is consistent with our previous observation from Fig. 2 (a).
Gd/Gafluxratio(solidsquares). Thesolidlineisalinearfittothe
ThetwocurvescoincideattheCurietemperatureT ,whenthe
datarepresentingsampleC,EandF.TheGdconcentrationforsam- c
ple A, B and D (open squares) is obtained from the corresponding hysteresisdisappears. Clearly,Tc isaround360Kforsample
Gd/Gafluxratiobyextrapolation. Theinsetofthefigureshowsthe A while it is much larger for sample C. The separation be-
SIMSprofileobtainedforsampleC. tweentheFCandZFCcurvesmeasuredat360Kisplottedas
afunctionofGdconcentrationintheinsetofFig.2(c),andis
seentoincreasewithincreasingGdconcentrationrevealinga
peraturerange5–100K,inacontinuousHe-flowcryostat,and shift of T towardshigher temperatures. We have also inves-
c
in magnetic fields up to 12 T using the backscattering Fara- tigateda Gd-implantedGaN sample(sampleI)with a higher
day geometry. In all measurements, the magnetic field was Gdconcentrationthanwecouldreachbyincorporationduring
oriented parallel to the c-axis of the samples. The magnetic growth.Thissamplealsoexhibitsferromagnetismatandwell
fieldinducedcircularpolarizationofthe(D0,X)transitionwas above room-temperature. These observations are consistent
analyzed by passing the emitted light through a photoelastic withtheresultsobtainedbyTeraguchietal., whoobserveda
modulator(PEM),aquarter-wave-plate,andalinearpolarizer. Curie temperaturelargerthan 400K in Ga Gd N alloys
0.94 0.06
GaN:GdlayersA–GweregrownwiththeGd/Gafluxratio [6].
increasingfromAtoGinalphabeticorder.Theconcentration TheeffectivemagneticmomentperGdatomp canbeob-
eff
of Gd (NGd) in samples C, E, F and G is measured by sec- tainedfromthevalueofthesaturationmagnetizationMs (peff
ondaryionmassspectrometry(SIMS).InFig.1,N asmea- =M /N ). InsampleC, p isfoundtobe935and737m at
Gd s Gd eff B
suredbySIMSisplottedasafunctionoftheGd/Gafluxratio 2Kand300K,respectively.Thesevaluesareabouttwoorder
f . SamplesC, EandF(solidsquares)arelyingonastraight ofmagnitudeslargerthanthe puremomentof Gd. In Fig. 3,
line with a slope of unity indicating a linear dependence of p obtainedatdifferenttemperaturesisplottedasafunction
eff
Gdincorporationonf . TheGdconcentrationofsampleGis ofN . DataobtainedfromsampleIarealsoincludedinthis
Gd
smallerthanexpectedfromthislineardependence.Infact,we figure(solidsquares).Bothat2K[Fig.3(a)]and300K[Fig.
haveobservedastronglyfacetedsurfaceforsampleG,indicat- 3(b)], p isfoundtobeextraordinarilylarge,particularlyfor
eff
ingthatGdisaffectingthegrowthmodeatthesehighconcen- lowGdconcentrations.AthighGdconcentrations,p isseen
eff
trations.N forsampleA,BandD(opensquares)isobtained to saturate. It is interesting to note that at 300K, the satura-
Gd
bylinearlyextrapolatingthecurvepassingthroughsamplesC, tionvalueisclosetothatoftheatomicmomentofGd(8m ),
B
E and F. The inset of the figure shows the SIMS profile ob- while at 2 K, it is clearly higher. This is true even for sam-
tained for sample C. The concentrationof Gd is found to be pleI.Suchacolossalmomentcanbeexplainedintermsofa
constantovertheentiredepthforsampleCandallothersam- veryeffectivespin-polarizationof the GaN matrix bythe Gd
plesinvestigatedbySIMS,rulingoutanyaccumulationofGd atoms. In fact, in certain diluted metallic alloys, the solute
onthesurfaceduringgrowth. Allsamplesweresubjecttoan atoms exhibit an average magnetic moment larger than their
extensiveinvestigationbyhigh-resolutionx-raydiffractionin atomic value. This effect is called giant magnetic moment.
a wide angular range. No reflections related to a secondary There are severalreportson a giant magneticmomentof Fe,
phase was detected. Furthermore, we have investigated one Mn and Co when they are either dissolved in or residing on
sample(C)bytransmissionelectronmicroscopy. Noclusters the surface of Pd [7, 8, 9]. This effect is explained in terms
orprecipitateswereobserved.Electrically,allGddopedsam- of a spin polarization of the surroundingPd atoms. Very re-
plesarefoundtobehighlyresistive. cently, a giant magnetic moment was observed in Co doped
Figure 2 (a) shows the magnetization loops obtained for SnO2−d [10], a DMS. High-temperatureferromagnetismand
sampleCat2Kand300K.Atbothtemperatures,themagneti- an unusually large magnetic moment were observed also in
zationsaturatesathighmagneticfields(unlikesuperparamag- Fe-dopedSnO ,whichwasarguedtooriginatefromferrimag-
2
neticmaterials)andexhibitsaclearhysteresisatlowerfields. netic coupling mediated by electrons trapped on bridging F-
Thesetwo featuresclearlyindicatea ferromagneticbehavior. centers[11].
Wehaveobservedqualitativelysimilarhysteresisloopsforall The above conclusion of a long-rangespin-polarizationof
3
0.6 2 K (a) 104 2 K
300 K 3m) 10
3m) 0.3 103 mu/c
(emu/cM-00..30 3 (emu/cm)M 00..03 mp ()eB102 (eMS0.11 N1G01d7 (cm-3)1019
-0.3
-2 0 2
-0.6 H (kOe) 101 (a)
-30 0 30
H (kOe) 1016 1017 1018 1019 1020
N (cm-3)
0.08 FC (b) Gd
300 K

103 3m) 10
c
3) u/
m m 1
(emu/cM0.04 mp ()eB102 (eMS0.1 10N17Gd (cm1-03)19
ZFC
101 (b)
0.00
0 100 200 300
T (K) 1016 1017 1018 1019 1020
0.12 N (cm-3)
FC (c) Gd

T = 360 K FIG. 3: Magnetic moment per Gd atom (p ) as a function of Gd
) MZFC3cm) 10-2 concentrationat(a)2Kand(b)300K.Theseaffturationmagnetization
3cm0.09 - MFC emu/ 10-3 t(hMesr)easspaecftuinvectiinosneotsf.GOdpceonnscqeunatrreastioarnearte2praensden3t0in0gKthiseaelxspoesrhimowenntianl
u/ ( dataforsampleA–GandsolidsquaresforsampleI.Solidlinesare
m
(eM ZFC 1016 1N0G17d (1c01m8-31)019 thetheoreticalfitobtainedfromourmodel(discussedinthetext).
0.06
neticfield. Figure4showsthePLspectraforaGaNreference
0 100 200 300
sample [Fig. 4 (a)] and sample C [Fig. 4 (b)] under a mag-
T (K)
netic field of B=10 T. The transition is polarized for both
samples,whichisevidentfromthedifferenceinintensitiesof
FIG.2: (a)MagnetizationloopsobtainedforsampleCat2K(solid
line)and300K(dottedline).Theinsetof(a)showstheloopsatsmall thetwocircularlypolarizeds + (opensquares)ands − (solid
fields.Temperaturedependenceofmagnetizationatfield-cooled(FC) squares) components. Most importantly,the polarizationhas
andzero-field-cooled(ZFC)conditionsatamagneticfieldof100Oe opposite sign for sample C when compared to the reference
for(b)sampleAand(c)sampleC.ThedifferencebetweenFCand sample,whichclearlyindicatesthattheexcitonicgroundstate
ZFCmagnetizationmeasuredat360KisplottedasafunctionofN
Gd insampleCissubjectedtoaninternalmagneticfieldwhichis
intheinsetof (c). Thesolidcurve through thedataisguide tothe
effectivelystrongerthantheexternalfieldandisactinginthe
eye.
oppositedirection. ConsideringthatthemeanGd-Gdsepara-
tionin sampleCis 25nm, andthatthe averagedistanceofa
the GaN matrix by the Gd atomsis independentlyconfirmed (D0,X)sitefromaGdatomwillthusbeaslargeas12nm[13],
bymagneto-PL.Intheabsenceofanexternalmagneticfield, thisfindingdirectlyconfirmsourpreviousconclusionthatthe
Gdatomsareintroducingalongrangespinpolarizationinthe
the PL spectra of all samples are characteristic for undoped
epitaxialGaN layersin thattheyaredominatedby a neutral- GaN matrix. We also observethatthe relative changeof po-
donor bound exciton (D0,X) transition at ∼3.458 eV. The larizationwithrespecttothereferencesampleincreaseswith
lowerenergyofthistransitionwhencomparedtohomoepitax- the Gd concentration, as intuitively expected. These results,
ial GaN is consistent with the tensile in-plane strain in these togetherwithaquantitativeanalysisofthedependenceofthe
layers of 0.15% [12]. In all cases, the donor responsible for polarization on the magnetic field, will be reported in detail
thistransitionisOwithaconcentrationofabout1018cm−3as elsewhere[14].
measured by SIMS. However, clear differences between un- Inordertogetaquantitativeunderstandingoftherangeof
dopedandGd-dopedGaN layersareevidentwhenanalyzing thespinpolarization,wehavedevelopedaphenomenological
the circular polarization of the PL in the presence of a mag- modelas explainedin the following. The polarizationof the
4
N
(a) + (cid:2)p0−(p0+p1NGdv)e−vNGd(cid:3) 0 (3)
Reference GaN N
Gd
AtlowGdconcentrations,mostofthespheresarewellsep-
aratedand p hasits maximumvalue. As the concentration
s - ofGdisincreeaffsed,moreandmorespheresoverlapandp de-
eff
ts) s + creases.Finally,ataveryhighGdconcentrationtheentirema-
ni trix becomespolarized, and p approachessaturation. Note
u eff
thatthevalueofsaturationislargerthanthemagneticmoment
.
b
ar ofbareGdatomsbyanamountof p1N0v. WeuseEqn.3tofit
( ourexperimentaldatawithpGd=8m Bandp0, p1andrasfree
y parameters. The agreement is quite satisfactory as shown in
nsit Sample C (b) Fig.3. Thefityields p0=1.1×10−3m B, p1=1.0×10−6m B,
e and r=33 nm at 2 K and p = 8.4×10−4 m , p ≈0, and
t 0 B 1
n r=28nmat300K.Thefinitevalueofp at2Kexplainswhy
I 1
s - peff saturates at a value which is still higher than the atomic
momentofGd. Mostimportant,however,isthatthevaluefor
s +
rissufficientlylargetoaccountforthestrongeffectofGdon
theexcitonicgroundstateoftheGaNmatrix(cf. Fig.4).
The second remarkable property of our GaN:Gd layers is
thehigh-temperatureferromagnetismobservedinallsamples
(wellaboveroomtemperature,comparedtoaT of289Kfor
c
3.42 3.44 3.46 3.48
bulkGd).Webelievethattheferromagnetismandthecolossal
Photon Energy (eV) moment of Gd observed in these samples are in fact closely
related. An overlap of the spheres of influence establishes a
(long-range)couplingbetweentheindividualspheres. Within
FIG. 4: Circularly polarized PL spectra for (a) the reference GaN
sampleand(b)sampleC,measuredat6Kunderamagneticfieldof the framework of percolation theory, ferromagnetism is ex-
B=10TinFaradayconfiguration(Bkc-axis). pected to occur at the percolation threshold, when an ”infi-
nite cluster” spanning macroscopic regions of the sample is
formed. The percolation threshold is reached for our model
GaNmatrixbytherandomlypositionedGdatomsisdescribed
at v = 0.28955 [15, 16]. With increasing Gd concentration,
asarigidsphereofinfluencearoundeachGdatom,meaning weewouldthusexpectaphasetransitionfromparamagneticto
that all the matrix atoms within the sphere are polarized by
ferromagneticbehavior. Furthermore,T whichdependsupon
c
anequalamountwhereasmatrixatomsfallingoutsideofthis
thestrengthoftheoverlapisexpectedtoincreasewiththeGd
spherearenotaffected.Letusassociateaninducedmomentof
concentration.Thisisclearlyconsistentwiththeresultsshown
p witheachofthematrixatomslyingintheregionoccupied
0 intheinsetofFig.2(c).
byonesphere. Asoneshouldexpectanincreaseofthepolar-
Unfortunately, the well-established percolation formalism
izationofmatrixatomsiftheybelongtoaregionwheretwo(or
cannotbe straightforwardlyadoptedto quantitativelyexplain
more)spheresofinfluenceoverlap,weattributeanadditional
the currentproblem. Itis intuitivelyclear thatthe spheresof
momentnp tomatrixatomsoccupyingsitesinregionswhere
1 influence are not hard but soft, i. e., the polarization of the
n (n=2,...N ) spheres overlap. Since their radius r is pre-
Gd matrix induced by the Gd atoms must decay with increasing
sumablymuchlargerthanthelatticespacinginGaN,wefur-
distance.Theonsetofferromagneticordernowdependsupon
therassumethatthespheresarerandomlyarrangedinathree-
the precise shape of this polarizationcloud as well as on the
dimensionalcontinuum(continuumpercolation). Within this
overlap of two or more of these clouds. A quantitative pre-
framework,thesaturationmagnetizationcanbeexpressedas
diction of the onset of ferromagnetism in this situation thus
N(cid:229) Gd requires a detailed understanding of the nature of the ferro-
Ms=pGdNGd+p0vN0+p1N0 nvn (1) magneticcouplinginthismaterial.
e n=2 e Regardingthemicroscopicoriginofthiscoupling,itisclear
whereN0istheconcentrationofmatrixatomsperunitvolume, that it cannot be explained simply in terms of direct, double
v is the volume of each sphere, v =1−exp(−vNGd) is the or superexchange between Gd atoms since the average Gd-
volumefractionoccupiedbythespeheres,and Gddistanceistoolargeforsuchacouplingtoexist. Further-
(vN )n more,allsamplesarefoundtobeelectricallyhighlyresistive,
vn= Gd e−vNGd (2) ruling out free-carrier mediated RKKY (Rudermann–Kittel–
e n!
Kasuya–Yosida)typelong-rangecoupling. Finally, also very
is the volume fraction of the regions contained within n
recentproposalsaimedatexplainingagiantmagneticmoment
spheres. The average magnetic moment per Gd atom p is
eff and/or high-temperature ferromagnetism in various material
thenobtainedas
systems [7, 8, 9, 10, 11] do not apply to the currentrequire-
p = p +p N v ment of a long-range coupling. An actual understanding of
eff Gd 1 0
5
thephenomenonobservedinthepresentpaperwillrequirede- AcademyofSciences,194021St.Petersburg,Russia
tailed ab initio studies, particularly of the f-d coupling be- [1] H.Ohnoetal.,Appl.Phys.Lett.69,363(1996).
tween Gd and Ga. Considering the long spatial range of the [2] T.Dietl,H.Ohno, F.Matsukura, JCibertandD.Ferrand,Sci-
ence287,1019(2000).
couplingevidentfromourexperiments,suchcalculationsare
[3] S.Dharetal.,Appl.Phys.Lett.82,2077(2003).
computationallyverydemandingandarethereforebeyondthe
[4] T.Storyetal.,Phys.Rev.Lett.77,3447(1996).
scopeofthepresentpaper.Animportantresultforanytheoret-
[5] ThepurityoftheGdingothasbeendeterminedbythemanufac-
icalapproachwasrecentlyobtainedbyHashimotoetal.,who turer(StanfordMaterialsCorporation) viainductively-coupled
showedthatGdoccupiesprimarilyGasitesinGaNevenata plasmamassspectroscopy. Thedatasheet ofouringotcertifies
concentrationashighas6%(twoordersofmagnitudehigher that the ferromagnetic elements Fe, Ni and Co are present in
thanthehighestconcentrationinvestigatedhere)[17]. residualtracesof≪100ppm,≪50ppm,andbelowthedetec-
tionlimit(0.5ppm), respectively. Notethat the magnetization
Our study has revealed an extraordinarily large magnetic
observedinthisworkfor,e.g.,samplesAandCwouldrequire
moment of Gd in GaN which can be explained in terms of
anFe(Ni,Co)concentrationof1019cm−3andabove,threeor-
a long-range spin-polarization of the GaN matrix by the Gd
dersofmagnitudehigherthantheGdconcentration.Alsonote
atoms. Thematerialisfoundtoexhibitferromagnetismabove thatthevaporpressureofalltheseelementsisalmostidentical
room temperature even with a Gd concentration less than tothatofGd.
1016 cm−3. Thisfindingoffersanexcitingopportunity,since [6] N.Teraguchietal.,Sol.StateCommun.122,651(2002).
GaN:Gd maybe easily dopedwith donors(acceptors)with a [7] G.Bergmann,Phys.Rev.B23,3805(1981).
[8] J. Flouquet, O. Taurian, J. Sanchez, M. Chapellier, J. L. Tho-
concentrationexceedingthatofGdtogeneratespinpolarized
lence,Phys.Rev.Lett.38,81(1977).
electrons(holes)intheconductionband(valenceband). Gd-
[9] J.CrangleandW.R.Scott,J.Appl.Phys.36,921(1965).
dopedGaNwithitsT aboveroomtemperaturemightthusbea
c [10] S.B.Ogaleetal.,Phys.Rev.Lett.91,077205(2003).
veryattractivecandidateasasourceofspin-polarizedcarriers [11] J.M.D.Coey,A.P.Douvalis,C.B.Fitzgerald,M.Venkatesan,
forfuturesemiconductor-basedspintronics[18]. Appl.Phys.Lett.841332(2004).
We are indebted to A. Trampert, K. J. Friedland and U. [12] P.Waltereitetal.,Appl.Phys.Lett.74,3660(1999).
Jahnforimportantcontributionstothiswork.Furthermore,we [13] It can be easily shown that the average distance of an exciton
thankJ.Herfort,M.BowenandR.Kochforvaluablediscus- bindingsitefromitsnearestGdatomis=0.480296a,wherea
istheaverageGd-Gdseparation
sionsandsuggestions. Wealsoacknowledgepartialfinancial
[14] V.Sapegaetal.,unpublished.
support of this work by the Bundesministerium fu¨r Bildung
[15] R. Consiglio, D. R. Baker, G. Paul, H. E. Stanley, Physica A
undForschungoftheFederalRepublicofGermany.
319,49(2003).
[16] D.R.Baker,G.Paul,S.Sreenivasan,H.E.Stanley,Phys.Rev.
E66,046136(2002).
[17] M.Hashimotoetal.,phys.stat.sol.(c)7,2650(2003).Seealso
Ref.6.
∗ Electronicaddress:[email protected] [18] S.A.Wolfetal.,Science294,1488(2001).
† Permanent address:Ioffe Physico-Technical Institute, Russian