APS/123-QED Dynamics of exciton magnetic polarons in CdMnSe/CdMgSe quantum wells: the effect of self-localization I. A. Akimov,1,2 T. Godde,3 K. V. Kavokin,2 D. R. Yakovlev,1,2 I. I. Reshina,2 I. V. Sedova,2 S. V. Sorokin,2 S. V. Ivanov,2 Yu. G. Kusrayev,2 and M. Bayer1,2 1Experimentelle Physik 2, Technische Universita¨t Dortmund, 44221 Dortmund, Germany 2Ioffe Physical-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia 3Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom (Dated: January 10, 2017) 7 We study the exciton magnetic polaron (EMP) formation in (Cd,Mn)Se/(Cd,Mg)Se diluted- 1 0 magnetic-semiconductorquantumwellsusingtime-resolvedphotoluminescence(PL).Themagnetic 2 field and temperature dependencies of this dynamics allow us to separate the non-magnetic and magnetic contributions to the exciton localization. We deduce the EMP energy of 14 meV, which n is in agreement with time-integrated measurements based on selective excitation and the magnetic a field dependence of the PL circular polarization degree. The polaron formation time of 500 ps is J significantly longer than the corresponding values reported earlier. We propose that this behavior 7 is related to strong self-localization of the EMP, accompanied with a squeezing of the heavy-hole envelope wavefunction. This conclusion is also supported by the decrease of the exciton lifetime ] i from 600 psto 200 - 400 ps with increasing magnetic field and temperature. c s PACSnumbers: - l r t m I. INTRODUCTION creases its binding energy, which can reach values up to 30 meV. However, truly free MPs have not been . t foundexperimentally sofar,only partialself-localization a In diluted magnetic semiconductors (DMS) carriers m are coupled with the localized spins of the magnetic during MP formation has been established from study- - ions by strong exchange interaction1,2. This leads to ing the MP dynamics6,16. The properties of two- d giant magneto-optical effects that have been investi- dimensional EMPs have been studied in great detail n gatedin depth for II-VI DMS with magnetic Mn2+ ions, for(Cd,Mn)Te/(Cd,Mg)Teheterostructures. Thedepen- o dencies of the polaron energy on the structure design like (Cd,Mn)Te, (Cd,Mn)Se and (Zn,Mn)Se and their c [ heterostructures2–4. The giant Zeeman splitting of the andexperimentalconditions,likeexternalmagnetic field band states, the giant Faraday and Kerr rotation and strength and temperature were measured by means of 1 optical selective excitation7,17–20. The spin dynamics of the existence of magnetic polaron are among the most v carriers and localized magnetic ions during the polaron widely studied phenomena. 4 formation process were studied by time-resolved spec- 2 The magnetic polaron (MP) formation is caused by troscopy and polarization sensitive techniques. Based 8 ferromagnetic alignment of the localized magnetic ions 1 in the vicinity of a carrier. Carrier localization plays on the current understanding it is important to extend 0 a crucial role for the MP stability and controls the po- these investigations to other material systems in order . to check whether the conclusions drawn for EMPs in 1 laron energy. Carriers may be bound to impurity cen- (Cd,Mn)Te/(Cd,Mg)Te heterostructures can be general- 0 ters (donors or acceptors) or localized by electrostatic 7 ormagneticpotentialfluctuations,like alloyfluctuations ized,andalsotosearchfornewEMPregimeswhichmay 1 in ternary semiconductors or well width fluctuations in be offered by novel DMS systems. : v quantum wells. As a result, bound or localized mag- i netic polarons can be studied in optical spectra, see e.g. In this paper we present the results of optical studies X Refs. 2,5–7. Also criteria for the stability of free mag- of exciton magnetic polarons in (Cd,Mn)Se/(Cd,Mg)Se r a netic polarons,i.e. for magneticpolaronformationwith- DMS heterostructures. These structures were addressed out initial localization of the involved carrier, have been using continuous wave photoexcitation only21. Thereby considered theoretically for II-VI semiconductors8,9. In the formation of EMP was established and the polaron particular,ithasbeenshownthatfreemagneticpolarons energy was measured. Here we study the EMP dynam- are not stable in three dimensional systems so that their ics using time-resolved photoluminescence (PL) as func- formationcannotbeexpectedinbulksamples. However, tions of magnetic field and temperature. The following reduction of the system’s dimensionality to two favors Section II presents the short theoretical background of free MP stability. the exchange interaction in DMS and the EMP parame- These predictions stimulated experimental studies of ters. Section III describes the investigated samples and excitonmagneticpolarons(EMP)inquantumwell(QW) the experimental technique. The experimental results structures based on (Cd,Mn)Te and (Zn,Mn)Se10–15. and discussion are given in Sections IV and V for time- The reduction of dimensionality provided by decreasing integratedandtime-resolvedmeasurements,respectively. the QW width indeed favors EMP formation and in- The discussion of the results is presented in section VI. 2 II. THEORETICAL BACKGROUND with reduction of dimensionality, because the relatively weak primary localization of the exciton (e.g. on inter- InII-VIDMSthe conductionbandelectronswithspin face fluctuations in QWs) can be sufficient for further s = 1/2 and the valence band holes with angular mo- self-localization leading to a gain in exchange energy. mentum J = 3/2 are subject to the sp − d exchange Suchself-localizationimpliesamodificationofthecarrier interaction with the localized spins of the Mn2+ ions, wavefunctionsintheEMPformationprocess,particulary which have angular momentum SMn = 5/2. This re- squeezing of the hole wavefunction,which contributes to sultsingiantZeemansplittingofconductionandvalence thepolaronenergyandaffectsthepolarondynamicsand bandsunderappliedmagneticfieldB. IntheFaradayge- exciton radiative lifetime6,25,26. ometry, when the magnetic field B is oriented along the The polaron energy EMP is related to the exchange QW growth axis coinciding with the optical axis z, the field Bex by27 heavy-hole exciton splits into two components with spin 1 −1, which is composed of s = +1/2 and J = −3/2, E = γB , (3) z z MP 2 ex and spin +1 constructed of s = −1/2 and J = +3/2. z z The energy splitting between these Zeeman sublevels is whereγ =d∆Ehh/dB| isthe slopeofthe heavy-hole described by the well known relation22 giant Zeeman spzlittingBm=0easured in the Faraday geom- etry in the limit of weak magnetic fields. ∆Ehh(B) is ∆E (B)=xN (α−β)hSMn(B)i, (1) z z 0 z connectedwiththeexcitongiantZeemansplittingbythe relation: wherexistheMn2+ concentration,N αandN β arethe 0 0 exchangeconstantsfortheconductionandvalencebands, |β| respectively,andhSzMn(B)iis thethermalaverageofthe ∆Ezhh(B)= |α|+|β|∆Ez(B). (4) Mn spin projection along B. The latter is given by the modified Brillouin function BS for S =5/2: It is important to note here, that Eq. (3) is derived for localized magnetic polarons where the hole localization 5µ g B hSMn(B)i=S B B Mn , (2) volume,andcorrespondinglytheholeexchangefieldBex, z eff 5/2(cid:20)2kB(T +T0)(cid:21) do not change during EMP formation. This condition is fulfilled for the most studied (Cd,Mn)Te/(Cd,Mg)Te where µ is the Bohr magneton, k is the Boltzmann B B structures. constant, T is the lattice (bath) temperature andg = Mn Experimentally, selective excitation of localized exci- 2.01 is the Mn2+ g factor. S is the effective spin eff tonsgivesthemostdirectandreliableaccesstotheEMP and T0 is the effective temperature. These parameters parameters7,18. Thereby excitons are excited in the tail permit a phenomenological description of the antiferro- of localized states below the mobility edge, where fur- magnetic Mn-Mn exchange interaction. We use here the ther spectraldiffusion along the tailof localizedstates is bulk values for the exchange integrals in Cd1−xMnxSe: suppressed. Excitonscandecreasetheirenergy,however, N α = 0.258 eV and N β = −1.238 eV2,23. Typically 0 0 by magnetic polaron formation and the energy shift of the intrinsic Zeeman splittings of electron and hole and the emission line maximum ~ω relative to the excita- PL the electron-hole exchange interaction are much smaller tionenergy~ω issolelycontributedbythepolaronex- exc comparedwiththeeffectsinducedbythesp−dexchange changeshift∆E. TheEMPformationtime,τ ,typically f interaction. Therefore, they are neglected. is in the rangeof50 to 200ps6,16. Attimes exceeding τ f The exciton magnetic polarons are formed due to po- the polaron shift approaches the EMP energy larizationofthemagneticionspinsbythe exchangefield of the holes Bex, which are dominant in the exchange ∆E(t>>τf)=EMP. (5) interaction with the magnetic ions because the hole ex- change integral is almost five times larger than that of However, exciton recombination occurring with charac- the electrons. The resulting cloud of polarized Mn spins teristictimeτ mayinterruptthepolaronformationpro- 0 can be consideredas magnetic molecule with a magnetic cess. In this case the polaron shift observed in time- moment of hundreds of Bohr magnetons. The exchange integrated PL spectra is smaller than E . Therefore, MP fieldB isinverselyproportionaltotheholelocalization time-resolved experiments, which allow one to measure ex volume24. both τ and τ , are required for evaluation of the EMP f 0 The EMP formation is accompanied by the decrease energy. of the associated exciton energy by the polaron energy An alternative technique for evaluating the EMP pa- and can be treated as localization process. The primary rameters is based on monitoring the magnetic-field- localizationof the excitonplays animportant rolein the induced polarization of magnetic polarons, which re- EMP formation. Theory predicts that the stability con- flects the orientation of the magnetic fluctuations in- ditions for free magnetic polarons can be hardly fulfilled sidethe polaronvolume,andthereforecontainsinforma- in bulk DMS based on II-VI materials, where strong ini- tion about the hole localization volume and the hole ex- tial localization on alloy and/or magnetic fluctuations is changefield24,27,28. Time-resolvedmeasurementsarenot required for EMP formation7–9. The situation changes required in this case. The circular polarizationdegree of 3 the EMPemission, ρ (B), is measuredas functionofthe c external magnetic field. Its slope in weak magnetic field MQW DQW θ =dρ /dB| allows evaluation of the polaron energy c B=0 E c 1 γ 2 E = . (6) MP 2πk T θ B (cid:16) (cid:17) It was shown for (Cd,Mn)Te based samples that both techniques give very similar EMP values.6,24,27 Never- 1.845 eV 2.125 eV 1.765 eV theless,ifthelocalizationvolumechangesduringthe po- laron formation process the theoretical approach should account for the self-localization effect. E v e e e e e e S S S S e S S g n g g S n g M M M M d M M III. EXPERIMENTAL DETAILS d d d d C d d C C C C C C Theinvestigated(Cd,Mn)Se/(Cd,Mg)Sequantumwell FIG. 1: Band gap diagram of a single period of the structures were grown by molecular-beam epitaxy on Cd0.935Mn0.065Se/Cd0.83Mg0.17Se MQW sample and the (001) oriented InAs substrates. Details of the growth CdSe/Cd0.8Mg0.2Se/Cd0.927Mn0.073SeDQW structure. technique were reported previously29,30. Most of the studies presented here were done on a multiple quan- tum well (MQW) structure (#372) with five periods of focusedintoaspotwithadiameterofabout300µmand Cd Mn Se/Cd Mg Se layers. The wells are 0.935 0.065 0.83 0.17 with the excitation densities kept low enough to exclude composed of the DMS material with a width of 3.8 nm, heating effects. sandwiched between nonmagnetic barriers with thick- Forreflectivitymeasurementsahalogenlampwasused nesses of 9.7 nm. The barriers are sufficiently thick to as white light source. Photoluminescence (PL) was ex- decouple the electronic states in the neighboring QWs cited by a cw semiconductor diode laser with excitation and, therefore, the QWs can be treated as isolated. On energy at 2.54 eV, which exceeds the band gap of the topofthisstructurea0.1µm-thickCd Mg Selayer 0.83 0.17 Cd Mg Se barriers (2.125 eV) and is referred to as and a 5 nm-thick CdSe cap layer were grown. 0.83 0.17 above-barrier excitation. The circular polarization de- AnotherstudiedCdSe/Cd Mg Se/Cd Mn Se 0.8 0.2 0.927 0.073 greeofthe PLinducedbyanexternalmagneticfieldwas double quantum well (DQW) structure (#309) contains measuredas well. For that purpose the PL was detected sequences of two QWs separated by a thin nonmagnetic in σ+ and σ− polarizationselected by rotation of a λ/4- barrier. The one, nonmagnetic CdSe QW has a width of wave plate in front of a Glan-Thomson prism placed be- 3.8 nm and the other, DMS Cd Mn Se QW has 0.927 0.073 foretheinstalledmonochromator. Thedegreeofcircular a width of 3.4 nm. A nonmagnetic Cd Mg Se barrier 0.8 0.2 with thickness of 1.2 nm allows electronic coupling polarizationisdefinedasρc =(I+−I−)/(I++I−),where between the wells. The whole structure comprises 5 I+ andI− arethe PLintensitiesforσ+ andσ− polariza- tions, respectively. periods of these DQW layers whih are separated by 6.7 nm Cd Mg Se barriers. This sample has also a For time-resolved measurements we used a mode- 0.8 0.2 0.1 µm-thick Cd Mg Se layer and a 5 nm-thick CdSe lockedTi:Sapphirelasercombinedwithasynchronously- 0.8 0.2 caplayer. Inthis studyweusethis sampleasareference pumped optical parametric oscillator equipped with an for the properties of nonmagnetic CdSe QWs. internal frequency-doubling unit for excitation. The The band gap diagrams of both structures are pre- system emitted pulses with a duration of about 1 ps sented in Fig. 1. The band offsets in CdMnSe/CdMgSe and a spectral width of 1 nm at a repetition frequency arenotyetwellelaborated. Theiropticalpropertieswere of 76 MHz. The laser photon energy was tuned to reported in Refs. 21 and 29 where the valence band off- ~ωexc =2.06eVinorderto achievebelow-barrierexcita- setwasestimatedtobe38%oftheenergygapdifference. tionoftheinvestigatedsamples. Time-resolvedmeasure- This corresponds to potential barriers of about 180 and ments were alsoperformed with above-barrierexcitation 100 meV for electrons and holes, respectively. ~ωexc = 2.95 eV. In this case the second harmonic unit The samples were held in the variable temperature was used directly after the Ti:Sapphire laser. inset of a cryostat with a split-coil superconducting The photoluminescence signal was dispersed in a 0.5- solenoid capable of generating magnetic fields B ≤ 7 T. meter monochromator with 6.33 nm/mm linear disper- They were either immersed in pumped liquid helium to sionandwasdetectedwitha streakcamera. Thesystem reach a temperature T = 2 K or were in contact with timeresolutionwas20ps. TheEMPlifetimesweredeter- coldheliumgastomeasuretemperaturedependenciesup mined from the decay of the integral PL intensity, while to 30 K. The magnetic field was applied in Faraday ge- the energy shift of the PL maxima allows one to trace ometry parallelto the structure growthaxis (Bkz) and the EMPformationdynamics6,7. Verysimilarresultsfor paralleltothelightwavevector. Thelaserexcitationwas the EMP dynamics were obtained for above- and below- 4 1.898 Refl. 1.92 PL units) X B=0T B=0T b. 1.896 ar gy (eV)1.90 eflectivity ( B=7T y (eV) 1.894 y ner R 1.9 2.0 erg 1.892 ensit T = 2 K E1.88 Energy (eV) En L int 8 K 1.890 P 16 K 1.85 1.90 1.86 1.888 Energy (eV) 0 2 4 6 8 0 5 10 15 20 25 Magnetic field (T) Temperature (K) FIG. 2: Magnetic field dependence of the exciton (X) en- FIG. 3: Temperature dependence of the PL peak maxi- ergy in the MQW sample measured from reflectivity (cir- mum at B = 0 T. Inset: Time integrated PL spectra for cles) at T = 2 K. The dashed line is the fit with Eqs. (1, T = 2,8 and 16 K measured under cw excitation with 2m)e.asTuhreedpeuankdeerneprugliseesdoefxtchiteattiiomne-winittehgr~aωteexdcP=L2s.p0e6cterVa ~ωexc =2.54 eV. is shown by the triangles. Inset: Reflectivity spectra for 80 B=0and7T.Thearrowsindicatetheexcitonresonance T = 2 K position. ) V 60 e m barrierexcitation. Also time-integratedPL spectra were (L measuredwith1.35nm/mmdispersionunderpulsedpho- ωP 40 h toexcitation using a charge-coupled-device detector con- - c nectedtothesamemonochromatorasthestreak-camera. ωex 20 ∆E=12 meV h IV. SPECTROSCOPY OF EXCITON 0 1.90 1.92 1.94 1.96 1.98 MAGNETIC POLARON hω (eV) exc The giant Zeeman splitting of the exciton resonance FIG. 4: Energy separation between the PL peak maxi- in MQW sample was measured by means of reflectivity. mumandtheexcitationenergyasfunctionof~ωexc. Data Examples of reflectivity spectra at B = 0 and 7 T are weremeasuredwithpulsedexcitationandtimeintegrated shown in the inset of Fig. 2. The heavy-hole exciton detection. (X) resonance shows up as clear minimum, its energy position is marked by the arrow. In magnetic field the lowerZeemansublevelcanbeclearlyidentified,whilethe The temperature dependence of the PL maximum at upper one is broadened. The former one shifts to lower B = 0 T is shown in Fig. 3. Here a high-energy shift energieswithincreasingmagneticfieldbyhalfofthetotal by10meVisobservedwithincreasingtemperature from giant Zeeman splitting of the excitons, see closed circles 2 to 20 K. The temperature and magnetic field depen- in Fig. 2. Fitting the shift data with Eqs. (1,2), see the denciesclearlyevidencetheEMPcontributiontothe PL dashed line, we find S = 0.98 and T =1.5 K. In the spectra13,18. Magnetic fieldapplicationleadstosuppres- eff 0 limitoflowmagneticfieldsweevaluated∆E /dB| = sion of the EMP and, therefore, the difference in the re- z B=0 42.8 meV/T. This gives γ = 35 meV/T, which we will flectivity andPL peak positions vanishes. The EMP can use for evaluation of the EMP parameters. be also destroyed by a temperature increase due to re- Additionally, Fig. 2 shows the dependence of the PL duction of the magnetic susceptibility of the Mn2+ ions. maximumonmagneticfield. AnexamplaryPLspectrum First, we evaluate the polaron shift ∆E from time- at B = 0 T is presented in the inset of Fig. 3. The PL integrated PL measurements under selective excitation peak is red shifted at T = 2 K by almost 20 meV with of localized exciton states13,17,18,20. Figure 4 gives the respect to the free exciton resonance deduced from the energy separation between the PL maximum ~ω and PL reflectivity spectrum (compare open and closed symbols the excitation laser energy ~ω as function of ~ω . exc exc in Fig. 2). Increasing the magnetic field leads to vanish- The energy of 1.91 eV, where this dependence changes ing of the shift and narrowing of the PL line. its character, can be associated with the exciton mobil- 5 ρc e 1.0 V) egre 0.8 on (e 1.91 2.0h6ω0e excV B=0 ation d 0.6 k positi 11..8990 11..980945 eeVV T=2K ular polariz 00..24 EΘM =P 9 =. 21 3T −m1 eV Energy pea 11..8878 0 500 1000 1500 2000 1hω.9e0xc4=e V c Time (ps) Cir 0.0 0.0 0.1 0.2 0.3 0.4 0.5 Magnetic field (T) 300 FIG. 5: Magnetic field dependence of the PL circular polarization degree ρc(B). The line corresponds to a ) linear fit in weak magnetic fields. cw excitation with s ~ωexc =2.54 eV,andtime-integrated detection. T =2K. e (p 837 m Ti 1374 ity edge within the band of localized states. Below this energy spectral diffusion of the exciton due to phonon- assistedtunneling does notoccurduringthe excitonlife- 1910 time. Then the PL shift with respect to the excitation energy is determined by the magnetic polaronformation 1.84 1.86 1.88 1.90 1.92 Energy (eV) only and the PL peak starts to follow ~ω . The cut- exc off energy in the dependence corresponds to the polaron FIG.6: Time-resolved PLspectraatdifferenttimedelaysaf- shift of ∆E =12 meV. Second, we analyze the magnetic field dependence of ter quasi-resonant pulsed excitation with ~ωexc = 1.904 eV. The red spectrum corresponds to t = 0. The green line fol- the circular polarization degree due to exciton thermal- lowsthePLmaximum. Insetshowsthetemporaldependence ization on the Zeeman sublevels. Figure 5 shows this of the PL maximum energy for different excitation energies. dependence of ρc(B), which grows with B before it sat- Arrows indicate thephoton excitation energy. urates at a level of 0.99 already at B = 0.3 T. In the range of weak magnetic fields we find θ = 9.2 T−1. Us- ing Eq. (6) together with the value of γ = 35 meV/T trally integratedPL transients I(t) and the PL peak en- evaluated from the reflectivity measurements we find ergy position E(t) at B = 0 and 7 T for low and high E = 13 meV. This result is consistent with previ- MP temperatures are shown in Figs. 7(a) and 7(b), respec- ousmeasurements21. TheEMPenergyE determined MP tively. As mentioned above,atB =0 T andT =2 K we with this method is comparable to the polaron shift ∆E observe a strong low energy shift relative to the initial measuredunderselectiveexcitonexcitation. Thiscanbe value of E(t = 0) = 1.904 eV to E(t → ∞) = 1.886 eV interpreted as fast EMP formation with τ < τ . How- f 0 at the longest measured delay of t = 2 ns. Application ever,adirectmeasurementofthepolarondynamicsusing of magnetic field or increase of temperature leads to a time-resolved PL spectroscopy is required to assess this significant suppression of this energy shift, which we at- claim in detail. tributetoreductionoftheEMPenergy. Interestingly,we observeasignificantshorteningoftheexcitonpopulation decay with increase of B or T [see Fig. 7(a)]. V. DYNAMICS OF MAGNETIC POLARON In order to quantify the results, we evaluate the en- ergy positions E(0) and E(∞) as function of magnetic Temporally-resolved and spectrally-resolved PL spec- fieldandtemperature. ThedataareplottedinFigs.8(a) tra measured with the streak-camera allow us to study and 8(b). The final energy E(∞) is taken at the longest the EMP formation dynamics. PL spectra at different delay time t where the position of the PL peak could be delay times t after the excitation pulse are shown in still reliably determined. Additionally, the dependencies Fig. 6 at zero magnetic field. The PL line shifts contin- of the energy difference δE =E(0)−E(∞) on magnetic uously to lower energies with increasing time indicating field and temperature are shown in Figs. 8(c) and 8(d). the non-magnetic exciton localization and magnetic po- ThemagneticfielddependenceofE(0)followscloselythe laron formation. The polaron formation can be treated data for the lowest exciton resonance deduced from the as magnetic localization of excitons. This shift is main- reflectivity measurements (see Fig. 2), as expected if the tainedalsounder resonantexcitationofthe excitonwith laser excitation pulses photogenerate free excitons. Due ~ω =1.895 eV as seen from the inset of Fig. 6. Spec- to EMP suppression the energy difference δE decreases exc 6 s) B=0T, T=2K 1.91 (a) T = 2K B=0 (b) nit B=0T, T=28K u b. 103 B=7T, T=2K V) 1.90 ar B=7T, T=26K e y ( (a) y ( 1.89 sit g n er 1.88 nte En t =0 ps B=7T L i 102 1.87 P 1.905 1.86 t = 0 t = 1500 ps 1.900 1.85 1500 ps t = 750 ps 1.895 20 T = 2K (d) V) 1.890 V) B = 0T e e 15 ( m gy 1.885 E( 10 er δ n E 5 (c) 1.865 7T (b) 0 1.860 0 2 4 6 8 0 10 20 30 Magnetic field (T) Temperature (K) 1.855 0 500 1000 1500 2000 FIG.8: Magneticfield(a)andtemperature(b)dependencies Time (ps) of the PL peak positions at zero (t = 0 ps) and maximum (t = 1500 or 750 ps) delay times after the excitation pulse. Magnetic field (c) and temperature (d) dependencies of the FIG. 7: Temporal dependence of integral emission inten- energy difference between the values at minimum and maxi- sfiietlyds(aa)ndantdemPpLerpaetuakresp.o~siωtieoxnc =(b2).0fo6redVi.fferent magnetic mum delay. ~ωexc =2.06 eV. where the polaron energy shift is most pronounced, the from 18 to 4 meV with increasing magnetic field up to intensity transientand the energy peak position follow a B > 4 T, above which it stays constant, see Fig. 8(c). non-exponential decay. Therefore τ and τ are deter- 0 E This behavior indicates the existence of additional lo- mined as the moments when I(t) and δE(t) are reduced calization, which does not vanish in magnetic field and, by the factor of e=2.72. therefore, has a non-magnetic origin. First,wefocusonτ ,whosemagneticfielddependence E The existence ofnon-magneticlocalizationunder non- ispresentedinFig.9. InstrongmagneticfieldstheEMP selective exciton excitation is quite typical. Often it is is suppressed and only non-magnetic localization occurs related with exciton localization on composition fluctu- on a time scale of τNM =180 ps. At zero magnetic field E ations in ternary alloys as well as interface fluctuations bothnon-magneticandmagneticlocalizationarepresent in QWs. Thus we conclude, that at B > 4 T the EMP producingthetotalshiftofδE =E +E =18meV. NM MP is almost fully suppressed while the δE = 4 meV shift The timescale of this localization at T =2 K is given by corresponds to non-magnetic localization with a charac- τ = 480 ps, which is slightly shorter than the exciton E teristic energy ENM. The temperature dependence at recombinationtime τ0. Assumingthatthe non-magnetic B = 7 T in Fig. 8(d) shows that the non-magnetic lo- localization is independent of B we put E = 4 meV NM calization contribution slightly increases from 4 meV at andevaluatethe EMPenergyE =14meV.Here,the MP T =2 K to 6 meV at 26 K. Simultaneously, at B =0 T nonmagnetic contribution is significantly smaller than the energy shift δE decreases with temperature and fi- the EMP energy and therefore we attribute the localiza- nally tends to the value of ENM at T = 28 K. Such tiontimeatB =0totheformationtimeoftheMPτf ≈ behavioris expected since the EMPenergy decreasesfor 500ps. SuchlongEMPformationtimeisquiteasurpris- alowermagneticsusceptibility ofthe Mn2+ spinsystem. ing result compared to previous studies for (Cd,Mn)Te Further insight in the magnetic polaron dynamics is and (Zn,Mn)Se based heterostructures for which times obtainedfromthemagneticfieldandtemperaturedepen- in the order of 50−200 ps were reported6,15,16. denciesofthetimeconstantsτ andτ characterizingthe ThedependenciesofthePLdecaytimeonB andT are 0 E decayofthe excitonpopulationI(t) andthe energyshift showninFig.10. Weobservedecreasesofτ from600ps 0 δE(t), respectively. Note that at B =0 T and T =2 K, to either 200 ps or400 ps with increase of magnetic field 7 ) 800 energy, but also the formation time s p τ (E600 τ τf =τs EMP , (7) f ∆Eeq(0) , e m where τ is the EMP formation time without self- ti 400 localizatison and ∆E (0) is the equilibrium EMP en- n eq o τ NM ergy at t = 0, i.e. without self-localization. Since zati 200 E ∆Eeq(0) < EMP, the formation time becomes longer ali than τs. oc Previous studies reported no strong deviations of τf L 0 fromτ ,exceptfor(Cd,Mn)TeQWquantumwells,where s 0 2 4 6 8 forsampleswithlowMn2+concentration(x=0.1)atwo- Magnetic field (T) fold increase of the formation time was reported16. The intrinsic formationtime τ in (Cd,Mn)Te QWstructures s FIG.9: Magneticfielddependenceofthelocalizationtime wasmeasuredtobe inthe rangeof150ps. Similartimes τE. ~ωexc = 2.06 eV. Arrows indicate the magnetic po- are expected for (Cd,Mn)Se. However, we find that in laron formation time τf and the non-magnetic exciton lo- the studied (Cd,Mn)Se structures τf = 500 ps which is calization time τENM. more than 3 times longer than τs. Obviously, in these structures exciton self-localizationhas to play an impor- tant role in the EMP formation. (a) (b) The equilibrium EMP energy at the initial moment of s) 600 T = 2 K B = 0 time ∆Eeq(0) = 4 meV can be evaluated from Eq. (7) p using τf = 500 ps, τs = 150 ps and EMP = 14 meV. ( 0 Theconsiderableself-localizationofEMPin(Cd,Mn)Se- τ 400 basedQWs canbe relatedto different factors: First, the e, 7T smaller heavy-hole effective mass of only m∗ =0.45 in m hh CdSe ascomparedto 0.8inCdTe, whichleadsto weaker eti 200 confinement in the magnetic quantum well and a larger f Li penetration of the wavefunction into the non-magnetic barriers. Second, the relatively small concentration of 0 Mn2+ ions. Bothfactorsmayleadtoweakerinitialmag- 0 2 4 6 8 0 10 20 30 netic localizationin the studied structure, which is criti- Magnetic field (T) Temperature (K) cal for self-localization. The polaronshift ∆E =12 meV evaluated from time- FIG.10: Magneticfield(a)andtemperature(b)dependen- integrated measurements under resonant exciton excita- ciesoftheexcitonlifetime. Opencirclesin(a)correspond tion is in good agreement with the time-resolved data to the lifetime of the exciton in the non-magnetic CdSe yielding E =14 meV. In fact, no large difference be- well of theDQW structure. ~ωexc =2.06 eV. tween thesMePvalues is expected because the polaron for- mation time, although being long, does not exceed the exciton radiative lifetime of 600 ps. We note, however, or temperature, respectively. Additionally, in Fig. 10(a) that the small value of ∆E (0)=4 meV does not coin- eq we present the data for the B-dependence of τ0 in the cide with the polaron energy of 13 meV extracted from non-magnetic well of the DQW structure. In this case themagneticfielddependenceofthePLcircularpolariza- τ0 =250 ps is independent of magnetic field strength as tion degree. The latter reflects the initial distribution of expected, i.e. we obtain the same recombinationtime as magnetic fluctuations and, therefore, should correspond in the magnetic QW, when the EMP is suppressed. to∆E (0). Thisfactdeservesattentionandthedynam- eq icsofmagneticpolaroninweakmagneticfieldsshouldbe studied more detailed in that respect in the future. The self-localization process is accompanied by a VI. DISCUSSION shrinkage of the heavy-hole envelope wavefunction. As a result the overlap of the electron and the hole wave A slow EMP dynamics is expected in case of self- functions changes, leading to a deceleration or acceler- localization which may take place if the initial localiza- ation of the PL intensity decay. Indeed we observe a tion on magnetic fluctuations is relatively weak. During non-exponential decay of I(t) with a rather long radia- EMPformationtheexcitonlocalizationisenhancedlead- tive lifetime of 600ps atB =0 T and low temperatures, ingtoanincreaseofE . Thetheoreticalconsideration where the polaron localization is most pronounced (see MP in Ref. 6 shows that the polaron self-localization in a Fig. 7). Moreover, the radiative decay becomes signifi- two-dimensional system increases not only the polaron cantly shorter, when the EMP is suppressed by applica- 8 tion of magnetic fields B ≥4 T and/or at elevated tem- tion supports the conclusion about the presence of self- peratures above 20 K. The exciton lifetime τ drops to localization. Note that previous observations of self- 0 200 ps at B ≥4 T. For an elevated temperature of 28 K localization were based on the comparison of magnetic we find τ =400 ps. QWswithdifferentwellwidths16. Hereweshowdirectly 0 Itisimportanttodistinguishbetweenoutofplaneand how EMP suppression by magnetic field or temperature lateral squeezing of the heavy hole wavefunction in the can change the exciton dynamics. QWduringtheprocessofEMPformation. Thefirstsce- nario takes place if the hole confinement in the QW is weak. Then, in narrow QWs, e.g. of 3.8 nm as studied VII. CONCLUSIONS experimentallyinthispaper,theelectronwavefunctionis strongly localized in the DMS QW, while the hole wave- We have studied time-resolved PL spectra of functionhasconsiderablepenetrationinthenonmagnetic (Cd,Mn)Se/(Cd,Mg)Se quantumwells in magnetic fields barriers. That would result in: (i) a longer exciton re- up to 7 T applied in the Faraday geometry and in the combination, due to a smaller overlap of the electron temperaturerangebetween2and30K.Theformationof and hole wavefunctions, and (ii) a specific dynamics of excitonmagneticpolaronshasbeenestablishedusingdif- the EMP in whose formation the self-localization pro- ferent spectroscopic techniques. We distinguish between cess of the hole wavefunction should contribute consid- magneticandnon-magneticlocalizationintheformation erably. Both features are in line with our experiment. process. The magnetic polaron energy at zero magnetic However,we exclude this scenario because it should also field extracted from time-resolveddata gives amounts to lead to a nonlinear dependence of the Zeeman splitting 14meV,whilenon-magneticcontributionatlowtemper- in small magnetic fields, which is in contrastto the data atures of 2 K is around 4 meV. The magnetic polaron presented in Fig. 2. Moreover, previous estimations of formation time of 500 ps is comparable with the exci- the valence band offset show that the QW potential in ton recombinationtime of 600 ps. We associate the long thestudiedstructuresisabout100meV,whichissignifi- formation time to strong self-localization, accompanied cantlylargerthanE . The secondscenarioofin-plane MP with squeezing of the heavy-hole envelope wavefunction. self-localization is realized if electron and hole become This conclusionis supported by the decrease ofthe exci- separatedspatially in the QWplane due to different ori- tonlifetime downto200psinstrongmagneticfieldsand gins of their localization potentials. The electrons are to 400 ps at elevated temperatures. localized on non-magnetic potential fluctuations, while theholeswithstrongexchangeinteractionwiththemag- neticionsarelocalizedonthemagneticfluctuations. Due VIII. ACKNOWLEDGEMENTS to self-localization of the EMP the in-plane squeezing of theheavyholewavefunctionreducestheoverlapwiththe electron wavefunction and consequently the exciton life- We acknowledge the financial support of the Russian time increases. This second scenario is most relevant for Science Foundation (Grant No. 14-42-00015) and the our case. Deutsche Forschungsgemeinschaft in the frame of ICRC We emphasize that the strong correlation between TRR 160. The MBE growth studies at Ioffe Institute the radiative lifetime and the magnetic polaron forma- were supported by RFBR Grant No. 15-52-12014. 1 J. K. Furdyna,Diluted magnetic semiconductors, J. Appl. conductors,Eds.J.KossutandJ.A.Gaj(Springer-Verlag, Phys. 64, R29 (1988). Berlin, 2010), pp. 221-262, ISBN 978-3-642-15855-1. 2 T. Dietl, Diluted magnetic semiconductors in: Handbook 8 C. Benoit a la Guillaume, Free Magnetic Polarons in of semiconductors, Vol. 3b, ed. by S. Mahajan (North- Three, Quasi-Two, and Quasi-One Dimensions, Phys. Holland, Amsterdam 1994) p.1252 Stat. Sol. (b) 175, 369 (1993) 3 Semiconductors and Semimetals Vol. 25, eds. J. K. Fur- 9 A. V. Kavokin and K. V. Kavokin, Theory of two- dynaand J. Kossut (AcademicPress, London, 1988). dimensional magnetic polarons in an external magnetic 4 J.CibertandD.Scalbert,in: SpinPhysicsinSemiconduc- field, Semicond. Sci. Technology 8, 191 (1993). tors, Ed. M. I. Dyakonov (Springer-Verlag, Berlin, 2008), 10 D. R. Yakovlev, W. Ossau, G. Landwehr, R. N. Bicknell- Ch. 13, p. 389. Tassius, A. Waag, and I. N. Uraltsev, First observation 5 P. A. Wolff, in: Semiconductors and Semimetals Vol. 25, and experimental proof of free magnetic polaron formation eds.J.K.FurdynaandJ.Kossut(AcademicPress,London, inCdTe/(Cd,Mn)Te quantum wells,SolidStateCommun. 1988) p. 413. 76, 325 (1990). 6 D. R. Yakovlev and K. V. Kavokin, Exciton magnetic po- 11 G. Mackh, W. Ossau, D. R. Yakovlev, A. Waag, T. Litz, larons in semimagnetic quantum wells and superlattices, andG.Landwehr,Exciton magnetic polarons insemimag- Comments Cond. Mat. Phys. 18, 51 (1996). netic quantum wells with nonmagnetic and semimagnetic 7 D.R.YakovlevandW.Ossau,Magneticpolarons,Chapter barriers, Solid StateCommun. 88, 221 (1993). 7inIntroduction tothe Physics ofDilutedMagnetic Semi- 12 D. R. Yakovlev, W. Ossau, G. Landwehr, R. N. Bicknell- 9 Tassius, A.Waag, S.Schmeusser, andI.N.Uraltsev,Two (2008)]. dimensional exciton magnetic polaron in CdTe/CdMnTe 22 J.A.Gaj,R.Planel,andG.Fishman,Relationofmagneto- quantum well structures, Solid State Commun. 82, 29 optical properties of free excitons to spin alignment of (1992). Mn2+ ions in Cd1−xMnxTe, Solid State Commun. 29, 13 D. R. Yakovlev, G. Mackh, B. Kuhn-Heinrich, W. Ossau, 435 (1979). A.Waag,G.Landwehr,R.Hellmann,andE.O.G¨obel,Ex- 23 M. Arciszewska, M. Nawrocki, Determination of the band citon magnetic polarons in short-period CdTe/(Cd,Mn)Te structureparametersofCd0,95Mn0.05Sefrommagnetoabor- superlattices, Phys.Rev. B 52, 12033 (1995). rption measurements, J. Phys.Chem. Sol. 47, 309 (1986). 14 C. D. Poweleit, L. M. Smith, B. T. Jonker, Ob- 24 K. V. Kavokin, I. A. Merkulov, D. R. Yakovlev, W. Os- servation of long-lived exciton magnetic polarons in sau, and G. Landwehr, Exciton localization in semimag- Zn1−xMnxSe/ZnSe multiple quantum wells, Phys. Rev. netic semiconductors probed by magnetic polarons, Phys. B 50, 18662 (1994). Rev.B 60, 16499 (1999). 15 V. V. Rossin, F. Henneberger, and J. Puls, Magnetic- 25 A.V.Kavokin,Thelifetimeof quasi-free exciton magnetic field-induced formation of exciton magnetic polarons in polaron in a quantum well with semimagnetic barriers, J. ZnSe/Zn1−xMnxSe quantum-well structures, Phys. Rev. dePhysiqueIV, Colloque C5, Vol. 3, 79 (1993). B 53, 16444 (1996). 26 M. Dahl, W. Gebauer, R. Prediger, and A. Waag, Proc. 16 E. O. G¨obel, R. Hellmann, G. Mackh, D. R. Yakovlev, Int.Conf.HighMagneticFieldsinSemiconductorPhysics, W.Ossau,A.Waag,andG.Landwehr,Picoseconddynam- p. 670, ed.by D. Heimann (World Scientific,1995). ics of magnetic polarons in semimagnetic quantum well 27 I.A.Merkulov,D.R.Yakovlev,K.V.Kavokin,G.Mackh, structures, Materials Science Forum, Vols. 182-184, 519 W.Ossau,A.Waag,andG.Landwehr,Hierarchy ofrelax- (1995), Trans Tech Publication (Switzerland). ation times in the formation of an exciton magnetic po- 17 B.P.Zakharchenya,Yu.G.Kusrayev,Opticalmanifestation laron in (Cd,Mn)Te, JETP Lett.62, 335 (1995). of spin-glass properties of semimagnetic semiconductors, 28 I.A.Merkulov,G.R.Pozina, D.Cocuillat, N.Paganotto, Zh. Eksp. Teor. Fiz. 50, 199 (1989) [JETP Lett. 50, 225 J. Siviniant, J. P. Lascaray, and J. Cibert, Parameters of (1989)]. themagneticpolaronstateindilutedmagneticsemiconduc- 18 G. Mackh, W. Ossau, D. R. Yakovlev, A. Waag, tors Cd-Mn-Te with low manganese concentration, Phys. G. Landwehr, R. Hellmann, and E. O. G¨obel, Localized Rev.B 54, 5727 (1996). exciton magnetic polarons in CdMnTe, Phys. Rev. B 49, 29 I.I.Reshina,S.V.Ivanov,D.N.Mirlin,I.V.Sedova,and 10248 (1994). S. V. Sorokin, Direct and indirect excitons and magnetic 19 G. Mackh, M. Hilpert, D. R. Yakovlev, W. Ossau, polarons in CdSe/CdMgSe/CdMnSe semimagnetic double H. Heinke, T. Litz, F. Fischer, A. Waag, G. Landwehr, quantum wells,Phys. Rev.B 74, 235324 (2006). R.Hellmann,andE.O.G¨obel,Exciton magnetic polarons 30 S. V. Ivanov, O. G. Lyublinskaya, Yu. B. Vasi- in the semimagnetic alloys CdMnMgTe, Phys. Rev. B 50, lyev, V. A. Kaygorodov, S. V. Sorokin, I. V. Se- 14069 (1994). dova, V. A. Solov’ev, B. A. Meltser, A. A. Sitnikova, 20 B.P. Zakharchenya, A.V. Kudunov,Yu. G. Kusraev. Hid- T. V. L’vova, V. L. Berkovits, A. A. Toropov, and den magnetic anisotropy in Cd1-xMnxTe spin glasses, Zh. P.S.Kop’ev,AsymmetricAlAsSb/InAs/CdMgSequantum Eksp. Teor. Fiz. 110, 177 (1996) [JETP 83, 95 (1996)]. wells grown by molecular-beam epitaxy, Appl. Phys. Lett. 21 I. I. Reshina and S. V. Ivanov, Magnetooptic of a 84, 4777 (2004). CdMnSe/CdMgSe single quantum well, Semiconductors 42, 1318 (2008) [Fiz. Tekh. Poluprovodnikov 42, 1348