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Nanoscale spin-polarization in dilute magnetic semiconductor (In,Mn)Sb A. Geresdi, A. Halbritter, M. Csontos, Sz. Csonka, G. Mihály Department of Physics, Budapest University of Technology and Economics and Condensed Matter Research Group of the Hungarian Academy of Sciences, 1111 Budapest, Budafoki ut 8., Hungary T. Wojtowicz Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland X. Liu, B. Jankó, and J.K. Furdyna Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA 8 (Dated: February 2, 2008) 0 0 Results of point contact Andreev reflection (PCAR) experiments on (In,Mn)Sb are presented 2 and analyzed in terms of current models of charge conversion at a superconductor-ferromagnet n interface. Weinvestigatetheinfluenceofsurfacetransparency,andstudythecrossoverfromballistic a to diffusive transport regime as contact size is varied. Application of a Nb tip to a (In,Mn)Sb J samplewithCurietemperatureTC of5.4Kallowedthedeterminationofspin-polarizationwhenthe 9 ferromagnetic phase transition temperature is crossed. We find a striking difference between the temperature dependence of the local spin polarization and of the macroscopic magnetization, and ] demonstrate that nanoscale clusters with magnetization close to the saturated value are present r e even well above themagnetic phase transition temperature. h t PACSnumbers: 72.25.-b,75.50.Pp,74.45.+c o . t a Controlling the spin state of electrons provides an im- assuming no Andreev reflection for the fully polarized m portant versatility for future electronics [1]. Most of the current and applying the original BTK theory for the - envisioned spintronic devices are based on spin transfer unpolarized part [10]. An alternative, more rigorously d n mechanisms onthe nanoscale. For this purpose new ma- founded quantification of P can be obtained based on o terials have been synthesized with highly spin polarized theimbalanceofspin-dependenttransmissioncoefficients c bands, and novel experimental techniques are being ap- P =(T −T )/(T +T ) [11, 12]. Both models assume T ↑ ↓ ↑ ↓ [ plied to characterizethe spin state of the charge carriers ballistic transport, but due to the difference in the ap- 1 [2, 3]. proaches they cannot be mapped to each other mathe- v (III,Mn)V dilutemagneticsemiconductorsarepromis- matically. 4 ing spintronic materials with high spin polarization InthispaperpointcontactAndreevreflection(PCAR) 6 [4,5, 6]andwithawide varietyofspin-dependenttrans- spectraarepresentedfor(In,Mn)Sbfilmswithferromag- 4 1 port properties [7]. While considerable effort is concen- netic transition temperature of TC = 5.4K, and for its . trated to enhance the ferromagnetic transition temper- (In,Be)Sb non-magnetic counterpart. We analyze the 1 0 ature [8, 9], studies of low TC alloys are also of great data in terms of the above models for various surface 8 interest, as they contribute to a better understanding of barriers, and show that the deduced spin-polarizations 0 theunderlayingphysics. Herethealloy(In,Mn)Sb–with agree well for the transparent contact limit. We also in- : v Curietemperaturesbelowthetransitiontemperaturesof vestigate the crossover from the ballistic to the diffusive i conventional superconductors – is especially interesting transport regime as the contact diameter is varied in a X inthatitallowsonetostudythespinpolarizationbyAn- controlledmanner. Furthermore the PCAR experiments r a dreev spectroscopy both in the ferromagnetic and para- allow us to compare the temperature dependence of the magnetic phases. measured local spin polarization to that of the macro- The Andreev reflection experiment provides a direct scopic magnetization as the ferromagnetic phase transi- measureofthe current spin polarization, P. The current tion temperature is crossed. throughaferromagnet/superconductorinterfaceisdeter- Thin In Mn Sb and In Be Sb film with typical 1-x x 1-y y minedbythechargeconversionofindividualelectronsto thicknesses of 200nm were grown by molecular beam Cooper pairs. As a Cooper pair consists of two elec- epitaxy in a Riber 32 R&D system, and were charac- trons with opposite spins, the conversion is suppressed terized by structural, transport and magnetic measure- in case of spin polarized bands, so that P can be de- ments [13]. The hole concentration of these samples is duced from the voltage dependence of the conductance. n ≈ 2·1020cm−3, resulting in a metallic conductivity P isoftenderivedintheframeworkofthemodifiedBTK with σ ≈ 3·103Ω−1cm−1. In the PCAR experiments theory [3], which simply splits the current to unpolar- mechanically-edged Nb tips were used as the supercon- ized and fully polarized parts. The net current is then ductingelectrodes. Thepositionofthe tipwasregulated calculated as I = (1 − P )I + P I by by a screw mechanism and a piezo actuator. The ac- total BTK unpol BTK pol 2 1.2 ters for the transmissions T = 0.99 and T = 0.246 ob- ↑ ↓ G)N (In,Mn)Sb tained by this approach correspond to a polarization of G/ 1.1 P=0.5 e ( PT =0.605, which agrees very well with that derived by nc 1.0 the BTK theory. A more detailed analysis was carried a ct out by acquiring data using several different contacts. u nd 0.9 We conclude that, despite the fact that the two models Co P=0.6 d 0.8 are based on quite different assumptions and cannot be e (a) aliz P=0.7 mappedontoeachother,theyleadtoidenticalresultsfor m 0.7 highqualitytransparentcontacts(denotedbyZ →0and or N T →1). For less transparent contacts, i.e. for Z > 0.3, 0.6 ↑ -4 -2 0 2 4 which correspondto T <0.9, the fitting curves obtained Bias Volt age (mV) using the two methods are still almost identical, but the 0.02 aboveexcellent agreementin the deduced polarizationis RelativeDeviation 0.00 (b) ldoastta. BobetloawinewdeopnrevseanritotuhsesBamTKpleasnbalyysciosnotfaactlafrogremsaettioonf -0.02 at different positions on the sample surface. -4 -2 0 2 4 We displayourresultsusingseveralcontactswithvar- FIG. 1: (Color online) a) Normalized conductance of a Nb- ious transparencies in the standard way. Figure 2 shows (In,Mn)Sb contact at T = 4.2K, with fits using the BTK thefittingparametersontheP-Zplanebothforthemag- method. The red curve withP =0.60±0.01 yields the best fit netic semiconductor (In,Mn)Sb andfor its non-magnetic (the other fitting parameters are: Z =0.13, T =4.17K, ∆= counterpart, (In,Be)Sb. Test results on a simple param- 1.13meV).Thedashedlinesarefitswithintentionallydetuned agnetic metal (gold) are also shown. The decay of spin- polarizations(P=0.5,P=0.7)usingthesametemperatureand polarization with increasing barrier strength observed gap parameters as for the best fit, and with Z as a fitting parameter. b) Red curve: deviation of measured data and with Nb-(In,Mn)Sb contacts is attributed to spin-flip BTK fitting; black curve: deviation between the two fitting scattering in the contact area, and the intrinsic spin po- methods as discussed in the text. larization of the sample is deduced from fitting the data to a Gaussian shape [14], P(Z → 0) = 0.62±0.01. In contrast, the Nb-Au and the Nb-(In,Be)Sb contacts do curacy of the positioning is 0.1nm, as determined from not exhibit a finite spin polarization, as expected. It is currents measured in the tunneling regime, i.e. before worth noting that the accuracy of the polarization de- touching the sample surface. In the present study the termined from an individual measurementis reduced for voltage-dependent differential conductance was acquired high-Z contacts. using standardfour-probe measurements,applying noise The high-accuracy piezo positioning of the Nb tip al- filtersinthe lowtemperaturestageofthe sampleholder. lows controlled variation of the contact diameter in the A typical PCAR spectrum is shown in Fig. 1 for range of about 5 to 50nm. The Andreev spectra of the (In,Mn)Sb at T = 4.2K. The bias dependence of the normalized conductance was analyzed in terms of the two models discussed earlier. The best fit obtained with the modified BTK model is shown by the red curve in 0.6 Fig. 1(a). This represents an almost transparent con- P tact (the Z = 0.13 barrier strengths corresponds to on, T = 1/(1+Z2) = 0.98 transmission) and high spin po- ati 0.4 z larization P = 0.60±0.01, in good agreement with ari BTK ol earlier experimental data [5]. It is to be noted that sim- P 0.2 n ulated curves for spin polarizationof 0.50 or 0.70 are far pi S awayfromthemeasureddata,i.e. thevalueofPBTK can 0.0 really be determined with a high accuracy within this formalism. 0.0 0.4 0.8 1.2 Similar high quality fit can also be obtained by cal- Interface Barrier, Z culating the imbalance of spin-dependent transmission coefficients, P [11, 12]. There is a small but clear sys- T FIG. 2: (Color online) Experimental results for several con- tematic deviation between the two fitting methods, as tacts on the P-Z plane. Extracted polarization data for Nb- expected due to differences in the two formalisms [see (In,Mn)Sb contacts are denoted by red circles, while the solid Fig. 1(b)]. However, the difference between simulations red line represents a Gaussian fit based on Ref. [14]. Refer- based on the two methods is within the scatter of ex- ence data on Nb-(In,Be)Sb and Nb-Au contacts are shown by perimental data and – surprisingly – the fitting parame- gray squares and green triangles, respectively. 3 characteristic time determined by this energy difference, N (In,Be)Sb (In,Mn)Sb G t = h¯/∆E . Indeed, no peak is observable for the Nb- ce, G/1.5 R=88(cid:58) R=125(cid:58) (NφIont,Me,nh)oSwbevcmoern,tathcat,taasssihmopwlenminetahnefireilgdhtappparnoealcohffFoirgt.h3e. ctan local magnetic interaction, ∆Em ≈ kBTC, would mean u only a slight broadening of the peak instead of its com- d R=175(cid:58) R=226(cid:58) on1.0 plete suppression, since in our case kBTC is almost as C smallasthethermalenergyatliquidheliumtemperature d ze R=1050(cid:58) at which the experiment was performed (TC = 5.4K). ali R=714(cid:58) Consequently, the absence of the coherence peak implies m0.5 a much more radical reduction of phase coherence time, r o N i.e.,thatthemagneticsplittingtestedonthelengthscale -5 0 5 -5 0 5 of a few nm is ∆Em ≫kBTC. Bias Voltage (mV) 1.0 FIG. 3: Normalized conductance of several contacts with different contact resistances fornonmagnetic (In,Be)Sb samples 0.8 (left panel) and magnetic (In,Mn)Sb samples (right panel). The experiments were performed at T =4.2K. The fits based 0.6 on modified BTK-theory assuming finite lifetime (Γ>0) are (cid:42)(cid:18)(cid:39) d=15nm shown in the red, the curves are shifted vertically for clarity. 0.4 0.2 magneticandnonmagneticsamplespreparedbythesame MBE technique and having nearly identical bulk param- 0.00 0.03 0.06 0.09 eters [13] are shown in Fig. 3. In these experiments the 1/d(nm-1) contactdiameterwasincreasedabovetheliteraturevalue of the heavy hole mean free path l ≈15nm, i.e. to the FIG. 4: (Color online) Normalized quasiparticle lifetime pa- m rameter as a function of contact size. Red circles and black regionwherediffusivetransportisexpected. Thecontact squares denote data acquired on InMnSb and InBeSb sam- sizewasestimatedfromthequasiclassicalformulaofcon- ples respectively. The onset of finite damping appears at tact resistance, applicable both to ballistic and diffusive d≈15nm. The dashed line is a guide for the eye. transport [15]: 4ρl l ρ Anotherfeatureoflow-resistancecontactsisthesmear- R= 1+Z2 m +γ m , (1) ing of the Andreev spectra onlargervoltage scales,both (cid:18)3πd2 (cid:18) d (cid:19)2d(cid:19) (cid:0) (cid:1) for the magnetic and for nonmagnetic samples. We have where d is the diameter of the contact, ρ is the bulk found that for contacts with d >∼ 15 nm the BTK the- resistivityofthe material[13,16], andγ is a prefactorof orygivesunphysicalparameters. Thefittingtemperature the order of unity. obtained by this approach is above the superconducting For large contact areas (small resistances), an un- transition temperature of Nb, while the value of the su- ambiguous qualitative feature of diffusive transport is perconducting gap ∆ still corresponds to that measured the narrow zero-bias peak observed in the nonmagnetic at liquid helium temperature. If, on the other hand, the (In,Be)Sb sample (Fig. 3, left panel). This is attributed temperatureisfixedatthecorrectvalue,theBTKtheory to multiple phase-coherent reflections occurring when givesaratherpoorfit. Thisbroadening,however,canbe d > l and the phase-coherence length l > d, similarly taken into account by introducing a finite quasiparticle m φ to the reflectionless tunneling phenomenon observed in lifetime (denoted by Γ) on the superconductor side [20]. superconductor normal metal tunnel junctions [17, 18]. The physical meaning of this phenomenological parame- In our case the peak is broadened by the thermal en- ter is the enhanced probability of inelastic scattering in ergy corresponding to about 350µV. A detailed quanti- thediffusiveregime. Plottingthedimensionlessquasipar- tative description of multiple reflections in diffusive con- ticle lifetime parameterΓ/∆as afunction ofthe contact tact regime based on scattering matrix calculations is diameter, we also see that the onset of the diffusive pro- given elsewhere [19]. cess appears aroundd≈15nm,as shownin Fig.4. This In general, such zero-bias coherence peak is not ex- feature is independent on whether the sample is mag- pected if the Cooper pair conversion occurs in a magnetic or not: typical fits to data are shown in Fig. 3. We netic sample where the energy of the resulting quasipar- conclude that the smoothing can be attributed to diffu- ticles of opposite spins differs due to the exchange split- sivescatteringinthecontactarea,andthatitdisappears ting. In that case the phase coherence is lost within a when the contact size is below the mean free path. 4 1.00 2.0 3m) different surface barriers were analyzed in terms of the c extended BTK theory and ofthe “spin-dependenttrans- ation 0.75 30% 1.5 emu/ mission model”; and it was shown that for the transpar- ariz on ( entcontactlimitthetwoformalismsleadtoidenticalspin Spin Pol 0.50 1.0 gnetizati psiozlearinizaaticoonn:trPol=led0.m61a±nn0e.r0,1w. eByweinrecraebalseintgotehnetecronfrtaocmt cal 0.25 0.5 Ma theballisticto thediffusivetransportregime,wherezero Lo ulk bias peak due to multiple phase-coherentreflections and B smearing of the Andreev spectra were observed. Ana- 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 lyzing the quasiparticle lifetime in (In,Mn)Sb, we found Normalized Tem perature, T/T that reliable experiments in the ballistic limit can only C be obtained if the contact diameter is less than 15nm, FIG. 5: (Color online) Temperature dependence of the spin- that corresponds to the heavy hole mean free path. The polarization acquired from point contact measurement (cir- temperature dependence of the spin-polarization P was cles); andthe remanent magnetization determined by SQUID alsoinvestigated,anda striking difference wasfound be- measurement (squares). The PCAR results are reproducible tween P and the remanent magnetization. Our obser- for contacts prepared at various surface positions. vation directly confirms the percolation scheme of the phase transition, with clusters characterized by nearly Wehavealsoinvestigatedthetemperaturedependence saturated magnetization even well above the magnetic of the Andreev spectra of (In,Mn)Sb. This study is es- phase transition temperature. pecially interesting because the use of Nb tip allowed This research was supported by the National Science us to cross the ferromagnetic phase transition tempera- Foundation Grants DMR 02-10519 and DMR 06-3752; ture. The results are summarized in Fig. 5. Although NSF-NIRT awardECS-0609249;US. Department of En- temperatures much above the Curie-temperature had ergy, Basic Energy Sciences contract W-31-109-ENG-38; been reached, only thermal broadening is observed, and and by the Hungarian Scientific Research Fund OTKA the dip in the differential conductance remains clearly under Grant NK72916 and F49330. A. Halbritter is a present. In the analysis of the curves the temperature grantee of the Bolyai János Scholarship. was used as a fitting parameter, and the values deduced from the measured Andreev spectra agree within 0.1K with the actual temperature measured independently. 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