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Spin dependent non-tunneling transport in granular ferromagnet Soumik Mukhopadhyay and I. Das Saha Institute of Nuclear Physics, 1/AF, Bidhannangar, Kolkata 700064, India 6 We have shown that, at low temperature, the effect of localization of charge carriers in granular 0 metals cannot be ignored. The electron localization in granular ferromagnetic metals can give rise 0 tonon-lineartransportinthemoderateelectricfieldregime,whichisdominatedbyspindependent 2 inter-grainnon-tunnelingemission. Incontrasttothegeneralopinionthatspindependenttunneling y gives rise to low field magnetoresistance in granular ferromagnetic metals we observe that spin a dependentnon-tunnelingtransportisprimarilyresponsibleforthesharpmagneticfielddependence M of resistance, at least in the low temperature and moderate electric field regime. 9 PACSnumbers: 72.25.-b,73.63.-b,85.75.-d 1 ] Recent emergence of spin based electronics or spin- sulating [8, 9]. ll tronics has initiated extensive studies on spin polarized Thick films of LSMO,having thickness 3000˚A,were a ∼ h transport in magnetic tunnel junctions, granular ferro- grown on LaAlO3(100), using pulsed laser deposition. - magnetic films and nanocomposites. The low field mag- The surface morphology of the film was inspected, using s netoresistance in magnetic tunnel junctions (MTJ), and atomic force microscopy which shows orderly arrange- e m granular ferromagnetic systems is attributed to spin de- mentofconnectedgrainswithaveragesize80nm(Fig:1). pendent tunneling [1, 2, 3]. However, it has been shown In order to prove that this is not a mere surface corru- . t recently that the superposition of tunneling conduction gation, the x-ray diffraction θ 2θ scan around (002) a − m and ballistic channels can lead to inversion of magne- peaksofLSMO/LAOareshowninFig:2Aandthemag- toresistance [4] in MTJs. This letter explores the possi- netic measurements in Fig: 3. The Bragg peak corre- - d bility of whether there exists any transport mechanism sponding to that portion of the film which matches with n other than spin dependent tunneling which might af- the in-plane lattice parameters of the substrate leading o fect low field magnetoresistance in granular ferromag- to higher c-axis parameter is indicated in the figure as c [ nets. Althoughthe studyofgranularferromagneticmet- (1) which gradually relaxes to the bulk lattice param- als spans more than three decades [2], recently, there is eter value shown by the higher angle peak among the 2 a renewed interest in this field with the granular sys- twin peaks separated by a plateau indicated as (2). The v 9 tems based on “half metallic” materials like CrO2 and intensity of Bragg peak which corresponds to strain re- 3 La0.67Sr0.33MnO3showingenhancedlowfieldmagnetore- laxed part of the film is much higher compared to the 7 sistance [3] leading to the possibility of their application strainedpartindicatingthatthegranularityextendsdeep 6 as magnetic field sensors. We will analyze the effect of insidethefilmandhenceboundtoinfluencethetransport 0 electronlocalizationingranularferromagneticsystemsat and magnetic properties of the film. The magnetic char- 5 0 sufficiently lowtemperature. The consequentdominance acterization was done using a Quantum Design SQUID / ofspindependentinter-grainnon-tunnelingemissionover magnetometer which shows the ferromagnetic transition t a inter-graintunnelinginthemoderateelectricfieldregime temperature T at around 360 K. The large irreversibil- c m will be discussed. ity in the temperature dependence of zero field cooled - For the preparation of granular film with almost uni- (ZFC)andfieldcooled(FC)magnetization(M)together d form grain size distribution and quasi-homogeneous dis- with the hysteric M H loop, where the magnetization n − o tribution of conducting and non-conducting regions, we does not saturate even at 2 kOe, are typical of granu- c haveutilizedthewellstudiedstrainrelaxationproperties lar ferromagnets (Fig: 3A,B). The virgin M H curve − v: of manganite films. Manganites like La0.67Sr0.33MnO3 shows(Fig:3)an‘S’-likeshapewiththepointofinflexion i (LSMO) can be grown epitaxially on single crystal in- around 100 Oe indicating non-ferromagnetic inter-grain X sulating substrate LaAlO3 (LAO). However, due to fi- coupling. Thecoercivityofthefilmhasroughlythesame r nite lattice mismatch ( a a /a +2%) value. a LSMO LAO LAO { − } ∼ with the substrate, thin films of La0.67Sr0.33MnO3 un- Thetransportpropertieswerestudiedusingfourprobe dergoes a biaxial in plane compressive stress leading to technique with the magnetic field being in-plane to the higher out of plane lattice parameter compared to the electric field. The granular film exhibits a sharp rise in substrate [5, 6, 7]. Relatively thick films (usually above resistance (Fig: 4B) with lowering of temperature below 50 nm) become strain relaxed forming granular nanos- around6 K in the absenceof externalmagnetic field. At tructures and the grain size depends on the thickness of higher bias current, the rise in resistance reduces drasti- the film. In granular manganite systems, it is an estab- callysuggestingnon-ohmictransportatlowtemperature. lished fact that the core of grain is ferro-magnetically Asignificantreductionofpercentageriseinresistanceon ordered but the grain surface is spin-disordered and in- application of magnetic field is observed. Hence Ziese’s 2 where β is a constant. PF However, in this case what is fundamentally different from traditionally observed PFE is the tunability of the phenomenon by application of even a small amount of magneticfield. ItisevidentfromFig:5Athatthethresh- oldelectric fieldfor the onsetofchargeemissionE (in- th dicated by the vertical arrow)and the slope of the curve are higher at 100 Oe magnetic field compared to that FIG.1: AFMpictureofthestrainrelaxedfilmover2×2µm2 at 1 kOe. The origin of PF type emission in granular area showing the granular surface morphology along with a metal can be explained following Mostefa’s model [12]. schematic cross-sectional blown-up view with strain-relaxed This model considers a granular metallic system with a granular part and a thin strained bottom part, the grains narrow grain size distribution with almost equal Fermi (theferromagneticallyorderedcorepart)beingassimilatedto levels for all grains and as a result the activation energy localized sites at low temperature, leading to the dominance is entirely due to the potential barrier between two ad- of inter-grain non-tunnelingtransport. jacent grains. In each grain, electrons can be considered as being localized at sufficiently low temperature. At low temperature, the leakage of electron wave function 5 10 (A) LAO(002) outside the grain is minimal, which is particularly true c (2) e S for insulating grain surfaces, as in this case [8, 9]. This unts/104 (1) justifiestheassumptionofgrainsaslocalizedsitesatsuf- o C ficiently low temperature. In the weak field regime, the 3 10 transportispurelythermallyactivated. Theelectricfield will affect two important parameters of the system if it 44 45 46 47 48 49 is above the weak field regime. 2 Firstly,theshapeofthepotentialbarriersandhencethe decay of the wave function associated with the electronic FIG. 2: A: X-ray diffraction pattern of the LSMO film on states. The tunneling probability P(R ) between two LAO substrate. The c-axis parameter of the film relaxes ij gradually to the bulk value of LSMO. The broad hump at grainsassumedtobelocatedatsitesR~iandR~j separated the lower angle (1) indicates the strained part whereas the byadistanceR = R~ R~ canbewritten,usingWKB ij j i two broad peaks (2) and theplateau in between corresponds | − | approximation, tothegradual relaxation of thestrain. B:The conduction is due to the combined effect of tunneling through the barrier 2 R~j andthermalactivation overthebarrier. Theeffectivebarrier P(R ) exp 2m[V(x) ε ] 1/2dx ij i height depends on the relative spin orientation of adjacent ≃ "−¯hZR~i { − } # sites. The conduction is in themoderate electric field regime where Rj−R1M <<Rj−Ri Here V(x) is barrier height, x is the position of the electron on the path R~ and ε is the electron energy in the ij i grainlocatedatithsite. Itis assumedthatthepotential model of quantum interference effect [10] is not applica- barrierisinthemoderatefieldregimewheretheelectron ble here. Below 6 K, the strain relaxed film exhibits low isemittedasafreeparticleintotheinsulatoroverapath field magnetoresistance which is extremely sensitive to muchshorterthanthe totaldistancebetweenthe grains. the applied bias (Fig: 4C). The effective barrier height is φ (x)=V(x) ε . Taking i i The electric field dependence of conductivity at 2 K, − these factors into consideration and assuming directed plottedinFig:4B,showsthatthelogarithmofconductiv- flow of electrons we get, P(R ) exp A , where A ity is linearly proportional to square root of the electric ij ≃ −E is a constant. field(E). At5K,verycloseto thepointofupturninre- (cid:8) (cid:9) Secondly, the activation energy E required for one a sistance with lowering of temperature, the transport be- electron to hop from a neutral grain to another neutral comes nearly ohmic (Fig: 4D). Such electric field depen- grain. In the non-negligible field regime, the activation denceisstrikinglysimilartothechargetransportmecha- energyrequiredto transferan electronfromsite i to site nismcalledPoole-Frenkelemission(PFE)[11]. ThePFE, j is,E ij =ε eE~.R~ ,where,ε =ε ε . Hence the a ij ij ij i j usually observed in disordered semiconducting systems, − − activation probability, is a non-tunneling transport phenomenon where the charge carriers are thermally activated over the poten- ε eER cosθ P(E ij) exp − ij + ij tialbarrierfromlocalizedchargetrapsinthe presenceof a ≃ KT KT electricfield. Thereductioninbarrierheightφ ispro- (cid:26) (cid:27) PF portional to the square root of applied electric field and The electrical conductance G between sites i and j ij theconductivityisgivenbyG=G0exp βPFE1/2/KT , canbecalculatedfromthetotaltransport probability Pij, (cid:0) (cid:1) 3 T (K) 1/2 E (E in mV/cm) 0 100 200 300 1 2 3 4 5 K) 4 (A) 2 0.12 50 %) T = 2 K H=100 Oe (3M )]0.09 R ( 0 T)/ 2 (0G M-2 (M H=100 Oe )/ -4 0.10 H=20 Oe V 0.0 0.5 1.0 (0.06 H (kOe) 0 G 0.9 (B) (C) 1.0 [ln H=1 kOe 0.08 MS 0.5 M/0.6 T = 2K 0.0 0.03 (A) T=2 K 0.3 -0.5 ) %) 0 (I) -1.0 K2.46 MR(-10 H=0 0.00 500 10001500 -2000-1000 0 10002000 n -20T=3K 2.67 H (Oe) H (Oe) G i 0 3H (k6Oe)9 H =10 kOe fifiFeeIllGdd.sc3oH:olAe=d:(T2F0hCeO)ze(efiralolnefiddeslHdymc=boooll1es0d)0M(OZvFesC.s)hTo(wocpuinervgnessiryarmetvbmeoralssgi)bniaelitntidyc (ln G(V)22..4403 T300K()/()11222.....26048 (II)--000.0..2122..6614 betweentheZFCandFCcurveswhich isanevidencefor the (B) 0 100T (K)200 300 granularityofthefilm. B:VirginMvs. Hcurveforthestrain 0.6 0.8 1.0 1.2 relaxed film at 2 K, exhibiting inflexion at 100 Oe shown by 1/2 theslopeofthecurveplottedascontinuousline. C:Mvs. H V (V in volt) hysteresis loops at 2 K,showing coercivity of about 100 Oe. FIG.5: SensitivityofthePFtypeemissiontomagneticfield. Plotoflogarithmofdcconductivityvs. E1/2intheantiparal- lelandparallelmagneticconfigurationwiththecorresponding (A) (B) magnetic field dependence of magnetoresistance at the same R ()111...344505I=1mA MR(%)-1--0284 T0 = 3 K20 40 II 6= =0 2 10 mm8A0A n {G(V)/G(0)}0000....01118024 T=2 K adt(oeLdledmnSdcMipeteleieOorocna)ftta1rru−ilecrxiseni(fissAeitenlaLtdnOt(chEIe)Iext)hoicinfniosstmeh(itBnepfd)osoisadrcimtaetestehcewerdsiiabstbmtheyrspaxtitlnehh=eewr0evti.ltee5ahmrxt(epaiBcdea)rr.alfiapTatlmuirhdrreoe(iwnAtdhc.)errpeTeaaesnhhnsdee-- H (kOe) l 0.06 T=5 K in slope below 10 K shown by thecontinuous line. 1.30I=10 mA 0.04 0 4 8 12 16 20 1 2 3 4 5 6 T (K) E1/2 (E in mV/cm) FIG. 4: A: Rise in resistance with lowering of temperature below 6 K at different bias currents, suggesting non-ohmic transportbelow6K.Inset: MagneticfielddependenceofMR one site to another. The value of E depends on the at 3 K at different bias currents. B: Plot of logarithm of dc m conductivity vs. E1/2 in absence of magnetic field at 2 K overlap of electronic wave function across the grains. If and 5 K for the same sample. The linear region in the curve the spin orientation is anti-parallel an additional energy (for2K)indicatesthermally assisted non-tunnelingemission +Em is necessary for charge carrier emission while less duetolocalizationofchargecarriersatlowtemperature. The energy E isrequirediftheorientationisparallel. Ob- m − non-tunnelingemission is almost suppressed at 5 K. viously, the value of E can easily be manipulated by m applying even a tiny magnetic field H. Hence the pre- scription is to simply replace the effective potential bar- which is given by the product of the tunneling probability rierφ (x) by φm(x)=φ (x) Eij(H) andthe activation across the barrier and the activation probability over the energyi E ij byiE ij,m =iε ±eE~m.R~ Eij(H). Now we barrier. Assuming that the temperature is low enough a a ij− ij± m employ the percolation criterion G G , where G ij C C to help the hopping transport, the conductance can be ≥ is the critical conductance for percolation. This sets a calculated employing percolative treatment. limit on the energy and the length scales (ε ε and ij M However, Mostefa’s model alone cannot explain R R )involvedandonearrivesat, εij Ri≤j 1 [12] the sharp magnetic field dependence discussed earlier. ij ≤ M εM−RM ≤ Therefore,we incorporateanadditionalinter-grainmag- where,εM = 1K±ξTm Y′,SM = KeET Y′ andY′ =lnGGC′0 netic exchange energy (Em) term in the model. It arises Herethemagn(cid:16)eticex(cid:17)changeener(cid:0)gyh(cid:1)asbeenexpressedin duetotherelativespinorientationofthetwoadjacentlo- the unit of ε as E =ξ ε , where ξ is a dimension- ij m m ij m calized sites when the spin is conserved in hopping from less quantity. Then following Mostefa’s derivation one 4 obtains, composite with x = 0.5 at 3 K. The temperature dependence of resistance shows a low temperature upturn G E1/2 log C =B(H) with a rapid increase in the slope below 10 K (Inset II, G′ KT (cid:18) 0(cid:19) Fig: 5B). All other samples with different values of x, where B √1 ξ for a given system, with exhibit similar behavior. This suggests that the effect ↑↓,↑↑ m and indicat∝ing the±antiparallel and parallel magnet↑i↓c of localization at low temperature and the consequent confi↑g↑urationbetweennearestneighboringgrains,respec- dominance of non-tunneling effect might be generic to tively. Evidently, the value of B is higher in the antipar- a large variety of granular ferromagnetic metals. Em- allel configuration compared to the parallel one. ploying the same method for estimation of magnetic ex- Itisinterestingtocomparethemagnetoresistance(In- change energy described in the previous paragraph we set, Fig: 5A) with the conductivity curves at different obtain ξm = 0.04 only. The temperature dependence of magneticfieldsinFig:5Aatlowtemperature. Themag- resistance can be fitted using the parallel channel con- netoresistanceispositiveat100Oe,whichisequaltothe duction model of ref. [13], which gives a rough estimate coercivity and the inflexion point in the virgin M H of activation energy to be 0.8 K. The reduction in the curve (Fig: 3). This suggests that at this point,−the slope of the curve as well ∼as Eth with applied magnetic spin orientation between the adjacent grains becomes fieldis notaspronouncedasinthe case ofstrain-relaxed anti-parallel, resulting in increase of exchange energy. film indicating that the value of exchange energy should The increase in the slope of the logarithmic conductiv- be comparatively smaller. The small value of exchange ity vs. E1/2 curve at H = 100 Oe in Fig: 5 compared energy in this case can be understood considering the to that at H = 1 kOe is consistent with our model. largeraverageinter-particleseparationinthe composite. The value of exchange energy can be estimated from Thus the sensitivity of the slope of the logarithmic con- the slope of the curves at 100 Oe (antiparallel config- ductance vs. E1/2 curves in the non-tunneling regime uration) and 1 kOe (parallel configuration) using the re- as well as that of Eth to the magnetic field depends on lation ξ = (B 2 B 2)/(B 2+B 2) which gives therelativecontributionofthemagneticexchangetothe m ↑↓ ↑↑ ↑↓ ↑↑ ξ = 0.79 and ther−efore E = 0.79ε . The validity total activation energy. This factor is determined by the m m ij of the non-tunneling emission being limited to the mod- microstructureofthegranularsystemalongwiththespin erateelectricfieldregime(asdefinedinFig:2B)isdeter- polarization of the ferromagnetic grains. mined partly by the potential barrier height. Therefore, To conclude, we have observed spin dependent theshiftinthethresholdelectricfield(Eth)fortheonset non-tunneling transport in LSMO granular film and of PF type emission should be magnetic field dependent LSMO/ALO metal-insulator nanocomposites, a phe- sincemagneticexchangeenergycontributessubstantially nomenon which appears to be generic to ferromagnetic to the total barrier height. In the antiparallel configura- granular metallic systems, particularly at low tempera- tion, the value of Eth should be higher in comparison ture. In contrast to the usual Poole-Frenkel emission, with the parallel configuration, which is consistent with the electric field dependence of conductivity is sensitive our observation. A roughestimationof the averagetotal to external magnetic field. The observed phenomenon activation energy (including the magnetic contribution) has been analyzed considering the dominance of ther- is possible from the fitting of temperature dependence mally assisted inter-grain non-tunneling transport (with of resistance (at low temperature and bias) in absence the grainsacting aslocalizedsites)in the moderate elec- of magnetic field by an activation term with a metallic tric field regime and the existence of anadditional inter- contribution in parallel. The metallic channel includes grain magnetic exchange barrier. whatever the effect of the thin continuous strained part The authors acknowledge Prof. A. K. Raychaudhuri might have. Consequently, the magnetic exchange en- and Dr. Barnali Ghosh of SNBNCBS, Kolkata for pro- ergy turns out to be E 0.24K. Similar value ( 0.23 m ∼ ∼ viding some experimental facilities. K) can be extracted from the difference in the total activation energy values in the absence and in presence of magnetic field, respectively. In order to find out whether the same phenomenon is operative in a different micro-structure, we have stud- [1] J. S. Moodera, Lisa R. Kinder, Terrilyn M. Wong, R. ied magnetotransport properties in a nanocrystalline Meservey, Phys. Rev.Lett., 74, 3273 (1995) LSMO/ Al2O3(ALO) granular composite with different [2] Helman J. S. and Abeles B., Phys. Rev. Lett., 37, 1429 weight concentrations x of Al2O3 (where x = 0 0.5). (1976) − [3] H. Y. Hwang, S-W. Cheong, N. P. Ong, and B. Batlogg The average grain size of the sol-gel prepared LSMO Phys. Rev.Lett. 77, 2041 (1996) was measured, using Transmission Electron Microscope [4] Soumik Mukhopadhyay, I. Das, Phys. Rev. Lett, 96, (TEM) and Scanning electron microscope (SEM), which 026601 (2006) turns out to be about 50 nm. Fig: 5B shows similar [5] S. I. Khartsev, P. Johnson, and A. M. Grishin, J. Appl. spin dependent non-tunneling emission in LSMO/ALO Phys. 87, 2394 (2000) 5 [6] Mandar Paranjape, A. K. Raychaudhuri,N. D. Mathur, [10] M. Ziese, Phys.Rev.B, 68, 132411 (2003) and M. G. Blamire, Phys. Rev.B 67, 214415 (2003) [11] Frenkel J., Phys. Rev., 54, 647 (1938) [7] M. Ziese, H. C. Semelhack, K. H. Han, S. P. Sena, and [12] M. Mostefa, D.Bourbieand G. Olivier, PhysicaB, 160, H.J. Blythe,J. Appl.Phys. 91, 9930 (2002) 186 (1989) [8] L.Balcells,J.Fontcuberta,B.Martnez,andX.Obradors [13] A.deAndres,M.Garcia-Hernandez,andJ.L.Martinez, Phys.Rev.B 58, R14697 (1998) Phys. Rev.B 60, 7328 (1999) [9] BarnaliGhosh,SohiniKar,LoveleenK.Brar,A.K.Ray- chaudhuri,J. Appl.Phys. 98, 094302 (2005)