Table Of Content

Angular dependence of domain wall resistivity in SrRuO films. 3 Michael Feigenson and Lior Klein Physics Department, Bar Ilan University, Ramat Gan 52900, Israel ∗ James W. Reiner and Malcolm R. Beasley T. H. Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305 (Dated: February 2, 2008) 3 0 SrRuO3 is a 4d itinerant ferromagnet (Tc ∼150 K) with stripe domain structure. Using high- 0 quality thin films of SrRuO3 we study the resistivity induced by its very narrow (∼ 3 nm) Bloch 2 domain walls, ρ (DWR), at temperatures between 2 K and T as a function of the angle, θ, DW c n between the electric current and the ferromagnetic domains walls. We find that ρDW(T,θ) = a sin2θρ (T,90)+B(θ)ρ (T,0)whichprovidesthefirstexperimentalindicationthattheangular DW DW J dependence of spin accumulation contribution to DWR is sin2θ. We expect magnetic multilayers 2 toexhibit a similar behavior. 2 ] I. INTRODUCTION oftheDWRwithperpendicularcurrentwasshowntobe el qualitatively and quantitatively consistent with resistiv- - Followingthediscoveryofthegiantmagnetoresistance ity induced by two sources relevant to magnetic multi- r t (GMR) effect in magnetic multilayers1 and related phe- layers: spin accumulation and potential step. We should s . nomenaconsideredtolaythefoundationfortheemerging note that spin accumulation was also claimed to be the at field of spintronics,2 there has been an intensive effort sourceofDWRinnanowiresofcobalt12;however,thisat- m to elucidate the mechanisms involved in spin polarized tribution was later challengedon grounds that the effect - transport in the presence of magnetic interfaces. One is expected to be suppressed in the 15 nm thick DWs.13 d of the outcomes of this effort was the realization that Here we explore DWR in SrRuO3 as a function of the n naturally obtained domain structure in itinerant ferro- angle, θ, between the electric current and the ferromag- o magnets may offer an important opportunity to study netic DWs. We find that DWR for any angle θ is given [c basicissuesrelevanttospintronicswhileavoidingdifficul- by a temperature−independent linear combination of ties encountered when artificially grown multilayers are DWR for parallel (ρDW(T,θ = 0)) and perpendicular 2 studied. These difficulties arise due to the intrinsic un- (ρDW(T,θ = 90)) currents. As we demonstrate below, v certainties and complications associated with the nature thisfitprovidesthefirstexperimentalindicationthatthe 0 0 of magnetic interfaces in these systems. angulardependenceofspinaccumulationcontributionto 4 Two major hurdles were encountered along this route DWRisproportionaltosin2θ,asexpectedbasedonsim- 1 when domain wall resistivity (DWR) of iron,3 nickel,4 ple theoretical considerations. This behavior is likely to 0 cobalt4,5 and FePd6 was studied: (a) The resistivity be found in magnetic multilayers, as well. 3 (or interface resistance) is quite small and hardly dis- 0 tinguished from the anisotropic magnetoresistance effect / t which is unavoidable in these systems due to the pres- II. EXPERIMENT a m ence of closure domains.7 (b) The estimated width of ferromagnetic domain walls (DWs) in these systems is SrRuO is a pseudocubic perovskite and an itinerant - 3 d relatively large (e.g., 10 nm in FePd,6 15 in cobalt and ferromagnetwithCurietemperatureof∼160 Kforbulk n 100innickel4). Consequently,modelsapplicabletomag- and∼150 Kforthinfilms(providedthefilmthicknessis o neticmultilayerswithatomicallysharpinterfacesarenot morethan10nm). Thinfilmsexhibithighmagnetocrys- c relevant and other models were used to interpret the tallineanisotropyfield(∼10 T)withuniaxialanisotropy : v obtained results.8,9,10 Therefore, limited understanding with the easy axis roughly14 along the crystallographic i of the physics governing magnetic multilayers could be b axis in the orthorhombic notation. For this study we X achieved from studying DWR in such systems. usedhigh-qualitythinfilms ofSrRuO grownonSrTiO 3 3 ar These problems are absent in the itinerant ferromag- substratesbyreactiveelectronbeamcoevaporation.15To netSrRuO . This compoundhas relativelylargemagne- avoidtwinningintheSrRuO filmandobtainafilmwith 3 3 tocrystalline anisotropy field (∼ 10 T) that yields stripe the same orientation of the uniaxial anisotropy through- structure with domain wall separation of 200 nm with- outthesample,thecubicsymmetryofthesubstratesur- out closure domains and with narrow Bloch DWs whose faceneedstobebroken. Thisisachievedbyslightlymis- estimated width is only δ ∼ 3 nm. These features make cutting(∼2degrees)theSrTiO substrateswhichforms 3 SrRuO a model system on which models suggested for atomicallyflat terracesseparatedby unit cellsteps. The 3 magnetic multilayers can be tested. film whose growth starts at the steps grows uniformly Initialevidencethatthesamephysicalmechanismsare with the projection of the easy axes on the plane of the relevantbothtoDWRinSrRuO andmagneticmultilay- film perpendicular to the miscut-induced steps. 3 erswasgiveninapreviousreport11 wherethemagnitude The domain structure of similarly grown films was 2 thoroughly studied using Lorentz microscopy on free standing films after removing the SrTiO substrate with 3 a chemical etch.16 It was found that in the domain state magneticstripesareformedparalleltotheeasyaxispro- jection on the film. Figure 1 shows DWs image taken from Ref.11. The DWs are 200 nm apart with no detectable dependence on film thickness (in the studied range of 30 nm - 100 nm) and no detectable dependence ontemperatureexceptforfewdegreesbelowT . Thees- c timated thickness of the Bloch wall, δ, is ∼3 nm.17 Clo- sure domains were not observed as expected for SrRuO 3 whose Q = K ≫ 1 (here K is the anisotropy en- 2πMs ergyandM is the saturatedmagnetization). Thestripe s structureformsspontaneouslywhenthesampleiscooled belowT inzerofield. Whenasufficientlyhighfieldisap- c plied below T the magnetization becomes uniform with c no stripes. An important observation is that the uniform magnetization state remains stable when the field is set back to zero. A substantial (temperature depen- dent)fieldneedstobeappliedinthenegativedirectionto startmagnetizationreversal(withmanyfewerDWsthan in the initial zero-field-cooled state). These features are essential for facilitating clear identification of DWR in this system. Usingphotolithographywepatternedfilmsintheform shownin Figure 1. It includes patterns at eightdifferent anglesrelativetothestripes: 0,15,30,45,-45,60,75and 90degrees. Thedistancebetweenthetwodistantvoltage FIG. 1: (a) Image of stripe domain walls in SrRuO3 with transmission electronmicroscopyinLorentzmode(from Ref. leads is 500µm and the width of the currentpath in the 11). The bright and dark lines image walls that diverge or patterns is 50 µm. Therefore, for θ = 90 the current converge the electron beam, respectively. Background fea- crosses ∼ 2500 domain walls between the voltage leads, tures are related to buckling of the free standing film and andforθ=0thereare∼250parallelDWsrunningalong are not related to magnetic variations. The average spacing the current path. between the walls is ∼ 200 nm. (b) Schematic figure of the photolitography patternsused for angular dependencestudy. Thepatternsareateightdifferentorientationsrelativetothe DWs(markedbythearrow): 0,15,30,45,-45,60,75and90 TheDWRmeasurementswereperformedforeachfilm degrees. on all eight patterns at temperatures between 2 K and 140 K. To measure the excess resistivity induced by do- mainwallsataspecifictemperatureT ,wecooled measure III. RESULTS AND DISCUSSION the sampleinzeromagneticfieldfromaboveT downto c T and measured the resistivity there. As noted measure before,11whencoolinginzerofieldastripedomainstruc- Fig. 2ashowsthetemperaturedependenceofDWRfor thecurrentflowingineightdifferentanglesrelativetothe ture forms; therefore, the zero-field-cooled resistivity is DWs. Ourmainobjectiveistounderstandthemeasured measured with the magnetic domains present. While DWR changes as a function of the angle between the staying at the same temperature we increased the field current and the DWs. to obtain uniform magnetization in the film. We then decreased the field to zero and measured the resistivity As noted before, we analyze our results by applying once again. The uniform magnetization remains stable models used for magnetic multilayers for which two im- at zero field. Therefore, the second resistivity is mea- portant contributions to resistivity were considered the- sured in the absence of any DWs. Consequently, we can oretically: spin accumulation18 and potential step.19 For attribute the difference between the two values of resis- parameters appropriate for SrRuO3 the two effects are tivity to DWR. For each temperature where DWR was expected to yield interface resistance for perpendicular measured,the processwasrepeatedbyfirstwarmingthe current on the order of 10−15 Ω m2, as experimentally sample above T andcooling in zero field to the temper- observed.11 c ature where DWR was to be measured. Spin accumulation is generated when spin-polarized 3 current crosses an interface between two domains with As a sensitivity check on our assumption of the sin2θ opposite magnetization. Valet and Fert18 showed that dependence of ρSA , we looked for the best fit (allowing DW such a current yields spin accumulation near the inter- B(θ) to vary) when sin2θ is replaced by sinθ or sin3θ. face that induces a potential barrier which results in in- The differentfits are showninFigure 3afor θ =45. Fig- terface resistancer givenby r =2β2ρ l (see Eq. 25in ure 3b shows an alternative comparison of the three fits F sf Ref. 18) where β is the spin asymmetry coefficient (zero which is independent of any fitting parameter. It shows forunpolarizedcurrentand1forfullypolarizedcurrent), (ρ (T,45)−f(θ)ρ (T,90))/ρ (T,0)asa function DW DW DW ρ is the average resistivity (for spin-up and spin-down of temperature with f(θ) being sinθ, sin2θ, or sin3θ. F currents) and l is the spin diffusion length which is A fit consistent with the assumption that the sources of sf the characteristic length over which the polarization of DWR for parallel current (that do not include spin ac- crossing current equilibrates with the equilibrium polar- cumulation)are presentat other anglesas wellandtheir ization. The spin-accumulation resistivity, ρSA , is pro- relativeeffectatotheranglesistemperatureindependent DW portional to the interface resistance, r, with the number should yield a temperature independent curve. Figure of domain walls per unit length being the proportional- 3bdemonstratesthatthebestfitisindeedobtainedwith ityfactor. ρSA isexpectedtodecreasewithtemperature f(θ)=sin2θ. DW due to the expected fast decrease in lsf due to increase The fitting function is B(θ)=A(θ)−A(90)sin2θ. To in magnetic scattering (e.g., due to magnons) which be- identify the spin accumulation part in the DWR of the comes more probable with increasing temperature. perpendicular current we need to determine A(90). To Sincespinaccumulationisassociatedwiththenetcur- identify A(90) we consider that the closer we are to T c rent crossing the interface, no spin accumulation contri- the less is the relative contribution of spin accumulation bution to DWR is expected for current parallel to the toDWR;hence,theangulardependenceofDWRisdom- domain walls. Here we explore in what way spin accu- inatedbytheangulardependenceofA(θ). Therefore,we mulation contribution, that we note by ρSA , changes as look for A(90) for which A(θ) is the most similar to the DW a function of angle. angular dependence of DWR obtained at high tempera- Two factors relevant to spin accumulation resistivity ture. Figure 4a presents A(θ) for two different samples change as a function of angle (see inset to Figure 3a): andFigure4bshowstheangulardependenceoftheDWR the net current flowing perpendicular to the interface is at different temperatures. The main feature is the non multiplied by sinθ and the number of domain walls per monotonic or even oscillatory (note correlation between unit length crossedby a currentis multiplied by another the two samples) behavior of A(θ) which is reflected in factorofsinθ. Thebottomlineisthatspinaccumulation theangulardependenceoftheDWRparticularlynearT c contribution to DWR for any angle θ is expected to be where ρSA diminishes. It is likely that the source that DW the spin accumulation resistivity for perpendicular cur- displaysthisbehaviorisrelatedtointerfaceresistanceas- rent multiplied by sin2θ. The problem, however, is to sociatedwith potentialsteps; however,the specific cause determine the spin accumulation part in the DWR with of this behavior is unclear at the moment. It is impor- perpendicular current. tant to note that the exact form of A(θ) depends on the As we noted before, no spin accumulation contribu- thicknessofthe film sowe hope thatmorestudy focused tionisexpectedforparallelcurrent. Therefore,assuming onthethicknessdependence ofDWRwillyieldmoreun- that the sources responsible for DWR for parallel cur- derstanding. rent (presumably, related to potential steps) are present Having found A(90), we can determine the spin ac- for other angles as well and assuming that (similarly to cumulation interface resistance as a function of temper- spin-accumulation) the contribution at other angles is a ature. Figure 5 shows the spin accumulation interface temperature−independent function of the angle alone, resistance for two different samples and the inset shows A(θ), we canexpect thatDWR for any temperature and their extracted l using Valet-Fert equation.18 It is im- sf angle will be given by the following equation: portant to note that this derivation of l is expected sf to be reliable only in the low-temperature limit where Valet-Fert equation is valid. From the low temperature ρDW(T,θ)= sin2θ(ρDW(T,90)−A(90)ρDW(T,0)) limit we find lsf on the order of 40-50 nm. This value is + A(θ)ρ (T,0) consistentwithourfindingsthatDWRforperpendicular DW current scales with the density of DWs20 which implies = sin2θρ (T,90)+B(θ)ρ (T,0) (1) DW DW that the scattering at neighboring DWs is independent, suggesting that spin diffusion length is smaller than the The term (ρ (T,90)−A(90)ρ (T,0)) is the spin DW DW separation between the DWs (200 nm). accumulationpartintheDWRforperpendicularcurrent and B(θ)=A(θ)−A(90)sin2θ. To test this model we check whether Equation 1 can IV. SUMMARY AND CONCLUSION reproduce, using measured ρ (T,90) and ρ (T,0), DW DW the measured DWR at all other angles by using a single fitting function, B(θ). The success of this fit is visible in We present here for the first time data on the angu- Figure 2b. lar dependence of resistivity induced by stripe domain 4 structure in a system that can adequately serve as a Humanities. modelsystemformagneticmultilayers. Wefindasimple fitting equation whose success provides the first exper- imental indication that the angular dependence of the spin-accumulation resistivity ρSA is sin2θ. DW Acknowledgments L.K.acknowledgessupportbytheIsraelScienceFoun- dation founded by the Israel Academy of Sciences and ∗ Current location: Department of Applied Physics, Yale 13 E. Simanek Phys.Rev.B 63, 224412 (2001). University,New haven,Connecticut 06520-8284 14 The easy axis is along the b direction near Tc; however, 1 M. N.Baibich et al.,Phys.Rev. Lett.61, 2472 (1988). there is a reorientation transition where the easy axis 2 S. A.Wolf et al.,Science 294, 1488 (2001). changes is orientation from 45 degrees to the film normal 3 A. D.Kent et al., J. Appl.Phys. 85, 5243 (1999). at Tc to30degrees tothenormalinthezero-temperature 4 M. Viret et al., Phys.Rev.B 53, 8464 (1996). limit. 5 J. F. Gregg et al.,Phys. Rev.Lett. 77, 1580 (1996). 15 S.J.Benerofeetal.,J.Vac.SciTecjnol.B12,1217(1994). 6 D. Ravelosona et al., Phys.Rev.B 59, 4322 (1999). 16 A.F. Marshall et al.,J.Appl. Phys85, 4131 (1999). 78 UG..RTuatdaigraeraentdalH.,.PFhuyksu.yRaemva.,BP5h9ys1.1R91e4v.(1L9e9t9t.).79, 5110 17 BthaeseadniosontrtohpeykcnoonwsntanretlaatnidonCδ==2πJS(cid:0)22.KCH1e(cid:1)r1e/2JwisheexrechKan1gies (1997). a 109 RP..MP..vLaenvyGaonrkdomZh,aAn.g,BPrahtyasa.sRaenvd.LGe.tEt.. 7W8.,B37a7u3er(,1P99h7y)s.. 1189 TeJn..eBVragarylne,taSsainasdnsdpAiAn.F.Fearnetrd,t,PaPhiyhssyd.si.RstReaven.vc.BeBb4e48t9,w,7e0e19n298s3p(51in9(s91.39)9.4). 11 RL.evK.leLientte.t8a3l.,,4P4h0y1s.(1R9e9v9.).Lett. 84, 6090 (2000). 20 L. Klein et al., J. Magn. Magn. Mater. 226-230, 780-781 12 U. Ebels et al., Phys.Rev.Lett. 84, 983 (2000). (2001). 5 0.8 m) c 0.7 0 (a) 15 mW y ( 0.6 3405 vit 0.5 60 sti 75 esi 0.4 90 R all 0.3 W n 0.2 ai m 0.1 o D 0 0.7 m) 75 c 0.6 (b) mW vity ( 0.5 45 sti 0.4 si e R 0.3 all 15 W 0.2 n ai m 0.1 o D 0 0 20 40 60 80 100 120 140 Temperature (K) FIG.2: (a): DWRasafunctionoftemperaturewithcurrent flowing at different angles relative to the DWs: θ=0, 15, 30, 45, 60, 75 and 90 degrees. The data points for θ=-45 are on topofthedatapointsforθ=45andarenotshowninthefigure (b)DWRasafunctionoftemperaturewithθ=15,45,and75. Thesymbolsaretheactualdatapointsforthedifferentangles whereas the line is the one-parameter fit based on Equation 1. 6 0.6 m) d c (a) 0.5 mW vity ( 0.4 J q sti esi 0.3 R Wall 0.2 n mai 0.1 o D 0 1 (b) 0.8 0.6 0.4 q)B( 0.2 0 -0.2 -0.4 0 20 40 60 80 100 120 140 Temperature (K) FIG.3: (a)ρ (T,45)withthreedifferentfitsassumingdif- DW ferentangulardependenceofthespinaccumulationcontribu- tion toDWR:sinθ (dotted),sin2θ (full) andsin3θ (dashed). Inset: Schematic illustration of a current path with current J at an angle θ relative to the DWs. The current flowing perpendicular to the wall is Jsinθ and the distance the current flows between the walls d is (domain width)/sinθ. (b) (ρ (T,45)−f(θ)ρ (T,90))/ρ (T,00) as a function of DW DW DW θ with f(θ) = sinθ (circles), f(θ) = sin2θ (squares) and f(θ) = sin3θ (triangles). Following Equation 1, the quality of the fit is manifested in temperature independence of (ρ (T,45)−f(θ)ρ (T,90))/ρ (T,00) DW DW DW 1.3 (a) 1.2 7 1.1 ) qA ( 1 0.9 0.8 0.7 0.8 m) (b) 2 K c 0.7 mW y ( 0.6 vit sti 0.5 40 K si e R 0.4 all W 0.3 n 90 K ai m 0.2 140 K o D 0.1 0 20 40 60 80 100 Angle (degree) FIG.4: (a) A(θ)asafunction ofangle fortwodifferentsam- ples(b)ρ (T,θ)asafunctionofangleatdifferenttemper- DW atures. The symbols are the actual data points whereas the line is the oneparameter fit based on Equation 1. 8 1 5 -10 m) 60 1 n 50 ) x 0.8 ngth ( 40 2 e m n l 30 0.6 usio 20 We ( n diff 10 c pi n S 0 a st 0.4 0 20 40 60 80 100120140 si Temperature (K) e r e 0.2 c a rf e nt 0 i 0 20 40 60 80 100 120 140 Temperature (K) FIG.5: Spinaccumulationcontributiontotheinterfaceresis- tance as a function of temperature for two different samples. The inset shows the extracted spin diffusion length based on Valet-Fert18 relation.