二次谐波具体公式1.3502596

Tilting of the spin orientation induced by Rashba effect in ferromagnetic metal layerUng Hwan Pi, Kee Won Kim, Ji Young Bae, Sung Chul Lee, Young Jin Cho, Kwang Seok Kim, and SunaeSeoCitation: Applied Physics Letters 97, 162507 (2010); doi: 10.1063/1.3502596View online: /10.1063/1.3502596View Table of Contents: /content/aip/journal/apl/97/16?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inQuaternary memory device fabricated from a single layer Fe filmJ. Appl. Phys. 111, 07C704 (2012); 10.1063/1.3670973Monitoring magnetization reversal and perpendicular anisotropy by the extraordinary Hall effect andanisotropic magnetoresistance.J. Appl. Phys. 108, 043924 (2010); 10.1063/1.3475690Tunable quaternary states in ferromagnetic semiconductor GaMnAs single layer for memory devicesAppl. Phys. 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Downloaded to IP:Tilting of the spin orientation induced by Rashba effect in ferromagnetic metal layerUng Hwan Pi,a͒Kee Won Kim,Ji Young Bae,Sung Chul Lee,Young Jin Cho,Kwang Seok Kim,and Sunae SeoSamsung Advanced Institute of Technology(SAIT),Gyeonggi-Do446-712,Republic of Korea͑Received3June2010;accepted14September2010;published online22October2010͒We devised a method to measure the virtual magneticfield induced by Rashba effect inferromagnetic metal layer.Transverse Rashba magneticfield makes the magnetization directiontilted out of the easy axis,which could be detected by the change in anomalous hall resistances.Through a specified measurement of the second harmonics of the hall resistance,the Rashbafieldcould be obtained with high sensitivity even at low current regime.The results are compared withthe prior reports based on the measurement of the transversefield required for the nucleation ofreversed domain.©2010American Institute of Physics.͓doi:10.1063/1.3502596͔Control of the magnetization in the nanodevices usinglocal electric currents or electricfields instead of externallyapplied magneticfields has been of great interest,because itcan open the possibility of various novel devices that are farsuperior in integration and functionalities.1Conventionalmethod to control the magnetization reversal with electriccurrent is to use the spin transfer torque effect,where thespin polarized electrons from a pinned ferromagnetic layerare injected into a free layer through a nonmagnetic spacer.Another way is to use so called Rashba effect2orDresselhaus effect,3both of which are related to the spin-orbit coupling between the spin of the electron and its mo-mentum.Electrons moving in an electricfield experience arelativistic magneticfield in the electron’s rest frame.Thedirection of the spin can be manipulated by the electricfieldor unpolarized currents.Recently,several groups reportedthe evidences of the Rashba effect in magnetic metallicsystems,4,5and the existence of the Rashbafield͑H ra͒has been confirmed through a direct measurement.6The mea-sured H ra value was much larger than the current inducedOesterdfield.A simple and sensitive method to measure H ra is essen-tial for the study of this promising way of magnetizationcontrol.In the prior report,6H ra has been estimated by mea-suring the transversefield required for the nucleation of thereversed domain.In this method,H ra can be measured onlywhen a reversed domain can be nucleated.In case of thesample that has very large anisotropyfield͑H k͒,this method requires very high externalfield or large current density for the nucleation of the reversed domain,rendering its applica-tion limited.Instead,one can directly measure the tilting angle of the spins by the anomalous hall measurements. Since the tilting angle has one-to-one correspondence with the magnitude of the transversefield,the measurement of the tilting angle can give a quantitative estimation of H ra.In this paper,we present the H ra estimation based on the measure-ment of the spin orientation angle.Two different kinds of ferromagnetic layers of Ta͑5͒/Pt͑3͒/Co͑0.6͒/AlO x͑1.8͒͑sample A͒and Ta͑5͒/Pt͑3͒/ Co͑0.6͒/Pt͑3͒͑sample B͒grown on Si/SiO2substrates have been fabricated to form hall cross structures as shown in Fig. 1͑a͒.Here the numbers in the parenthesis represent thefilm thickness in nanometers.Due to the crystalfield induced by the structural inversion asymmetry,sample A is expected to show larger Rashba effect than sample B.The widths of the nanowire and hall bar were500nm and200nm,respec-tively.The magnitude of H ra under a current density J is given by7H raϷ␣R P␮B M͑zˆϫJ͒,͑1͒where␮B is the Bohr magneton,P is a parameter that de-pends on the s−d coupling strength,and␣R represents the coefficient of Rashba interaction.When an alternating cur-rent͑I sin␻t͒flows through the nanowire under a transversea͒Electronic mail:ilovesuyoung@.V VH yH yxH raH raI sinωtspinyz(c)0.00.5(T)FIG.1.͑Color online͒͑a͒shows the experimental setup of the Rashbafield͑H ra͒measurement.The spin orientations are modulated by the alternatingH ra induced by the alternating current bias of400Hz as shown in the inset.The modulation of the spin angle is measured by the anomalous hall effect,from which H ra are estimated.͑b͒and͑c͒show the in-phasefirst harmonics͑C␻͒of the hall voltages measured under the perpendicularfields͑H z͒andtransversefields͑H y͒,respectively.APPLIED PHYSICS LETTERS97,162507͑2010͒0003-6951/2010/97͑16͒/162507/3/$30.00©2010American Institute of Physics97,162507-1This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: /termsconditions. Downloaded to IP:externalfield͑H y͒as depicted in Fig.1,the tilting angles of the spins out of the easy axis are also modulated by the H ra induced by the alternating current as shown in the inset of Fig.1͑a͒.The anomalous hall resistance͑R hall͒,that repre-sents z component of magnetization,has a signal modulated with the same frequency as the current͑␻component͒by R hall͑H͒=R hall͑H y+H ra sin␻t͒ϷR hall͑H y͒+͑dR hall/dH͒H ra sin␻t.͑2͒Since both R hall and the alternating current have␻compo-nents,the hall voltage͑V hall͒,which is the product of the R hall and current,has both␻and2␻components asV hall͑H͒=R hall͑H͒I sin␻tϷ͓R hall͑H y͒+͑dR hall/dH͒H ra sin␻t͔I sin␻t=I͑dR hall/dH͒H ra/2+C␻sin␻t−C2␻cos2␻t.͑3͒Here C␻=IR hall and C2␻=−͑IH ra/2͒͑dR hall/dH͒are the in-phase␻and out-of-phase2␻components of the modulated hall voltage,respectively.From this,H ra can be obtained asH ra=−2C2␻dC␻/dH.͑4͒Figures1͑b͒and1͑c͒show thefirst harmonic hall volt-age͑C␻͒of sample A measured at an alternating current density͑J ac͒of2.1ϫ106A/cm2under a perpendicular ex-ternalfield͑H z͒and transversefield H y,respectively.Before the H y sweep shown in Fig.1͑c͒,the magnetization of the sample was initialized to a single domain state by a perpen-dicularfield H z=−300mT.Since our sample holder is not perfectly aligned with the electromagnet axis,the H y sweep from0.94toϪ0.94T did not show symmetric behavior.As shown in the inset of Fig.1͑c͒,the application of positive ͑negative͒H y accompanies negative͑positive͒H z due to the slight misalignment of the sample.The jump of C␻observed inϪ0.85T in Fig.1͑c͒represents the initiation of the mag-netization reversal by the misalignment-induced perpendicu-larfield larger than the coercivefield H c=119mT.In the field range of͉H z͉ϽH c,C␻values have no dependence upon H z as one can see in Fig.1͑b͒.Therefore,the additional perpendicularfield due to the slight misalignment does not affect the C␻values,and the Eqs.͑2͒and͑3͒,where only H y is considered,are still valid.For the measurement of H ra based on Eq.͑4͒,we per-formed H y sweep only in the positive range͑from0to0.94 T͒,where the additional H z induced by the sample misalign-ment supported the initial magnetization direction͑−z͒and did not cause any abrupt change due to the magnetization reversal͓cf.Figs.1͑b͒and1͑c͔͒.The C␻and C2␻values measured at several different current densities J ac in sample A are depicted as a function of H y in Figs.2͑a͒and2͑b͒, respectively.In case of sample B,only C2␻data are pre-sented in the inset of the Fig.2͑b͒because C␻of sample B has similar behavior with that of sample A.In contrast to the similar behavior of C␻on both samples,C2␻shows distinct difference between the two samples.While sample B has negligible C2␻values in the whole ranges of H y and J ac, sample A has significant C2␻values that have linear behavior with H y.This reveals that the structural inversion asymmetry is essential to the formation of the Rashbafield.The linear behavior of C␻in sample A can also be easily understood ifwe consider that C2␻is the derivative of the C␻with respectto H y according to Eq.͑3͒.The estimated H ra values of sample A are depicted as afunction of H y and J ac in Figs.2͑c͒and2͑d͒,respectively.H ra shows negligible dependence upon H y but increases lin-early as J ac goes higher.We performed the measurementonly up to J ac=1.0ϫ107A/cm2,beyond which the mea-surement became very noisy due to the heating of thesample.The conversion factor from current density to theRashbafield is about2.9ϫ10−9T cm2/A.If the conversion factor works even at a higher current density,a Rashbafieldof0.29T is expected on a current density of108A/cm2.This value is about 3.4times smaller than the reportedvalue.6But it is58times larger than the calculated Oesterdfield,revealing that the measured H ra surely comes from theRashba effect.To compare our result with the prior report,we per-formed the Rashbafield measurement based on the detectionof the reversed domain.As described by the prior report,6areversed domain begins to nucleate from a threshold trans-versefield.Since the total transversefield is the sum of H yand H ra,the external transversefield required for the nucle-ation of the reversed domain͑H nuc͒depends on H ra.Thedependence of H ra upon the current density J can be ob-tained from the difference between the two H nuc values mea-sured with and without currentflow asH ra͑J͒=H nuc͑0͒−H nuc͑J͒.͑5͒In our experiment,the nucleation of the reversed domainwas detected by the abrupt change in the hall voltage.Con-trary to the experiments depicted in Fig.2,we measured thehall voltages while sweeping H y in the negative range from0toϪ0.94T.In this negative H y range,the misalignment in-duced H z is opposite to the initialized magnetization direc-Hy(T)Jac(106A/cm2)FIG.2.͑Color online͒In-phasefirst harmonics͑C␻͒and out-of-phase sec-ond harmonics͑C2␻͒of the hall voltages have been measured as a function of H y at several ac current densities͑J ac͒.͑a͒and͑b͒show the C␻and C2␻dependences of sample A upon the transversefield H y,respectively.In the inset of͑b͒,the behavior of C2␻in sample B is depicted for the comparison. From the C␻and C2␻values shown in͑a͒and͑b͒,one can estimate the Rashbafields͑H ra͒from Eq.͑4͒in the text.The resulting values of H ra are displayed as a function of H y and J ac in͑c͒and͑d͒,respectively.This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: /termsconditions. Downloaded to IP:tion,supporting a nucleation of a reversed domain.For the control of the Rashba field,100ns long current pulses with densities ͑J p ͒from 0to 1.9ϫ107A /cm 2have been continu-ously applied with a period of 1Hz through bias tee.The hall voltages were measured with a 400Hz alternating current bias whosedensity was 5.0ϫ105A /cm 2much smaller than the current pulses for the Rashba field.The results obtained in sample A are shown in Fig.3.As expected,the behaviors of hall voltages show distinct differ-ence depending upon the polarity of the current pulses,i.e.,the direction of H ra .When the current pulses J p are positive ͑electron flow toward −x ͒,the positions of the abrupt jump moves to the lower H y as J p goes higher.On the other hand,the positions of the jump remain unchanged in the case of negative current pulses ͓cf.Figs.3͑a ͒and 3͑b ͔͒.From this current polarity dependence,one can find that the direction of H ra is −y ͑parallel to external field H y ͒when current is positive ͑electron flow toward −x ͒and the spin direction is −z .This agrees with the previous report by Miron et al.6In case of the negative J p ,the H ra is antiparallel to H y ,reducing the total transverse field.The jump due to the reversed do-main nucleation is expected to appear at even higher H y .But this does not happen because the current pulses acts only a very short period,and most of the time in the experiment,the situation is the same without current pulse,i.e.,J p =0A /cm 2.Therefore,the position of the jump remains the same in the negative current pulses as shown in Fig.3͑b ͒.Figure 3͑c ͒shows the current dependence of H nuc and H ra .Up to about 1.5ϫ107A /cm 2,H ra shows linear behav-ior with J p but it suddenly increases from J p =1.5ϫ107A /cm 2.This nonlinear behavior comes from the heat-ing of the nanowire.The energy barrier for the nucleation of the reversed domain is reduced due to the increased tempera-ture,yielding much smaller H nuc .Equation ͑5͒is not valid any more in this case.In the inset of Fig.3͑c ͒,the values of H ra estimated from H nuc measurement ͑black square ͒are compared with those from the second harmonics method ͑red triangles ͒in the cur-rent range of negligible heating,i.e.,J p Ͻ1.1ϫ107A /cm 2.One can notice that they coincide with each other.The sec-ond harmonics method presented in this paper gives the Rashba field as well as the previous method by Miron et al.6In summary,the current induced Rashba fields have been estimated in ferromagnetic layers by the anomalous hall measurement.With the special method that measures the tilt-ing angle of the spin orientation,the Rashba field could be measured sensitively even at low current density regime.1C.Chappert,A.Fert,F.Nguyen,and V .Dau,Nat.Mater.6,813͑2007͒.2H.C.Koo,J.H.Kwon,J.Eom,J.Chang,S.H.Han,and M.Johnson,Science 325,1515͑2009͒.3A.Chernyshov,M.Overby,X.Liu,J.K.Furdyna,Y .Lyanda-Geller,and L.P.Rokhinson,Nat.Phys.5,656͑2009͒.4T.A.Moore,I.M.Miron,G.Gaudin,G.Serret,S.Auffret,B.Rodmacq,A.Schuhl,S.Pizzini,J.V ogel,and M.Bonfim,Appl.Phys.Lett.93,262504͑2008͒.5I.M.Miron,P.-J.Zermatten,G.Gudin,S.Auffret,B.Rodmacq,and A.Schuhl,Phys.Rev.Lett.102,137202͑2009͒.6I.M.Miron,G.Gaudin,S.Auffret,B.Rodmacq,A.Schuhl,S.Pizzini,J.V ogel,and P.Gambardella,Nat.Mater.9,230͑2010͒.7A.Manchon and S.Zhang,Phys.Rev.B 79,094422͑2009͒.m T )J (106A/cm 2)H r a (p FIG.3.͑Color online ͒C ␻values have been measured as a function of transverse field H y in sample A with additional positive ͑a ͒and negative ͑b ͒current pulses of 100ns.The position of the distinct jumps representing the nucleation of the reversed domain moves toward smaller H y as the height of the positive current pulses increases.However,no change is observed in the negative current pulses.The nucleation field ͑H nuc ͒and the corresponding Rashba field ͑H ra ͒are depicted as a function of current density of the pulses ͑J p ͒in ͑c ͒.In the inset,the H ra values estimated from the H nuc measurement ͑black square ͒are compared with those from the second harmonics method ͑red triangles ͒in the current range J p Ͻ1.1ϫ107A /cm 2.This article is copyrighted as indicated in the article. 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