二次谐波具体公式1.3502596

Tilting of the spin orientation induced by Rashba effect in ferromagnetic metal layer

Ung Hwan Pi, Kee Won Kim, Ji Young Bae, Sung Chul Lee, Young Jin Cho, Kwang Seok Kim, and Sunae

Seo

Citation: Applied Physics Letters 97, 162507 (2010); doi: 10.1063/1.3502596

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Tilting of the spin orientation induced by Rashba effect in ferromagnetic metal layer

Ung Hwan Pi,a?Kee Won Kim,Ji Young Bae,Sung Chul Lee,Young Jin Cho,

Kwang Seok Kim,and Sunae Seo

Samsung Advanced Institute of Technology(SAIT),Gyeonggi-Do446-712,Republic of Korea

?Received3June2010;accepted14September2010;published online22October2010?

We devised a method to measure the virtual magnetic?eld induced by Rashba effect in

ferromagnetic metal layer.Transverse Rashba magnetic?eld makes the magnetization direction

tilted out of the easy axis,which could be detected by the change in anomalous hall resistances.

Through a speci?ed measurement of the second harmonics of the hall resistance,the Rashba?eld

could be obtained with high sensitivity even at low current regime.The results are compared with

the prior reports based on the measurement of the transverse?eld required for the nucleation of

reversed domain.?2010American Institute of Physics.?doi:10.1063/1.3502596?

Control of the magnetization in the nanodevices using

local electric currents or electric?elds instead of externally

applied magnetic?elds has been of great interest,because it

can open the possibility of various novel devices that are far

superior in integration and functionalities.1Conventional

method to control the magnetization reversal with electric

current is to use the spin transfer torque effect,where the

spin polarized electrons from a pinned ferromagnetic layer

are injected into a free layer through a nonmagnetic spacer.

Another way is to use so called Rashba effect2or

Dresselhaus 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 electric?eld experience a

relativistic magnetic?eld in the electron’s rest frame.The

direction of the spin can be manipulated by the electric?eld

or unpolarized currents.Recently,several groups reported

the evidences of the Rashba effect in magnetic metallic

systems,4,5and the existence of the Rashba?eld?H ra?has been con?rmed through a direct measurement.6The mea-

sured H ra value was much larger than the current induced

Oesterd?eld.

A simple and sensitive method to measure H ra is essen-

tial for the study of this promising way of magnetization

control.In the prior report,6H ra has been estimated by mea-

suring the transverse?eld required for the nucleation of the

reversed domain.In this method,H ra can be measured only

when a reversed domain can be nucleated.In case of the

sample that has very large anisotropy?eld?H k?,this method requires very high external?eld 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 transverse?eld,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 Ta?5?/Pt?3?/Co?0.6?/AlO x?1.8??sample A?and Ta?5?/Pt?3?/ Co?0.6?/Pt?3??sample B?grown on Si/SiO2substrates have been fabricated to form hall cross structures as shown in Fig. 1?a?.Here the numbers in the parenthesis represent the?lm thickness in nanometers.Due to the crystal?eld 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 by7

H ra?

?R P

?B M

?z??J?,?1?

where?B is the Bohr magneton,P is a parameter that de-pends on the s?d coupling strength,and?R represents the coef?cient of Rashba interaction.When an alternating cur-rent?I sin?t??ows through the nanowire under a transverse

a?Electronic mail:ilovesuyoung@https://www.360docs.net/doc/703558367.html,.

V V

H y

H y

x

H ra

H ra

I sinωt

spin

y

z

(c)

0.00.5

(T)

FIG.1.?Color online??a?shows the experimental setup of the Rashba?eld

?H ra?measurement.The spin orientations are modulated by the alternating

H 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.?b?and?c?show the in-phase?rst harmonics

?C??of the hall voltages measured under the perpendicular?elds?H z?and

transverse?elds?H y?,respectively.

APPLIED PHYSICS LETTERS97,162507?2010?

0003-6951/2010/97?16?/162507/3/$30.00?2010American Institute of Physics

97,162507-1

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external?eld?H y?as 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.1?a?.The anomalous hall resistance?R hall?,that repre-sents z component of magnetization,has a signal modulated with the same frequency as the current??component?by R hall?H?=R hall?H y+H ra sin?t??R hall?H y?

+?dR hall/dH?H ra sin?t.?2?Since both R hall and the alternating current have?compo-nents,the hall voltage?V hall?,which is the product of the R hall and current,has both?and2?components as

V hall?H?=R hall?H?I sin?t??R hall?H y?

+?dR hall/dH?H ra sin?t?I sin?t

=I?dR hall/dH?H ra/2+C?sin?t?C2?cos2?t.

?3?Here C?=IR hall and C2?=??IH ra/2??dR hall/dH?are the in-phase?and out-of-phase2?components of the modulated hall voltage,respectively.From this,H ra can be obtained as

H ra=?2

C2?

dC?/dH

.?4?

Figures1?b?and1?c?show the?rst harmonic hall volt-

age?C??of sample A measured at an alternating current density?J ac?of2.1?106A/cm2under a perpendicular ex-ternal?eld?H z?and transverse?eld H y,respectively.Before the H y sweep shown in Fig.1?c?,the magnetization of the sample was initialized to a single domain state by a perpen-dicular?eld H z=?300mT.Since our sample holder is not perfectly aligned with the electromagnet axis,the H y sweep from0.94to?0.94T did not show symmetric behavior.As shown in the inset of Fig.1?c?,the application of positive ?negative?H y accompanies negative?positive?H z due to the slight misalignment of the sample.The jump of C?observed in?0.85T in Fig.1?c?represents the initiation of the mag-netization reversal by the misalignment-induced perpendicu-lar?eld larger than the coercive?eld H c=119mT.In the ?eld range of?H z??H c,C?values have no dependence upon H z as one can see in Fig.1?b?.Therefore,the additional perpendicular?eld due to the slight misalignment does not affect the C?values,and the Eqs.?2?and?3?,where only H y is considered,are still valid.

For the measurement of H ra based on Eq.?4?,we per-formed H y sweep only in the positive range?from0to0.94 T?,where the additional H z induced by the sample misalign-ment supported the initial magnetization direction??z?and did not cause any abrupt change due to the magnetization reversal?cf.Figs.1?b?and1?c??.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.2?a?and2?b?, respectively.In case of sample B,only C2?data are pre-sented in the inset of the Fig.2?b?because 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 signi?cant C2?values that have linear behavior with H y.This reveals that the structural inversion asymmetry is essential to the formation of the Rashba?eld.The linear behavior of C?in sample A can also be easily understood if

we consider that C2?is the derivative of the C?with respect

to H y according to Eq.?3?.

The estimated H ra values of sample A are depicted as a

function of H y and J ac in Figs.2?c?and2?d?,respectively.

H ra shows negligible dependence upon H y but increases lin-

early as J ac goes higher.We performed the measurement

only up to J ac=1.0?107A/cm2,beyond which the mea-

surement became very noisy due to the heating of the

sample.The conversion factor from current density to the

Rashba?eld is about2.9?10?9T cm2/A.If the conversion factor works even at a higher current density,a Rashba?eld

of0.29T is expected on a current density of108A/cm2.

This value is about 3.4times smaller than the reported

value.6But it is58times larger than the calculated Oesterd

?eld,revealing that the measured H ra surely comes from the

Rashba effect.

To compare our result with the prior report,we per-

formed the Rashba?eld measurement based on the detection

of the reversed domain.As described by the prior report,6a

reversed domain begins to nucleate from a threshold trans-

verse?eld.Since the total transverse?eld is the sum of H y

and H ra,the external transverse?eld required for the nucle-

ation of the reversed domain?H nuc?depends on H ra.The

dependence 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 current?ow as

H ra?J?=H nuc?0??H nuc?J?.?5?

In our experiment,the nucleation of the reversed domain

was detected by the abrupt change in the hall voltage.Con-

trary to the experiments depicted in Fig.2,we measured the

hall voltages while sweeping H y in the negative range from0

to?0.94T.In this negative H y range,the misalignment in-

duced H z is opposite to the initialized magnetization direc-

H

y

(T)J

ac

(106A/cm2)

FIG.2.?Color online?In-phase?rst harmonics?C??and out-of-phase sec-ond harmonics?C2??of the hall voltages have been measured as a function of H y at several ac current densities?J ac?.?a?and?b?show the C?and C2?dependences of sample A upon the transverse?eld H y,respectively.In the inset of?b?,the behavior of C2?in sample B is depicted for the comparison. From the C?and C2?values shown in?a?and?b?,one can estimate the Rashba?elds?H ra?from Eq.?4?in the text.The resulting values of H ra are displayed as a function of H y and J ac in?c?and?d?,respectively.

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tion,supporting a nucleation of a reversed domain.For the control of the Rashba ?eld,100ns long current pulses with densities ?J p ?from 0to 1.9?107A /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 whose

density was 5.0?105A /cm 2much smaller than the current pulses for the Rashba ?eld.

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 ?ow 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.3?a ?and 3?b ??.From this current polarity dependence,one can ?nd that the direction of H ra is ?y ?parallel to external ?eld H y ?when current is positive ?electron ?ow 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 ?eld.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.3?b ?.

Figure 3?c ?shows the current dependence of H nuc and H ra .Up to about 1.5?107A /cm 2,H ra shows linear behav-ior with J p but it suddenly increases from J p =1.5?107A /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 ?5?is not valid any more in this case.

In the inset of Fig.3?c ?,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 ?1.1?107A /cm 2.One can notice that they coincide with each other.The sec-ond harmonics method presented in this paper gives the Rashba ?eld as well as the previous method by Miron et al.6

In summary,the current induced Rashba ?elds 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 ?eld could be measured sensitively even at low current density regime.

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m T )

J (106

A/cm 2

)

H r a (p FIG.3.?Color online ?C ?values have been measured as a function of transverse ?eld 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 ?eld ?H nuc ?and the corresponding Rashba ?eld ?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 ?1.1?107A /cm 2.

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