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

View online: /10.1063/1.3502596

View Table of Contents: /content/aip/journal/apl/97/16?ver=pdfcov

Published by the AIP Publishing

Articles you may be interested in

Quaternary memory device fabricated from a single layer Fe film

J. Appl. Phys. 111, 07C704 (2012); 10.1063/1.3670973

Monitoring magnetization reversal and perpendicular anisotropy by the extraordinary Hall effect and

anisotropic magnetoresistance.

J. Appl. Phys. 108, 043924 (2010); 10.1063/1.3475690

Tunable quaternary states in ferromagnetic semiconductor GaMnAs single layer for memory devices

Appl. Phys. Lett. 90, 152113 (2007); 10.1063/1.2721144

Influence of spin polarization enhancement layer to rare earth–transition metal thin films for perpendicular

tunneling magnetoresistance evaluated by ferromagnetic Hall effect

J. Appl. Phys. 99, 08C513 (2006); 10.1063/1.2177420

Perpendicular magnetization reversal, magnetic anisotropy, multistep spin switching, and domain nucleation

and expansion in Ga 1 − x Mn x As films

J. Appl. Phys. 98, 063904 (2005); 10.1063/1.2043233

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: /termsconditions. Downloaded to IP:

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

Ung Hwan Pi,a͒Kee 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 online22October2010͒

We devised a method to measure the virtual magneticfield induced by Rashba effect in

ferromagnetic metal layer.Transverse Rashba magneticfield makes the magnetization direction

tilted 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 Rashbafield

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 transversefield required for the nucleation of

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

Control of the magnetization in the nanodevices using

local electric currents or electricfields instead of externally

applied magneticfields 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 electricfield experience a

relativistic magneticfield in the electron’s rest frame.The

direction of the spin can be manipulated by the electricfield

or unpolarized currents.Recently,several groups reported

the evidences of the Rashba effect in magnetic metallic

systems,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 induced

Oesterdfield.

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 transversefield 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 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 by7

H raϷ

␣R P

␮B M

͑zˆϫJ͒,͑1͒

where␮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 transverse

a͒Electronic mail:ilovesuyoung@.

V V

H y

H y

x

H ra

H ra

I sinωt

spin

y

z

(c)

0.00.5

(T)

FIG.1.͑Color online͒͑a͒shows the experimental setup of the Rashbafield

͑H ra͒measurement.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.͑b͒and͑c͒show the in-phasefirst harmonics

͑C␻͒of the hall voltages measured under the perpendicularfields͑H z͒and

transversefields͑H y͒,respectively.

APPLIED PHYSICS LETTERS97,162507͑2010͒

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

97,162507-1

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: /termsconditions. Downloaded to IP: