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Careful study ofCareful study of

Ultrafast Magneto-OpticsUltrafast Magneto-Optics

ITOH Lab. Yoshitaka Sakamoto

( 坂本　圭隆 )

[Referenece] “Ultrafast Magneto-Optics in Nickel: Magnetism or Optics?”

B.Koopmans, M.van Kampen et al. Phys.Rev.Lett. 85,844(2000)

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ContentsContents

Introduction　　・ Background

　　・ Aim of the reference

Main talk　　・ light, Kerr effect, and TRMOKE

　　・ Measurement configuration

・ Predictable signal

　　・ Result and Analysis (in the reference)

Summary

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BackgroundBackground

Problem:

10

100

1000

1980 2005

year

Clock per second

CPU speed

Writing speed to a RAM

・ storage

(capacity, writing speed)

↓

・ spin memory

Solution:

(rapid writing by using light,

large capacity [lamellar magnetic layer])薄　層　磁　性　膜

⇒TRMOKE (time-resolved MO Kerr effect) is used.

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Aim of the referenceAim of the reference

Cu 3nm

Cu(111)or(001)

Ni0~15nm

1.Ni thickness

2.field

3.temperature

MO

sig

nal

0 delay time0.5ps(10sec)

-12

Ultrafast demagnetization?

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TRMOKE measurementTRMOKE measurement

T RT R M OM O K EK ETime-resolved Magnetic optical Kerr effect

時間分解 磁気光学 カー効果

pulse laser

time

amplitude

Kerr effect

polarization

is changed

Field H

reflection

pump pulse

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PolarizationPolarization

x

→E(t) = E1 exp(-iωt) x

+E2 Eoexp(-iωt) y

^

^

E(t) = Eoexp(-iωt) x̂→

z

y

x

y

z

<<<<Linearly

Polarization

<<<<Elliptical

Polarization

: How a electromagnetic wave goes…

偏　　光

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Elliptical polarizationElliptical polarization

→E(t) = E1 exp(-iωt) x

+E2 exp(-iωt) y

^

^⇔

E(t) = ½(E1+E2)exp(-iωt) (x+iy)

+ ½(E1-E2)exp(-iωt) (x-iy)

^→ ^

^ ^

Elliptical Polarization>>>>>x

y

+ =

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Magnet-Optic Kerr effectMagnet-Optic Kerr effect

Field H Field HField H

One of the Magnetic-Optics which contains many

property of the target.

Polar Kerr

effect

Longitudinal

Kerr effect

Transverse

Kerr effect極カー効果 縦カー効果 横カー効果

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Reflective indexReflective indexN±=n±+iκ±N: complex refractive index 　 n: refractive index κ: extinction coefficient

複屈折率　 屈折率　 消光係数

ψ0 ψ1

ψ2

x

z

E0PE0S

E1S

E2S

E1P

E2P

rP=E0P

E1P―= ―――――tan(ψ0 ＋ ψ2)tan(ψ0 － ψ2)

rS=E0S

E1S―= － ―――――sin(ψ0 ＋ ψ2)sin(ψ0 － ψ2)

Complex reflective index of amplitude 複素振幅反射率

(Fresnel coefficient)

^

^

n0

N

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Reflective index of amplitudeReflective index of amplitudefor Circular Polarized lightfor Circular Polarized light

r±= ―――N± - n0

N±+n0

r ＋ :for right circular light

r － :for left circular light

^^

^^

^

≡r ＋exp(iθ ＋ )

≡r －exp(iθ － )

ηK

θK = - ―――2

θ ＋ -θ －

= ――――|r ＋ |+^

|r ＋ |- ^

|r － |^|r － |^

： Kerr rotation angle

： Kerr ellipticity

カー回転角

カー楕円率

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Kerr rotation angle, elliptical indexKerr rotation angle, elliptical index

x

y

z

ΦK=θK+iηK

Rr

ηK=r /R

①Kerr rotation angle ②Kerr ellipticity:difference of phase shift :difference of reflectivity

complex Kerr rotation angle

R = R+ + R-

r = R+ - R-

位相差 反射率の違い

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Kerr rotation and MagnetizationKerr rotation and Magnetization

θK∝M

ΦK∝M

ηK∝M

It is known that

⇔

Kerr rotation angle is proportional to

Magnetization. It is called “Magnetic Kerr

effect”.

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Measurement configurationMeasurement configuration

Ti:sapph LASER (femto sec. pulse)

probe line

PEM

pump line

photodiode

delay stagetarget

polarizer

to amplifier

targetpump pulseprobe pulse

delay time

⇒ 　 relaxation process

can be measured

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In this paper…In this paper…

complex Kerr rotation

Ψ=Ψ’+ iΨ’’

Ψ’: Kerr rotation angle

Ψ’’: ellipticity

⊿Ψ=Ψ – Ψ0

Ψ0: original Kerr effect value

⊿Ψ’/Ψ’= Ψ’’/Ψ’’⊿ ～⊿ M/M

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Result AResult A

Comparison of the induced ellipticity ( ψ’’/ψ⊿ 0’’, opencircles) and rotation ( ψ’/ψ⊿ 0’, filled diamonds) as a function of pump-probe delay time.

It is strange that the changing of the both ratio which

don’t same reaction if it is because of magnetism.

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Result BResult B

(a)(b) dependence on the applied field

Instantaneous decrease of ΔΨ’’ doesn’t

relate to applied field.

delay1ps 200ps0ps 0ps

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Result CResult C

(c)(d) Temperaure dependence at 4.6nm and no applied field.

(d) is well explained by a thermal softening

of the effective magnetic potintial.

delay1ps 200ps0ps 0ps

Pay attention

to the scale of y.

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SummarySummary

☆ An instantaneous demagnetization is unlikely.

☆ Rough estimate of the spin relaxation is 0.5-1ps, and may be explained by a highly efficient spin-lattice relaxation.

☆ We should pay attention to the Kerr effect which is not always the reaction of magnetism.

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Measurement methodMeasurement method

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Argument for ultrafastArgument for ultrafast

No H dependence and

only a relatively weak T and dNi dependence.

state filling effects may well account for the

initial response in the TRMOKE experiments.

↓

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Argument for subnano signalArgument for subnano signal

Surprisingly appeared after 30ps.

strong dependence on applied field.

This can identified the oscillations as a precession

of M.

An intuitive illustration of the process is found by

solving the Landau-Lifshitz-Gilvert equation

in the limit of weak damping.

↓

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N±=n±+iκ±N: complex refractive index 　 n: refractive index κ: extinction coefficient

α±=2ωκ±/c複屈折率　

Rr

屈折率　 消光係数

α: absorption coefficient 　 ω: frequency c: speed of light 吸収係数　 周波数 光速

ηF=ωΔκ/2cηF: Faraday elliptical index

ファラデー楕円率

(=r /R)

R = R+ + R-

r = R+ - R-

CalculationCalculation

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pump light

(pulse laser)

probe light

(pulse laser)

TRMOKE measurementTRMOKE measurement

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Kerr effect and MagnetizationKerr effect and Magnetization

tanΦK== ――――――――――――――― ―――――――――――――――√εxx(cosψ0 ＋√ εxx cosψ2)√εxx(cosψ2 ＋√ εxx cosψ0)

εxy cosψ0

zz

yyyx

xyxx

00

0

0~

permittivity誘電率

※polar Kerr effect

εij = εij(M) change of Kerr effect depends ⇒

on magnetization.

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Result DResult D

(e)(f) Ni thickness dependence at 300K and

2800Oe(e) and 0Oe(f).

With in a couple of picoseconds the excess

energy rapidly diffuses out of the Ni film.

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☆ On about 100ps time scale, they have observed optically induced spin movement.