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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.