1 Careful study of Ultrafast 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)

2 Contents Introduction ・ Background ・ Aim of the reference Main talk ・ light, Kerr effect, and TRMOKE ・ Measurement configuration ・ Predictable signal ・ Result and Analysis (in the reference) Summary

3 Background Problem: 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.

4 Aim of the reference Cu 3nm Cu (111)or(001) Ni 0~15nm 1.Ni thickness 2.field 3.temperature MO signal 0 delay time 0.5ps(10sec) -12 Ultrafast demagnetization?

5 TRMOKE measurement T R M O K E Time-resolvedMagnetic 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

6 Polarization x → E(t) = E 1 exp(-iωt) x +E 2 Eoexp(-iωt) y ^ ^ E(t) = E o exp(-iωt) x ^ → z y x y z <<<<Linearly Polarization <<<<Elliptical Polarization : How a electromagnetic wave goes… 偏 光

7 Elliptical polarization → E(t) = E 1 exp(-iωt) x +E 2 exp(-iωt) y ^ ^ ⇔ E(t) = ½(E 1 +E 2 )exp(-iωt) (x+iy) + ½(E 1 -E 2 )exp(-iωt) (x-iy) ^ → ^ ^^ Elliptical Polarization>>>>> x y + =

8 Magnet-Optic Kerr effect Field 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

9 Reflective index N ± =n ± +iκ ± N: complex refractive index n: refractive index κ: extinction coefficient 複屈折率 屈折率 消光係数 ψ0ψ0 ψ1ψ1 ψ2ψ2 x z E 0P E 0S E 1S E 2S E 1P E 2P rP=rP= E 0P E 1P ― = ――――― tan(ψ 0 ＋ ψ 2 ) tan(ψ 0 － ψ 2 ) rS=rS= E 0S E 1S ― = － ――――― sin(ψ 0 ＋ ψ 2 ) sin(ψ 0 － ψ 2 ) Complex reflective index of amplitude 複素振幅反射率 (Fresnel coefficient) ^ ^ n0n0 N

10 Reflective index of amplitude for Circular Polarized light r±=r±= ――― N ± - n 0 N ± +n 0 r＋:r＋: for right circular light r－:r－: for left circular light ^ ^ ^ ^ ^ ≡ r ＋ exp(iθ ＋ ) ≡ r － exp(iθ － ) ηKηK θKθK = - ――― 2 θ ＋ - θ － = ―――― |r ＋ |+ ^ |r ＋ |- ^ |r － | ^ ^ ： Kerr rotation angle ： Kerr ellipticity カー回転角 カー楕円率

11 Kerr rotation angle, elliptical index x y z Φ K =θ K +iη K R r η K =r /R ① Kerr rotation angle ② Kerr 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

12 Kerr rotation and Magnetization θK∝MθK∝M ΦK∝MΦK∝M ηK∝MηK∝M It is known that ⇔ Kerr rotation angle is proportional to Magnetization. It is called “Magnetic Kerr effect”.

13 Measurement configuration Ti:sapph LASER (femto sec. pulse) probe line PEM pump line photodiode delay stage target polarizer to amplifier target pump pulseprobe pulse delay time ⇒ relaxation process can be measured

14 In this paper… complex Kerr rotation Ψ=Ψ’+ iΨ’’ Ψ’: Kerr rotation angle Ψ’’: ellipticity ⊿ Ψ=Ψ – Ψ 0 Ψ 0 : original Kerr effect value ⊿ Ψ’/Ψ’= ⊿ Ψ’’/Ψ’’ ～⊿ M/M

15 Result A Comparison of the induced ellipticity ( ⊿ ψ’’/ψ 0 ’’, open circles) 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.

16 Result B (a)(b) dependence on the applied field Instantaneous decrease of ΔΨ’’ doesn’t relate to applied field. delay 1ps 200ps 0ps

17 Result 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. delay 1ps 200ps0ps Pay attention to the scale of y.

18 Summary ☆ An instantaneous demagnetization is unlikely. ☆ Rough estimate of the spin relaxation is ps, 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.

19

20 Measurement method

21 Argument for ultrafast No H dependence and only a relatively weak T and d Ni dependence. state filling effects may well account for the initial response in the TRMOKE experiments. ↓

22 Argument 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. ↓

23 N ± =n ± +iκ ± N: complex refractive index n: refractive index κ: extinction coefficient α ± =2ωκ ± /c 複屈折率 R r 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 η F =ωΔκ /2c η F : Faraday elliptical index ファラデー楕円率 (=r /R) R = R + + R - r = R + - R -Calculation

24 pump light (pulse laser) probe light (pulse laser) TRMOKE measurement

25 Kerr effect and Magnetization tanΦK = = ――――――――――――――― ――――――――――――――― √ε xx (cosψ0 ＋ √ε xx cosψ2)√ ε xx (cosψ2 ＋ √ε xx cosψ0) ε xy cosψ0 permittivity 誘電率 ※ polar Kerr effect εij = εij(M) ⇒ change of Kerr effect depends on magnetization.

26 Result 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.

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