Careful study of Ultrafast Magneto-Optics

1. Careful study ofUltrafast Magneto-Optics [Referenece] “Ultrafast Magneto-Optics in Nickel: Magnetism or Optics?” B.Koopmans, M.van Kampen et al. Phys.Rev.Lett. 85,844(2000) ITOH Lab. Yoshitaka Sakamoto (坂本　圭隆)

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: ・storage (capacity, writing speed) Clock per second 1000 ↓ 100 CPU speed Solution: 10 Writing speed to a RAM ・spin memory year 1980 2005 (rapid writing by using light, large capacity [lamellar magnetic layer]) 薄　層　磁　性　膜 ⇒TRMOKE (time-resolved MO Kerr effect) is used.

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

5. TRMOKE measurement T RM OK E Time-resolved Magnetic optical Kerr effect 時間分解 磁気光学 カー効果 pump pulse amplitude reflection polarization is changed time Field H Kerr effect pulse laser

6. → ^ E(t) = Eoexp(-iωt) x → ^ E(t) = E1 exp(-iωt) x +E2 Eoexp(-iωt)y ^ Polarization 偏　　光 : How a electromagnetic wave goes… x z <<<<Linearly Polarization y x z <<<<Elliptical Polarization y

7. → ^ 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 Elliptical Polarization>>>>> y ⇔ = +

8. Magnet-Optic Kerr effect One of the Magnetic-Optics which contains many property of the target. Field H Field H Field H 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. E1S ― rS= =－ ――――― E0S sin(ψ0＋ψ2) Reflective index N±=n±+iκ± N: complex refractive indexn: refractive index κ: extinction coefficient 屈折率　 複屈折率　 消光係数 Complex reflective index of amplitude z 複素振幅反射率 E0S (Fresnel coefficient) E0P E1S tan(ψ0－ψ2) E1P E1P ψ0 ψ1 ^ ― rP= = ――――― E0P tan(ψ0＋ψ2) n0 sin(ψ0－ψ2) x ^ N ψ2 E2P E2S

10. ^ ^ ^ ^ |r－| |r＋|- |r＋|+ |r－| Reflective index of amplitude for Circular Polarized light ^ ^ r＋: N± - n0 for right circular light ^ ――― r±= ≡r＋exp(iθ＋) ^ N±+n0 ^ r－: for left circular light ≡r－exp(iθ－) θ＋ -θ－ θK = - ――― 2 ：Kerr rotation angle カー回転角 ηK = ―――― ：Kerr ellipticity カー楕円率

11. x z y r R R = R+ + R- r = R+ - R- Kerr rotation angle, elliptical index complex Kerr rotation angle ΦK=θK+iηK ηK=r /R ①Kerr rotation angle ②Kerr ellipticity :difference of phase shift :difference of reflectivity 位相差 反射率の違い

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

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

14. 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

15. Result A Comparison of the induced ellipticity (⊿ψ’’/ψ0’’, open circles) and rotation (⊿ψ’/ψ0’, 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. delay Result B 0ps 1ps 0ps 200ps (a)(b) dependence on the applied field Instantaneous decrease of ΔΨ’’ doesn’t relate to applied field.

17. delay Result C Pay attention to the scale of y. 0ps 200ps 1ps 0ps (c)(d) Temperaure dependence at 4.6nm and no applied field. (d) is well explained by a thermal softening of the effective magnetic potintial.

18. Summary ☆ 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.

20. Measurement method

21. Argument 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.

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. R = R+ + R- r = R+ - R- Calculation N±=n±+iκ± N: complex refractive indexn: refractive index κ: extinction coefficient 屈折率　 複屈折率　 消光係数 α±=2ωκ±/c α: absorption coefficientω: frequency c: speed of light 吸収係数　 周波数 光速 ηF=ωΔκ/2c (=r /R) ηF: Faraday elliptical index r ファラデー楕円率 R

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

25. Kerr effect and Magnetization εxy cosψ0 tanΦK= =―――――――――――――――――――――――――――――― √εxx(cosψ0＋√εxx cosψ2)√εxx(cosψ2＋√εxx cosψ0) ※polar Kerr effect permittivity 誘電率 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.