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Recent Advances in Magneto-Optics

Recent Advances in Magneto-Optics. Katsuaki Sato Department of Applied Physics Tokyo University of Agriculture & Technology. CONTENTS. Introduction Fundamentals of Magneto-Optics Magneto-Optical Spectra Experiments and theory Recent Advances in Magneto-Optics

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Recent Advances in Magneto-Optics

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  1. Recent Advances inMagneto-Optics Katsuaki Sato Department of Applied Physics Tokyo University of Agriculture & Technology ICFM2001 Crimia October 1-5, 2001

  2. CONTENTS • Introduction • Fundamentals of Magneto-Optics • Magneto-Optical Spectra • Experiments and theory • Recent Advances in Magneto-Optics • Magneto-optics in nano-structures • Nonlinear magneto-optical effect • Scanning near-field magneto-optical microscope • Current Status in Magneto-Optical Devices • Magneto-optical disk storages • Magneto-optical isolators for optical communication • Other applications • Summary ICFM2001 Crimia October 1-5, 2001

  3. 1. Introduction • Magneto-Optical Effect：Discovered by Faraday on 1845 • Phenomenon：Change of Linear Polarization to Elliptically Polarized Light Accompanied by Rotation of Principal Axis • Cause：Difference of Optical Response between LCP and RCP • Application： • Magneto-Optical Disk • Optical Isolator • Current Sensors • Observation Technique ICFM2001 Crimia October 1-5, 2001

  4. 2.Fundamentals of Magneto-Optics • MO Effect in Wide Meaning Any change of optical response induced by magnetization • MO Effect in Narrow Meaning Change of intensity or polarization induced by magentization • Faraday effect • MOKE(Magneto-optical Kerr effect) • Cotton-Mouton effect ICFM2001 Crimia October 1-5, 2001

  5. 2.1 Faraday Effect • (a) Faraday Configuration: • Magnetization // Light Vector • (b)Voigt Configuration: • Magnetization  Light Vector ICFM2001 Crimia October 1-5, 2001

  6. Faraday Effect • MO effect for optical transmission • Magnetic rotation（Faraday rotation）F • Magnetic Circular Dichroism（Faraday Ellipticity）F • Comparison to Natural Optical Rotation • Faraday Effect is Nonreciprocal (Double rotation for round trip) • Natural rotation is Reciprocal (Zero for round trip) • Verdet Constant • F=VlH (For paramagnetic and diamagnetic materials） ICFM2001 Crimia October 1-5, 2001

  7. Illustration of Faraday Effect Rotation of Principal axis • For linearly polarized light incidence, • Elliptically polarized light goes out (MCD) • With the principal axis rotated (Magnetic rotation) Elliptically Polarized light Linearly polarized light ICFM2001 Crimia October 1-5, 2001

  8. Materials rotation (deg) figure of merit(deg/dB) wavelength (nm) temperature (K) Mag. field (T) Fe 3.825･105 578 RT 2.4 Co 1.88･105 546 〃 2 Ni 1.3･105 826 120 K 0.27 Y3Fe5O12 250 1150 100 K Gd2BiFe5O12 1.01･104 44 800 RT MnSb 2.8･105 500 〃 MnBi 5.0･105 1.43 633 〃 YFeO3 4.9･103 633 〃 NdFeO3 4.72･104 633 〃 CrBr3 1.3･105 500 1.5K EuO 5･105 104 660 4.2 K 2.08 CdCr2S4 3.8･103 35(80K) 1000 4K 0.6 Faraday rotation of magnetic materials ICFM2001 Crimia October 1-5, 2001

  9. 2.2 Magneto-Optical Kerr Effect • Three kinds of MO Kerr effects • Polar Kerr（Magnetization is oriented perpendicular to the suraface） • Longitudinal Kerr（Magnetization is in plane and is parallel to the plane of incidence） • Transverse Kerr （Magnetization is in plane and is perpendicular to the plane of incidence） ICFM2001 Crimia October 1-5, 2001

  10. Magneto-optical Kerr effect Polar Longitudinal Transverse M M M ICFM2001 Crimia October 1-5, 2001

  11. Materials rotation Photon energy temperature field (deg) (eV) (K) (T) Fe 0.87 0.75 RT Co 0.85 0.62 〃 Ni 0.19 3.1 〃 Gd 0.16 4.3 〃 Fe3O4 0.32 1 〃 MnBi 0.7 1.9 〃 PtMnSb 2.0 1.75 〃 1.7 CoS2 1.1 0.8 4.2 0.4 CrBr3 3.5 2.9 4.2 EuO 6 2.1 12 USb0.8Te0.2 9.0 0.8 10 4.0 CoCr2S4 4.5 0.7 80 a-GdCo * 0.3 1.9 RT CeSb 90 2 MO Kerr rotation of magnetic materials ICFM2001 Crimia October 1-5, 2001 * "a-" means "amorphous".

  12. 2.3 Electromagnetism and Magnetooptics • Light is the electromagnetic wave. • Transmission of EM wave：Maxwell equation • Medium is regareded as continuum→dielectric permeability tensor • Effect of Magnetic field→mainly to off-diagonal element • Eigenequation • →Complex refractive index：two eigenvalues eigenfunctions：right and left circularpolarization • Phase difference between RCP and LCP→rotation • Amplitude difference →circular dichroism ICFM2001 Crimia October 1-5, 2001

  13. Dielectric tensor Isotromic media；M//z Invariant C4 for 90°rotation around z-axis ICFM2001 Crimia October 1-5, 2001

  14. MO Equations (1) Maxwell Equation Eigenequation Eigenvalue Eigenfunction：LCP and RCP Without off-diagonal terms：No difference between LCP & RCP No magnetooptical effect ICFM2001 Crimia October 1-5, 2001

  15. MO Equations (2) Both diagonal and off-diagonal terms contribute to Magneto-optical effect ICFM2001 Crimia October 1-5, 2001

  16. Phenomenology of MO effect Linearly polarized light can be decomposed to LCP and RCP Difference in phase causes rotation of the direction of Linear polarization Difference in amplitudes makes Elliptically polarized light In general, elliptically polarized light With the principal axis rotated ICFM2001 Crimia October 1-5, 2001

  17. 2.4 Electronic theory of Magneto-Optics • Magnetization→Splitting of spin-states • No direct cause of difference of optical response between LCP and RCP • Spin-orbit interaction→Splitting of orbital states • Absorption of circular polarization→Induction of circular motion of electrons • Condition for large magneto-optical response • Presence of strong (allowed) transitions • Involving elements with large spin-orbit interaction • Not directly related with Magnetization ICFM2001 Crimia October 1-5, 2001

  18. Dielectric functions derived from Kubo formula where ICFM2001 Crimia October 1-5, 2001

  19. E - + + Wavefunction perturbed by electric field Unperturbed wavefunction + - +　・・ = + + S-like P-like Microscopic concepts of electronic polarization Expansion by unperturbed orbitals ICFM2001 Crimia October 1-5, 2001

  20. Orbital angular momentum-selection rules and circular dichroism py-orbital px-orbital p+=px+ipy Lz=+1 Lz=-1 p-=px-ipy s-like Lz=0 ICFM2001 Crimia October 1-5, 2001

  21. Roleof Spin-Orbit Interaction Jz=-3/2 Jz=-1/2 L=1 Jz=+1/2 LZ=+1,0,-1 Jz=+3/2 Jz=-1/2 L=0 Jz=+1/2 LZ=0 Exchange +spin-orbit Without magnetization Exchange splitting ICFM2001 Crimia October 1-5, 2001

  22. 1.Diamagnetic lineshape ’xy ”xy Excited state Lz=-1  Lz=+1 0 1 2 1+2 Ground state Lz=0 Without magnetization With magnetization Photon energy Photon energy MO lineshapes (1) ICFM2001 Crimia October 1-5, 2001

  23.  f=f+ - f- ’xy excited state dielectric constant 0 f+ f- ”xy ground state photon energy without magnetic field with magnetic field (b) (a) MO lineshapes (2) 2.Paramagnetic lineshape ICFM2001 Crimia October 1-5, 2001

  24. 3. Magneto-Optical Spectra • Measurement technique • Magnetic garnets • Metallic ferromagnet：Fe, Co, Ni • Intermetallic compounds and alloys：PtMnSb etc. • Magnetic semiconductor：CdMnTe etc. • Superlattices：Pt/Co, Fe/Au etc. • Amorphous：TbFeCo, GdFeCo etc. ICFM2001 Crimia October 1-5, 2001

  25. i /4 B D j PEM A quartz fused silica CaF2 Ge etc. Isotropic medium P Retardation =(2/)nl sin pt =0sin pt Piezoelectric crystal amplitude l position Measurement of magneto-optical spectra using retardation modulation technique Light source chopper filter ellipsoidal mirror monochromator polarizer eletromagnet sample sample analyzer detector computer ICFM2001 Crimia October 1-5, 2001

  26. Magnetic garnets • One of the most intensively investigated magneto-optical materials • Three different cation sites; octahedral, tetrahedral and dodecahedral sites • Ferrimagnetic • Large magneto-optical effect due to strong charge-transfer transition • Enhancement of magneto-optical effect by Bi-substitution at the dodecahedral site ICFM2001 Crimia October 1-5, 2001

  27. Jz= Jz= J=7/2 -3/2 3/2 6P (6T2, 6T1g) 5/2 -7/2 7/2 - J=5/2 -3/2 3/2 -3/2 J=3/2 -3/2 3/2 P+ P+ P- P- 6S (6A1, 6A1g) spin-orbit interaction -5/2 without perturbation 5/2 octahedral crystal field (Oh) tetrahedral crystal field (Td) Electronic level diagram of Fe3+in magnetic garnets ICFM2001 Crimia October 1-5, 2001

  28. x104 Faraday rotation (deg/cm) 0.8 experiment +2 Faraday rotation (arb. unit) 0 0.4 -2 calculation 0 -0.4 300 400 500 600 Wavelength (nm) Experimental and calculated magneto-optical spectra of Y3Fe5O12 ICFM2001 Crimia October 1-5, 2001

  29. (a) (b) Electronic states and optical transitions of Co2+ and Co3+ in Y3Fe5O12 ICFM2001 Crimia October 1-5, 2001

  30. Theoretical and experimental magneto-optical spectra of Co-doped Y3Fe5O12 ICFM2001 Crimia October 1-5, 2001

  31. Theoretical and experimental MO spectra of bcc Fe Katayama Krinchik theory ICFM2001 Crimia October 1-5, 2001

  32. MO spectra of PtMnSb Magneto-optical Kerr rotation θK and ellipticity ηK Off-diagonal Dielectric function Diagonal dielectric functions (a) (b) (c) ICFM2001 Crimia October 1-5, 2001

  33. (a) (b) (c) (d) Comparison of theoretical and experimental spectraof half-metallic PtMnSb After Oppeneer ICFM2001 Crimia October 1-5, 2001

  34. Faraday rotation spectra (deg) Photon Energy (eV) Magneto-optical spectra of CdMnTe ICFM2001 Crimia October 1-5, 2001

  35. Pt(10)/Co(5) Pt(18)/Co(5) simulation experiment PtCo alloy rotation Kerr rotation and ellipticity(min) Kerr rotation and ellipticity(min) elliptoicity Pt(40)/Co(20) Photon energy (eV) Photon energy (eV) Pt/Co superlattices ICFM2001 Crimia October 1-5, 2001

  36. Wavelength (nm) Polar Kerr rotation (min) MO spectra in RE-TM (1) ICFM2001 Crimia October 1-5, 2001

  37. Wavelength (nm) 300 400 500 600 700 0 -0.2 Polar Kerr rotation (deg) -0.4 -0.6 5 4 3 2 Photon Energy (eV) MO spectra in R-Co ICFM2001 Crimia October 1-5, 2001

  38. MO spectra of Fe/Au superlattice ICFM2001 Crimia October 1-5, 2001

  39. Calculated MO spectra of Fe/Au superlattice By M.Yamaguchi et al. ICFM2001 Crimia October 1-5, 2001

  40. Au/Fe/Au sandwich structure By Y.Suzuki et al. ICFM2001 Crimia October 1-5, 2001

  41. 4. Recent Advances in Magneto-Optics • Nonlinear magneto-optics • Scanning near-field magneto-optical microscope (MO-SNOM) • X-ray magneto-optical Imaging ICFM2001 Crimia October 1-5, 2001

  42. NOMOKE（Nonlinear magneto-optical Kerr effect） • Why SHG is sensitive to surfaces? • Large nonlinear magneto-optical effect • Experimental results on Fe/Au superlattice • Theoretical analysis • Future perspective ICFM2001 Crimia October 1-5, 2001

  43. l=810nm Pulse=150fs P=600mW rep80MHz LD pump SHG laser Ti: sapphire laser Mirror l=532nm Electromagnet Filter Berek compensator Stagecontroller Mirror Sample Chopper Analyzer lens polarizer Lens Photon counting Filter PMT Photon counter Computer MSHG Measurement System ICFM2001 Crimia October 1-5, 2001

  44. Sample Optical arrangements 試料回転 Sample stage w (810nm) Pole piece P-polarized or S-polarized light 45° Rotating analyzer w (810nm) Analyzer Filter 2w (405nm) ICFM2001 Crimia October 1-5, 2001

  45. Azimuthal dependence of ・　Linear optical response(=810nm) The isotropic response for the azimuthal angle ・　Nonlinear optical response (=405nm) The 4-fold symmetry pattern Azimuthal pattern show 45-rotation by reversing the magnetic field MSHG linear 45 SHG intensity (counts/10sec.) SHG intensity (counts/10sec.) (a)Linear (810nm) (b)SHG (405nm) [Fe(3.75ML)/Au(3.75ML)] 超格子の　（Pin Pout）配置の線形および非線形の方位角依存性 ICFM2001 Crimia October 1-5, 2001

  46. (a) Pin-Pout (b) Pin-Sout 103 103 SHG intensity (counts/10sec.) APP=1310, B=26, C=-88 APS=-300, B=26, C=-88 (c) Sin-Pout (d) Sin-Sout 103 103 SHG intensity (counts/10sec.) ASP=460, B=26, C=-88 ASS=100, B=26, C=-88 Calculated and experimental patterns :x=3.5 Dots：exp. Solid curve：calc. ICFM2001 Crimia October 1-5, 2001

  47. Electromagnet S-polarized light ω(810nm) Rotating Analyzer 45° Analyzer Filter 2w (405nm) Nonlinear Kerr Effect Df = 31.1° The curves show a shift for two opposite directions of magnetic field Fe(1.75ML)/Au(1.75ML)Sin ICFM2001 Crimia October 1-5, 2001

  48. Sample P F1 L F2 Objective lens A CCD Schematic diagram 50m Linear and nonlinear magneto-optical images of domains in CoNi film Nonlinear Magneto-optical Microscope ICFM2001 Crimia October 1-5, 2001

  49. MO-SNOM(Scanning near-field magneto-optical microscope) • Near-field optics • Optical fiber probe • Optical retardation modulation technique • Stokes parameter of fiber probe • Observation of recorded bits on MO disk ICFM2001 Crimia October 1-5, 2001

  50. Medium 1 Evanescent wave ic Propagating wave Medium 2 Critical angle c ic Evanescent field d Scattered wave Near-field Scattered wave by a small sphere placed in the evanescent field produced by another sphere Total reflection and near field ICFM2001 Crimia October 1-5, 2001

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