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Nonlinear Magneto-Optical Studies in Magnetic Superlattices and Magnetic Nano Structures K. Sato, A. Kodama, M. Miyamoto, M. Tsuruga, T. Matsumoto, T. Ishibashi Y. Morishita, Department of Applied Physics, Tokyo University of Agriculture and Technology, Koganei, Tokyo, Japan K. Takanashi, S. Mitani, Institute of Materials Science, Tohoku University, Sendai, Miyagi, Japan 1st International Conference on Quantum Photonic Science TUAT COE Project “Future Nano Materials”
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Nonlinear Magneto-optics What is the nonlinear magneto-optical effect? Magnetization-induced nonlinear optics What is the nonlinear Kerr rotation? When P-polarized primary light is incident both P- and S-polarized SH light emits: which leads to rotation of E vector from the plane of incidence. In centrosymmetric materials such as Fe and Au no SHG occurs due to cancellation of P and –P.
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Azimuthal angle dependence of SHG from Si and GaAs wafer Si wafer (001) centrosymmetric GaAs wafer (001) Non-centrosymmetric
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Theoretical prediction and experimental verification Nonlinear magneto-optical Kerr rotation larger than linear rotaion was theoretically predicted 1), and was experimentally proved 2,3). 1) W. Hübner and K.-H. Bennemann: Phys. Rev. B40, 5973 (1989) 2) Th. Rasing et al.: J. Appl. Phys. 79, 6181 (1996) 3) Th. Rasing: J. Mag. Soc. Japan 20 (Suppl. S1), 13 (1996)
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Application of MSHG Sensitive toEvaluation of the break ofMultilayers symmetry at surfaceImaging of domains ・ This effect cannot be expected to be applied to some practical memory devices but is thought to be useful for characterization of surfaces and interfaces of materials. Surface and interface sensitivity of MSHG
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・ For strong incident laser field E( ) : Second harmonic generation (SHG) ・ Nonlinear polarization P (2) for incident field of E=E 0 sin t Third rank tensor is not allowed in centrosymmetric materials. ・ For weak incident laser field E( ) : linear response Nonlinear response Nonlinear magneto-optical effect
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SHG process Light rectification parametric process Nonlinear polarization of 2nd order
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Centrosymmetric materials: all the χ ijk (2) components vanish. (from symmetry operations) Surfaces and interfaces: symmetry breaks, leading to appreciable amount of nonlinear magneto-optical effect even in the centrosymmetric materials Definition of nonlinear susceptibility
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(1) yz, 0 (1) = xx -1=N 2 -1 K K i K (複素カー回転角) Wave equation of linear magneto- optical effect
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Source term does not depend on optical constants of materials, leading to special solution associated with the second order susceptibility. Wave equation of nonlinear magneto-optics.
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Nonlinear Kerr roation
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Different from the linear case χ (2)odd /χ (2)even contributes 。 This term is zero in centrosymmetric materials And takes a finite value at surfaces Surface sensitivity useful for surface magnetism studies ! Nonlinear Kerr rotaion
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Linear : factor reduces the magnitude Also χ xy is order of magnitude smaller that χ xx Nonlinear : no such factor exists Also χ odd and χ even are of the same order 。 Difference between linear and nonlinear Kerr rotation
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SHG 3 photon proicess Here | k q // l >→ | k+q // l‘> | k+q // l’>→ | k+2q // l" > | kl> → | k+2q//l”> Intermediate state Ground stateExcited state Microscopic origin of MSHG
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Illustration of microscopic process of MSHG
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Nonlinear Kerr rotation of Fe
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Nonlinear Kerr rotation of Fe/Cu Nonlinaer Kerr effect nolinear
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Cu cover layer-thickness dependence of Co/Cu Cu の層厚 SH 信号
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Non-integer: x=1.25, 1.5, 1.75, 2.25, 2.5, 2.75, 3.25, 3.5, 3.75 Fe seed MgO(100) Au buffer Fe(xML) Au(xML) { { { { 1 2 3 N Fe Au 1 x=3.75ML 2 0.250.500.751 Superlattices : 〔 Fe(xML)/Au(xML) 〕 N Integer: x=1, 2, 3, 4, 5, 6, 8, 10, 15
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Atomic arrangement in a unit cell of Fe-Au with a L1 0 suructure. 4.079 Å fcc-Au (001) 2.867 Å 4.054 Å bcc-Fe (001) Au Fe L1 0 Fe seed layer Au buffer layer Fe(xML) Au(xML) 1 2 MgO (100) N [Fe(1ML)/Au(1ML)] Schematic structure for the Fe/Au superlattice Fe(1ML)/Au(1ML) superlattice
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LD pump SHG laser lens Mirror Chopper Lens Analyzer Filter PMT Ti: sapphire laser Mirror Filter polarizer Berek compensator Sample Stage controller Electromagnet Photon counterComputer =532nm =810nm Pulse=150fs P=600mW rep80MHz Photon counting MSHG Measureing System
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Laboratory Experimental setup for MSHG measurement
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P-polarized or S-polarized light nm) nm) Analyzer Filter nm) Pole piece Rotating analyzer 試料回転 Sample stage 45° Sample Optical Setups (Longitudinal Kerr)
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Result Analyzer angle-dependence for [Fe(3.5ML)/Au(3.5ML)] (Sin) Nonlinear Kerr rotation & ellipticity K (2) = 17.2 3 The curves show a shift for two opposite directions of magnetic field Analyzer angle (deg.) SHG intensity (counts/10sec.) 10 4 2 K (2) =34.3 S-polarized light ω(810nm) 2 (405nm) Analyzer 45° Electromagnet Rotating Analyzer Filter Nonlinear Kerr Rotation and Kerr Ellipticity
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Analyzer angle (deg.) SHG intensity (counts/10sec.) Fe(1.75ML)/Au(1.75ML) Sin = 31.1° Largest nonlinear Kerr rotation observed in the Fe/Au series
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Azimthal angle-dependence of MSHG intensity for [Fe(3.75ML)/Au(3.75ML)] superlattice. ( P in P out ) (a) Linear (810nm)(b) SHG (405nm) ・ 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 SHG intensity (counts/10sec.) 45 Electromagnet 2 (405nm) Analyzer 45° Rotation of sample Filter P-polarized light (810nm) linear nonlinear Azimuthal Angle Dependence
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Pin-Pout Sin-Sout
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Discussion A: Surface nonmagnetic term ・ The electric dipole origin give rise to isotropic signal. B: Bulk nonmagnetic term ・ The quadrupole origin causes an anisotropic contribution for four rank tensor. The equation of the azimuthal angle- dependence by the theoretical analysis C: Surface magnetic term ・ The time reversal symmetry is lifted by magnetization ・ Mirror symmetry operations should be supplemented with an additional reversion of M.
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Kerr rotation calculated from parameters Axx,B,C S in P in Calculated azimuthal angle dependence of SHG and MSHG signals
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Surface non-magnetic term ・ SHG response causes an isotropic contribution only. ・ For crystallographic contribution the electric quadrupole should be introduced to get four rank tensor. SHG response causes an anisotropic contribution (parameter B). Bulk non-magnetic term Surface magnetization induced term ・ The surface magnetic response comes from the electric dipole term expanded by magnetization and contributes to the parameter C.
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(a) A=5, B=0, C=0.85 (b) A=5, B=0.85, C=0.85 (a) A=5, B=0, C=0.85 ・ For B much smaller than C, the polar pattern shows 45 rotation for the magnetization reversal. ( b) A=5, B=0.85, C=0.85 ・ For B comparable C, the polar pattern undergo a smaller rotation. The azimuthal pattern was interpreted in terms of combination of B and C. The equation of the azimuthal angle- dependence by theoretical analysis Without nonlocality With nonlocality Calculated polar patterns of the azimuthal angle-dependence (Sin-Pout)
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Sin-Sout A SP (surface nonmagnetic term)= 460 A SS (surface nonmagnetic term)= 100 B(bulk nonmagnetic term)= 26 C(surface magnetic term)= -88 (a) Sin-Pout 10 3 SHG intensity (counts/10sec.) The equation of the azimuthal angle- dependence by theoretical analysis (b) Sin-Sout 10 3 SHG intensity (counts/10sec.) Sin-Pout Azimuthal angle-dependence of MSHG for a [Fe(3.5ML)/Au(3.5ML)] superlattice (Sin-Pout, Sin-Sout configuration)
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A SP =460, B=26, C=- 88 (c) Sin-Pout 10 3 SHG intensity (counts/10sec.) A SS =100, B=26, C=- 88 (d) Sin-Sout 10 3 A PP =1310, B=26, C=-88 (a) Pin-Pout 10 3 SHG intensity (counts/10sec.) A PS =-300, B=26, C=-88 (b) Pin-Sout 10 3 Dots : exp. Solid curve : calc. Calculated and experimental patterns :x=3.5
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Nonlinear Kerr rotation (deg.) (a) Experimental pattern (Sin) (b) Calculated pattern (Sin) Nonlinear Kerr rotation (deg.) The azimuthal angle-dependences of nonlinear Kerr rotation angle and ellipticity in [Fe(3.75ML)Au(3.75ML)] (c) Exp.(d) Calc. Nonlinear Kerr ellipticity Azimuthal angle (deg.) Calculated and experimental pattern of Nonlinear Kerr rotation and ellipticity
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Fe(2.75ML)/Au(2.75ML) Nonlinear Kerr rotation (deg.) Experimental and calculated patterns of Kerr rotation angle Fe(2.5ML)/Au(2.5ML) Nonlinear Kerr rotation (deg.) Fe(3.25ML)/Au(3.25ML) Nonlinear Kerr rotation (deg.) Fe(3.5ML)/Au(3.5ML) Nonlinear Kerr rotation (deg.) Sin configuration: (a) Experimental data, (b) Calculated usingparameters determined by fitting to the azimuth patterns Fe(2. 5ML)/Au(2.5ML) Nonlinear Kerr rotation (deg.) Fe(2.75ML)/Au(2.75ML) Nonlinear Kerr rotation (deg.) Fe(3.25ML)/Au(3.25ML ) Nonlinear Kerr rotation (deg.) Fe(3.5ML)/Au(3.5ML) Nonlinear Kerr rotation (deg.) (a) Experiment (b) Calculation ( a) Experiment (b) Calculation
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Calculation and experimental result ・ The experimental maximum K (2) for x=1.75 superlattice was 31.1 . ・ The calculated K (2) reproduced the muximum K (2) for x=1.75 superlattice. The nonlinear Kerr rotation was explained by theoretical analysis. Fig. Nonlinear Kerr rotation angle of [Fe(xML)/Au(xML)] (1.25 x 3.75) superlattices [(a)Calculation, (b)Experiment] (a) Exp. Modulated rate x (ML) Nonlinear Kerr rotation angle (deg.) (b) Calc. x=1.75 K (2) =31.1 Calculated nonlinear Kerr rotation angle K (2) using the fitting parameter A SP, A SS, B, C of the azimuthal pattern (The maximum K (2) was selected for azimuth angle) Nonlinear Kerr rotation angle of [Fe(xML)/Au(xML)] (1.25 x 3.75) superlattices (Sin)
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・ The azimuthal angle dependence was analyzed in terms of nonlinear electrical susceptibility tensor taking into account the magnetic symmetry of the superlattice. ・ The azimuthal pattern was explained by symmetry analysis, taking into account the surface non- magnetic A, bulk non-magnetic B and surface magnetic C contributions. The four-fold pattern clearly reflects the symmetry of the MgO(100) substrate. This suggests that the Fe/Au superlattice is perfectly epitactic to the substrate. Summary: MSHG of Fe/Au superlattice
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・ The azimuthal angle-dependence of the nonlinear Kerr rotation were explained using parameters determined from azimuthal patterns of MSHG response ・ MSHG was shown to lead to a nonlinear Kerr rotation (2) K that can be orders of magnitude larger than its linear equivalent (0.2 ), e.g., (2) K for x=1.75 was 31.1 We observed azimuthal angle-dependence of the nonlinear Kerr rotation for the first time. Modulation period dependence of parameters: A (Surface nonmagnetic) is large for short period B (Bulk nonmagnetic) is nearly constant C (Surface magnetic) becomes larger with modulation Period. Summary (cont ’ d)
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Fabrication of permalloy nanostructure by Damascene technique ① Preparation of substrate: Spin-coating of ZEP resist with high etching resistance ② EB-exposition: Write patterns by EB ③ Development: Formation of mask-pattern by development ④ Etching : By dry-etching process mask-pattern is transferred to the substrate ⑤ Deposition of magnetic film: Deposition of magnetic films by sputter or evaporation ⑥ Polishing: Obtain flat buried structure using chemical- mechanical polishing Process is simplified by abbreviation of lift-off and repeated spin-coating
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EB-patterning process 〔1〕 Dot size 100nm×300nm rectangular dot with 300nm- spacing 100nm square dot with 300nm-spacing 〔2〕 Patterned area: 3mm×3mm 〔3〕 EB-resist thickness: 300 nm ・・・ by spin-coating with 5000 rpm rotation 〔4〕 Baking 160 ℃ 20min Spin coating of resist EB exposure Si substrate Development
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Electron beam lithography Clean Room Laboratory
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EtchingResist removal 〔1〕 Etching gas:CF 4 〔2〕 Vacuum 3.0×10 -3 Pa 〔3〕 Gas pressure 9.2Pa 〔4〕 RF power:400W 〔5〕 Etching rate: 0.1μm/min 300nm 100nm Silicon surface after etching Dry etching process
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Dry-etching
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Laboratory EB deposition RF magnetron sputtering
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Embedding of permalloy film by electron beam deposition 〔1〕 material: permalloy ( Ni 80 Fe 20 ) 〔2〕 Vacuum 3.0×10 -6 Torr 〔3〕 Accelerating voltage 4kV 〔4〕 Deposition rate 1.0 Å /sec 〔1〕 Polishing chemicals: Si wafer grain-size ~ 20nm 〔2〕 pH 11 〔3〕 polishing rate: 60nm/min flatting Embedding of permalloy Chemical mechanical polishing
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Observation FE-SEM AFM /MFM
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3μm 0.6μm 300nm×100nmsquare dot, 300 nm space SEM observation
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100nm Dot depth? Cross sectional SEM observation
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Cross section SEM image of Line and space pattern (width =100nm) 0.3 μm
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MFM observation of a permalloy film
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1μm AFM Line scan ・・・ Surface roughness~10nm MFM image ・・・ magnetization axis along the longer side direction AFM and MFM observation
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5kOe Comparison between two scans after magnetization in opposite direction
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MFM-image for different scanning direction
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Scan-direction dependence
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Pattern variation with scan direction 0°0°15°30°45°60°90°75°
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-2012 -0.0004 -0.0002 0 0.0002 0.0004 H(kOe) M(emu) Longer axis Shorter axis In-plane Perpendicular VSM measurement
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0.5μm Surface roughness ~10nm 100nm circular dots with 300 nm spacing AFM SEM
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Parallel to the plane Perpendicul ar to the plane VSM measurement of circular dot array
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Demagnetized Magnetic field applied Perpendicular to the plane MFM measurement of circular dots
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Influence of stray field from the MFM probe tip MFM measurenment Magnetization AB AFM sensing (2- 3nmlevitation) MFM probe Magnetization AB 80nm Recording by first scan Reading by second scan
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MFM image Magnetization AB A BC MFM image Models to explain MFM images
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1 m square dot array AFM MFM
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MFM image of 300nm x 100nm dot with a low-moment probe tip AFM MFM
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300nm x 100nm dot ( wide scan ) with a low-moment probe tip AFMMFM
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Simulation by Nakatani
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MSHG studies of Nano-structured magnetic patterns
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Azimuthal angle dependence of SHG from unpatterned permalloy film PinPout Unstructured permalloy film: H=±2.5kOe Longitudinal (counts/10sec)
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PinPout (counts/10sec) H=±2.5kOe Azimuthal angle dependence of SHG from unpatterned Si wafer
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Azimuthal angle dependence of SHG from GaAs wafer
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PinPout Longitudinal Kerr configuration (counts/10sec) H=±4kOe Azimuthal angle dependence of MSHG from 1 m square dot array
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PinPoutSinPout Longitudinal configuration (counts/10sec) H=±4kOe (counts/10sec) Azimuthal angle dependence of MSHG from 300nm x 100nm rectangular dot array (Longitudinal)
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polar Kerr configuration PinPout (counts/10sec) H=±6kOe Azimuthal angle dependence of MSHG from 300nm x 100nm rectangular dot array (Polar)
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PinPout SinPoutSinSout PinSout 縦カー配置 (counts/10sec) 丸ドット (100nm) の方位角依存性:磁場 ±4kOe
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非線形カー回転角 6.00°
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