Gianluca Gubbiotti. CNR-Istituto Officina dei Materiali (IOM) -Unità di Perugia. Italian School on Magnetism, Pavia 8 th February 2011

Transcription

1 Brillouin Light Scattering Spectroscopy Gianluca Gubbiotti CNR-Istituto Officina dei Materiali (IOM) -Unità di Perugia Italian School on Magnetism, Pavia 8 th February 2011 gubbiotti@fisica.unipg.it 1

2 Outline Spin waves in magnetic thin film and nanostructures Brillouin light Scattering:Experimental setup Conventional In-situ Micro-focused Experiments in magnetic thin film and nanostructures Magnonic crystals Microwave and Spin Tranfer Torque excited spin waves Conclusions 2

3 Spin Waves (Magnons) Ferromagnetic resonance Raman Light scattering Brillouin Light scattering 3

4 Publications on Spin Waves in magnetic nanostructures Thin films period Phase transition YIG period Magnetic films Multilayers Lateral structures 4 4

5 One dimensional chain of identical atoms One dimensional chain of spin a a a a U s-2 U s-1 U s U s+1 U s+2 r ϕ( ) = r r q a ω λ/2-2 - ω 4c 1 M π 0 a π a C. Kittel, Introduction to Solid State Physics. 5 k π a 0 π a k 5

6 r M r ( t) = M + m( r,t) s r r Landau-Lifshitz torque equation << s r r r r m(, t) = m ( ) e 0 rr i( qr- ωt ) exch, intra eff = + exch, intra +, Zeeman field intralayer exchange field anisotropy field (magnetocrystalline, surface), interlayer exchange field (layered structures) Wave front λ is the field generated by fluctionating Maxwell equations: =0 =0 k 6

7 ω γ 2 Dipolar Damon-Eshbach Modes ( ) 2 = + ( ) 2 2q d H 2πM 2πM e Magnetostatic dipolar modes in magnetic thin film S S Uniform precession Mode (Kittel mode) Non- reciprocity The amplitude of the DE mode decreases exponentially from the film surface k MSSBVW MSSW R. W. Damon and J. R. Eshbach J. Phys. Chem. Solids 19, 308 (1961) 7

8 r q Exchange dominated Perpendicular Standing Spin Waves (PSSW) r r = q + q M r, H r = r q + n π d 30 = 4 25 Frequency (GHz) Frequency (GHz) d=50 nm Thickness (nm) q // (10 5 rad/cm -1 ) 8 P. Grunberg et al. J. Appl. Phys. 53, 2078 (1982).

9 Spin waves in confined elements x z DE BA EM y H Plane spin waves are not eigen modes of the system due to: broken translational symmetry New effects: spin wave quantization (lateral boundaries) self-localization (non-uniform internal field) 9

10 Neutrons Techniques to study spin wave excitations Providing access to the entire Brillouin-Zone but their sensitivity is too low for thin films Time Domain Technique Time resolved Kerr-Effect-Experiments (q=0) Frequency Domain Technique Ferromagnetic Resonance (FMR) (q=0) Inelastic light scattering (BLS) ( cm -1 ) 30 GHz = 1cm -1 = 0.12 mev In BLS, the magnetic system is treated using a continuun approach (λ >>a) and the discrete nature of spin can be neglected. Magnetic properties are described by macroscopic parameters. Anisotropies, magnetic moments, magnetic exchange constant 10

11 Brillouin light scattering technique Detector Laser ω L,k L ω s,k s Analyzer,,,, Polarizer,,,,,,,, Doppler frequency shift Stokes process Anti-Stokes process Conservation laws: Energy Momentum k I k S =k I -k k ω s = ω L -ω k I k S =k I +k k ω s = ω L +ω 11

12 Brillouin light scattering setup k I k S θ z y Probed area diameter ~30 µm Laser Power on the sample: ~ 200 mw k φ H x beam-splitter Solid State Laser λ=532 nm polariser COMPUTER P.D. FP2 Elastic peak Stokes SAMPLE analyzer Incidence angle of light Intensity of the external magnetic field In-plane direction of the applied field FP1 FABRY-PEROT TANDEM 3+3 PASS INTERFEROMETER Anti-Stokes Frequency shift (GHz) 12

13 Sandercock type Farby-Perot Interferometer frequency range: GHz resolution: 0.1 GHz (or 1% of free spectral range) contrast: > 1:10 10 (multipass arrangement: 3+3) laser spot diameter: 40 µm 250 nm magnetic sensitivity: Monolayer regime wavevector range: cm -1 k k S k I θ k//= 2k I sin(θ)=2(2π/λ) sin(θ)= (4π/λ) sin(θ) NOTES Light does not excite spin waves; it serves only as a probe of the magnetic modes which exist already inside the film (Thermally excited or externally driven SW). Light is scattered efficiently from those modes that have a large transverse magnetization components. BLS technique is surface sensitive: penetration depth of light in metallic ferromagnet δ opt 15 nm. The frequency of the SW is determined by the whole thickness of the sample. Uncertainty in the perpendicular component of the exchanged wave vector is K 1/δ opt =10 6 cm -1 Wave vector conservation applies only to the in-plane wavevector components 13

14 UHV chamber for in-situ BLS measurements Load-lock system Ion gun Sputtering Annealing up to 1200 K e-beam evaporators quartz microbalance Temperature: 110 K-1200 K LEED RHEED-Auger apparatus 14

15 Main features of the micro-bls setup In Conventional BLS: Spatial resolution is limited by the spot size dimension (30-40 µm) No direct information about the modes localization is obtained. Some modes are not detected because of their spatial symmetry. With micro-focused BLS: We want to study magnetization dynamics of magnetic object A 2D map of spatial distribution of magnetic modes is possible (scanning probe technique with lateral resolution of 250 nm or less). 15

16 Fully automatized optical setup for micro-focused BLS FABRY-PEROT TANDEM 3+3 PASS INTERFEROMETER+TFPDAS4 Photodetector CCD Camera Lens FP2 Band pass filter Blue LED Polarizing Beam Splitter Cube Beam Splitter Cube Glan laser prism polarizer Beam expander Beam Splitter FP1 λ/2 Solid state laser (532nm) Illuminating System Power on the sample ~ 3mW Lateral resolution of ~250 nm G. Gubbiotti et al., JAP 105, 07D521 (2009). XYZ Piezoelectric Stage Microscope objective 100 X Electromagnet FOCALIZATION STAGE Photodiode Active stabilization of sample positioning to compensate position drift over long time acquisition.

17 Epitaxial Co films on a Cu(110) substrate k eff = J. Fassbender et al, Phys. Rev. B 57, 5870 (1998). Bulk fcc Co Epitaxial Fe films on GaAs(001) substrate R. J. Hicken, et al., J. Magn. Magn. Mater. 145, 278 (1995). 17

18 In sity study of epitaxial Fe films on a GaAs(001) substrate Frequency (GHz) GaAs 6 Å Å 4 Å Cu capping Å Å 100 Å Frequency (GHz) Frequency (GHz) [110] [100] [110] [010] H= 1 koe [110] 100 Å 50 Å 30 Å 15 Å 10 Å 6 Å Ag capping [110] In plane angle ( ) In-plane angle ( ) 10 Å Frequency (GHz) Au capping [110] In plane angle ( ) 10 Å In plane angle ( ) Tacchi et al. Surf. Sci. 601, 4311 (2007) 18

19 Perpendicular Magnetic anisotropy in thin Ni films 3 ML Fe/Cu(001) fcc Ni/Cu(001) > 0 in-plane < 0 out-of-plane M M J. Dutcher et al. PRB 39, (1989) C. Vaz et al., Rep. Prog. Phys. 71, (2008) 19

20 Interlayer exchange coupling d Cr 20

21 homogeneous internal field H=0.3 koe Damon-Eshbach geometry 20 H q Intensity (arb. units) q=1.81x10 5 cm x10 5 cm x10 5 cm x10 5 cm -1 Spin-wave Frequency (GHz) n=7 n=6 n=5 n=4 n=3 n=2 n=1 n=0 0.41x10 5 cm Frequency shift (GHz) q (10 5 cm -1 ) NiFe wires width w= 0.65 µm, d=30nm modes with quantized frequencies are observed over final q-intervals nm nm mode intensity is changing with wavevector -0.5 x/w

22 MSBVW geometry H Standard H=1.6 koe µ -BLS center Internal Field (koe) M GHz x q y Frequency shift (GHz) Width =1 µm, L=30nm, Separation= 1 µm Stripe center µ -BLS edge Stripe edge Dynamical magnetization (arb. units) GHz 12.3 GHz Laser spot Laser spot x/w 22

23 Outer diameter 1060 nm 660 nm Inner diameter 380 nm 120nm 2D maps of modes intensity in the vortex state M. Madami, IEEE Trans. on Magn. 46, 199 (2010) (2,0)-loc AS(1,0) S(2,0) Intensity (arb. units) S(1,0) S(0,0) (0,1) (2,0)-loc S(1,0) AS(1,0) 4.9 GHz 7.16 GHz 7.83 GHz Frequency (GHz) S (2,0)-loc 5.53 GHz Near Field Brillouin light scattering S (1,0) 7. 6 GHz AS (1,0) 7.94 GHz 1.3x2.4 µm 2 J. Jersch et al., Appl. Phys. Lett. 97, (2010)

24 Nano-optics with spin waves at microwave frequencies V. Demidov, Appl. Phys. Lett. 92, (2008); PRB 79, (2009) 24

25 Spatial control of spin-wave modes in NiFe antidot lattices by embedded Co nanodisks Py thickness = 26 nm Etching depth = 7 nm Co thickness = 15 nm Diameter 435 nm Lattice period = 1 µm H CPW H=10mT m(t) M s Duerr et al., Appl. Phys. Lett. 99, (2011) µ-bls Simul. 25

26 Magnonic Crystal (MC) are a new class of metamaterials with periodicallymodulatedmagneticproperties. The spin wave dispersion is characterized by bands of allowed magnonic states (magnonic band) separated by frequency regions where propagation is prohibited(magnonic bandgap). E Magnonic Crystals Electron Photons Magnons 26

27 Magnonic vs Photonic Crystals MCs be considered as the counterpart of photonic crystal operating with spinwave (SW) at the GHz or THz frequency range. Dipolar interaction Exhange interaction BG position controlled by magnetic field. Reconfigurable MCs. SW wavelength much shorter that EM radiation in the GHz frequency range. Refractive index Internal field Air is not a medium for SW propagation. SWs are strongly damped in FM materials 27

28 1. Discrete MCs: Starting from uncoupled resonators make them coupled by dynamic dipolar interaction. Frequency (GHz) Separation (nm) 1-DE F 1-BA EM M We start from a discrete set of energy levels for SWs and magnonic band of finite width are introduced by the dynamical dipolar stray field which couples resonances of individual elements and removes their degeneracy. ( ) inside + outside (, ) 2. Continuous MCs: Processing a continuous medium to make a periodical profile of magnetic properties. We start from a continuous density of states and band gaps are introduced because of the artificial periodicity of the crystal H 0 Band gap depends on the magnetic contrast between the two ferromagnets. Fe rods in EuO Matrix J. O. Vasseur et al. 54, 1043 (1996) 28

29 Spin wave band diagram in 1D MCs H k Frequency (GHz) H Coupled nanowires π/a 2π/a =55nm M-Band Gap M-Band Wave number (10 5 cm -1 ) Dynamic magnetization x/w Frequency (GHz) Isolated nanowire k x (10 5 cm -1 ) Frequency (GHz) =35nm π/a Frequency (GHz) π/a 2π/a =55nm Frequency (GHz) π/a =55nm 3π/a 5π/a Wave number (10 5 cm -1 ) Wave number (10 5 cm -1 ) Wave number (10 5 cm -1 ) a= 210 nm a= 405 nm a= 905 nm G. Gubbiotti et al., PRB 72, (2005); APL 90, (2007). 29

30 k // φ Band diagram of spin waves in a two-dimensional MC y Y (0,π/a) M(π/a, π/a) Thickness= 50 nm Diameter= 600 nm, =65 nm 1 BZ=π/a= rad/cm x Γ(0,0) H=1.0 koe Γ H=1.0 koe Y M X X (π/a,0) (0.5) (0.25) (0.7) (1.8) (0.5) S. Tacchi, PRL (2011), (2011) 30

31 Modes classification Γ point λ infinite y H=200Oe q x X point λ = 2a Period= 800 nm Diameter= 120 nm λ infinite λ infinite DE 1BZ λ = 2a Extended modes spreading in the horizontal channels (along the x direction) comprised between adjacent rows of holes. These modes are dispersive and are the analogous of the surface magnetostatic mode of a continuous film. Localized modes mainly concentrated along the horizontal rows of holes. These modes are weakly dispersive. λ infinite λ = 2a EM Edge-modes are strong localized in the regions adjacent to edges of ADs, where the internal field is highly inhomogeneous. 31

32 Band structure: Experiment and DMM theory DE loc 2BZ DE 2BZ DE loc 1BZ DE 1BZ Γ 1 st BZ EM X 2 nd BZ DE loc 1BZ DE 1BZ Γ' 3 rd BZ DE loc 3BZ DE 3BZ DE 2BZ 4 th BZ DE loc 4BZ DE 3BZ 5 th BZ DE 5BZ DE 4BZ Wave vector q (10 5 rad/cm) H q 6 th BZ DE 6BZ y x Frequency (GHz) y (nm) DE 2BZ DE 1BZ DE 1BZ λ = 2a x (nm) a a y (nm) a 0 DE 2BZ λ = 2a x (nm) a cos( The appearance of BGs at BZ boundaries is due to the different spatial localization of the modes. R. Zivieri et al, Phys. Rev. B 85, (2012). <Hint > PC λ/ x sin( 32

33 Spin transfer Torque effect M fixed M free 33 33

34 Magnetization dynamics with Spin transfer Landau-Lifshitz-Gilbert-Slonczewski equation r r r τ M I M I sinθ st For sufficiently large current spin-transferinduced negative damping overwhelms the natural positive magnetic damping and equilibrium orientation becomes unstable magnetization precession at microwave frequency 34

35 Nanopillars Point-Contact Current induced magnetization switching Current density of the order of 10 7 A/cm 2 1mA across (100x100 nm 2 ) Magnetization deviation detected by GMR effect Katine at al. PRL 84, 3149 (2000) Rippard et al. PRL 92, (2004) 35

36 Current induced spin wave modes: theory Slavin-Tiberkevich: localized spin wave Cu Sample magnetized in-plane Excitation of a nonlinear self-localized spin wave mode, spin wave bullet Precessional frequency lower than FMR frequency red shifts with current. FL POL H Slonczewski: propagating spin wave Cu Free layer magnetized perpendicularly with respect to the film plane The excitation is a propagating spin wave with wave vector k ~ 1/R c Frequency higher than FMR frequency blue shifts FL POL H A.N. Slavin et al, Phys. Rev. Lett. 95, (2005) J. C. Slonczewski, J. Magn. Magn. Mater. 159, L261 (1999). V. Demidov et al. Nature materials 9, 984 (2010). 36

37 µ-bls observation of propagating spin waves SW Frequency f (GHz) experimental simulation FMR FMR µ 0 H ext = 0.6 T µ 0 H ext = 0.7 T Modulus of the applied DC I (ma) 20 nm 6 nm 4.5 nm J Integrated intensity J(r) (a.u.) λr ( ) = 0 e λ v g r = = 2. 1 µ m r J r µ-bls measurements calculated intensity distance from the contact r (µm) 37 M. Madami et al, Nature Nanotechnology 6, 635 (2011) r 2αω

38 Conclusions Brillouin light scattering is a powerful tool for measuring spin waves in magnetic nanostructures. Conventional BLS Determination of magnetic parameters is possible by measuring the SW dispersion and/or field dependence. In-situ BLS Spin wave properties in thin and ultrathin magnetic films Micro-focused BLS 2D intensity maps of thermally and microwave excited spin waves 38

39 Usefull textbooks 39