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Spectroscopic ellipsometry

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Spectroscopic ellipsometry

Spectroscopic ellipsometry

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    Spectroscopic ellipsometry Spectroscopic ellipsometry Presentation Transcript

    • Alexander BORIS Max Planck Institute for Solid State Research Stuttgart Spectroscopic ellipsometry: application to electrodynamics of correlated electron materials and oxide superlattices.September 1, 2011, Vancouver MAX-PLANCK-UBC CENTRE FOR QUANTUM MATERIALS International Summer School on Surfaces and Interfaces in Correlated Oxides
    • Outline Outline • the complex dielectic function spectra - one of the first steps in research of the physical properties of a new material • spectroscopic ellipsometry - basic principles and experimental implementation • advantages of ellipsometry - illustrative examples - i) exact numerical inversion, no i) superconductivity-induced Kramers-Kronig transformation, transfer of the spectral weight in allows for K-K consistency check high temperature cuprate SCs ii) no reference measurements, very ii) superconductivity-induced optical accurate and highly reproducible anomalies and iron pnictide superconductors iii) oblique and variable angle of iii) dimensionality-controlled incidence, very sensitive to collective charge and spin* order thin-film properties in nickel-oxide superlattices * combined with low-energy muons which serve as a sensitive local probe of the internal magnetic field distribution
    • Outline Outline • the complex dielectic function spectra - one of the first steps in research of the physical properties of a new material
    • Electromagnetic waves Electrodynamics of Solids ‫ܧ = ܧ‬଴ ݁ [௜(ఠ௧ିk‫ ݔ‬ାఋ)]
    • Dielectric polarization, susceptibility, pemittivity Electrodynamics of Solids ࡱ ࡼ + +q - - - - Polarization + Electric field - + ݈ - - - + -q - ߤ ൌ ‫݈∙ݍ‬ Electric Ionic (phonon) Dipole moment Polarization ࡼ ൌ ∑࢏ ࣆ࢏ ൌ ߝ଴ χ ࡱ ࡼ ࢿ ൌ 1 ൅ χ ൌ 1 ൅ ఌబ ࡱ
    • 4π Electrodynamics of ∂E ∇× H = j + ε 0ε SolidsMaxwell’s equations for wave c ∂t propagation in a conductor: ∂H ∇ × E = −µ0 ∂t  ∂E ∂ 2E  ⇒ ∇ × (∇ × E) = −∇ E = − µ0 σ 2 + ε 0ε 2   ∂t ∂t  plane wave : ‫ܧ = ܧ‬଴ ݁ [௜(ఠ௧ିk‫ ݔ‬ାఋ)] ⇒ k ଶ = ߤ଴ ݅߱ߪ + ߤ଴ ߝ଴ ߝ߱ଶ 4ߨ 1 SI → CGS: ߤ଴ → ଶ , ߝ଴ → ܿ 4ߨ ఠమ ସగ ఠ ସగ k ଶ = ߝ+݅ ߪ , k ≡ N, Nଶ = ߝ + ݅ ߪ ௖మ ఠ ௖ ఠComplex dielectric function optical conductivity ߝ̃ ߱ = ߝଵ (߱) + ݅ ∙ ߝଶ (߱) ߪ ߱ = ߪଵ ߱ + ݅ ∙ ߪଶ (߱) ෤ 4ߨ ߝଶ ߱ = ߪଵ (߱) ߱
    • Dielectric response of Drude metal dv mb equation of motion for electrons mb = eE − v dt τ damping term momentum transferred to phonons and impurities per unit time eτ 1 solution v= E mb 1 − iωτ nb e 2 τ current density j = nb e v = E mb 1 − iωτ σ0 γ = 1/ τ ω pl 2 σ (ω) = ε1 (ω) = 1 − 2 2 1 − iωτ ω +γ 4π nbe2 ne2τ ω pl = 2 ω pl γ 2 2 σ0 = mb σ1 (ω) = 1 mb collective oscillations of 4π γ ω 2 + γ 2 electron charge density
    • Complex dielectric functionElectrodynamics of Solids ߝଵ (߱) 4ߨ ߝଶ ߱ = ߪ (߱) ߱ ଵ
    • Optical sum rules: ∞ Spectral Weight and Sum Rules π ne e 2 f-sum rule: SW (0, ∞) = ∫ σ 1 (ω )dω = = const 0 2me ݊௘ - total number of electrons in the system, ݉௘ - free electron mass D.Y. Smith and E. Shiles, PRB 17, (1978) 4689-4694 Ω = 2 Al ∫ σ (ω )dω 2m neff πe N 0 Ω ω pl 2 π nb e 2 intra-band spectral weight: SW intra (0, ∞) = = = f (T ) ≠ const 8 2mb
    • Kramers-Kronig relations 1926-1927 response follow causality: P = ε 0 χ E applied field ∞ P(t ) = ε 0 ∫ χ (t − t )E(t )dt , χ (t − t ) = 0 for t < t −∞ P(ω) = ε 0 χ (ω)E(ω) ∞ ω ε 2 (ω ) ε 1 (ω ) − 1 = 2 KKR: ⋅ P∫ dω π 0 ω −ω 2 2 2ω ∞ ε 1 (ω ) − 1 ε 2 (ω ) = − ⋅ P∫ dω π 0 ω −ω 2 2 ∆σ 1 (ω ) ∞ consistency check: ∆ε 1 (ω ) = 8 ⋅ P ∫ 2 dω 0 ω −ω 2
    • Normal incidenceReflectivity by normal incidence reflectivity Incident light ‫ܧ‬଴௜ sin ߱‫ݐ‬ ߶௥ r Ei Reflected light ‫ܧ‬଴௥ sinሺ߱‫ ݐ‬൅ ߶௥ ሻ 2 E0 r ~2 r R= =r Er E0 i 2 ~ = ε − 1 = R (ω ) exp{iφ (ω )} r ε +1 r ∞ 2ω ln R (ω ) KKR: φr (ω ) = − ∫ ω 2 − ω 2 dω π 0
    • Outline Outline • spectroscopic ellipsometry - basic principles and experimental implementation
    • Analogy with electric circuit electric circuit admittance Analogy with impedance Lissajous figure a b resistance & reactance (complex impedance) X Y Z = R+iωL R Vmaxsinωt ϕ Imaxsin(ωt-ϕ) L Vmax Imax ϕ= arctan(ωL/R)= = arcSin(a/b) Time
    • Polarization of light Electrodynamics of Solids ࡱ-field vector ࡱ = ࡱ࢞ + ࡱ࢟ Y Linear polarization phase delay ߮=0 X Y Curcular polarization phase delay ߮=ߨ/2 X Y Elliptical polarization Ψ ‫ܧ‬௫ phase delay ߮=0.35·2ߨ X ‫ܧ‬௬
    • Spectroscopic ellipsometry Sample Analyzer near Brewster angle Polaryzer tan ߠ஻ = ݊௧ ⁄݊௜
    • Spectroscopic ellipsometry Sample Analyzer near Brewster angle Polaryzer tan ߠ஻ = ݊௧ ⁄݊௜ ϕ
    • Spectroscopic ellipsometry Detector: 2,0 Elliptically polarized light determined by: Intensity 1. Relative phase shift, ∆= ∆௣ − ∆௦ ; ௥೛ 2. Relative attenuation, tan Ψ = 1,0 ௥ೞ Sample 0,0 0 90 180 270 360 Analyzer angle (Ai ) Analyzer I(Ai)/I0 = 1 + α sin(2Ai) + β cos(2Ai) 1+ߙ tan Ψ = tan ܲ , Polaryzer 1−ߙ ̃ ‫ݎ‬௣ (߱) ߚ ෤ ߩ ߱ = = tan Ψ(߱) ݁ ௜∙୼(ఠ) cos Δ = ̃ ‫ݎ‬௦ (߱) 1 − ߙଶ 1 + tan Ψ(߱) ∙ ݁ ௜∆(ఠ) ଶ Ψ(߱) ൠ ⇒ ߝ̃ ߱ = (sin ߮)ଶ +(sin ߮)ଶ (tan ߮)ଶ Δ(߱) 1 − tan Ψ(߱) ∙ ݁ ௜∆(ఠ)
    • Spectroscopic ellipsometry Paul Drude ellipsometer ~ 1890 2007
    • ANKA Synchrotron, Karlsruhebeamline at ANKA IR IT IR-1 beamline Y.-L. Mathis, B. Gasharova, D. Moss Current: 80 -180 mA lifetime: 12-23 hours
    • ANKA Synchrotron, Karlsruhebeamline at ANKA IR IT IR-1 beamline Y.-L. Mathis, B. Gasharova, D. Moss 1.5 Magnetic Field [T] Magnetic profile 1.0 of a dipole 0.5 Edge and dipoleSpatial distribution radiation in the visiblefrom the edge at 0.03 m from the source(calculated for 100µm) 1.0m 0.5 0.0 -0.5 -1.0 Position on particle trajectory [m] Photons/s/.1%bw/mm^2 x10 40 150 20 at λ=10 µm y [mm] 100 0 -20 50 -40mm 9 0 -40mm -20 0 20 40 x [mm]
    • wide-band spectroscopic ellipsometry THz to UV Ellipsometry: from ANKA Synchrotron edge radiation 1m 10m 100m 1 eV 6.2 0.2 THz 1 2 far-IR mid-IR near-IR UV 10 100 1000 10000 cm-1 near-IR to deep-UV far-IR homebuilt ellipsometer spectroscopic at ANKA IR1- beam line, ellipsometer (VASE) @ Karlsruhe IT Woollam Co., @ MPI-FKF IR homebuilt ellipsometer based on Bruker 66v/S FTIR spectrometer, @ MPI-FKF
    • wide-band spectroscopic ellipsometry THz to UV Ellipsometry: from ANKA Synchrotron edge radiation 1m 10m 100m 1 eV 6.2 0.2 THz 1 2 far-IR mid-IR near-IR UV 10 100 1000 10000 cm-1 near-IR to deep-UV far-IR homebuilt ellipsometer spectroscopic at ANKA IR1- beam line, ellipsometer (VASE) @ Karlsruhe IT Woollam Co., @ MPI-FKF IR homebuilt ellipsometer based on Bruker 66v/S FTIR spectrometer, @ MPI-FKF
    • Outline Outline • advantages of ellipsometry - i) exact numerical inversion, no Kramers-Kronig transformation, allows for K-K consistency check ii) no reference measurements, very accurate and highly reproducible iii) oblique and variable angle of incidence, very sensitive to thin-film properties
    • Outline Outline • advantages of ellipsometry - illustrative examples - i) exact numerical inversion, no i) superconductivity-induced Kramers-Kronig transformation, transfer of the spectral weight in allows for K-K consistency check high temperature cuprate SCs
    • Kramers-Kronig consistency check ∆σ 1Exp (ω ) ∞ ∆ε 1Exp (ω0 ) ∆ε KK (ω0 ) = 8 ⋅ P ∫ 2 2 dω 0 ω −ω0 1 This additional constraint unique to ellipsometry allows one to determine with high accuracy changes in the spectral weight in the extrapolation region beyond the experimentally accessible spectral range: hω < 10 meV ......... hω > 6.6 eV
    • T-dependent Drude ω pl π e 2 nb 2 SW Drude = = 8 2 mb σDC γ (T1 ) > γ (T2 ) γ2 σ1 (ω) = σ DC T1 > T2 ω2 + γ 2 0 ω pl 2 ε1 (ω) = ε ∞ − 2 2 -20 ε1 ω +γ -40 0.0 0.5 1.0 1.5 2.0 hν (eV)
    • T-dependent Drude SW ω pl π e 2 nb 2 SW Drude = = 8 2 mb electron correlation effects σDC UHB Daniel Khomslii’s lecture 0 nb = f (T ) ≠ const -20 mb ε1 -40 0.0 0.5 1.0 1.5 2.0 hν (eV)
    • Kramers-Kronig consistency check 1.2 1.0 σ1,A- σ1,B 0.8 A ωp= 1.5 eV ∆σ1 (10 Ω cm ) 6 SWA-SWB -1 0.6 -1 +0.1 % γΑ = 0.05 eV 3 σ1 (10 Ω cm ) -1 0.4 -0.25 % 4 γB = 0.06 eV -1 B 0.2 3 0.0 2 -0.2 0.00 0.02 0.04 0.06 0.08 photon energy (eV) 0 0.00 0.05 0.10 0.15 0.20 0.0 photon energy (eV) -0.5 ∆σ (ω ) ∞ ε1,A- ε1,B ∆ε 1 (ω0 ) = 8 ⋅ P ∫ 2 1 2 dω -1.0 ∆ε1 0 ω −ω0 -1.5 SWA-SWB +0.1 % -2.0 -0.25 % 0.18 0.21 0.24 0.27 photon energy (eV)
    • in-plane Ba2Sr2CaCu2Oin-plane Ba2Sr2CaCu2O8 8 Tc=91 K Tc = 91 K 6000 10 K 100K 200 Kσ1 (Ω cm ) 4000-1 0-1 2000 -1000 ε1b 10 K 0 100 K 0.01 0.1 -2000 200 K Photon energy (eV) -3000 0.01 0.1 Photon energy (eV)
    • in-plane Ba2Sr2CaCu2O8 (T>Tc) 8 exp N ∆ε1 0 ∆SW > 0 6 exp from ∆σ1 (0 < ω < 1.0 eV) as measured∆σ1 (mΩ cm ) -2 100K 200K-1 extrapolated with with SW = SW 4 100K SW > SW 200K -4-1 (by ≈ 1.5%) ∆ε1 SW head = − SW tail 2 -6 SW head > − SW tail -8 ∆T = 200 K - by ≈ 1.5% 100 K (0.007eV 2 ) 0 -10 0.00 0.02 0.04 0.06 0.08 0.10 0.1 0.2 0.3 0.4 0.5 Photon energy (eV) Photon energy (eV) ∆SW total > 0 SW 100 K = SW 200 K + 0.007 eV 2
    • Perfect conductor ω plτ → ∞ σ0 σ0 ne2 purely reactive σ(ω) = = = 1 − iωτ iωτ iωm* Cooper pairs ms = 2m, es = 2e, ns = n / 2 1 ns es2 r 1 1 r j (ω) = E(ω) = E(ω) r iω ms iω µ0λ2 ms r r i ( kr⋅rr −ωt ) penetration depth λ= , E = E0e µ0ns es 2 r dj The first London equation: E = µ0λ2 r dt
    • R.A. Ferrell, R.E. Glover, M. Tinkham1958-1959FGT-sum fule KKR 1 1 ε1 (ω) = − ⇒ σ1 (ω) = δ (ω) λL ω2 2 8λL 2 >6 ∆SC 1λL 2 =8 ∫ ∆σ (ω)dω 0+ 1
    • Optical response of NbN SC film J.Demsar et al., 2011 Mach-Zander interferometer with movable mirror: ω 1 1 σ 2 (ω) = − ε1 (ω) = σ1 (ω) = δ (ω) 4π 4π λL ω 2 8λL 2
    • D-wave gap in cuprates
    • in-plane Ba2Sr2CaCu2Oin-plane Ba2Sr2CaCu2O8 8 Tc=91 K Tc = 91 K 6000 10 K 100K 200 Kσ1 (Ω cm ) 4000-1 0-1 2000 -1000 ε1b 10 K 0 100 K 0.01 0.1 -2000 200 K Photon energy (eV) -3000 0.01 0.1 Photon energy (eV)
    • in-plane Ba2Sr2CaCu2O8 (T<Tc) ∆σ 1Exp (ω ) ∞ ∞ ∆ε 1 (ω ) = 2 2 + 8 ⋅ P ∫ 2 = 8 ∫ ∆σ 1Exp (ω )dω ( FGT − sum rule) 1 1 dω with λLω 0+ ω −ω 2 λ2 L 0+ 8 exp ∆ε1 as measured 6 exp from ∆σ1 (0 < ω < 1.0 eV) extrapolated with∆σ1 (mΩ cm ) 2 1/λ L=∆SW-1 ° with λL = 2300 Α 4-1 ° λL = 2000 Α ∆ε1 2 ∆T = 100 K - 10 K 0 SC 0 ∆SW ≈0 0.00 0.02 0.04 0.06 0.08 0.10 Photon energy (eV) 0.1 0.2 0.3 0.4 0.5 Photon energy (eV) ∞ ≈ 8 ∫ ∆σ 1Intra (ω )dω 1 λ2 L 0+
    • in-plane Ba2Sr2CaCu2O8 (T<Tc) ∆σ 1Exp (ω ) ∞ ∞ ∆ε 1 (ω ) = 2 2 + 8 ⋅ P ∫ 2 = 8 ∫ ∆σ 1Exp (ω )dω ( FGT − sum rule) 1 1 dω with λLω 0+ ω −ω 2 λ2 L 0+ 8 exp ∆ε1 as measured 6 exp from ∆σ1 (0 < ω < 1.0 eV) extrapolated with∆σ1 (mΩ cm ) 2 1/λ L=∆SW+1%-1 ° with λL = 2300 Α 4 2 1/λ L=∆SW-1%-1 ° λL = 2000 Α ∆ε1 2 ∆T = 100 K - 10 K 0 SC 0 ∆SW ≈0 0.00 0.02 0.04 0.06 0.08 0.10 Photon energy (eV) 0.1 0.2 0.3 0.4 0.5 Photon energy (eV) ∞ = 8 ∫ ∆σ 1Intra (ω )dω ± 0.5% (0.0008 eV 2 ) 1 λ2 L 0+
    • SW transfer in Ba2Sr2CaCu2O8 Ba2Sr2CaCu2O8 in-plane Tc=91 K SW 100 K = SW 200 K + 0.007 eV 2 8 exp ∆ε1 (∆T=200K-100K) 6 exp ∆ε1 (∆T=100K-10K) 4 N ∆SW > 0 ∆ε1 2 0 SC ∆SW ν0 0.1 0.2 0.3 0.4 0.5 Photon energy (eV) ∞ = ∫ ∆σ 1Intra (ω )dω ± 0.0008 eV 2 1 λ2 L 0+H.J.A. Molegraaf & D. van der Marel,Science, 295, 2239 (2002)
    • SW transfer in Ba2Sr2CaCu2O8 Ba2Sr2CaCu2O8 in-plane Tc=91 K Bi2212H.J.A. Molegraaf & D. van der Marel,Science, 295, 2239 (2002)
    • SW transfer in Ba2Sr2CaCu2O8 Ba2Sr2CaCu2O8 in-plane Tc=91 K Bi2212 Y123H.J.A. Molegraaf & D. van der Marel,Science, 295, 2239 (2002)
    • Conclusions Science, 304, 708 (2004)
    • Outline Outline • advantages of ellipsometry - illustrative examples - ii) no reference measurements, very ii) superconductivity-induced optical accurate and highly reproducible anomalies and iron pnictide superconductors
    • Iron arsenide superconductors Ba lattice structuremultiband electronic structure Fe Assuperconductivity Ba0.68K0.32Fe2As2 Tc=38.5 K
    • SC-reduced absorption in visible ω ∆ ! ħω > 200∆SCmax
    • Thermal modulation ellipsometry
    • inter-band excitations: LDAexcitations: LDA assignment inter-band assignment A.N. Yaresko Γ M
    • SC-induced anomalies in visible (single-band BCS) ! Ν ouSC ≡ Ν ouNS 2∆A.L. Dobryakov et al.,Optics Communications 105, 309 (1994)
    • SC-reduced absorption in visible (Ba1-xKxFeAs) ! Ν ouSC < Ν ouNS ∆Εg 0.5 eV
    • SC-induced lowering of the chemical potential Single band BCS: e.g. D.J. Scalapino, “SC-ty” (1969) 1 ∆ SC 2 µ SC ≈ µN − 4 µN ∆ SC / ε F ~ ∆F SC (0) ~ 0.1 meV 2
    • SC-induced lowering of the chemical potential Single band BCS: e.g. D.J. Scalapino, “SC-ty” (1969) 1 ∆ SC 2 µ SC ≈ µN − 4 µN ∆ SC / ε F ~ ∆F SC (0) ~ 0.1 meV 2 Multi band BCS: ∆iSC ≠ ∆ jSC   j→  ⇒ nSC = nN + ∆nSC i i i µ = µ = µ SC  i j  • self-consistent treatment of a variable chemical potential at the SC transition is required
    • SC-induced inter-band charge transferSingle band BCS: e.g. D.J. Scalapino, “SC-ty” (1969) 1 ∆ SC 2 µ SC ≈ µN − 4 µN ∆ SC / ε F ~ ∆F SC (0) ~ 0.1 meV 2Multi band BCS: ∆iSC ≠ ∆ jSC   j→  ⇒ nSC = nN + ∆nSC i i i µ = µ = µ SC  i j  Two el’s subsystems in cuprates: D. I. Khomskii and F.V. Kusmartsev, PRB 46 (1992) N CuO2 ∆2 µ SC = µ N − N CuO2 + N chain 4µ N  N CuO2 ∆2  nSC =n N 1 +  ~ 1% CuO2 CuO2  N CuO + N chain 4µ N 2   2 
    • SC-induced inter-band charge transfer Fe3dxz,zy+Fe3dxy ∆SC < ∆SC  h e  nh < nh SC N ⇒ mh < me h  ∆F SC (0) > ∆ SC / ε F * * 2  Fe3dxy
    • ConclusionsBa0.68K0.32Fe2As2 - SC-reduced absorption in visible: • assigned to excitations from As-px,y/Fe-dz2 to Fe-dyz,zx and Fe-dxy states • charge transfer between the Fe-dyz,zx and Fe-dxy bands below Tc could explain the optical anomaly • self-consistent treatment of a variable chemical potential at the SC transition is required • in the presence of large Fe-As bond polarizability it can potentially enhance superconductivity in iron pnictides.
    • Outline Outline • advantages of ellipsometry - illustrative examples - iii) oblique and variable angle of iii) dimensionality-controlled incidence, very sensitive to collective charge and spin* order thin-film properties in nickel-oxide superlattices * combined with low-energy muons which serve as a sensitive local probe of the internal magnetic field distribution
    • 2D e-gas in semiconductors Band Bending picture QHE v Klitzing 1980 FQHE H. Störmer 1984 Jochen Mannhart’s lecture
    • Dimentionality control in oxides LaAlO3 “solid-state chemistry approach” wide-band-gap (~ 5eV) insulator LaNiO3 Ruddlesden–Popper (R–P) homologous paramagnetic series of Srn+1RunO3n+1 metal
    • Why RNiO3? J.-S. Zhou, J.B. Goodenough et al., LaAlO3 PRL 84, 526 (2000) wide-band-gap (~ 5eV) insulator Ni3+ 3d7 t62ge1g ∆CF >> JH eg LaNiO3 S=1/2 W ~ EG~ JH ~ U paramagnetic t2g metal
    • RNiO3-based Heterosctructures LaAlO3 wide-band-gap Possible 3D-to-2D- and interface- (~ 5eV) insulator induced “engineered” properties of correlated electrons:• metal- insulator transition with unusual magnetic and charge ordering• orbital reconstruction• multiferroicity G. Giovannetti et al., PRL 103, 156401 (2009)• superconductivity J. Chaloupka and G. Khaliullin, PRL 100, 016404 (2008) P. Hansmann et al., PRL 103, 016401 (2009) “… possible orbital occupancy analogous to the cuprates …” LaNiO3 paramagnetic metal
    • Theory Experiment Perfect sample Real sample Technology Extrinsic properties Intrinsic properties (stacking faults, inter-diffusion(collective quantum phases) substrate contribution) high oxygen pressure PLD, MPI-FKF G. Cristiani and H.-U. Habermeier
    • LaNiO3|LaAlO3 superlattices compressive tensile (001) LaSrAlO4 (001) SrTiO3 N = 4 u.c. x 10, d = 290 ± 10 Å N = 3 u.c. x 13, d = 312 ± 10 ÅMF-MPI beam line @ANKA, A. Frano, E. Benckiser, P. Wochner
    • Reciprocal-space maps N = 4 u.c. N = 2 u.c. N = 2 u.c.Alex Frano’s poster
    • Reciprocal-space maps N = 4 u.c. N = 2 u.c. N = 2 u.c.TEM: MF-MPI StEM E. Detemple, W. Sigle, P. van Aken
    • Theory Experiment Perfect sample Real sample Technology Extrinsic properties Intrinsic properties faults, inter-diffusion (stacking (collective quantum phases) contribution) substrate inevitable defects + local probes! vs. macro probes optical spectroscopy dc conductivitycharge: (ellipsometry) and permittivity muon-SR magnetic spin: (slow muons) susceptibility AFM, charge order FM, ferroelectric, SC
    • Charge dynamics via spectroscopic ellipsometry Y Ai sample detector E Es analyzer IrsI P Ep ϕ IrpI ~ ~ r p (ω ) polarizer ρ (ω ) = ~ = tan Ψ (ω )ei∆ (ω ) light source r s (ω ) oblique incidence - sensitive to thin-film properties intrinsic SL’s electrodynamics is not flawed by a substrate, contacts and extended defects
    • Isotropic film on isotropic substrate in vacuum ૚⁄૛ ଶ ଶ ૛ ߮௜ ܰ cos ߮ − ܰ − sin ࣐ ‫ݎ‬଴ଵ೛೛ = ૚⁄૛ 01 ܰ ଶ cos ߮ + ܰ ଶ − sin ࣐ ૛ d ܰ SL ଶ ଶ ૛ ૛ ૚⁄૛ 12 −݊ cos ߚ + ܰ ݊ − ࡺࡿ sin ࢼ ‫ݎ‬ଵଶ೛೛ = ૚⁄૛ ૛ ߚ௜ ݊ଶ cos ߚ +ܰ ݊ଶ − ࡺࡿ sin ࢼ ૛ ࡺ࢙ substrate ૚⁄૛ cos ߮ − ܰ ଶ − sin ࣐ ૛ ‫ݎ‬଴ଵೞೞ = ‫ݎ‬௣ (߱) ̃ cos ߮ + ܰ ଶ − sin ࣐ ૛ ૚⁄૛ ߩ ߱ = ෤ = tan Ψ(߱) ݁ ௜∙୼(ఠ) ‫ݎ‬௦ (߱) ̃ ૚⁄૛ ଶ ૛ ૛ −ࡺࡿ cos ߚ + ܰ − ࡺࡿ sin ࢼ ‫ݎ‬଴ଵ೛೛ + ‫ݎ‬ଵଶ೛೛ ݁ ି௜ଶఈ ‫ݎ‬ଵଶೞೞ = ૚⁄૛ ‫ݎ‬௣ (߱) = ̃ cos ߚ + ܰ ଶ − ࡺࡿ ૛ sin ࢼ ૛ 1 + ‫ݎ‬଴ଵ೛೛ ‫ݎ‬ଵଶ೛೛ ݁ ି௜ଶఈ ‫ݎ‬଴ଵೞೞ + ‫ݎ‬ଵଶೞೞ ݁ ି௜ଶఈ Snell‘s law: sin ߮ = ܰ௦ sin ߚ ‫ݎ‬௦ (߱) = ̃ 1 + ‫ݎ‬଴ଵೞೞ ‫ݎ‬ଵଶೞೞ ݁ ି௜ଶఈ ૚⁄૛ ௗ ଶ ૛ Phase thickness: ߙ = 2ߨ ܰ − sin ࣐ ఒ Known: ߩ ߱ , ߮, ࡺࡿ ෤ ߱ Unkown: ࡺ ߱ , ݀
    • complex dielectric function of bare SLs numerical inversion Drude parameters: N = 4: ω p ≈ 1.10 eV , γ ≈ 87 meV m* = 10 N = 2: ω p ≈ 1.05 eV , γ ≈ 196 meV m V EF = 0.5eV , VF = 1.33 ⋅107 cm , l = F s 2π cγ o o mean free path: N = 4: l = 9.7 A, N = 2: l = 4.4 A
    • from itinerant to localized electronsLaNiO3
    • from itinerant to localized electronsLaNiO3
    • from itinerant to localized electronsLaNiO3 ΔNeff=0.03 Effective number of electrons localized: ω ∆N eff (ω ) = 2 0 ∫ ∆σ (ω ′)dω ′ 2m π e N Ni 0
    • from itinerant to localized electronsLaNiO3 ΔNeff=0.03 Effective number of electrons localized: bulk NdNiO3 - ΔNeff=0.058 ω ∆N eff (ω ) = 2 0 ∫ ∆σ (ω ′)dω ′ 2m T.Katsufuji, Y.Tokura et al., (1995): π e N Ni 0
    • from itinerant to localized electronsLaNiO3 ΔNeff=0.03 Effective number of electrons localized: bulk NdNiO3 - ΔNeff=0.058 ω ∆N eff (ω ) = 2 0 ∫ ∆σ (ω ′)dω ′ 2m T.Katsufuji, Y.Tokura et al., (1995): π e N Ni 0
    • Metal – Insulator Transition (MIT) in LaNiO3 Continuing the analogy with bulk RNiO3 series, one would then expect another second-order transition due to the onset of antiferromagnetic ordering at TN < TMI in the N = 2 SLs, as in RNiO3 with small R (Lu through Sm).
    • Low-Energy µSR measurements Rob Kiefl’s lecture Thomas Prokscha, Zaher Salman, Andreas Suter, Elvezio Morenzoni
    • LaNiO3|LaAlO3 SLs : µ+ Spin Relaxation F (t ) − B (t ) BTF = 0 AZF (t ) = = aoG (t ) F (t ) + B(t ) G(t) is the Fourier transform of the field distribution averaged over all muon sites. Fast depolarization rate: Ni spins are AFM ordered
    • LaNiO3|LaAlO3 SLs : µ+ Spin Rotation BTF=100 G The time evolution of the muon polarisation in a transverse field BTF is µ+ F (t ) − B(t ) ATF (t ) = = aoG (t ) cos(ω L t ) F (t ) + B (t ) where Larmor frequency ωL= γµBTF , γµ= 2π×13.55 MHz/kG
    • LaNiO3|LaAlO3 SLs : µ+ Spin Rotation BTF > 0 The time evolution of the muon polarisation in a transverse field BTF is µ+ F (t ) − B(t ) ATF (t ) = = aoG (t ) cos(ω L t ) F (t ) + B (t ) where Larmor frequency ωL= γµBTF , γµ= 2π×13.55 MHz/kG BTF =100 Gauss BTF =1000 Gauss BTF =3000 Gauss
    • LaNiO3|LaAlO3 SLs : charge and spin order
    • LaNiO3|LaAlO3 SLs : charge and spin order
    • LaNiO3|LaAlO3 SLs : charge and spin order
    • Science, 332, 937 (2011)
    • SUMMARY i) superconductivity-induced transfer of the spectral weight in high temperature cuprate SCs ii) superconductivity-induced optical anomalies and iron-based pnictide superconductors iii) dimensionality-controlled collective charge and spin* order in nickel-oxide superlattices
    • Thank you !