![Electromagnetic waves Electrodynamics of Solids
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![4π
Electrodynamics of ∂E
∇× H = j + ε 0ε Solids
Maxwell’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 ఠ
Complex dielectric function optical conductivity
ߝ̃ ߱ = ߝଵ (߱) + ݅ ∙ ߝଶ (߱) ߪ ߱ = ߪଵ ߱ + ݅ ∙ ߪଶ (߱)
4ߨ
ߝଶ ߱ = ߪଵ (߱)
߱](https://image.slidesharecdn.com/borismpg-ubcschool2011-120810172845-phpapp02/85/Spectroscopic-ellipsometry-6-320.jpg)
![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 dipole
Spatial distribution radiation in the visible
from the edge at
0.0
3 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]](https://image.slidesharecdn.com/borismpg-ubcschool2011-120810172845-phpapp02/85/Spectroscopic-ellipsometry-20-320.jpg)
Spectroscopic ellipsometry
- 1. 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
- 2. 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
- 3. Outline Outline • the complex dielectic function spectra - one of the first steps in research of the physical properties of a new material
- 4. Electromagnetic waves Electrodynamics of Solids ܧ = ܧ ݁ [(ఠ௧ିk ݔାఋ)]
- 5. Dielectric polarization, susceptibility, pemittivity Electrodynamics of Solids ࡱ ࡼ + +q - - - - Polarization + Electric field - + ݈ - - - + -q - ߤ ൌ ݈∙ݍ Electric Ionic (phonon) Dipole moment Polarization ࡼ ൌ ∑ ࣆ ൌ ߝ χ ࡱ ࡼ ࢿ ൌ 1 χ ൌ 1 ఌబ ࡱ
- 6. 4π Electrodynamics of ∂E ∇× H = j + ε 0ε Solids Maxwell’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 ఠ Complex dielectric function optical conductivity ߝ̃ ߱ = ߝଵ (߱) + ݅ ∙ ߝଶ (߱) ߪ ߱ = ߪଵ ߱ + ݅ ∙ ߪଶ (߱) 4ߨ ߝଶ ߱ = ߪଵ (߱) ߱
- 7. 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
- 8. Complex dielectric functionElectrodynamics of Solids ߝଵ (߱) 4ߨ ߝଶ ߱ = ߪ (߱) ߱ ଵ
- 9. 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
- 10. 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
- 11. 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
- 12. Outline Outline • spectroscopic ellipsometry - basic principles and experimental implementation
- 13. 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
- 14. 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
- 15. Spectroscopic ellipsometry Sample Analyzer near Brewster angle Polaryzer tan ߠ = ݊௧ ⁄݊
- 16. Spectroscopic ellipsometry Sample Analyzer near Brewster angle Polaryzer tan ߠ = ݊௧ ⁄݊ ϕ
- 17. 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)
- 18. Spectroscopic ellipsometry Paul Drude ellipsometer ~ 1890 2007
- 19. 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
- 20. 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 dipole Spatial distribution radiation in the visible from the edge at 0.0 3 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]
- 21. 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
- 22. 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
- 23. 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
- 24. 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
- 25. 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
- 26. 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)
- 27. 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)
- 28. 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)
- 29. in-plane Ba2Sr2CaCu2Oin-plane Ba2Sr2CaCu2O8 8 Tc=91 K Tc = 91 K 6000 10 K 100K 200 K σ1 (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)
- 30. 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
- 31. 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
- 32. R.A. Ferrell, R.E. Glover, M. Tinkham 1958-1959 FGT-sum fule KKR 1 1 ε1 (ω) = − ⇒ σ1 (ω) = δ (ω) λL ω2 2 8λL 2 >6 ∆SC 1 λL 2 =8 ∫ ∆σ (ω)dω 0+ 1
- 33. 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
- 34. D-wave gap in cuprates
- 35. in-plane Ba2Sr2CaCu2Oin-plane Ba2Sr2CaCu2O8 8 Tc=91 K Tc = 91 K 6000 10 K 100K 200 K σ1 (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)
- 36. 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+
- 37. 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+
- 38. 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)
- 39. SW transfer in Ba2Sr2CaCu2O8 Ba2Sr2CaCu2O8 in-plane Tc=91 K Bi2212 H.J.A. Molegraaf & D. van der Marel, Science, 295, 2239 (2002)
- 40. SW transfer in Ba2Sr2CaCu2O8 Ba2Sr2CaCu2O8 in-plane Tc=91 K Bi2212 Y123 H.J.A. Molegraaf & D. van der Marel, Science, 295, 2239 (2002)
- 41. Conclusions Science, 304, 708 (2004)
- 42. 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
- 43. Iron arsenide superconductors Ba lattice structure multiband electronic structure Fe As superconductivity Ba0.68K0.32Fe2As2 Tc=38.5 K
- 44. SC-reduced absorption in visible ω ∆ ! ħω > 200∆SCmax
- 46. inter-band excitations: LDAexcitations: LDA assignment inter-band assignment A.N. Yaresko Γ M
- 47. SC-induced anomalies in visible (single-band BCS) ! Ν ouSC ≡ Ν ouNS 2∆ A.L. Dobryakov et al., Optics Communications 105, 309 (1994)
- 48. SC-reduced absorption in visible (Ba1-xKxFeAs) ! Ν ouSC < Ν ouNS ∆Εg 0.5 eV
- 49. 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
- 50. 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
- 51. SC-induced inter-band charge transfer 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 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
- 52. 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
- 53. Conclusions Ba0.68K0.32Fe2As2 - 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.
- 54. 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
- 55. 2D e-gas in semiconductors Band Bending picture QHE v Klitzing 1980 FQHE H. Störmer 1984 Jochen Mannhart’s lecture
- 56. 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
- 57. 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
- 58. 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
- 59. 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
- 60. 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 Å MF-MPI beam line @ANKA, A. Frano, E. Benckiser, P. Wochner
- 61. Reciprocal-space maps N = 4 u.c. N = 2 u.c. N = 2 u.c. Alex Frano’s poster
- 62. 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
- 63. 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 conductivity charge: (ellipsometry) and permittivity muon-SR magnetic spin: (slow muons) susceptibility AFM, charge order FM, ferroelectric, SC
- 64. 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
- 65. Isotropic film on isotropic substrate in vacuum ⁄ ଶ ଶ ߮ ܰ cos ߮ − ܰ − sin ࣐ ݎଵ = ⁄ 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 ࣐ ݎଵೞೞ = ݎ (߱) ̃ cos ߮ + ܰ ଶ − sin ࣐ ⁄ ߩ ߱ = = tan Ψ(߱) ݁ ∙(ఠ) ݎ௦ (߱) ̃ ⁄ ଶ −ࡺࡿ cos ߚ + ܰ − ࡺࡿ sin ࢼ ݎଵ + ݎଵଶ ݁ ିଶఈ ݎଵଶೞೞ = ⁄ ݎ (߱) = ̃ cos ߚ + ܰ ଶ − ࡺࡿ sin ࢼ 1 + ݎଵ ݎଵଶ ݁ ିଶఈ ݎଵೞೞ + ݎଵଶೞೞ ݁ ିଶఈ Snell‘s law: sin ߮ = ܰ௦ sin ߚ ݎ௦ (߱) = ̃ 1 + ݎଵೞೞ ݎଵଶೞೞ ݁ ିଶఈ ⁄ ௗ ଶ Phase thickness: ߙ = 2ߨ ܰ − sin ࣐ ఒ Known: ߩ ߱ , ߮, ࡺࡿ ߱ Unkown: ࡺ ߱ , ݀
- 66. 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
- 67. from itinerant to localized electrons LaNiO3
- 68. from itinerant to localized electrons LaNiO3
- 69. from itinerant to localized electrons LaNiO3 ΔNeff=0.03 Effective number of electrons localized: ω ∆N eff (ω ) = 2 0 ∫ ∆σ (ω ′)dω ′ 2m π e N Ni 0
- 70. from itinerant to localized electrons LaNiO3 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
- 71. from itinerant to localized electrons LaNiO3 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
- 72. 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).
- 73. Low-Energy µSR measurements Rob Kiefl’s lecture Thomas Prokscha, Zaher Salman, Andreas Suter, Elvezio Morenzoni
- 74. 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
- 75. 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
- 76. 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
- 77. LaNiO3|LaAlO3 SLs : charge and spin order
- 78. LaNiO3|LaAlO3 SLs : charge and spin order
- 79. LaNiO3|LaAlO3 SLs : charge and spin order
- 80. Science, 332, 937 (2011)
- 81. 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
- 82. Thank you !