Photoemission and the electronic structure of magnetic oxides. Dan Dessau University of Colorado, Boulder Duane F625

Transcription

1 Photoemission and the electronic structure of magnetic oxides Dan Dessau University of Colorado, Boulder Duane F625

2 Einstein s Photoelectric effect XPS, UPS, ARPES BE e- hn D.O.S. occupied DOS

3 Expt LDA

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5 Valence Bands Copper 2p core levels Experiment Intensity LDA

6 Correlated vs. uncorrelated systems Static Dynamic remove one Si, Ge, Cu, etc. Band theory Works even though 1 23 electrons! Correlated systems Many-body theories Dynamic interactions --> Novel and rich physics and materials systems.

7 a c Crystal structure of the manganites b MnO 6 octahedra Cubic perovskite manganite (ie. La.6 Sr.4 MnO 3 ) cation (Sr or La) 1 4 x=.4 Monolayer perovskite Manganite (i.e. La.6 Sr 1.4 Mn 2 O 4 ) Bilayer perovskite manganite (ie. La 1.2 Sr 1.8 Mn 2 O 7 ) resistivity (W-cm) T c n=1 n=2 T c rock-salt layer 1-4 n= cubic Temperature (K) monolayer bilayer

8 Bilayer manganite - La 2-2x Sr 1+2x Mn 2 O 7 c b a } } } (La,Sr)MnO 3 (La,Sr)O (La,Sr)MnO 3 Cleavage Plane C.D. Ling et al. TN/TC (K) CMR FM PI type A-AFI resistivity (W-cm) (x=.4) Y. Moritomo et al Doping level x x Temperature (K)

9 Evidence for half-metallicity Strong spin polarization in La.67 Sr.33 MnO 3 epi-films: T = 4K J.H. Park et al., PRL 81, 1953 (1998), Nature 392, 794 (1998).

10 Double Exchange Theory Kinetic energy gain for ferromagnetic alignment e g LaMnO 3 t 2g large t ~ Mn 3+ 3d 4 La 1-x Sr x MnO 3 (T<<T c ) small t ~ La 1-x Sr x MnO 3 (T>T c ) La 1-x Sr x MnO 3 (T>T c ) H large t ~ H Susceptibility (emu/mol) Ferro Para Temperature (K) Ferromagnetism and Metallicity go together.

11 Double Exchange Theory Kinetic energy gain for ferromagnetic alignment ~ t = t o cos(q/2) e g electron itinerant Ferro ~ t = t o Para ~ t ~.77 t o q t 2g electrons core-like S=3/2 Change in conductivity going across Ferro-Para transition: ~ 3% Real materials - many orders of magnitude effect! Why? D(E) E F Para Change in t --> change in W Can study with ARPES Ferro J E W o ~.7 W o

12 Polarons and conductivity Transport without polarons Transport with polarons a1) e- b1) e- a2) e- b2) e- To help manganite problem, polaronic effect must be stronger above T c than below T c Feedback effect necessary - Polaronic effect cooperates with Double-exchange and/or other phenomena (charge ordering). Resistivity (ohm-cm) negative magnetoresistance H=T H=1T H=2T H=3T H=5T H=7T Temperature (K)

13 Temperature dependent pseudogaps in CMR Oxides ARPES experiments Yi-De Chuang, Zhe Sun, Adam Gromko, Alexei Fedorov, Fraser Douglas, Max Bunce, D.S.D. University of Colorado Samples T. Kimura, Y. Tokura University of Tokyo John Mitchell Argonne Nat l Labs Thanks to: X.J. Zhou, P. Bogdanov, Z. Hussain K. Altmann, SRC Madison Support from the DOE and NSF ALS Berkeley Y.D. Chuang et al., Science 292,159 (21)

14 Questions How to explain very poor conductivity In the metallic state of the manganites? M-I transition into the high T insulating state? (--> CMR) Resistivity (ohm-cm) negative magnetoresistance H=T H=1T H=2T H=3T H=5T H=7T Very poor metal Temperature (K) Insulator Possible mechanisms. Polarons? Large scattering? Charge/orbital ordering? Temperature dependent pseudogap (includes some of above).

15 Arbitrary Unit Angle Resolved Photoemission (ARPES) BE spectral weight loss due to Fermi function cutoff E vs k relation hn e- D.O.S. Binding Energy k occupied DOS kf Fermi Surface crossing point EF EDC emission angle MDC EDC: Energy Distribution Curve (ARPES intensity versus binding energy) MDC: Momentum Distribution Curve (ARPES intensity versus momentum) binding energy

16 ARPES on La 1.2 Sr 1.8 Mn 2 O 7 (n=2, x=.4) (Low T Ferromagnetic state) Integrated spectral weight over (.2eV,-.2eV) window 3d x 2 -y 2 hole pockets 3d 3z 2 -r 2 electron pocket Y.D. Chuang et al., Science 292, 159 (21) LSDA Fermi surface topology (N. Hamada unpublished)

17 Angle-scanned (unsymmetrized) Fermi Surface bilayer manganite x=.4 (Low T Ferromagnetic state)

18 ARPES on bilayer x=.4 samples - Low T (2K) ferro state Fermi surface topology k y k x E LDA+U dispersion relation emission angle (degree) EDCs Binding energy (ev) 6 MDCs Double Lorentzian fit to MDCs eV EF Binding energy (ev)

19 ARPES on bilayer x=.4 samples - Low T (2K) ferro state MDCs EDCs 6 emission angle (degree) eV EF Binding energy (ev) Binding energy (ev) binding energy (ev) LDA dispersion MDC centroid EDC centroid Double Lorentzian fit to MDCs (,) (p,) (p,p)

20 Double Exchange Theory Kinetic energy gain for ferromagnetic alignment ~ t = t o cos(q/2) e g electron itinerant Ferro ~ t = t o Para ~ t ~.77 t o q t 2g electrons core-like S=3/2 Change in conductivity going across Ferro-Para transition: ~ 3% Real materials - many orders of magnitude effect! Why? D(E) E F Para Change in t --> change in W Can study with ARPES Ferro J E W o ~.7 W o

21 Temperature dependence of (LaSr)Mn 2 O 7 x=.4 T c ~ 13K hv=22.4 ev 2K spectra taken first (/) (p/) 5K Ferro 2K Para (/) (p/) (p,p) (p,p) 22/.6 ev 18/ 14/ 1/ 6/ 4/ 2/ / 22/1 22/8 22/6 22/4 22/2 22/ Energy Relative to EF (ev) Bandwidth change :.6 ev/1.5 ev = 4%. Much less than the DE prediction of 3%. ==> DE relevant but not key effect. T. Saitoh et al., PRB (2)

22 Extraction of the key transport parameters - low T ferrometal state emission angle (degree) Weight fitting results centroid of peak 2 centroid of peak 1 width Binding energy (mev) expected behavior weight of peak Binding energy (mev) emission angle (degree) Pseudogap (loss of weight) 1)Fermi velocity (from band dispersion near E F ) v F ~.38 c 2)Band mass (fitting dispersion with parabola) m ~.27 m e 3)Number of carriers (measurement of the FS volume) n ~ 3.4*1 21 holes/cm 3 4)Momentum width (HWHM) Dk ~1.2 o ~.9 p/a ~.7 A -1 (original) 4b)Mean free path (lower limit) l=1/ Dk ~ 14 A ~7 times the Mn-O bond length 4c) Mean free time between scattering (lower limit) t=l/v F ~1.24 fs r ARPES = 1/s = m* / n e 2 t ~ 1.3*1-4 W-cm (Drude) Real value r ~ 2*1-3 W-cm (more resistive) Key ingredient not considered in the Drude calculation: pseudogap. Presence of the pseudogap can effectively remove carriers from conduction process thus increasing the resistivity

23 Temperature dependence of the pseudogap Binding Energy (ev) Energy spectra averaged across the entire slice intensity Average Average intensity Energy (ev) 5K 8K 1K 11K 12K 13K 15K analyzer angle (degrees) weight Tc weight (-1.7eV,.3eV) weight (-.2eV,.5eV) Pseudogap correlates with and may drive the M-I transition Temperature (K) Weak pseudogap Poor metal Strong pseudogap Insulator

24 Dimensionality dependence of near-e F weight The pseudogap affects all families of the manganites - some very strongly (single layer) and some less so (pseudocubic). Resistivity varies in kind.

25 Optical Conductivity of layered manganite Spectral weight transfer with temperature over large energy scale Gapped low energy spectral weight (no Drude peak) T. Ishikawa et al., Phys. Rev B 57, R879 (1998)

26 Loss of near-e F weight (pseudogap) Simple superposition of metallic and insulating regimes? Spectral Weight (density of states) insulator metal Spectral Weight Experiment Binding energy (mev) Binding energy (mev) (Need many many types of regions, all with different size gaps) - May consider fluctuations in space and time to get this. Also, FS volume matches total # carriers expected by chemical doping (no regions with extra # holes, regions with fewer # holes).

27 Real-space Charge Density Waves (CDW s) and CDW gaps Example: LaSr 2 Mn 2 O 7 (x=.5) commensurately doped insulator Commensurate/static CE ordering Mn 3+ Mn 3+ Extra periodicity induced by CDW observable in diffraction experiments as weak superlattice spots at (1/4,1/4,). Mn 3+ AF FM Mn 4+ Mn 3+ Mn 3+ Mn 4+ Mn 3+ Mn 3+ d 3x 2 -r K 1.75,2.25, ,1.75, 2 D.Argyriou et al., Argonne/APS E(k) G 2 k System gains energy when gap is centered at E F (commensurate doping levels). G

28 k-space driven CDW s and Fermi Surface nesting We can guarantee that CDW gap is centered at E F in a k-space driven CDW --> gain extra energy. If many parts of the Fermi Surface connect (nesting condition) the instability is greatly enhanced. E(k) Q 2 k G charge density Real space atom position Charge density wave incommensurate with lattice. Short range in space. Fluctuates in time. Elusive! Entire measured FS of La 1.2 Sr 1.8 Mn 2 O 7 is gapped due to large parallel segments (nearly perfect nesting).

29 Real space picture of the k-space driven CDW fluctuations From an analysis of the intensity of 18 superlattice reflections (only observed in the high temperature paramagnetic state) x ~ 6a Temperature Dependence ARPES Weight at E F Diffraction I(.3,,1) c a Mn O La/Sr O3b O2 O1 O3a Intensity T c Fermi-Surface-driven CDW cooperates with the Jahn-Teller effect to distort MnO 6 octahedra. --> increased energy scale of gap. Elastic strain mediates the correlations. Incommensurability with the lattice --> order is short ranged in real space B. Campbell et al, (Phys. Rev. B 21) (K) Temperature Weak Pseudogap Poor metal Fluctuating CDW (not observed in diffraction!) Strong Pseudogap Insulator Semi-static CDW

30 Sharpness of the energy gap CDW with long range order E 2 k E 2 DOS With short range order E k E 2 DOS Including polaronic (Jahn- Teller) energy scale E DOS Looks like lower figure even in low T ferromag state! Polarons and/or charge order at all Temps (with varying strengths).

31 Temperature dependence of the pseudogap Binding Energy (ev) Energy spectra averaged across the entire slice intensity Average Average intensity Energy (ev) 5K 8K 1K 11K 12K 13K 15K analyzer angle (degrees) weight Tc weight (-1.7eV,.3eV) weight (-.2eV,.5eV) Pseudogap correlates with and may drive the M-I transition Temperature (K) Weak pseudogap Poor metal Strong pseudogap Insulator

32 Competition and cooperation electronic ARPES k-space Fermi surface topology r-space XRD,EXAFS (.3,,1) orbital stripe (k-space) CDW (short range) pseudogap charge/orbital charge modulation orbital + Jahn-Teller distortions lattice of various magnitude CMR effect Double Exchange spin