Theory of charge and spin ordering in the nickelates - Physics ...

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Comparisons FERMI SURFACES, ELECTRON-HOLE ASYMMETRY, AND… PHYSICAL REVIEW B 79, 115122 2009 Γ-X a R-M b X R Γ M X R Binding energy (eV) 0.0 0.5 1.0 0.5 0.0 1.0 0.5 0.0 Binding energy (eV) Binding energy (eV) k F 1 k F 2 k F 3 k F 4 1.0 X Γ X R M R soft x-ray ARPES, R. FIG. Eguchi 3. Color online a and et bal, EDCs along 2009 -X and R-M direction, respectively. c and d The intensity maps of EDCs. k F1-k F4 indicate the MDC peak positions at E F. we measured ARPES at a fixed photon energy of 630 eV k z 0 and 710 eV k z /c. The FS mapping in horizontal k x -k y planes “” and “” of Brillouin zone in Fig. 1a t’/t=0.15 was obtained as shown in Figs. 2b and 2c. In “” plane, FIG. 2. Color online Fermi-surface mapping in a a vertical the small electron FS around point is again observed. This k result indicates that the 3D spherelike FS around point can z-k x plane “” and b horizontal k x-k y planes “” and c “” of Brillouin zone in Fig. 1a. Solid white lines correspond to the be observed by ARPES experimentally. The squarelike intense area around M points obtained from raw data without cubic Brillouin zone and dotted white lines correspond to the highsymmetry lines. k F1-k F4 indicate the MDC peak positions at E F in symmetrization corresponds to the projection of the hole FS Figs. 3c and 3d. Blue gray lines show nesting character hole centered at R point. In “” plane, no small FS is observed. LNO FSs. All the intensity maps are measured data over the displayed Instead large FSs centered at R point were observed. From range and no symmetrization has been used to obtain the maps. the complete data set of energy and angle-dependent FS RH maps, the experimental FS obtained by soft x-ray ARPES is to the Ni 3d6t 2g bands. In addition, EDCs for 600–660 eV in overall agreement with that predicted by the band clearly show a dispersive band crossing at the E F arrows calculation. 24 However, the actual band dispersions reveal an around the point. This dispersive band originates in Ni 3d important difference in electron and hole FSs as discussed in e g states and forms a small electron pocket as predicted by the following. the local-density 4 approximation LDA band calculation. The In order to discuss the band structures forming these FSs, band disappears for energies below 600 eV and above 660 we measured the ARPES in the high-symmetry lines with eV photon energy and an increase in intensity is observed detailed momentum steps and an energy resolution E close to the M point at h=570 and 700 eV. 150 meV. The EDCs Figs. 3a and 3b and the intensity plots Figs. 3c and 3d along -X and R-M directions 2 Figure 2a shows the FS mapping in a vertical k z -k x plane “” of Brillouin zone as shown in Fig. 1a, which is are shown in Fig. 3. The FS crossing k F points are labeled as obtained by a plot of the integrated intensity from −0.05 to k F 1-k F 4. The intensity plots in both directions Figs. 3c and 0.05 eV binding energy in EDCs. A small circle centered at 3d show an intense feature around 0.0–0.2 eV at and M point is observed, while no 0.2 intensity is observed 0.1 around the 0.0points, corresponding 0.1 to the electron 0.2 t’/t band and the hole band X point. The existence of a nearly spherical small FS centered at point, corresponding to the electron FS, was pre- bottom at M point is around 0.25 eV, the band bottom at derived from Ni 3d e g states, respectively. While the band dicted by2 band calculations. 24 From photon energy point is not at 0.25 eV. The intensity remains in high bindingenergy region about 0.5–1.0 eV at point Fig. 3c, in- k z -dependent ARPES measurements, we can decide the photon energy tracing the -X and X-M directions as shown dicating that the bands extend to high binding energies. Because the t 2g bands also appear above 0.5 eV at X point, in Fig. 1b. 4 In order to observe the in-plane cuts of the FSs, the 6 115122-3 c d S/T 3 2 1 1 2 3 optics, D. Ouellette et al, 2010 LNO 0.4 0.2 0.0 0.2 0.4 t’/t “Hole like” Hall conductivity “Electron like” thermopower
Nesting Large fermi surface contains rather flat portions Approximate “nesting” leads to a large susceptibility at some wavevectors, and a tendency to CDW or SDW order
Page 1 and 2: Theory of charge and spin ordering
Page 3 and 4: Outline Introduction to Mott transi
Page 5 and 6: ates remain temperature ds, the key
Page 7 and 8: Bulk transitions Transitions are al
Page 9 and 10: Magnetic structure Neutron scatteri
Page 11 and 12: Charge and spin order CO CO+AF Torr
Page 13 and 14: Valence skipping Mazin et al, 2007:
Page 17 and 18: Hubbard Model A minimal model to co
Page 19 and 20: Phase Diagram Which is more appropr
Page 21 and 22: Tight-binding model Keep just σ-bo
Page 23: Fermi surfaces Variation with t’/
Page 27 and 28: Hartree-Fock Two SDW phases appear
Page 29 and 30: Landau Theory SDW order parameter i
Page 31 and 32: Cubic symmetry Landau free energy F
Page 33 and 34: Cubic symmetry Landau free energy F
Page 35 and 36: Cubic lattice “site centered”
Page 37 and 38: 1918 J B Good Orthorhombic Distorti
Page 39 and 40: SDW states Look along axis θ=0 θ
Page 41 and 42: Hartree-Fock With orthorhombicity,
Page 43 and 44: Back to the Mott Transition What ab
Page 45 and 46: Strong Coupling Approach Consider p
Page 47 and 48: Ordering of pairs Half of sites sho
Page 49 and 50: Magnetism The spin of each Ni 2+ el
Page 51 and 52: Put it together Strong coupling pic
Page 55 and 56: Electronic structure Another way to
Page 57 and 58: Hartree-Fock graphene-like band str
Page 59 and 60: Anisotropy SDW wavevectors cubic un
Page 61 and 62: Nesting Confinement affects Fermi s
Page 63: Summary Theory of the nickelates mu

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