Spin-correlated electronic state on the surface of a spin-orbit Mott system

We use angle-resolved photoemission spectroscopy to show that the near-surface electronic structure of a bulk insulating iridate ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ lying near a metal-Mott insulator transition exhibits weak metallicity signified by finite electronic spectral weight at the Fermi level. The surface electrons exhibit a spin structure resulting from an interplay of spin-orbit, Coulomb interaction and surface quantum magnetism. Our results shed light on understanding the exotic quantum entanglement and transport phenomena in iridate-based oxide devices.

Figure 1

Crystallographic properties and resistivity data of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. (a),(b) Crystal structure of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. CCW (CW) represents the 12${}^{\circ }$ counterclockwise (clockwise) rotation of the ${\mathrm{IrO}}_6$ octahedra. A and B denote two different types of magnetic moment direction for the central Ir atom of each octahedra below $T_{\mathrm{AF}}$. (c) Resistivity curve of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ up to 290 K, showing clear insulating behavior. $T_{\mathrm{AF}}\sim 280$ K marks the Néel temperature. Inset shows a picture of a typical ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ crystal. (d) Brillouin zone and notation of high-symmetry points of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$.

Figure 2

Surface electronic structure of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. ARPES measurements are carried out at 14 K with 35 eV photons. (a) Temperature dependence of the raw $a$-$b$ plane resistivity $\rho$ (right axis) and differentiated $a$-$b$ plane resistivity $\frac{\partial \log \rho }{\partial (1/T)}$ (left axis) for ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ [27]. (b) Sketch of ARPES constant energy map close to $E_F$. Red lines mark the in-plane bulk Brillouin zone at $k_z=0$. (c) Sketch of the experiment-derived in-plane band dispersion at $k_z=0$. (d) ARPES Fermi mapping [raw data in (e)]. Data is twofold symmetrized with respect to $k_{\left[110\right]}=0$. Blue and green colors represent the $\alpha$ and $\beta$ bands, respectively. (e) Raw ARPES mappings at 0 and 0.15 eV binding energies. (f) Band dispersion along three $k$-$E$ cuts shown in (b). Top: raw data; bottom: second derivative of raw data along the EDCs. (g) Analysis of the gap value at $X$. The two-peak structure of symmetrized EDC at $X$ near $E_F$ demonstrates the existence of a gap ${\Delta }_{\mathrm{ARPES}}\left(X\right)\sim 38$ meV.

Figure 3

Quasi two dimensionality of the electronic states. (a) $k_z$ dispersion data $(40<h\nu <80$ eV) along two high-symmetry directions. $k_z$ values are calculated using an inner potential $V_0=10$ eV. (b) MDC stacks of the corresponding panels in (a). Blue and green bars mark the $\alpha$ and $\beta$ bands, respectively. (c) ARPES Fermi mappings with 35, 50, and 25 eV photons, corresponding to $k_z$ values of $\sim$0, $\sim \pi /c$, and $\sim 2\pi /c$, respectively. (d) Sketches of experimental constant energy maps (CEMs) near $E_F$ for the corresponding photon energies in (c). (e) Brillouin zone and notation of high-symmetry points. (f) Schematics of the experiment-derived three-dimensional CEM.

Figure 4

ARPES constant energy maps of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ at elevated temperatures. Dark area represents higher intensity (see color scale). (a) ARPES constant energy maps at $T=100$ K, measured with 25 eV photons. Binding energy $\left(E_B\right)$ for each map is marked at the lower right corner of each panel. (b) Same as (a), but at $T=130$ K, measured with 30 eV photons. Red solid lines in (a) and (b) mark the Brillouin-zone boundaries. Note that the zone boundaries are different for 25 and 30 eV maps (same as in Fig. 3). (c) $k$-$E$ map along the $Y$-$X$-$Y$ direction for data in (b). (d) Symmetrized EDC stacks corresponding to data in (c). Red line indicates the top of the van Hove-like flat portion of the $\alpha$ band, showing a $\sim$35 meV spectral weight suppression similar to Fig. 2.

Figure 5

Detailed analysis for the plateaulike flat portion for bands around the zone corner $X$. Data is taken with 35 eV photons at $T=14$ K. (a) A series of ARPES $k$-$E$ maps near $X$. $k$-space locations of these maps (cuts 1–7) are marked by black arrows in (c). (b) Energy distribution curves (EDCs) for the corresponding map in (a). Note that the $X$ bands evolve to binding energies as low as $\sim$40 meV. (c) Sketch of the observed Fermi contours around $X$. (d) Black curve: Spectral weight at the zone corner—integration of EDCs within the $k$-space range given by an orange box in (c). Red curve: data of a polycrystalline gold sample in electrical contact with the ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ crystal, showing the exact location of $E_F$. Note that the energy scale for the spectral weight peak just below $E_F$ comes from the flat portion of the $X$ bands.

Figure 6

Spin polarization of electrons on the surface. (a) ARPES $k$-$E$ map along the $\Gamma$-$X$ direction. White solid line denotes the spin-resolved MDC studied in (c)–(e). (b) Summary of results from spin-resolved ARPES measurements, together with notations of the AF Brillouin zone and cut direction in (b)–(d). Blue contours represent the projected $\alpha$ band. Black arrows represent the Rashba-like in-plane spin-polarization direction; numbers represent the experimental in-plane spin-polarization angles $\left(\theta \right)$. (c) Spin-integrated ARPES intensity along $\Gamma$-$X$ at a binding energy of $\sim$50 meV. Data is taken at $T=20$ K with 35 eV photons. Lower curves represent the multiple Lorentzian fit of the spin-integrated curve. Black curve is the sum of all Lorentzians. (d) Polarization curve for spin component $S_{[1,-1,0]}$ along $\Gamma$-$X$. Insets show the Rashba-like in-plane spin fine structure of the $\beta$ band. (e) Spin-resolved ARPES intensity along the same direction as in (d). Arrows and symbols mark the apparent “shoulders” in the spin-polarized intensity that corresponds to the $\beta -$ and $\beta +$ bands in (d).

Figure 7

Complete spin-resolved ARPES data set along $X$-$\Gamma$-$X$. Top: Spin-resolved ARPES intensity for three spin components, $S_{[1,-1,0]}$, $S_{\left[110\right]}$, and $S_z$, along $X$-$\Gamma$-$X$. Bottom: Corresponding spin-polarization curves.

Figure 8

Layered iridate $\mathrm{GGA}+U$ theory vs ARPES experiment. (a) Calculated constant energy maps (CEMs) at different binding energies, indicated by purple lines in (c), vs the experimentally derived CEM at $E_B\sim 40$ meV (lower right panel). Black arrows show the Rashba-like fine texture of spin detected for the $\beta$ band. (b) Results of band calculation (detailed in text). Solid circles with different colors and sizes represent the contribution of different Ir 5$d$ orbitals. (c) Band calculation on top of ARPES band structure close to $E_F$ (same data set as Figs. 2 and 3). Red arrow points to the $\beta$ band approaching $E_F$ near $M$ that is not present in the calculation.

Figure 9

Spin texture of the $\beta$ band from slab calculations. Upper row: Slab calculation results for $({\lambda }_{\mathrm{SO}}$, $U$, $E_z)$ = (1.7, 1.5 eV, 0) (left) and (1.7, 1.5 eV, 0.02 eV/$\AA ·e)$ (right). Lower row: Slab calculation results (percentage of spin polarization) for $({\lambda }_{\mathrm{SO}}$, $U$, $E_z)$ = (1.7, 0 eV, 0.02 eV/$\AA ·e)$ (left) and (1.7, 1.5 eV, 0.02 eV/$\AA ·e)$ (right). The in-plane Rashba-like spin polarization changes sign, while the out-of-plane Zeeman-like spin polarization emerges once a finite $U$ is introduced in the calculation.