Direct visualization of spin-dependent orbital geometry on the Na 2 IrO 3 surface with ultra-high resolution

The honeycomb iridate Na2IrO3, as a candidate for the Kitaev model, has drawn increasing attention in recent years. It is a rare example of a strongly correlated, topologically nontrivial band structure that may have protected quantum spin Hall states. The nature of its intriguing insulating phase and magnetic order is still under debate. In the present work, we combine low-temperature scanning tunneling microscopy/spectroscopy and density functional theory calculations to show that Na2IrO3 exhibits a band gap of 420 meV at 77 K, indicating a novel relativistic Mott insulator rather than Slater-like states. In addition, it is demonstrated that the Ir-O-Ir bonds and the subtle local density of states variation of Ir atoms induced by spin correlations can be imaged in real space in ultra-high resolution utilizing a spin-polarized oxygen-functionalized scanning tunneling microscopy tip. The direct observation of the zigzag Ir-O-Ir bonds at 77 K strongly dictates the zigzag magnetic ordering below T N ≈ 15 K because of the strong spin-orbit interactions that lock the lattice and magnetic moments.


STM:
The cleaved sample was quickly transferred into a Unisoko-1300 commercial STM for measurement at a temperature of 77 K.A commercial Pt-Ir tip was prepared by gentle field emission above a clean Au(111) sample.The bias voltage was applied on the sample during the STM observations.The STM images were analyzed using WSxM (36).The resistivity of the samples increases dramatically upon further cooling (10), which prevents us to conduct the STM/S measurements at temperatures much lower than 77 K.

Preparation of O-decorated tip:
By applying a voltage pulse of −3 V with time duration about 100 ms on the Na2IrO3 sample so that the voltage pulse can excite and break Na-O bond, the oxygen anion will be released and attracted to the positive bias on the tip.Such procedure is performed in ultrahigh vacuum and at room temperature.
A monitor is used for monitoring the variation of tunneling current.Before functionalizing the tip with surface oxygen, a clean metal tip need be preheated by a tungsten wire ring with apply a current about 2 A in order to remove the oxide layer at the apex of tip.

Sample preparation:
A self-flux method was used to grow the Na2IrO3 single crystals from off-stoichiometric quantities of IrO2 and Na2CO3.The preparation details can be found elsewhere (10, 14, [51][52][53].The crystals used in this study have the typical sizes of 2 mm × 2 mm × 0.5 mm.Samples were cleaved in situ at room temperature (RT) under vacuum with pressure better than 1×10 −10 torr, resulting in shiny surfaces.

Calculation:
The first-principles DFT calculations were carried out with the Vienna Ab Initio Simulation Package (VASP) (37).The core and valence electronic interactions were described with the frozen-core projector augmented-wave (PAW) potentials (38).The Kohn-Sham single electron states were expanded in plane waves with a kinetic energy of up to 400 eV.The exchange correlation energy was calculated with the Perdew-Burke-Ernzerhof (PBE) of generalized gradient approximation (GGA) (39).The tolerance of 10 -4 eV was chosen for energy convergence of electronic calculations.The Na2IrO3 was modelled with a (2×2) unit cell.The metal STM tip was modelled with a pyramid of Ir(111) in which the apex is a single Ir atom.
The oxygen functionalized tip was mimicked by an Ir(111) pyramid with five oxygen atoms at the apex.A large vacuum of 25 Å along the direction normal to the surface was employed to separate surfaces from their periodic images.The Brillouin zone of 3 / 7 reciprocal space was modeled based on the Γ centered Monkhorst-Pack scheme, where a 4×2×1 gird was adopted in geometry optimizations, searches of the transition states and calculations of electronic properties.STM images were simulated using the revised Chen method implemented in the bSKAN code (40).

In situ annealing of the samples
According to the previous work (54), the strongly bonded IrO6 octahedra can keep intact during the cleaving process, while the pure Na layer and the Na atoms in the NaIr2O6 layer are volatile.In present work, a dominating 1×1 periodic Na surface (Fig. S1A) is obtained after the cleaving process except for a number of atomic defects (see Fig. 1B for details).In order to tune the content of the surface Na atoms, we annealed the sample at 300 °C for 5 min.As shown in Supplementary Fig. 1B, a (√3×√3)R30° unit cell is identified.Hence, This (√3×√3)R30° surface is consistent with previous reports (51), where two-thirds of the Na atoms are removed out of the surface NaIr2O6 layer during the annealing.In addition, more bright spots are found after annealing, which can be sort as oxygen vacancies (see the main text of this paper).4 / 7 We measured the dI/dV spectra on the surfaces before and after annealing (Supplementary Fig. S2).The insulating gap of the annealed surface is 300 meV, which is 120 meV narrower than that measured on the pristine one (420 meV).In addition, there is a small shift of the gap feature in the spectra, implying an electron doping during the annealing.In conclusion, both the surface morphologies and electronic properties can be tuned by the simple annealing, which provides a strategy for studying the lattice structure and doping characteristics of the A2IrO3 materials.

Functionalizing the STM tip with surface oxygen
By applying a voltage pulse of −3 V on the sample so that the voltage pulse can excite and break Na-O bond and the oxygen anion will be released and attracted to the positive bias on the tip .The process would create an oxygen vacancy on the surface, which can be visualized by the successive images (Fig. S4B).In addition, one can immediately notice from Fig. S4B that the resolution became better once the tip is decorated with oxygen atoms.

Bias dependent STM images with an O-tip
With an O decorated tip, The STM images vary with the sample biases.At -1.8 V, the entire surface exhibits a hexagonal lattice (Fig. S5A).At -1.6 V to -1.2 V, however, anisotropic pattern is observed at the regions that are away from the oxygen vacancies, while the hexagonal lattice maintains at the region adjacent to the oxygen vacancies, as shown in Fig. S5B.

2.
Fig S1.Top view (left) and side view (right) of the optimized Na2IrO3 surface.

Fig. S3 .
Fig. S3.Topographic image and dI/dV spectra taken on the samples after in situ annealing.(A) Topographic image after annealing at 300 °C for 5 min.(Vb = −2.0V, It = 50 pA, image size: 20 × 20 nm 2 ).(B) dI/dV spectra measured before and after annealing.(C) Spectra measured along the line marked in (A).The spectra across these bright spots shows similar gap features.dI/dV spectra were acquired using a lock-in technique with ac modulation of 10 mV.

Fig. S4 .
Fig. S4.Preparation of the O-decorated STM tip.(A) Schematic drawings illustrate the methodology to prepare the O-decorated tip.(B) Two STM images in successive scan at the same location.(left) the initial image; (right) the image showing the newly emerged, three O vacancies (marked as red stars) after applying the pulses, taken by O-decorated tip.

Fig. S5 .
Fig. S5.Bias dependent STM images with an O-terminated tip.The bias voltage is -1.8 V for (A) and -1.2 V for (B).The tunneling current is 20 pA and the image size is 20 × 20 nm 2 for both figures.