Termination and Verwey transition of the (111) surface of magnetite studied by scanning tunneling microscopy and first-principles calculations

Scanning tunneling microscopy and scanning tunneling spectroscopy combined with first-principles calculations have been applied to investigate the (111) surface of a naturally grown ${\text{Fe}}_3{\text{O}}_4$ single crystal. The commonly observed surface is determined as a layer of Fe cations at tetrahedral sites, known as the ${\text{Fe}}_{\text{tet}1}$ termination. A surface terminated with Fe cations at octahedral sites, another proposed termination in previous studies, is found only when the surface was prepared under oxygen-poor conditions. Scanning tunneling spectra at room temperature and at 77 K indicate that the (111) surface undergoes a metal-insulator transition.

Figure 1

(Color online) Schematic of atomic arrangement of the ${\text{Fe}}_3{\text{O}}_4\left(111\right)$ surface in cubic phase used in the calculations. (a) Top view and (b) side view for the ${\text{Fe}}_{\text{oct}2}$ termination are shown. The ${\text{Fe}}_{\text{tet}1}$ termination can be constructed just by removing the last ${\text{Fe}}_{\text{oct}2}$ layer from the schematics. Five outermost atomic layers (${\text{Fe}}_{\text{oct}2}$, ${\text{Fe}}_{\text{tet}1}$, ${\text{O}}_1$, ${\text{Fe}}_{\text{oct}1}$, and ${\text{O}}_2$) were relaxed to obtain a stable structure.

Figure 2

(Color online) STM images of the regular termination of the ${\text{Fe}}_3{\text{O}}_4\left(111\right)$ surface acquired at 77 K. (a) Large-scale image $\left(20\times 10{\text{nm}}^2\right)$. Step height was measured to be $\sim 480\text{pm}$, corresponding to the half the basis vector along the $c$ axis in the inverse spinel structure. Tunneling parameters are $V_{\text{sample}}=-2.1\text{V}$ and $I_{\text{t}}=0.4\text{nA}$. (b) and (c) Smaller-scale images $\left(10\times 5{\text{nm}}^2\right)$ acquired with different bias voltages: (b) $V_{\text{sample}}=+4\text{V}$ and $I_{\text{t}}=50\text{pA}$; (c) $V_{\text{sample}}=-4\text{V}$ and $I_{\text{t}}=50\text{pA}$. Three types of defects are marked in the images. White arrows indicate a vacancy of the protrusion forming the hexagonal lattice or ${\text{Fe}}_{\text{tet}1}$ vacancy; red circled (broken line) and blue circled (solid line) sites are named as P1 and P2 species, respectively.

Figure 3

(Color online) STM image $\left(20\times 10{\text{nm}}^2\right)$ of oxygen deficient area of the ${\text{Fe}}_3{\text{O}}_4\left(111\right)$ surface acquired at 77 K, showing a mixture of a triangular-shaped superstructure and the regular termination. Tunneling parameters are $V_{\text{sample}}=-3.0\text{V}$ and $I_{\text{t}}=0.2\text{nA}$.

Figure 4

(Color online) (a) STS obtained on the regular termination at 77 K. Inset: another spectrum that shows the energy gap region in detail. (b) Current-voltage $\left(I\text{−}V\right)$ curve (left y-axis) and STS (right y-axis) obtained at RT on the regular termination. (c) Site-dependent STS obtained on a protrusion forming the hexagonal lattice or ${\text{Fe}}_{\text{tet}1}$ site (black dotted line), P1 (red broken line), and P2 species (blue solid line).

Figure 5

STM images [(a) and (b) $9\times 15{\text{nm}}^2$; (c) and (d) $10\times 10{\text{nm}}^2$] showing bias and tip dependences of the appearances of two regions acquired at 77 K. Region A corresponds to the regular termination. Appearance of region B, either honeycomb or hexagonal lattice, depends both on the [(a) and (b)] bias and [(c) and (d)] tip conditions. Tunneling parameters (a) $V_{\text{sample}}=+2.0\text{V}$ and $I_{\text{t}}=0.2\text{nA}$; (b) $V_{\text{sample}}=-2.0\text{V}$ and $I_{\text{t}}=0.2\text{nA}$; (c) and (d) $V_{\text{sample}}=-1.0\text{V}$ and $I_{\text{t}}=0.2\text{nA}$.

Figure 6

(Color online) Simulated constant height STM images for the cubic phase using GGA and $\text{GGA}+U$ ($U=5\text{V}$ and $J=1\text{V}$) methods. Four images on the left correspond to the ${\text{Fe}}_{\text{tet}1}$ termination and four images on the right correspond to the ${\text{Fe}}_{\text{oct}2}$ termination. Sample bias voltages are set to $+2\text{V}$ (upper row) and $-2\text{V}$ (lower row). Rhombus in each image corresponds to the unit cell. Blue triangles and red circles indicate the ${\text{Fe}}_{\text{tet}1}$ and ${\text{Fe}}_{\text{oct}2}$ sites, respectively.