Anomalous Hall effect at the spontaneously electron-doped polar surface of $\mathrm{PdCo}{\mathrm{O}}_2$ ultrathin films

We revealed the electrical transport through surface ferromagnetic states of a nonmagnetic metal $\mathrm{PdCo}{\mathrm{O}}_2$. Electronic reconstruction at the Pd-terminated surface of $\mathrm{PdCo}{\mathrm{O}}_2$ induces Stoner-like ferromagnetic states, which could lead to spin-related phenomena among the highly conducting electrons in $\mathrm{PdCo}{\mathrm{O}}_2$. Fabricating a series of nanometer-thick $\mathrm{PdCo}{\mathrm{O}}_2$ thin films, we detected a surface-magnetization-driven anomalous Hall effect via systematic thickness- and termination-dependent measurements. Besides, we discuss that finite magnetic moments in electron doped $\mathrm{Co}{\mathrm{O}}_2$ triangular lattices may have given rise to additional unconventional Hall resistance.

Figure 1

Crystal structure and electronic structure of $\mathrm{PdCo}{\mathrm{O}}_2$. (a) Crystal structure of $\mathrm{PdCo}{\mathrm{O}}_2$. (b) Two-dimensional Pd layer. (c) $\mathrm{Co}{\mathrm{O}}_2$ sublattice (top) and $\mathrm{C}{\mathrm{o}}^{3+}$ spin arrangement (bottom). (d) The density of states (DOS) of surface Pd bands split by ${\mathrm{\Delta }}_{\mathrm{Stoner}}$ by Stoner instability [17, 18]. (e) Schematic illustration of a $\mathrm{PdCo}{\mathrm{O}}_2$ thin film with a surface ferromagnetic state extending over $d_{\mathrm{s}}$. Hall effect measurement probes the conduction throughout the entire film. (f) HAADF-STEM image of a $\mathrm{PdCo}{\mathrm{O}}_2$ thin film on $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ (0001), projected along the $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ $\left[\overline{1}100\right]$ direction. Pd and $\mathrm{Co}{\mathrm{O}}_2$ sublattices can be seen on the $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ substrate. (g) The electronic band dispersion along the Γ-Κ cut of a $\mathrm{PdCo}{\mathrm{O}}_2$ film with $d=8.0\mathrm{nm}$. The spin-split surface Pd bands are shown as α and β. The purple dotted square indicates the region where the Co-derived surface band is expected to appear if it existed [18, 22]. (h) Fermi surface of $\mathrm{PdCo}{\mathrm{O}}_2$ obtained by symmetrizing the ARPES data in (g).

Figure 2

AHE of $\mathrm{PdCo}{\mathrm{O}}_2$ thin films. (a)–(c) $R_{\mathrm{H}}\text{−}{\mu }_{0}H$ curves of $\mathrm{PdCo}{\mathrm{O}}_2$ films measured at 2 K with different thicknesses ($d$) ($d=13.0$, 5.4, and 3.2 nm, respectively). (d) Sheet resistance ($R_{\mathrm{sheet}}$) at $B=0\mathrm{T}$ and (e) $R_{\mathrm{H}}$ at $B=9\mathrm{T}$ (${R_{\mathrm{H}}}^{9\mathrm{T}}$) as functions of $d$, plotted as log-log graphs (the red and blue lines are fitting results). (f) Temperature dependence of ${R_{\mathrm{H}}}^{9\mathrm{T}}$ (red squares) and the saturation magnetization measured at ${\mu }_{0}H=7\mathrm{T}$ (${M_{\mathrm{s}}}^{7\mathrm{T}}$) (blue circles) for a film with $d=3.2$ nm. The black curves correspond to typical ferromagnetic and paramagnetic behaviors.

Figure 3

Control of AHE by $\mathrm{Co}{\mathrm{O}}_x$ capping. (a) Schematic illustration of the rock-salt type CoO (111) heterostructure and the delafossite-type $\mathrm{PdCo}{\mathrm{O}}_2$ (0001). (b) $R_{\mathrm{H}}$ vs ${\mu }_{0}H$ for $\mathrm{PdCo}{\mathrm{O}}_2$ (3.6 nm) (red) and $\mathrm{Co}{\mathrm{O}}_x$ (5 nm) / $\mathrm{PdCo}{\mathrm{O}}_2$ (3.6 nm) (blue).

Figure 4

Unconventional AHE of $\mathrm{PdCo}{\mathrm{O}}_2$ thin films. (a) Magnetic field (${\mu }_{0}H$) dependence of $R_{\mathrm{H}}$, $R_{\mathrm{AH}}$, and $R_{\mathrm{UH}}$ for $d=3.2$ nm at various temperatures. $R_{\mathrm{AH}}$ was calculated using the magnetization curves. (b) Temperature dependence of $R_{\mathrm{AH}}$ (red squares) and $R_{\mathrm{UH}}$ (blue circles). (c) The $R_{\mathrm{UH}}$ mapped as a function of temperature and magnetic field. (d) The electron configurations of $\mathrm{C}{\mathrm{o}}^{2+}$ in the high-spin (top) and in low-spin (bottom) states.

Figure 5

Spectroscopic investigation of the $\mathrm{Co}{\mathrm{O}}_2$ layers. (a) $\mathrm{Co}\text{−}{L}_{2,3}$ XAS spectra of the $\mathrm{PdCo}{\mathrm{O}}_2$ films with $d=2.7$ nm (red line) and 8.8 nm (blue line) measured at $T=300\mathrm{K}$. The $\mathrm{Co}\text{−}{L}_{2,3}$ XAS spectra of $\mathrm{LaCo}{\mathrm{O}}_3$ (black dotted line) and CoO (green dotted line) are also shown as references for the $\mathrm{C}{\mathrm{o}}^{3+}$ and $\mathrm{C}{\mathrm{o}}^{2+}$ states, respectively [34]. The peak and shoulder structures that are attributed to the $\mathrm{C}{\mathrm{o}}^{3+}$ and $\mathrm{C}{\mathrm{o}}^{2+}$ states are indicated by black and green arrows, respectively. (b) XMCD data of the $\mathrm{PdCo}{\mathrm{O}}_2$ thin films. $\mathrm{Co}\text{−}{L}_{2,3}$ XAS spectra of the $\mathrm{PdCo}{\mathrm{O}}_2$ film ($d=2.7$ nm) measured at $T=30\mathrm{K}$, by positive (${\mu }^{+}$, green line) and negative (${\mu }^{-}$, black line) circular polarized lights, respectively. XMCD spectra (${\mu }^{+}\text{–}{\mu }^{-}$) of the $\mathrm{PdCo}{\mathrm{O}}_2$ films for $d=2.7$ (red line) and 8.8 nm (blue line) measured under the magnetic field of 5 T at $T=30\mathrm{K}$. The gray dashed line indicates the energy positions of the features characteristic to the $\mathrm{C}{\mathrm{o}}^{2+}$ states. The spectra in (a) and (b) were offset for the easiness of comparison.