Resistance of domain-wall states in half-metallic $\mathrm{Cr}{\mathrm{O}}_2$

The half-metallic $\mathrm{Cr}{\mathrm{O}}_2$ with nearly 100% spin polarization is an ideal system to study magnetic domain-wall resistance, which differs from the resistance (or resistivity) inside a single domain. To experimentally measure the domain-wall resistance, we design and prepare a special $\mathrm{Cr}{\mathrm{O}}_2$ epitaxial nanostructure with an asymmetrical weak link to localize a domain wall, by using the techniques of chemical vapor deposition and selective-area growth. This structure provides a capability to generate and annihilate a domain wall near the weak link. By contrasting the resistance between a single-domain state and a domain-wall state, we observe a repeatable and reversible resistance jump, namely domain-wall resistance, in half-metallic $\mathrm{Cr}{\mathrm{O}}_2$. Using the Levy-Zhang model, we further obtain the spin asymmetry ratio ${\rho }_0^{\uparrow }/{\rho }_0^{\downarrow }$ between resistivities in the two spin channels. The ratio, 4256 ± 388 at 5.0 K, is much larger than that of conventional ferromagnetic metals, attesting to the half metallicity of $\mathrm{Cr}{\mathrm{O}}_2$.

Figure 1

(a) Scanning electron micrograph of fabricated $\mathrm{Cr}{\mathrm{O}}_2$ nanostructure sample used in this study (see details in the text). The yellow area is $\mathrm{Cr}{\mathrm{O}}_2$ and the gray area is $\mathrm{Si}{\mathrm{O}}_2$. ${\mathrm{V}}^{+}$, ${\mathrm{V}}^{-}$, ${\mathrm{I}}^{+}$, and ${\mathrm{I}}^{-}$ labels show the four-point resistance measurement configuration. (b) Characterizing the $\mathrm{Cr}{\mathrm{O}}_2$ nanostructure sample by measuring its resistivity as a function of temperature between 5.0 and 300.0 K.

Figure 2

(a) Magnetoresistance hysteresis loop at 5.0 K of the $\mathrm{Cr}{\mathrm{O}}_2$ nanostructure under a sweeping external magnetic field between −50.0 and 50.0 mT along the $x$ axis. The inset magnetization maps are from micromagnetic simulation and the red and blue areas represent magnetization along the positive and negative $x$ axis, respectively. (b) Magnetoresistance hysteresis loop under a sweeping field between −30.0 and 17.0 mT, revealing a low-resistance state of single domain and a high-resistance state of single-domain wall in the nanostructure. (c) Similar to (b), except under a sweeping field between −17.0 and 30.0 mT. The blue arrows are the magnetic-field sweeping direction.

Figure 3

(a) Temperature dependence of resistance difference ΔR between the high-resistance and the low-resistance state at zero field, obtained from the data shown in Figs. 1 and 1. The inset is an expanded view of ΔR within 5.0 to 60.0 K. (b) Ratio ($\mathrm{\Delta }R/R_0$) of resistance difference ΔR to the zero-field resistance $R_0$ in the low-resistance single-domain state.

Figure 4

Ratio of DW resistivity to the longitudinal resistivity based on different shape of domain-wall contour $b$/$r$. $b/r=5$ is the approximated value obtained from micromagnetic simulation. The inset shows the domain-wall contour shape.