Origin of ferromagnetism in ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x\mathrm{O}$ from magnetization and spin-dependent magnetoresistance measurements

In order to elucidate the nature of ferromagnetic signatures observed in (Zn,Co)O, we have examined experimentally and theoretically magnetic properties and spin-dependent quantum localization effects that control low-temperature magnetoresistance. Our findings, together with a through structural characterization, substantiate the model assigning spontaneous magnetization of (Zn,Co)O to uncompensated spins at the surface of antiferromagnetic nanocrystal of Co-rich wurtzite (Zn,Co)O. The model explains a large anisotropy observed in both magnetization and magnetoresistance in terms of spin Hamiltonian of Co ions in the crystal field of the wurtzite lattice.

Figure 1

Hysteresis loop of ${\mathrm{Zn}}_{0.95}{\mathrm{Co}}_{0.05}\mathrm{O}:\mathrm{Al}$ measured as a function of external magnetic field: (a) for different temperatures and (b) for two directions of the magnetic field with respect to the wurtzite $c$ axis. A temperature-independent contribution linear in the field is subtracted from the data.

Figure 2

Magnetization of ${\mathrm{Zn}}_{0.95}{\mathrm{Co}}_{0.05}\mathrm{O}:\mathrm{Al}$ measured as a function of temperature, at a magnetic field of $500\mathrm{Oe}$ in $H\Vert c$ configuration. The arrows indicate the direction of temperature ramp. The zero field cooled (ZFC) and field cooled (FC) data were obtained after earlier cooling of the sample from 280 down to $5\mathrm{K}$ without and with the applied magnetic field, respectively. A temperature-independent contribution linear in the field is subtracted from the data.

Figure 3

Magnetization of ${\mathrm{Zn}}_{0.95}{\mathrm{Co}}_{0.05}\mathrm{O}:\mathrm{Al}$ measured as a function of the external magnetic field: (a) for two directions of the magnetic field with respect to the wurtzite $c$ axis and (b) for different temperatures. The straight lines result from fitting to the data in a high-field range. A temperature-independent contribution linear in the field is subtracted from the data.

Figure 4

(a) Resistivity changes in the magnetic field $(H\Vert c)$ for ZnO:Al (points) measured at $T=1.5$, 2.3, 3.6, 4.2, 7, 10, 14, 17, 20, 25, 30, 40, 50, 60, 70, 100, and $150\mathrm{K}$. Curves are vertically shifted for clarity. The fitted curves (lines) are obtained within the weak localization (WL) theory. (b) Phase coherence length $L_{\phi }$ (which is the fitting parameter) as a function of temperature. The dots denote $L_{\phi }$ values determined by fitting the 2D WL theory(Refs. 11, 12, 13) and the squares by 3D one $(L_{\phi }<d)$ (Refs. 11, 13) Straight line shows the $T^{-3∕4}$ dependence expected for 3D disordered systems.

Figure 5

Resistivity changes of ${\mathrm{Zn}}_{0.95}{\mathrm{Co}}_{0.05}\mathrm{O}:\mathrm{Al}$ in the magnetic field, [(a) and (b)] measured and [(c) and (d)] simulated for temperatures $T=1.5$, 4.2, 6, 8, 10, 14, 17, 20, and $30\mathrm{K}$. Curves are vertically shifted for clarity. Simulation of magnetic field dependence of [(e) and (f)] Co-related spin-splitting are performed for the same set of temperatures. The configuration of the external magnetic field is $H\Vert c$ for (a), (c), and (e) and $H\perp c$ for (b), (d), and (f).

Figure 6

Low-temperature spontaneous magnetization of uncompensated Co spins at the surfaces of antiferromagnetic wurtzite CoO nanocrystals, calculated as a function of the nanocrystal size for different nanocrystal shapes as indicated in the legend. It is assumed that half (2.5%) of Co atoms in ${\mathrm{Zn}}_{0.95}{\mathrm{Co}}_{0.05}\mathrm{O}$ forms identical nanocrystals exhibiting type II or III aniferromagnetic ordering. The quoted radii correspond to spheres of the same volume. The magnetization value is given in Bohr magnetons per one cobalt ion in ${\mathrm{Zn}}_{0.95}{\mathrm{Co}}_{0.05}\mathrm{O}$.