Spin-related magnetoresistance of $n$-type ZnO:Al and ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{O}:\mathrm{Al}$ thin films

Effects of spin-orbit and $s\text{−}d$ exchange interactions are probed by magnetoresistance (MR) measurements carried out down to $50\mathrm{mK}$ on ZnO and ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{O}$ with $x=3$ and 7% and electron concentration $\sim {10}^{20}{\mathrm{cm}}^{-3}$. A description of the data for ZnO:Al in terms of weak-localization theory leads to the coupling constant ${\lambda }_{\mathrm{so}}=(4.4\pm 0.4)\times {10}^{-11}\mathrm{eV}\mathrm{cm}$ of the $kp$ hamiltonian for the wurzite structure, $H_{\mathrm{so}}={\lambda }_{\mathrm{so}}\mathit{c}(\mathit{s}\times \mathit{k})$. A complex and large MR of ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{O}:\mathrm{Al}$ is interpreted in terms of the influence of the $s\text{−}d$ spin-splitting on the disorder-modified electron-electron interactions, which explains positive MR. A large negative MR is tentatively assigned to a precursor effect of the magnetic polaron formation. It is suggested that the proposed model explains the origin of MR observed recently in many magnetic oxide systems.

Figure 1

Resistivity as a function of temperature (a) and magnetic field (b) for ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{O}$ and ${\mathrm{Zn}}_{0.93}{\mathrm{Mn}}_{0.07}\mathrm{O}$, respectively, revealing that the increase of resistance at low temperatures is destroyed by the magnetic field.

Figure 2

Resistance changes in the magnetic field for $n\text{−}\mathrm{Zn}\mathrm{O}$ (thin lines) compared to calculations (thick lines) within the weak localization theory for the 3D case. For $T=1.8$ and $5\mathrm{K}$ the phase coherence length $L_{\phi }$ is set to infinity, while the fitted values of $L_{\phi }$ at higher temperatures are plotted in (b) by squares. Dots denote $L_{\phi }$ determined by fitting the weak-field data presented in Fig. 3. Straight line shows the dependence $T^{-3∕4}$ expected for $L_{\phi }\left(T\right)$ in the 3D case.

Figure 3

Resistance changes in the magnetic field $B$ for $n\text{−}\mathrm{Zn}\mathrm{O}$ (symbols) compared to calculations (solid lines) within the weak localization theory for the 2D case with the diffusion coefficient calculated from the 3D formula. Curves are vertically shifted for clarity. The upper axis gives the magnetic field normalized by $B_{\mathit{tr}}\equiv \hslash ∕4eD\tau =14\mathrm{T}$.

Figure 4

Measured (a,c) and calculated within no adjustable parameter (b,d) resistivity changes in the magnetic field for $n\text{−}{\mathrm{Zn}}_{0.97}{\mathrm{Mn}}_{0.03}\mathrm{O}$ (a,b) and $n\text{−}{\mathrm{Zn}}_{0.93}{\mathrm{Mn}}_{0.07}\mathrm{O}$ (c,d). Theory neglects magnetic localization effects, which are thought to result in negative magnetoresistance not reproduced by computed results at low temperatures.