The key result of our work is presented in Figure 1, which clearly shows that the RT MR is strongly correlated with resistivity and therefore the transport behavior of Co/ZnO films. We found that the reproducibility of the films was very good and that there is no clear correlation between the ZnO thickness, the chamber sputtering pressure, and the values of MR. However, a clear pattern emerges when MR is plotted against the resistivity of the films. From Figure 1, the MR values are evidently larger than 8.1% in the intermediate regime (tunneling regime) with 0.08 Ω · cm < ρ < 0.5 Ω · cm, but they decrease markedly in the left and right regimes (metallic and hopping regimes). In the metallic regime, the MR effect becomes weaker with decreasing resistivity and finally trends toward zero as the resistivity decreases to approximately 0.004 Ω · cm. The MR also decreases with increasing resistivity in the hopping regime and retains at 3.7% when the resistivity reaches approximately 3.8 Ω · cm in the hopping regime, as shown in Figure 1.
To investigate the mechanisms behind the dependence of MR on resistivity, we selected three typical samples: Co/ZnO films with x = 0.5 sputtered at 0.4 Pa (marked as sample A), x = 0.4 sputtered at 0.8 Pa (marked as sample B), and x = 2.5 sputtered at 0.8 Pa (marked as sample C) (shown in Figure 1). Figure 2 shows the hysteresis loops of the three films measured with a magnetic field applied to the film plane at RT after subtracting the diamagnetic background. The magnetization curves of samples B and C exhibit a superparamagnetic-like nature, with negligible remanence and coercivity. This indicates that Co nanoparticles may exist in the films. Whereas, as shown in the inset of Figure 2, a coercivity value of 34 Oe is observed in sample A, which may be attributed to the formation of interconnected large Co particles in the films. The saturation magnetization decreases from 476 to 264 and 25 emu/cm3 for samples A, B, and C, respectively. This decrease may be attributed to the decreasing size of Co particles and the increasing ZnO content.
Figure 3a,b,c shows the temperature dependence of the zero-field-cooled and field-cooled (ZFC-FC) curves for samples A, B, and C measured in an applied field of 100 Oe. A large bifurcation is observed at low temperatures between the ZFC and FC curves for samples B and C, which suggests that superparamagnetic nanoparticles are embedded in the ZnO matrix [16, 17]. Assuming that interactions between Co particles are neglected for samples B and C, the Co particle size can be roughly estimated from the measured blocking temperatures (T
) identified by the maximum in the ZFC plots using the Bean-Livingston formula: KV = 25k
, where K = 2.7 × 105 J/m3 is the magnetic anisotropy constant, V is the average volume of the nanoparticles, and k
is the Boltzmann constant. The average size values are approximately 7.2 and 3.4 nm calculated for sample B (T
= 152 K) and sample C (T
= 16 K), respectively. However, for sample A, the ZFC and FC plots do not coincide at temperatures below 300 K. This observation is consistent with the ferromagnetic behavior as shown in the inset of Figure 2. The existence of Co nanoparticles and their different dispersion in the ZnO is expected to significantly influence the MR behavior, as will be discussed later.
We also carried out XRD measurements for samples A and B, as shown in Figure 4a,b. Sample B exhibits no peaks because of the small Co particles and amorphous ZnO. Broadened peaks of Co (002) and ZnO (002) appear in sample A, although the Co content of sample A is lower than that of sample B according to the nominal structure of the films. This finding indicates that the distribution of Co particles is inhomogeneous in sample A. Figure 4c shows the variation of the deposition rate of ZnO film with sputtering pressure. The deposition rate decreases from 0.113 to 0.054 nm/s with an increase in sputtering pressure from 0.4 to 0.8 Pa, which is attributed to the increase in collisions and the scattering of sputtered species under high processing pressure [18, 19]. In general, the surface of the ZnO film deposited at low pressure is very rough, and a ravine-like topography can form at the surface because of higher deposition rate [18, 20]. In our experiments, Co does not wet the surface of ZnO when Co deposits on the surface of ZnO. Co consequently may agglomerate into larger elongated particles in ravines because the surface energy of metallic Co (approximately 2.52 J/m2) is higher than that of ZnO (approximately 1.58 J/m2). For sample C, superparamagnetic Co particles with smaller size and larger distance between Co particles may form because of the increase in ZnO content and higher sputtering pressure.
From the above discussions, it can be concluded that the films of samples B and C contain Co nanoparticles with different particle sizes dispersed in the ZnO matrix, and some interconnected Co particles may exist in sample A. The plane-view schematic illustrations of the three samples are shown in Figure 3. The structural, magnetic, and transport measurements strongly suggest that the MR effect in these granular films should be related to the size and spatial distribution of Co particles. In the metallic regime, the value of MR decreases with decreasing resistivity probably because of the increase in the number of interconnected Co particles. When the resistivity is less than 0.004 Ω · cm, the value of MR is almost zero. Most Co particles connect with one another and provide few opportunities for spin-polarized electron tunneling. The MR ratio is also reduced as the resistivity in the hopping regime increases, but it still remains greater than 3.7% even when resistivity reaches 3.8 Ω · cm and the volume fraction of Co calculated according to the nominal structure of Co (0.6)/ZnO (2.0) is less than 24%. This observation can be ascribed to the relatively long spin-coherence length in our material [21, 22].
We turn to the spin polarization of electron in the films, which can be estimated roughly from the Inoue-Maekawa model as follows: MR = P2m2/(1 + P2m2) , where P is the spin polarization of the tunneling electrons, m is the relative magnetization of the film, and m2 = 〈 cos θ〉. m = 1 in the saturated state, and the above equation becomes MR = P2/(1 + P2). The RT spin polarization in the tunneling regime calculated from the MR value of 8.1% is approximately 30%, which is very close to the 35% of the bulk Co metal determined by tunneling . This large RT spin polarization indicates that the transport of polarized carriers in the semiconductor ZnO is very efficient in our films.
We focus on the electron transport properties in different regimes. We begin by discussing the intermediate regime (tunneling regime). Figure 5a shows the temperature dependence of the resistivity of sample B, which attests to a semiconductor behavior. As shown in the inset of Figure 5a, from the ln ρ vs T−1/2 plot, it can been seen that ln ρ is almost linear to T−1/2, which is a typical characteristic of interparticle spin-dependent tunneling in metal/insulator granular films [25, 26]. To investigate the transport mechanism further, we convert the temperature dependence of resistivity to the temperature dependence of conductivity (G), as shown in Figure 5b. The data were normalized to the conductivity at T = 5 K. For T < 130 K, the interparticle tunneling conductivity of sample B as a function of temperature can be fitted well by the following equation [23, 27]:
where Gtun is the tunneling conductivity, G0 is a free parameter, Δ = 4E/k
, E is the tunneling activation energy, and k
is the Boltzmann constant. That is, the ZnO matrix behaves as a tunneling barrier between Co nanoparticles, and the MR effect originates from interparticle spin-dependent tunneling. When T > 130 K, the conductivity starts to deviate slightly from Equation 1. This phenomenon suggests that Gtun is not the only conduction mechanism at high temperature, which may result from the essential physics of the conductance in the presence of localized states within the ZnO matrix. A power-law temperature dependence of conductivity, which is a characteristic of higher-order inelastic hopping, can be used at high temperature to fit the experimental data of sample B. The expression is as follows :
where G0 and C are free parameters, γ = N − [ N/(N + 1)], N is the number of localized states in the barriers, and Ghop is the spin-independent higher-order inelastic hopping conductivity. Equation 2 fits our experimental data well with γ = 1.33 (N = 2) at high temperatures, as shown in Figure 5b. At high temperature, the conduction in sample B mainly contains two channels: the tunneling channel and the second-order hopping. The suppression of spin-dependent contribution to the conductance can result in a decrease in the MR at high temperature when a spin-independent channel (i.e., higher-order inelastic hopping) influences the conductivity.
Figure 5c shows the temperature dependence of the resistivity of sample C located in the hopping regime. At low temperatures, an almost temperature-independent tunneling regime is observed. The direct tunneling may represent an important contribution to the total conductance at low temperature, which is similar to the result reported by de Moraes et al. . Figure 5d shows the temperature dependence of the conductivity of sample C and the curve fitted by Equation 2. It is obvious that not only the second-order hopping (γ = 1.33) but also the third-order hopping (γ = 2.5) and fourth-order hopping (γ = 3.6) evidently become non-negligible because a thicker ZnO barrier results in spin-independent higher-order inelastic hopping (see Figure 3c). In order to compare the fitting results of the tunneling and hopping regimes, the resulting parameters fitted by Equation 2 for samples B and C are given in Table 1. It can be seen that the number of localized states of sample C (N = 4) increases as compared to sample B (N = 2). Consequently, a much higher-order hopping gradually prevails during the transition from the tunneling regime to the hopping regime, which apparently suppresses the MR effect at RT (shown in Figure 1). Also, the tunneling activation energy (E) estimated from Δ is 1.64 meV for sample B. With the ZnO content increasing, the value appreciably increases to 44.3 meV due to smaller Co particles and thicker ZnO barriers between Co particles, which consists with the decrease of MR effect in the hopping regime with more defects.
For sample A, the resistivity as a function of temperature is shown in Figure 5e. Although the temperature coefficient of resistivity is negative below RT, the temperature dependence of resistivity between sample A and the others exhibits evident differences. The resistivity increases gradually with decreasing temperature and varies slightly from 0.0093 Ω · cm (T = 300 K) to 0.011 Ω · cm (T = 5 K). Combined with the structure of sample A, the transport process is probably dominated by metallic paths because of the large number of interconnected elongated Co particles (see Figure 3a), which decreases when the resistivity increases, accompanying an increased MR effect. The approximate linear relationship between ρ and ln T for sample A is shown in Figure 5f. The fitting value of straight slope is shown in Table 1. The same phenomenon was reported in a CoO-coated monodispersive Co cluster system corresponding to a small negative MR value in a metal/semiconductor transition regime  and in the CoFeB/MgO films, in which the sample with high magnetic metal concentration is not in the strongly localized regime of conduction and the resistivity is plotted as a linear function of log(T) . Further detailed studies are necessary and in progress to elucidate the mechanism behind this result.