Tunneling magnetoresistance in $\mathrm{Co}\text{−}{\mathrm{ZrO}}_2$ granular thin films

Granular films composed of well defined nanometric Co particles embedded in an insulating ${\mathrm{ZrO}}_2$ matrix were prepared by pulsed laser depositon in a wide range of Co volume concentrations $(0.15<x<0.43)$. High-resolution transmission electron microscopy (TEM) showed very sharp interfaces between the crystalline particles and the amorphous matrix. Narrow particle size distributions were determined from TEM and by fitting the low-field magnetic susceptibility and isothermal magnetization in the paramagnetic regime to a distribution of Langevin functions. The magnetic particle size varies little for Co volume concentrations $x<0.32$ and increases as the percolation limit is approached. The tunneling magnetoresistance (TMR) was successfully reproduced using the Inoue-Maekawa model. The maximum value of TMR was temperature-independent within 50–300 K, and largely increased at low $T$, suggesting the occurrence of higher-order tunneling processes. Consequently, the tunneling conductance and TMR in clean granular metals are dominated by the Coulomb gap and the inherent particle size distribution.

Figure 1

TEM images of $\mathrm{Co}\text{−}{\mathrm{ZrO}}_2$ granular films with $x=0.20$. Left-hand-side inset shows the magnification of one particle. Right-hand-side inset shows the histogram of the size distribution obtained from the TEM micrograph. The solid line is the fit to a logarithmic-linear distribution.

Figure 2

Temperature dependence of the ZFC and FC magnetization of films with various Co concentrations (circles). Solid lines are the fits of ZFC curves to a distribution of Langevin functions, given by Eq. (1).

Figure 3

(a) Field dependence of magnetization at different temperatures of films with various Co concentrations (circles). (b) Magnetization as a function of the reduced field $H∕T$. The solid lines represent the fits to Eq. (2).

Figure 4

(a) Magnetoresistance and (c) magnetization of a $\mathrm{Co}\text{−}{\mathrm{ZrO}}_2$ sample with $x=0.34$ at 10 K. (b) and (d) shows the low-field behavior.

Figure 5

(a)–(c) Field dependence of magnetoresistance at different temperatures of films with several Co concentrations (circles). (d), (e) Same data plotted as a function of $H∕T$. Solid lines are fits to Eq. (3).

Figure 6

Temperature dependence of the magnetoresistance of $\mathrm{Co}\text{−}{\mathrm{ZrO}}_2$ film with $x=0.37$ (circles). The solid line is the fit to Eq. (4).