Anomalous behavior of the tunneling magnetoresistance in (CoFeB)$_x$(LiNbO$_3$)$_{100-x}$/Si nanocomposite film structures below the percolation threshold: manifestations of the cotunneling and exchange effects

A strongly nonmonotonic temperature dependence of the magnetoresistance in (CoFeB)$_x$(LiNbO$_3$)$_{100-x}$ film nanocomposites ($x= 40$–$48$ at $\%$) is observed in the temperature range of $3$–$250$ K at the magnetic field up to $14$ T near the percolation threshold on its insulating side. The magnetoresistance has a minimum at $40$ K and increases steeply on cooling. Such behavior of the magnetoresistance is attributed to the coexistence of superferromagnetic regions with exchange-coupled granules separated by regions with superparamagnetic granules in the nanocomposite. In this case, an increase in the negative magnetoresistance at $T>40$ K is due to the destruction of superferromagnetic ordering, whereas an increase in the magnetoresistance at $T<40$ K is related to the processes involving simultaneous elastic tunneling via the chains of granules. At the saturation of the magnetization, an additional negative contribution arises, which is probably due to the quantum interference effects. At $T<4$ K, a double-well shape of the field dependence of the magnetoresistance is observed, which could be attributed to the effect of a positive contribution that competes with the negative magnetoresistance.