Flux pinning and critical current density in $TiO_2$-doped $MgB_2$ superconductor

$MgB_2$ doped with $TiO_2$ was prepared by the in-situ solid state reaction to study the effects of $TiO_2$ dopant on the flux pinning behavior of $MgB_2$ superconductor. From the field-cooled and the zero-field-cooled temperature dependences of magnetization, the realms of vortex-glass and vortex-liquid states of $TiO_2$-doped $MgB_2$ were determined in the H-T diagram (the temperature dependence of upper critical magnetic field and irreversibility line). The critical current density was estimated from the width of hysteresis loops in the framework of Beam's model at different temperatures. The results indicate that nano-scale $TiO_2$ inclusions play a role of the effective pinning centers and lead to the enhanced upper critical field and critical current density. It is suggested that the grain-boundary pinning mechanism is realized in $TiO_2$-doped $MgB_2$ superconductor.