Phase diagram of pressure-induced superconductor $\beta $-(BDA-TTP)$_{2}$\textit{MX}$_{4}$ ($M$=Fe, Ga and $X$=Cl, Br) with localized magnetic moments

We have investigated transport and magnetization properties of $\beta $-(BDA-TTP)$_{2}$\textit{MX}$_{4}$ ($M$=Fe, Ga and $X$=Cl, Br) as a function of pressure, temperature and magnetic field. The title material undergoes metal-insulator transitions above 100 K at ambient pressure. The insulating phase is suppressed with pressure and superconductivity eventually appears above $P_{c}$= 4.5 kbar ($X$=Cl) and 13 kbar ($X$=Br). The general temperature-pressure (\textit{TP}) phase diagram is similar each other, while higher pressure is required for $X$=Br compounds to suppress the insulating state and induce the superconductivity. Pressure dependent DC magnetization studies on $\beta $-(BDA-TTP)$_{2}$FeCl$_{4}$ compound revealed that the AFM ordering persist well above $P_{c}$. In spite of similarity of phase diagram between $M$=Fe and $M$=Ga compounds, magnetoresistance results show distinct behaviors, which indicates the magnetic interaction with the conduction electrons are still effective. The comparison between $X$=Cl and $X$=Br compounds suggests the anion-size effect rather than the existence of localized magnetic moments plays more important role in determining the ground state.