Pressure-driven transitions in the double perovskite ${\mathrm{La}}_2{\mathrm{CoTiO}}_6$: Antiferromagnetic insulator to nonmagnetic metal via antiferromagnetic metal in a double perovskite oxide

In double perovskite oxides ($A_2{BB}^{\prime }{O}_6$), magnetism often arises from diluted magnetic lattices, created by combining a perovskite structure with localized $3d$ magnetic elements ($B$) alongside another perovskite lattice containing nearly nonmagnetic delocalized $4d/5d$ elements ($B^{\prime }$). Alternatively, the magnetic lattice can consist entirely of $3d$ elements, with one being completely nonmagnetic with a $d^0$ state. ${\mathrm{La}}_2{\mathrm{CoTiO}}_6$ (LCTO), a representative double perovskite oxide, contains Ti in a nonmagnetic state with a $d^0$ electron configuration due to its $4^{+}$ oxidation state. Experimental evidence shows that LCTO possesses a monoclinic structure (space group $P{2}_1/n$) and behaves as an antiferromagnet with a Néel temperature of 14.6 K. Through first-principles electronic structure calculations, we uncover that adjusting external hydrostatic pressure induces a sequence of phase transitions: from antiferromagnetic insulator (AFM-I) to antiferromagnetic metal (AFM-M), and ultimately to itinerant nonmagnetic metal (NM-M). The transition from AFM-I to AFM-M at $\sim 42$ GPa pressure coincides with a shift in spin states, moving from a high-spin (HS) state to a low-spin (LS) state, while Co retains a $d^7$ configuration. Distortion within the monoclinic structure under pressure plays a pivotal role in the spin-state transition. At the AFM-I to AFM-M transition, we observe a sharp decrease in the ratio of the octahedral volumes occupied by Co and Ti. Such change in ratio is linked to variations in octahedral volumes, akin to a breathing mode distortion. We explore the impact of the breathing mode distortion by examining a highly symmetric theoretical structure (space group $I4/mmm$), achieved by optimizing the structure with all $\angle$ Co-O-Ti angles set to ${180}^{\circ }$. Remarkably, the LS state in the LCTO theoretical structure persists under ambient pressure conditions, underscoring the unique role of breathing mode distortion in the monoclinic phase, facilitating the HS to LS transition under pressure. In the LS state, LCTO displays metallic behavior, even with a substantial local correlation (Hubbard $U$) on Co, as large as $U$ = 6 eV. The spin-state transition is further elucidated through an energy level diagram, illustrating a significant modification in the crystal field splitting between Co-$t_{2g}$ and Co-$e_g$ levels, driven by the robust hybridization of Co-$d$ and O-$p$ orbitals. Finally, with a further increase in pressure, the system attains the NM-M phase at $\sim 130$ GPa, leading to the complete suppression of the magnetic moment on Co.