Magnetic exchange interactions in the BaM₂Si₂O₇(M= Cu, Co, Mn) system

A quasi 1D system with weak exchange coupling between the magnetic chains will exhibit a crossover from 1D magnetic behavior at high temperatures to a 3D ordered state at low temperatures. The BaM₂Si₂O₇(M = Cu, Co, Mn) with layered structure is an excellent system to study low-dimensional magnetic behaviors. BaCu₂Si₂O₇ has an orthorhombic structure with CuO₄ plaquettes, while BaCo₂Si₂O₇ and BaMn₂Si₂O₇ have a monoclinic crystal structure with CoO₄ and MnO₄ tetrahedrons. We have performed local spin-density approximation with onsite Coulomb interaction (LSDA + U) calculations to study the exchange interactions. By computing the total energies of various magnetic configurations and mapping these energies to a Heisenberg model, we extract the magnetic exchange interactions in the three materials. We also discuss the relations between the magnetic exchange interactions with their crystal and electronic structures. In the end, we make comparisons with experimental studies such as single crystal neutron diffraction measurements.