Interchain interaction effect on the magnetic properties of azurite material

Considering the interchain exchange interaction through dimer and monomer in the azurite, a two-dimensional Ising-Heisenberg model with dimer and monomer interlacing arrangement is established, and the magnetic and thermodynamic properties are calculated by Monte Carlo method. In the ground state, as the magnetic field increases from zero, the system changes from quantum antiferromagnetic (QAF) state with monomer in antiferromagnetic state and dimer in spin singlet to the quantum ferrimagnetism (QFI) state with monomer in saturated state and dimer in spin singlet, and finally reaches the saturated spin state (SP). In the QFI state, system shows 1/3 magnetization plateau. Starting from the QAF phase closing to the boundary with QFI phase, the specific heat and magnetic susceptibility of the system with temperature show beaks in the low temperature region, corresponding phase change, and in the whole range of temperature they may present double peak structure. Starting from the two phases of QFI and SP near the boundary between them, the magnetic susceptibility and specific heat with temperature also show peak, and the corresponding phase transition temperature is symmetry with respect to the phase boundary. Comparing with the specific heat data in the experiment, we conjecture the strength of the interchain interaction of azurite material is about half of the dimer interaction.