Magnetic and electronic properties of the recently discovered material Sr₈CaRe₃Cu₄O₂₄ are investigated by means of the quantum Monte Carlo method and the LSDA+U method. Based on the LSDA+U calculation, we show that the ground state is an insulator with magnetic moment 1.01μ_B, which is consistent with experimental results. Further, we specify magnetic sites and derive an effective model for the magnetic properties of this material. The resultant effective model is a three-dimensional Heisenberg model with spin-alternation. Cu sites with spin 1 (Cu1) form a cubic lattice, and Cu sites with spin 1/2 (Cu2) are located between them, where neighboring spins are coupled antiferromagnetically. Finite-temperature properties of this effective model are investigated by the quantum Monte Carlo method (continuous-time loop algorithm). Our numerical results are consistent with experimental results, indicating that the effective model is suitable for this material. Through the analysis of the effective model, we make some predictions for this material.

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