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Quasi-2D $J_1$-$J_2$ Antiferromagnet $Zn_2VO(PO_4)_2$ and its $Ti$-substituted Derivative - A Spin-wave Analysis

In this study, we present non-linear spin wave analysis of a quasi 2D spin-$\frac{1}{2}$ $J_1-J_2$ antiferromagnet at the parameter regime relevant for the recently studied compound $Zn_2VO(PO_4)_2$. We obtain the temperature dependence of the spin wave energy, susceptibility and magnetization using Green's function technique and Hartree-Fock factorization or Tyablikov's decoupling approximation. The comparison of our numerical results with the experimental findings is discussed. Magnetic structure factor is calculated and compared with powder neutron diffraction data. We also study the spin wave behavior of the compound $Zn_2Ti_{0.25}V_{0.75}O(PO_4)_2$ obtained by partial chemical substitution of $Ti$ at $V$ sites of the compound $Zn_2VO(PO_4)_2$ (Phys. Rev. B87, 054431). Due to the superlattice structure of the spin lattice, the substituted compound possess multiple spin wave modes. The spin wave analysis confirms the quasi-1D nature of the substituted system.