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In this study, we present non-linear spin wave analysis of a quasi 2Dspin-$\frac{1}{2}$ $J_1-J_2$ antiferromagnet at the parameter regime relevantfor the recently studied compound $Zn_2VO(PO_4)_2$. We obtain the temperaturedependence of the spin wave energy, susceptibility and magnetization usingGreen's function technique and Hartree-Fock factorization or Tyablikov'sdecoupling approximation. The comparison of our numerical results with theexperimental findings is discussed. Magnetic structure factor is calculated andcompared with powder neutron diffraction data. We also study the spin wavebehavior of the compound $Zn_2Ti_{0.25}V_{0.75}O(PO_4)_2$ obtained by partialchemical 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 spinlattice, the substituted compound possess multiple spin wave modes. The spinwave analysis confirms the quasi-1D nature of the substituted system.

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