Research On The Magnetic Properties Of Ba(TiO)Cu₄(PO₄)₄ Materials

By using linear spin wave approximation,we study a spin model proposed to describe a synthesized two-dimensional magnetic materials Ba(TiO)Cu4(PO4)4.In these magnets,the asymmetric Dzyaloshinsky-Moriya(DM)interactions play a key role for their anomalous properties.In our work,we focus on the effects of the DM interaction in these materials.We find that the spin-wave excitations depend strongly on the direction of the DM interaction.A nonzero in-plane component of DM interaction opens an excitation gap in spin-wave spectrum.However,the spin-wave spectrum is gapless if the DM interaction is along c-axis.We attribute the gapless model in the latter case to the spontaneous breaking of the global U(1)symmetry.In addition,based on linear spin wave approximation and Hellmann-Feynman theorem,we introduce a method to evaluate the critical magnetic field where the ground state transforms into a fully polarized ferromagnetism when a magnetic field is applied along c-axis.To confirm that we can get right results by using our method,we apply it to Ba(TiO)Cu4(PO4)4 and compare the results with numerical data.