Transition to disordered phase and spin dynamics in the two-dimensional ferrimagnetic model

Highlights: • The spectral function S(q, $\omega$) is studied at T = 0 K. • The AC spin conductivity evaluated in the neighborhood of QTP transition. • There is an influence of the transition to disorder paramagnetic phase on AC conductivity. • The AC spin conductivity tends to zero in the DC limit and the Drude's weight is zero indicating an insulator DC spin transport. The effect of transition to disordered phase on AC conductivity in the two-dimensional frustrated ferrimagnetic model in the square lattice at $T=0$ is investigated. The spin conductivity, ${\sigma }^{\mathrm{reg}}\left(\omega \right)$ is determined for different values of frustration parameters $J_{2S}$ and $J_{2s}$ that separates the different phases such as the ferrimagnetic phase and the collinear phase. We obtain a small influence of this phase transition on spin conductivity. Furthermore, we present the behavior of the half-width of $S(\overrightarrow{q},\omega )$ that gives the information about the scattering of magnons at long wavelength range.