Loss of classicality in alternating spin-$\frac{1}{2}$/spin-$1$ chain, in the presence of next-neighbor couplings and Dzyaloshinskii-Moriya interactions

Abstract: We have considered and alternating Heisenberg spin chain with nearest-neighbor ($J_1$), next-nearest neighbor ($J_2$) antiferromagnetic couplings along with z-component of the Dzyaloshinskii-Moriya(DM) ($D_z$) interactions. The Hamiltonian has been studied using (a) Linear Spin-Wave Theory(LSWT) and (b) Density Matrix Renormalization Group (DMRG). The system had been reported earlier as a classical ferrimagnet only when nearest neighbor exchange interactions are present. Both the antiferromagnetic next-nearest neighbor interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero $J_2$ introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of $J_1$ along with $D_z$ introduces a short range order but develops long range order along the XY plane. $J_1$ along with $J_2$ induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the $D_z$ term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.