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Progress of Theoretical Physics

Linear Classical Spin Chain with Nearest, Next-Nearest Neighbor and Spin-Lattice Interactions

Akihide Oguchi, Y. Tsuchida

Published Dec 1, 1976• 4 citations
Publisher
DOI
10.1143/ptp.56.1976

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Loss of classicality in alternating Spin Chain, in the presence of next-neighbor couplings and Dzyaloshinskii-Moriya interactions

Abhiroop Lahiri, Swapan Kumar Pati

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.

•Oct 13, 2020•0 citations
We have considered and alternating Heisenberg spin chain with nearest-neighbor (J1J_1J1​), next-nearest neighbor (J2J_2J2​) antiferromagnetic couplings along with z-component of the Dzyaloshinskii-Moriya(DM) (DzD_zDz​) 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 J2J_2J2​ 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 J1J_1J1​ along with DzD_zDz​ introduces a short range order but develops long range order along the XY plane. J1J_1J1​ along with J2J_2J2​ 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 DzD_zDz​ term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.