Phase Diagrams of Finite Spin Chains with Coupled Spin and Lattice Vibrations

Abstract: The spin-lattice coupling is due to itinerant electrons interacting with both spins of ions and phonons, mediating a coupling between magnetic spin moments and lattice vibrations. In this project, the coupling is studied systematically for finite quantum spin chains of size 2 – 10. The coupling is included in a Hamiltonian model with the Heisenberg exchange interaction and an external magnetic field resulting in an eigenvalue problem which is solved numerically to find phase diagrams of the magnetic moment of the system depending on an external magneticfield and the lattice vibration parameter. The eigenvalue problem is also solved analytically for the 2-ion chain, dimer, and 3-ion chain, trimer, systems. Based on these phase diagrams two propositions are made: the effect of the coupling is larger than an external magnetic field and the behavior of the coupling converges to a common phase diagram for larger spin chains.