Magnon-polaron formation in XXZ quantum Heisenberg chains

TL;DR

This paper investigates the formation of magnon-polaron excitations in XXZ quantum Heisenberg chains with magnetoelastic coupling, revealing critical interaction thresholds and the influence of different time scales on hybridized states.

Contribution

It introduces an original framework for hybridized magnon-polaron states in 1D chains considering vibrational degrees of freedom and magnetoelastic coupling.

Findings

Identification of a critical magnetoelastic interaction strength ($$) for stationary magnon-polaron formation.

Demonstration of how different time scales between magnon and lattice dynamics affect the regimes of magnon-polaron formation.

Discovery of a limiting magnetoelastic interaction value where magnon velocity becomes independent of coupling.

Abstract

We study the formation of magnon-polaron excitations and the consequences of different time scales between the magnon and lattice dynamics. The spin-spin interactions along the 1D lattice are ruled by a Heisenberg Hamiltonian in the anisotropic form XXZ, in which each spin exhibits a vibrational degree of freedom around its equilibrium position. By considering a magnetoelastic coupling as a linear function of the relative displacement between nearest-neighbor spins, results provide an original framework for achieving a hybridized state of magnon-polaron. Such state is characterized by high cooperation between the underlying excitations, where the traveling or stationary formation of magnon-polaron depends on the effective magnetoelastic coupling. A systematic investigation reveals the critical amount of the magnon-lattice interaction ($\chi_c$) necessary to emergence of the stationary magnon-polaron quasi-particle. Different characteristic time scales of the magnon and the vibrational dynamics unveiled the threshold between the two regimes, as well as a limiting value of critical magnetoelastic interaction, above which the magnon velocity no longer interferes at the critical magnetoelastic coupling capable of inducing the stationary regime.