Structural and magnetic instabilities of layered magnetic systems

TL;DR

This paper investigates how spin-lattice interactions influence the structural and magnetic properties of two-dimensional quantum spin systems, revealing tendencies toward plaquette formation, coexistence of distortions with magnetic order, and phonon spectrum softening.

Contribution

It provides a comprehensive analysis of static and dynamic spin-lattice effects in 2D magnetic systems, highlighting the conditions for plaquette formation and lattice instabilities.

Findings

Plaquette formation is the most favorable static dimerization in square lattices.

Spin-phonon coupling reduces magnetic moments but does not eliminate magnetic order.

Zone boundary phonons soften significantly at low temperatures, indicating lattice instabilities.

Abstract

We present a study of the magnetic order and the structural stability of two-dimensional quantum spin systems in the presence of spin-lattice coupling. For a square lattice it is shown that the plaquette formation is the most favourable form of static two-dimensional dimerization. We also demonstrate that such distortions may coexist with long range magnetic order, in contrast to the one-dimensional case. Similarly, the coupling to Einstein phonons is found to reduce, but not to eliminate the staggered magnetic moment. In addition, we consider the renormalization of the square lattice phonon spectrum due to spin-phonon coupling in the adiabatic approximation. Towards low temperatures significant softening mainly of zone boundary phonons is found, especially around the $(\pi,0)$ point of the Brillouin zone. This result is compatible with the tendency to plaquette formation in the static limit. We also point out the importance of a "magnetic pressure" on the lattice due to spin-phonon coupling. At low temperatures, this results in a tendency towards shear instabilities of the lattice.