Frustrated magnets often exhibit exotic spin correlations that defy conventional descriptions. A prominent example is the emergent molecular-like excitations discovered in a broad family of frustrated pyrochlore-lattice compounds. In these materials, despite the existence of a magnetic long-range order, spin dynamics is dominated by resonant-like excitations rather than dispersive spin wave excitations, and the structural factors of the resonant modes resemble those of free molecules (see e.g. Nature 2002, PRL 2013, PRL 2014, and PRL 2021). Although recent studies of the short-range spin correlations in MgCr2O4 casts doubt on the molecular picture, the proposed Heisenberg spin model only works in the paramagnetic regime and fails to explain the exotic excitations in the ordered regime. Therefore, in spite of two decades’ intensive research, the origin of the molecular-like excitations in frustrated pyrochlores still remains an open question.

The key to understand the emergent molecular-like excitations in frustrated pyrochlores may lie in the spin-lattice coupling. The importance of the lattice degree of freedom was first established through the analysis of the half-magnetization plateau that is often observed in this family of compounds (see e.g. PRL 2002 and PRL 2004). Assuming independent displacements of magnetic atoms and distance-dependent exchange strengths, a site-phonon model has been developed (PRB 2006 and PRL 2008). In this model, the spin-lattice coupling, after integrating out the lattice degree of freedom, leads to effective four-spin interactions. Recent classical Monte Carlo simulations for the site-phonon model on a pyrochlore lattice revealed the emergence of rich static orders as a function of the strength of the spin-lattice coupling (PRL 2016 and PRB 2019). In the dynamical regime, however, knowledge on the impacts of the spin-lattice coupling is still limited.

In our recent post, arXiv:2404.05523, we examine the spin dynamics of the site-phonon model on a pyrochlore lattice through an extended Landau-Lifshitz-Gilbert method under the random phase approximation. By adding a relatively weak spin-lattice coupling to the nearest-neighbor antiferromagnetic Heisenberg lattice model, we show that the site-phonon model provides an elegant yet encompassing explanation for the molecular-like dynamics in frustrated pyrochlores. Applications of this approach in both the long- and short-range ordered regimes are demonstrated for two model materials, MgCr2O4 and LiGaCr4O8, which represent the regular and breathing pyrochlore-lattice compounds, respectively. Based on our calculations, we conclude that the molecular excitations in frustrated pyrochlores are not real entities, but rather statistic approximations to dispersive spin wave excitations. The method demonstrated in our work, including the four-spin interactions that arise from the spin-lattice coupling, shall have broad applications in the magneto-elastic compounds beyond the frustrated pyrochlores.

This work utilizes JuliaMD.jl, a package developed in our lab for the calculations of spin dynamics in classical spin systems. This package is an implementation of the Landau-Lifshitz-Gilbert method, and works in both the long- and short-range ordered regimes.