Dynamic spin Jahn-Teller effect in small magnetic clusters

Abstract

We study the effect of spin-phonon coupling in small magnetic clusters, concentrating on a S=1/2 ring of 4 spins coupled antiferromagnetically. If the phonons are treated as classical variables, there is a critical value of the spin-phonon coupling above which a static distortion occurs. This is a good approximation if the zero point energy is small compared to the energy gain due to the distortion, which is true for large exchange interactions compared to the phonons energy ($J\gg \hslash \omega$). In the opposite limit, one can integrate out the phonon degrees of freedom and get an effective spin hamiltonian. Using exact diagonalizations to include the quantum nature of both spins and phonons, we obtain the spectrum in the whole range of parameters and explicit the crossover between the classical and quantum regimes. We then establish quantitatively the limits of validity of two widely used approaches (one in the quantum and one in the classical limits) and show that they are quite poor for small magnetic clusters. We also show that upon reducing $\hslash \omega /J$ the first excitation of a 4-site cluster becomes a singlet, a result that could be relevant for Cu${}_2$Te${}_2$O${}_5$Br${}_2$.

References in corpus (11)

• Phase diagram of a Heisenberg spin-Peierls model with quantum phonons
• Evidence for an unconventional magnetic instability in the spin-tetrahedra system Cu_2Te_2O_5Br_2
• Effective Spin Models for Spin-Phonon Chains by Flow Equations
• Peierls-like transition induced by frustration in a two-dimensional antiferromagnet
• Peierls Dimerization with Non-Adiabatic Spin-Phonon Coupling
• Longitudinal magnon in the tetrahedral spin system Cu2Te2O5Br2 near quantum criticality
• Incommensurate magnetic ordering in $C{u}_{2}T{e}_2{O}_5{X}_2$ (X=Cl,Br) studied by neutron diffraction
• Dynamical properties of low dimensional CuGeO3 and NaV2O5 systems
• Weak antiferromagnetism and dimer order in quantum systems of coupled tetrahedra
• Magneto-elastic instability in Molecular Antiferromagnetic Rings
• Quantum mechanics on Riemannian Manifold in Schwinger's Quantization Approach I

Cited by in corpus (2)

• Spin-phonon interaction induces tunnel splitting in single-molecule magnets
• Field-induced level crossings in spin clusters: Thermodynamics and magneto-elastic instability