Role of dipolar and exchange interactions in the positions and widths of EPR transitions for the single-molecule magnets ${\mathrm{Fe}}_8$ and ${\mathrm{Mn}}_{12}$

We examine quantitatively the temperature dependence of the linewidths and line shifts in electron paramagnetic resonance experiments on single crystals of the single-molecule magnets ${\mathrm{Fe}}_8$ and ${\mathrm{Mn}}_{12},$ at fixed frequency, with an applied magnetic field along the easy axis. We include intermolecular spin-spin interactions (dipolar and exchange) and distributions in both the uniaxial anisotropy parameter D and the Landé g factor. The temperature dependence of the linewidths and the line shifts are mainly caused by the spin-spin interactions. For both ${\mathrm{Fe}}_8$ and ${\mathrm{Mn}}_{12},$ the temperature dependence of the calculated line shifts and linewidths agrees well with the trends of the experimental data. The linewidths for ${\mathrm{Fe}}_8$ reveal a stronger temperature dependence than those for ${\mathrm{Mn}}_{12},$ because for ${\mathrm{Mn}}_{12}$ a much wider distribution in D overshadows the temperature dependence of the spin-spin interactions. For ${\mathrm{Fe}}_8,$ the line-shift analysis suggests two competing interactions: a weak ferromagnetic exchange coupling between neighboring molecules and a longer-ranged dipolar interaction. This result could have implications for ordering in ${\mathrm{Fe}}_8$ at low temperatures.