Role of dipolar and exchange interactions in the positions and widths of EPR transitions for the single-molecule magnets Fe8 and Mn12

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 Fe$_8$ and Mn$_{12}$, at fixed frequency, with an applied magnetic field along the easy axis. We include inter-molecular spin-spin interactions (dipolar and exchange) and distributions in both the uniaxial anisotropy parameter $D$ and the Land\'{e} $g$-factor. The temperature dependence of the linewidths and the line shifts are mainly caused by the spin-spin interactions. For Fe$_8$ and Mn$_{12}$, the temperature dependence of the calculated line shifts and linewidths agrees well with the trends of the experimental data. The linewidths for Fe$_8$ reveal a stronger temperature dependence than those for Mn$_{12}$, because for Mn$_{12}$ a much wider distribution in $D$ overshadows the temperature dependence of the spin-spin interactions. For 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 Fe$_8$ at low temperatures.