We have investigated the microwave response at 44.5 GHz with respect to temperature T and external magnetic field H in $\ensuremath{\lambda}\ensuremath{-}(\mathrm{BEDT}\ensuremath{-}\mathrm{TSF}{)}_{2}{\mathrm{FeCl}}_{4}$ forming a quasi two-dimensional electronic system with $\ensuremath{\pi}\ensuremath{-}d$ correlations. At 8.3 K $[{=T}_{\mathrm{MI}},$ the metal-insulator (MI) transition temperature] $<T<70\mathrm{K}$ ${(=T}_{\mathrm{FM}}),$ the microwave dielectric constant along the c axis, ${\ensuremath{\epsilon}}_{1}^{c},$ takes positive large values amounting to 1000--2000. Furthermore, the microwave conductivity ${\ensuremath{\sigma}}_{1}^{c}$ starts to deviate resistively from the dc conductivity ${\ensuremath{\sigma}}_{\mathrm{dc}}^{c},$ and the difference between ${\ensuremath{\sigma}}_{1}^{c}$ and ${\ensuremath{\sigma}}_{\mathrm{dc}}^{c}$ reaches about two orders of magnitude just above ${T}_{\mathrm{MI}}.$ The present results are consistent with the previous results at 16.3 GHz, and consequently the appearance of the anomalous metallic state is confirmed. An anomalous microwave response has also been observed in the ${a}^{*}$ and ${b}^{*}$ directions, and there exist large anisotropies depending sensitively on the orientations. The broad maximum of ${\ensuremath{\epsilon}}_{1}^{c}$ around 30 K is reminiscent not of a usual ferroelectric transition, but of relaxor ferroelectric behaviors. It is expected that dielectric domains or stripes with less metallic conductions emerge inhomogeneously in the $\ensuremath{\pi}$ electronic systems. Above ${T}_{\mathrm{FM}},$ where microwave anomalies are not present, the interplane and intraplane microwave conductivities hold anisotropies ${\ensuremath{\sigma}}_{1}^{c}/{\ensuremath{\sigma}}_{1}^{{b}^{*}}\ensuremath{\approx}{10}^{3}$ and ${\ensuremath{\sigma}}_{1}^{c}/{\ensuremath{\sigma}}_{1}^{{a}^{*}}\ensuremath{\approx}10.$ In the antiferromagnetic insulating state, ${\ensuremath{\sigma}}_{1}^{c}$ becomes much conductive in comparison with ${\ensuremath{\sigma}}_{\mathrm{dc}}^{c}.$ Together with low frequency data, ${\ensuremath{\epsilon}}_{1}^{c}$ is found to exhibit a large frequency dispersion. The microwave response is not attributed to single particle excitations, but to some collective mode excitations associated with charge degrees of freedom. The $H\ensuremath{-}T$ phase diagram of the MI transition determined by the present microwave measurements is independent of the orientations of H, and coincides well with the phase diagram obtained by the dc magnetoresistivity and magnetization. Spin waves for the hard axis are observed as an absorption peak in the width change for the microwave magnetic field applied parallel to both H and ${a}^{*}.$
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