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We present outstanding infrared spectra of the active star $\epsilon$ Eridani (K2V) and two inactive reference stars, 40 Eridani (K1V) and $\sigma$ Draconis (K0V). The spectra are the result of 9 hours of observations per star with the IR FTS at the 4--m Mayall Telescope at Kitt Peak National Observatory. The noise is 0.5--1.0\% with an unapodized spectral resolution of 120,000. The wavelength range covered is 1.54-1.59 $\mu$m (6290--6490 ${\rm cm}^{-1}$) in air, which includes two dozen moderate strength lines, notably the Land\'e--$g=3$ line at 1.5649 $\mu$m. This line is a superior magnetic diagnostic because of its high Land\'e--g factor, long wavelength, and large depth of formation. The Zeeman sensitivity of this line is at least a factor of 2--3 times greater than any optical line.
We employ a polarized radiative tranfer code to simultaneously model the profiles of clean neutral iron lines in our infrared spectra and high quality optical spectra. The inactive stars are used to determine and check oscillator strengths and to assess the accuracy of our models. We then model $\epsilon$ Eridani both with and without a magnetic field. The observed wings of the magnetically sensitive 1.5649 $\mu$m line are clearly deeper than predicted by the $B=0$ model. No such discrepency is observed in the insensitive lines or in inactive stars. We then fit the $\epsilon$ Eridani profiles with various magnetic models. A model with depth independent magnetic fields yields a (preliminary) field strength of 1.9 kG covering 12\% of the stellar surface. We also consider the observable effects of magnetic fields that vary with depth or across the stellar surface.
