Fe 1Àx Rh x layers are grown with varying rhodium fraction x on (001)-oriented MgO substrates by molecular-beam epitaxy. Film structural, morphological, magnetic, and transport properties are investigated. At room temperature, layers are ferromagnetic (FM) for x < 0.48 and antiferromagnetic (AF) for x > 0.48. Separating the two magnetically ordered phases at x ¼ 0.48 is an abrupt change in the Fe 1Àx Rh x lattice parameter of Da ¼ 0.0028 nm (Da/a ¼ À0.9%). For AF layers, the FM state is recovered by heating across a first-order phase transition. The transition leads to a large resistivity modulation, Dq/q ¼ 80%, over a narrow temperature range, DT ¼ 3 K, in stoichiometric Fe 0.50 Rh 0.50 /MgO(001). For samples with compositions deviating from x ¼ 0.50, fluctuations broaden DT and defect scattering reduces Dq/q.