  CeFe$_2$ is a geometrically frustrated ferromagnet that lies close to an
instability at which a subtle change in the lattice symmetry couples to a
transition to antiferromagnetism. We use x-ray diffraction, diamond-anvil-cell
techniques, and numerical simulation to identify the ground states and to
quantitatively illustrate effects of competing magnetic energy scales and
geometrical frustration on the magnetic phase diagram. Comparison of phase
transitions under both chemical substitution and applied pressure suggests a
general solution to the physics of pyrochlore rare earth inter-metallic
magnets.
