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Resolving magnetic frustration in a pyrochlore lattice

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.