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We present the experimental phase diagram of LiHo$_x$Er$_{1-x}$F$_4$, adilution series of dipolar-coupled model magnets.The phase diagram wasdetermined using a combination of AC susceptibility and neutron scattering.Three unique phases in addition to the Ising ferromagnet LiHoF$_4$ and the XYanti-ferromagnet LiErF$_4$ have been identified. Below $x=0.86$ an embeddedspin-glass phase is observed, where a spin-glass exists within theferromagnetic structure. Below $x=0.57$ an Ising spin-glass is observedconsisting of frozen needle-like clusters. For $x \sim 0.3 - 0.1$ anantiferromagnetically coupled spin-glass occurs. A reduction of $T_C(x)$ forthe ferromagnet is observed which disobeys the mean-field predictions thatworked for LiHo$_x$Y$_{1-x}$F$_4$.

Phase diagram with enhanced spin-glass region of mixed Ising / XY magnets LiHo$_{x}$Er$_{1-x}$F$_{4}$