Dysprosium, one of the most magnetic atoms in the periodic table, forms unusual states of matter at ultralow temperatures, such as quantum droplets and supersolids. So far, these experiments have been limited to a single spin state, because dipolar relaxation destroys mixtures. Using spin-dependent light shifts, our team has recently produced the first long-lived mixtures of the |−8⟩ and |+8⟩ states of ¹⁶²Dy, whose magnetic moments are exactly antiparallel. Theory predicts that such a mixture forms a self-bound crystal of alternating magnetic domains, held together by their dipolar attraction, much like an ionic crystal. This internship, followed by a PhD thesis, will focus on spin-dependent imaging, the measurement of the scattering length between |−8⟩ and |+8⟩, and the cooling of potassium. Potassium, which interacts differently with the two spin states, should act back on this crystal. Moreover, it will open up other directions, such as the stabilization of Efimov trimers a long-term goal of this experiment.