Quenched disorder may prevent the formation of the widely sought quantum spin-liquid states (QSLs) or mask their signatures by inducing a spin-glass state, which is why considerable experimental efforts are directed at purifying materials that may host QSLs. However, in geometrically frustrated (GF) magnets, the largest class of materials in which QSLs are sought, the glass-transition temperature $T_g$ grows with decreasing the density of vacancy defects, accompanied by a simultaneous growth of the magnetic susceptibility. In this Letter, we develop a phenomenological theory of glass transitions and magnetic susceptibility in three-dimensional geometrically frustrated magnetic materials. We consider a model of a GF magnet in which the glass transition occurs in the absence of vacancies, e.g., due to other types of quenched disorder. We show that disorder that creates weak local perturbations, e.g., weak random strain, leads to the growth of the transition temperature $T_g$. By contrast, vacancies reduce $T_g$ for small vacancy concentrations. Another consequence of the presence of vacancies is the creation of quasispins, effective magnetic moments localized near the vacancies, that contribute to the magnetic susceptibility of the system together with the bulk spins. We show that increasing the vacancy density leads to an increase of the total magnetic susceptibility.

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• Frustrated magnetism
• Mesoscopics
• Quantum spin liquid
• Disordered systems
• Spin ice