Complex investigations of thermal and magnetic properties of polycrystalline samples of diluted ferrimagnetic spinels Li0.5Fe2.5–xGaxO4 with a concentration x=0.9 and 1.0 of nonmagnetic Ga3+ ions show that at the initial concentration stage of the formation of spin-glass (SG)-type disordered states, when nonzero spontaneous magnetization for longitudinal spin components coexists with long-range SG order for transverse components, the low-energy excitations are spin waves with a quadratic energy-momentum relation and are responsible for the violation of the long-range SG order at the freezing temperature Tf. The existence of an uncorrelated disorder in the magnetic subsystem at T>Tf leads to the emergence of other types of modes (in addition to the spin waves) in the excitation spectrum. This is manifested in the form of peaks on the temperature dependences of the magnetic contributions to the heat capacity.

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