Spin liquid state in the three dimensional pyrochlore-like frustrated magnet MgCrGaO <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>4</mml:mn>

The three-dimensional frustrated spin lattice in MgCrGaO4, where Cr3+ ions occupy a pyrochlore-like network, exemplifies a quantum magnet with competing interactions, macroscopic degeneracy, and exotic low-energy excitations. Using thermodynamic, electron spin resonance (ESR), muon spin relaxation (muSR), and inelastic neutron scattering (INS) techniques, we observe no magnetic order or spin freezing down to 57 mK, despite a sizable exchange interaction (J= 58 K) between Cr3+ (S=3/2) moments and inherent site disorder. Below the characteristic exchange energy scale, all experimental probes detect the emergence of antiferromagnetic short-range spin correlations, corroborated by magnetic diffuse scattering in the wave vector dependence of low-energy magnetic excitations centered on Q = 1.5 A^-1 in inelastic neutron scattering experiments. The low-temperature specific heat follows a near-quadratic dependence without a gap, consistent with algebraic spin correlations. These results establish MgCrGaO4 as a rare three-dimensional classical spin liquid featuring a highly degenerate ground-state manifold and gapless excitations, offering a strong impetus for the experimental realization of spin liquids in higher-dimensional frustrated quantum magnets.