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The spinels CoB$_2$O$_4$ with magnetic Co$^{2+}$ ions on the diamond latticeA site can be frustrated because of competing near-neighbor ($J_1$) andnext-near neighbor ($J_2$) interactions. Here we describe attempts to tune therelative strengths of these interactions by substitution on the non-magneticB-site. The system we employ is CoAl$_{2-x}$Ga$_x$O$_4$, where Al issystematically replaced by the larger Ga, ostensibly on the B site. Asexpected, Ga substitution expands the lattice, resulting in Co atoms on theA-site being pushed further from one other and thereby weakening magneticinteractions. In addition, Ga distributes between the B and the A site in aconcentration dependent manner displacing an increasing amount of Co from the Asite with increasing $x$. This increased inversion, which is confirmed byneutron diffraction studies carried out at room temperature, affects magneticordering very significantly, and changes the nature of the ground state.Modeling of the magnetic coupling illustrates the complexity that arises fromthe cation site disorder.

Tuning magnetic frustration on the diamond lattice of the A-site magnetic spinels CoAl$_{2-x}$Ga$_x$O$_4$: Lattice expansion and site disorder