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