  Co3V2O8 is an orthorhombic magnet in which S=3/2 magnetic moments reside on
two crystallographically inequivalent Co2+ sites, which decorate a stacked,
buckled version of the two dimensional kagome lattice, the stacked kagome
staircase. The magnetic interactions between the Co2+ moments in this structure
lead to a complex magnetic phase diagram at low temperature, wherein it
exhibits a series of five transitions below 11 K that ultimately culminate in a
simple ferromagnetic ground state below T~6.2 K. Here we report magnetization
measurements on single and polycrystalline samples of (Co(1-x)Mg(x))3V2O8 for
x<0.23, as well as elastic and inelastic neutron scattering measurements on
single crystals of magnetically dilute (Co(1-x)Mg(x))3V2O8 for x=0.029 and
x=0.194, in which non-magnetic Mg2+ ions substitute for magnetic Co2+. We find
that a dilution of 2.9% leads to a suppression of the ferromagnetic transition
temperature by ~15% while a dilution level of 19.4% is sufficient to destroy
ferromagnetic long-range order in this material down to a temperature of at
least 1.5 K. The magnetic excitation spectrum is characterized by two spin-wave
branches in the ordered phase for (Co(1-x)Mg(x))3V2O8 (x=0.029), similar to
that of the pure x=0 material, and by broad diffuse scattering at temperatures
below 10 K in (Co(1-x)Mg(x))3V2O8 (x=0.194). Such a strong dependence of the
transition temperatures to long range order in the presence of quenched
non-magnetic impurities is consistent with two-dimensional physics driving the
transitions. We further provide a simple percolation model that
semi-quantitatively explains the inability of this system to establish
long-range magnetic order at the unusually-low dilution levels which we observe
in our experiments.
