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Co3V2O8 is an orthorhombic magnet in which S=3/2 magnetic moments reside ontwo crystallographically inequivalent Co2+ sites, which decorate a stacked,buckled version of the two dimensional kagome lattice, the stacked kagomestaircase. The magnetic interactions between the Co2+ moments in this structurelead to a complex magnetic phase diagram at low temperature, wherein itexhibits a series of five transitions below 11 K that ultimately culminate in asimple ferromagnetic ground state below T~6.2 K. Here we report magnetizationmeasurements on single and polycrystalline samples of (Co(1-x)Mg(x))3V2O8 forx<0.23, as well as elastic and inelastic neutron scattering measurements onsingle crystals of magnetically dilute (Co(1-x)Mg(x))3V2O8 for x=0.029 andx=0.194, in which non-magnetic Mg2+ ions substitute for magnetic Co2+. We findthat a dilution of 2.9% leads to a suppression of the ferromagnetic transitiontemperature by ~15% while a dilution level of 19.4% is sufficient to destroyferromagnetic long-range order in this material down to a temperature of atleast 1.5 K. The magnetic excitation spectrum is characterized by two spin-wavebranches in the ordered phase for (Co(1-x)Mg(x))3V2O8 (x=0.029), similar tothat of the pure x=0 material, and by broad diffuse scattering at temperaturesbelow 10 K in (Co(1-x)Mg(x))3V2O8 (x=0.194). Such a strong dependence of thetransition temperatures to long range order in the presence of quenchednon-magnetic impurities is consistent with two-dimensional physics driving thetransitions. We further provide a simple percolation model thatsemi-quantitatively explains the inability of this system to establishlong-range magnetic order at the unusually-low dilution levels which we observein our experiments.

Magnetic Order and Fluctuations in the Presence of Quenched Disorder in the Kagome Staircase System (Co(1-x)Mg(x))3V2O8