Magnetic order and fluctuations in the presence of quenched disorder in the kagome staircase system (Co _1-xMg _x) ₃V ₂O ₈

Co ₃V ₂O ₈ 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 11K that ultimately culminate in a ferromagnetic ground state below T∼6.2 K. Here we report magnetization measurements on single- and polycrystalline samples of (Co _1-xMg _x) ₃V ₂O ₈ for x<0.23, as well as elastic and inelastic neutron scattering measurements on single crystals of magnetically dilute (Co _1-xMg _x) ₃V ₂O ₈ for x=0.029 and x=0.194, in which nonmagnetic 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-xMg _x) ₃V ₂O ₈ (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-xMg _x) ₃V ₂O ₈ (x=0.194). Such a strong dependence of the transition temperatures on long-range order in the presence of quenched nonmagnetic impurities is consistent with two-dimensional physics driving the transitions. We further provide a simple percolation model that semiquantitatively explains the inability of this system to establish long-range magnetic order at the unusually low dilution levels which we observe in our experiments.