Scaling of nonlinear susceptibilities in an artificial permalloy honeycomb lattice

Two-dimensional artificial magnetic honeycomb lattice is predicted to manifest several magnetic phase transitions as a function of reducing temperature. We have performed the analysis of nonlinear susceptibility to explore the equilibrium nature of phase transition in artificial honeycomb lattice of ultrasmall connected permalloy (${\mathrm{Ni}}_0.81{\mathrm{Fe}}_0.19$) elements, typical length of $\ensuremath{\simeq}12$ nm. The nonlinear susceptibility ${\ensuremath{\chi}}_n1$ is found to exhibit an unusual crossover character in both temperature and magnetic field. The higher order susceptibility ${\ensuremath{\chi}}₃$ changes from positive to negative as the system traverses through the spin solid phase transition at ${T}_s=29$ K. Additionally, the static critical exponents, used to test the scaling of ${\ensuremath{\chi}}_n1$, do not follow the conventional scaling relation. We conclude that the magnetic phase transition, especially to the low temperature spin solid order, is not conventional in nature at this length scale.