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Two-dimensional artificial magnetic honeycomb lattice is at the forefront ofresearch on unconventional magnetic materials. Among the many emergent magneticphases that are predicted to arise as a function of temperature, the lowtemperature spin solid phase with zero magnetization and entropy is of specialimportance. Here, we report an interesting perspective to the consequence ofspin solid order in an artificial honeycomb lattice of ultra-small connectedelements using electrical dimensionality analysis. At low temperature, $T \leq$30 K, the system exhibits a very strong insulating characteristic. Theelectrical dimensionality analysis of the experimental data reveals afractional dimensionality of $d$ = 0.6(0.04) in the spin solid phase ofhoneycomb lattice at low temperature. The much smaller electrical dimension inthe spin solid phase, perhaps, underscores the strong insulating behavior inthis system. Also, the fractional dimensionality in an otherwisetwo-dimensional system suggests a non-surface-like electrical transport at lowtemperature in an artificial honeycomb lattice.

Fractional electrical dimensionality in the spin solid phase of artificial honeycomb lattice