In the submonolayer regime, fullerene molecules tend to form compact islands on dense-packed metal surfaces. On Cu(111), these islands exhibit various types of corrugation patterns caused by a compressive epitaxial stress and an atomic-scale reconstruction of the metal surface. Following a strategy we introduced in a previous study [Phys. Rev. Lett. 131, 186201 (2023)], we use scanning tunneling microscopy to study molecule-molecule correlations in stripelike corrugation patterns that develop in ${\mathrm{C}}_{60}$ islands. Overall, these correlations are well described by a frustrated on-lattice Ising spin Hamiltonian that includes spin-spin interactions up to the third-nearest neighbor. Careful comparison between the measured and computed correlations allows us to distinguish molecular islands that exhibit a corrugation pattern typical of an equilibrated spin configuration from those that appear nonequilibrated. The statistical analysis performed both in real and reciprocal space confirms the relevance of using a frustrated spin Hamiltonian to characterize nontrivial molecular arrangements on surfaces.

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• Adsorption
• Frustrated magnetism
• Fullerenes
• Molecules
• Monolayer films
• Transition metals
• Scanning tunneling microscopy