We predict the occurrence of unexpected magnetic ground states in ultrathin Mn films due to the frustration of higher-order interactions. Based on density functional theory we show that significant chiral-chiral interactions occur in hexagonal Mn monolayers due to large topological orbital moments which interact with the emergent magnetic field. Due to the competition with biquadratic and four-spin interactions superposition states of spin spirals such as the $2Q$ state or a distorted $3Q$ state arise. Simulations of spin-polarized scanning tunneling microscopy images suggest that the distorted $3Q$ state could be the magnetic ground state of a Mn monolayer on Re(0001).

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• Magnetic texture
• Magnetism
• Antiferromagnets
• Noncollinear magnets
• Density functional theory