Electric control over magnetic interactions at the level of individual spins is relevant for a variety of quantum applications, such as qubits, memory, and sensor functionality. We show here that spin lattices and magnon gaps can be controlled with a supercurrent. Remarkably, a spin-polarized supercurrent makes the interaction between magnetic adatoms placed on the surface of a superconductor depend not only on their relative distance, but also on their absolute position in space. This property permits electric control over the interaction not only between two individual spins, but over an entire spin lattice, allowing for tunable noncollinear ground states and a practical arena to study the properties of different spin Hamiltonians. Moreover, we show that a supercurrent controls the magnon gap in antiferromagnetic and altermagnetic insulators. These results provide an accessible way to realize electrically controlled spin switching and magnon gaps without dissipative currents.

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• Magnetism
• Superconductivity
• Spin lattice models