Nanomagnetism concerns the engineering of magnetic interactions in heterostructures that consist of layers of magnetic and nonmagnetic materials. Mostly, these interactions are dominated by the minimization of energy. Here, we propose an effective magnetic interlayer coupling that is dominated by the maximization of entropy. As an example, we consider the system that mediates the effective interactions to be square spin ice, in which case we find purely entropic interactions that are long-ranged. We argue that in the thermodynamic limit the entropic interlayer coupling gives rise to entropic torques on the magnetization direction. For small systems, the physical properties are well characterized by the mutual information between the two magnets that are coupled. Because entropic interactions typically become stronger for higher temperatures, our findings may benefit the development of nanomagnetic devices that require thermal stability.

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• Entropy
• Frustrated magnetism
• Magnetism
• Artificial spin ice
• Metropolis algorithm