Magnetic order typically emerges due to the short-range exchange interaction between the constituent electronic spins. Recent discoveries have found a crucial role for spin-phonon coupling in various phenomena from optical ultrafast magnetization switching to dynamical control of the magnetic state. Here, we demonstrate theoretically the emergence of a biquadratic long-range interaction between spins mediated by their coupling to phonons hybridized with vacuum photons into polaritons. The resulting ordered state enabled by the exchange of virtual polaritons between spins is reminiscent of superconductivity mediated by the exchange of virtual phonons. The biquadratic nature of the spin-spin interaction promotes ordering without favoring ferro- or antiferromagnetism. It further makes the phase transition to magnetic order a first-order transition, unlike in conventional magnets. Consequently, a large magnetization develops abruptly on lowering the temperature which could enable magnetic memories admitting ultralow-power thermally-assisted writing while maintaining a high data stability. The role of photons in the phenomenon further enables an in-situ static control over the magnetism. These unique features make our predicted spin-spin interaction and magnetism highly unconventional paving the way for novel scientific and technological opportunities.

磁序通常是由于组成电子自旋之间的短程交换相互作用而出现的。最近的发现发现自旋声子耦合在从光学超快磁化切换到磁态动态控制的各种现象中发挥着至关重要的作用。在这里，我们从理论上证明了自旋之间双二次长程相互作用的出现，这种相互作用是通过它们与与真空光子杂交成极化子的声子的耦合介导的。自旋之间虚拟极化子交换所产生的有序状态让人想起由虚拟声子交换介导的超导性。自旋-自旋相互作用的双二次性质促进有序化，而不利于铁磁性或反铁磁性。与传统磁体不同，它进一步使向磁序的相变成为一级转变。因此，在降低温度时会突然产生大的磁化，这可以使磁存储器允许超低功率热辅助写入，同时保持高数据稳定性。光子在该现象中的作用进一步实现了对磁性的原位静态控制。这些独特的特征使我们预测的自旋相互作用和磁性非常规，为新的科学和技术机会铺平了道路。