In solids, atoms are arranged in a regular pattern; however, atoms can vibrate from their equilibrium positions through vibrational modes known as phonons. In particular, the circularly polarized vibrational motions of ions are called chiral phonons (note that there is another definition for chiral phonons. In this study, we refer to two-dimensional (2D) rotational phonons as chiral phonons).

 Chiral phonons exhibit angular and magnetic moments owing to the rotational motion of the ions. The rotation of the ions also induces effective magnetic fields that can be relatively large (of the order of 1 T). Chiral phonons can couple with spins through the Zeeman effect of these magnetic fields.

 Recent experimental reports have suggested that the spin–spin interaction through an insulator is mediated by chiral phonons, which cannot be explained by electronic mechanisms. However, although this interaction may be attributed to chiral phonons, the microscopic mechanism remains unclear. The electronic origins of the mechanisms of spin–spin interactions have been extensively investigated. Thus, one fundamental question is: What is the signature of boson-mediated spin–spin interactions?

 To address these problems, we investigated the interaction between two localized spins on top of a 2D insulator in the presence of chiral phonons. We demonstrated that this interaction was mediated by chiral phonons through spin-chiral phonon coupling. The exchange interactions were always positive because of the bosonic nature of phonons. We found that the exchange interactions for acoustic and optical phonons (i.e., in-phase and out-of-phase motions of neighboring atoms) exhibited a power-law decay with respect to the distance between two localized spins and were proportional to the temperature of the system at high temperatures. Furthermore, the chiral phonon-induced spin-spin interaction exhibited a power-law decay, corresponding to the propagation of phonons in insulators. Therefore, this interaction can become the dominant mechanism for spin-spin interactions in magnetic insulators.

 Further, an extremely small rotation of atoms can induce a strong　magnetic field (on the order of 1 T); therefore, chiral phonons can be regarded as tiny magnets. The interaction between chiral phonons and spin (or magnetization), such as the magnetization reversal induced by chiral phonons, has been actively researched in recent years.  Applications to new device principles are anticipated in combination with studies on spintronics.

(Written by T. Yokoyama)

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