Floquet topological magnons

We introduce the concept of Floquet topologicalmagnons—amechanismbywhich a synthetic tunableDzyaloshinskii–Moriya interaction (DMI) can be generated in quantummagnets using circularly polarized electric (laser)field. The resulting effect is thatDiracmagnons and nodal-line magnons in two-dimensional and three-dimensional quantummagnets can be tuned tomagnon Chern insulators andWeylmagnons respectively under circularly polarized laserfield. The Floquet formalism also yields a tunable intrinsicDMI in insulating quantummagnets without an inversion center.We demonstrate that the Floquet topologicalmagnons possess afinite thermalHall conductivity tunable by the laserfield. Quantummagnets without an inversion center allow an intrinsicDzyaloshinskii–Moriya interaction (DMI) [1, 2], which is a consequence of spin–orbit coupling and it is usuallyfixed in differentmagnets. The associated magnon bands in themagnetically ordered systems have a nontrivial topologywithChern number protected chiralmagnon edgemodes in two-dimensional (2D) systems andmagnon surface states in three-dimensional (3D) systems. They are dubbed topologicalmagnonChern insulators [3–9] andWeylmagnons [10–13] respectively. They are the analogs of electronic topological (Chern) insulators [14–16] andWeyl semimetals [17–19]. However, due to the charge-neutral property ofmagnons, topologicalmagnonicmaterials are believed to be potential candidates for low-dissipationmagnon transports in insulating quantummagnets and they are applicable tomagnon spintronics andmagnetic data storage [20]. Topologicalmagnonicmaterials (i.e.magnon Chern insulators andWeylmagnons) also possess a thermalHall effect as predicted theoretically [21–25] and observed experimentally [26–28]. To date, topologicalmagnon bands have been realized only in a quasi-2D kagomé ferromagnet [29]. Generally, every quantum ferromagneticmaterial does not have a strong intrinsic DMInecessary for topologicalmagnons to exist. For instance, the single crystals of the ferromagnetic honeycomb compounds CrX3 (XoBr, Cl, and I) showno evidence ofDMI [30–35], and kagomé haydeeite also does not have afinite (topological) energy gap in the observed spin-wave spectra [36], suggesting that theDMI does not play a significant role in haydeeite. These 2D ferromagneticmaterials with negligibleDMI are candidates forDirac magnons [37], and the 3D ferromagnetic counterparts are candidates for nodal-linemagnons [13, 38]. By applying a circularly polarized laser field in these ‘topologically trivial’ systems, one can generate topological magnons (i.e.,magnonChern insulators andWeylmagnons) via a tunable synthetic laser-inducedDMI. This is particularly important as it offers away to tune theDMI inmagneticmaterials. The Floquet theory [39] of laser-driven systems provides a theoretical as well as experimentalmethod to engineer such topologically nontrivial systems. This formalism ismostly dominated by electronic systems [40–59] and also optical bosonic systems [60–65].Moreover, an applied laser field provides ameans for coherent control of themagnetization in 1Dquantummagnets [66–70]. In this Letter, we introduce the Floquet formalism to 2D and 3D ferromagnetic quantummagnets in the presence of a circularly polarized electric (laser)field.We show that the underlying charge-neutralmagnons acquire a time-dependent Aharonov–Casher phase [71], which generates a tunable synthetic DMI inmagnetic OPEN ACCESS