“…In the past decade, the research field of magnonics has rapidly grown due to its potential for the development of innovative low-energy computing devices, where spin waves (SWs), the collective excitations of electron spins, are used to carry and process information. − Progress in this field mainly relies on the capability to control and manipulate the SW propagation, for the implementation of SW-based devices with unprecedented functionalities in information and communication technologies. − In this context, the exploitation of the interfacial Dzyaloshinskii–Moriya interaction (i-DMI), − namely the antisymmetric exchange interaction arising at the interface of a ferromagnetic film and a heavy-metal substrate with high spin–orbit coupling, − can represent an effective method for achieving a nonreciprocal SW propagation, opening the way toward unidirectional devices such as insulators and diodes for nanomagnonic circuits. − The nonreciprocal magnonic propagation, induced by the presence of i-DMI, has been primarily used to quantify the i-DMI strength, D , in continuous metallic films and multilayers. − In this respect, a small i-DMI has also been observed in magnetic garnet systems in contact with heavy metals, − which are auspicious materials for magnonic applications due to their low damping. Nevertheless, typical values of the i-DMI strength are still 2 orders of magnitude smaller than for conventional ferromagnets. , A frequency nonreciprocity can also originate from any symmetry-breaking mechanism along the thickness, such as different anisotropies at the bottom and top surfaces, magnetization grading, and dipolar coupling in bilayers − and curved surfaces. , However, such effects are negligible in ultrathin films.…”