Fig. 5: The possible states produced by the magnons in FM, AFM, artificial FiM systems.
\(\langle {{{{{\bf{m}}}}}}\rangle\), \(\langle {{{{{\bf{M}}}}}}\rangle\) and magnon chirality are taken into account as the degrees of freedom. The first degree of freedom is \(\langle {{{{{\bf{m}}}}}}\rangle\) in AFM and \(\langle {{{{{\bf{M}}}}}}\rangle\) in FM or artificial FiM. In analogy to \(\langle {{{{{\bf{m}}}}}}\rangle\) in AFM, \(\langle {{{{{\bf{M}}}}}}\rangle\) is the DC component of the precessing magnetization in FM or in the specific magnetic sublayer of artificial FiM (black arrows). This degree of freedom is denoted by \(\langle \uparrow \rangle\) for \(\langle {{{{{\bf{m}}}}}}\rangle\) // +z or \(\langle {{{{{\bf{M}}}}}}\rangle\) // +z, and by \(\langle \downarrow \rangle\) for \(\langle {{{{{\bf{m}}}}}}\rangle\) // −z or \(\langle {{{{{\bf{M}}}}}}\rangle\) // −z. The colorful cones denote the precessing angles of magnetic moment in FM and magnetic sublattices in AFM. In our artificial FiM, Vsp is produced by one specific magnetic sublayer which is denoted by a single cone. Both sublattices in AFMs could have magnetic contributions so that being denoted by the double cones. The second degree of freedom is the magnon chirality which is denoted in red (RH) and green (LH). Overall, the combination of \(\langle {{{{{\bf{M}}}}}}\rangle\) and magnon chirality can produce four possible states in our artificial FiM while AFMs only host two states of opposite chiralities locked with the opposite \(\langle {{{{{\bf{m}}}}}}\rangle\).
