Frequency-division routing via spin-refractive-index locking.

Here we demonstrate spin-refractive-index locking (SRIL) in a composite right-left-handed transmission-line metamaterial, where the transverse spin of surface modes is locked to the sign of the effective refractive index. Unlike conventional spin-momentum locking (SML), the SRIL reverses the spin for the same energy propagation direction in right- and left-handed bands. Using this index-dependent spin control, we realize frequency-selective chiral photon-magnon interaction by placing a yttrium iron garnet (YIG) sphere above the metamaterial and achieving strong nonreciprocity, where magnons only couple to microwaves of matching spin and the required direction is determined by the operating band. Tuning the frequency across the two bands dynamically switches the coupling direction, enabling a compact, reconfigurable on-chip routing device for spin-selective microwave control and nonreciprocal signal processing.