  Vanadium tetracyanoethylene (V[TCNE]$_\text{x}$) is an organic-based
ferrimagnet that exhibits robust magnetic ordering (T$_\text{C}$ of over 600
K), high quality-factor (high-Q) microwave resonance (Q up to 3,500), and
compatibility with a wide variety of substrates and encapsulation technologies.
Here, we substantially expand the potential scope and impact of this emerging
material by demonstrating the ability to produce engineered nanostructures with
tailored magnetic anisotropy that serve as a platform for the exploration of
cavity magnonics, revealing strongly coupled quantum confined standing wave
modes that can be tuned into and out of resonance with an applied magnetic
field. Specifically, time-domain micromagnetic simulations of these
nanostructures faithfully reproduce the experimentally measured spectra,
including the quasi-uniform mode and higher-order spin-wave (magnon) modes.
Finally, when the two dominant magnon modes present in the spectra are brought
into resonance by varying the orientation of the in-plane magnetic field, we
observe anti-crossing behavior indicating strong coherent coupling between
these two magnon modes at room temperature. These results position
V[TCNE]$_\text{x}$ as a leading candidate for the development of coherent
magnonics, with potential applications ranging from microwave electronics to
quantum information.
