Orphan spins and bound in-gap states in the $S=\frac{5}{2}$ antiferromagnet CaFe${}_2$O${}_4$

CaFe${}_2$O${}_4$ is an anisotropic $S=\frac{5}{2}$ antiferromagnet with two competing $A$ ($\uparrow \uparrow \downarrow \downarrow$) and $B$ ($\uparrow \downarrow \uparrow \downarrow$) magnetic order parameters separated by static antiphase boundaries at low temperatures. Neutron diffraction and bulk susceptibility measurements, show that the spins near these boundaries are weakly correlated and a carry an uncompensated ferromagnetic moment that can be tuned with a magnetic field. Spectroscopic measurements find these spins are bound with excitation energies less than the bulk magnetic spin-waves and resemble the spectra from isolated spin-clusters. Localized bound orphaned spins separate the two competing magnetic order parameters in CaFe${}_2$O${}_4$.