Weak doping dependence of the antiferromagnetic coupling between nearest-neighbor Mn2+ spins in (Ba1−xKx)(Zn1−yMny)2As2

Dilute magnetic semiconductors (DMS) are nonmagnetic semiconductors doped with magnetic transition metals. The recently discovered DMS material (${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_x){({\mathrm{Zn}}_{1\ensuremath{-}y}{\mathrm{Mn}}_y)}₂{\mathrm{As}}₂$ offers a unique and versatile control of the Curie temperature ${T}_{\mathrm{C}}$ by decoupling the spin (${\mathrm{Mn}}²⁺$, $S=5/2$) and charge (${\mathrm{K}}⁺$) doping in different crystallographic layers. In an attempt to describe from first-principles calculations the role of hole doping in stabilizing ferromagnetic order, it was recently suggested that the antiferromagnetic exchange coupling $J$ between the nearest-neighbor Mn ions would experience a nearly twofold suppression upon doping 20% of holes by potassium substitution. At the same time, further-neighbor interactions become increasingly ferromagnetic upon doping, leading to a rapid increase of ${T}_{\mathrm{C}}$. Using inelastic neutron scattering, we have observed a localized magnetic excitation at about 13 meV associated with the destruction of the nearest-neighbor Mn-Mn singlet ground state. Hole doping results in a notable broadening of this peak, evidencing significant particle-hole damping, but with only a minor change in the peak position. We argue that this unexpected result can be explained by a combined effect of superexchange and double-exchange interactions.