Weak doping dependence of the antiferromagnetic coupling between nearest-neighbor ${\mathrm{Mn}}^{2+}$ spins in $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\left({\mathrm{Zn}}_{1-y}{\mathrm{Mn}}_y\right)}_2{\mathrm{As}}_2$

Dilute magnetic semiconductors (DMS) are nonmagnetic semiconductors doped with magnetic transition metals. The recently discovered DMS material (${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x){\left({\mathrm{Zn}}_{1-y}{\mathrm{Mn}}_y\right)}_2{\mathrm{As}}_2$ 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.

Figure 1

Intensity maps from TOF neutron spectroscopy (raw data) for II-II-V type DMSs with isovalent Mn substitution: (a), (b) undoped $\mathrm{Ba}{\left({\mathrm{Zn}}_{1-y}{\mathrm{Mn}}_y\right)}_2$ with $y=0.2$ and 0.15, (c) hole-doped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\left({\mathrm{Zn}}_{1-y}{\mathrm{Mn}}_y\right)}_2$ with $x=0.2$, $y=0.15$, and (d) the nonmagnetic reference sample ${\mathrm{BaZn}}_2{\mathrm{As}}_2$. The intensity in each panel was corrected for detector efficiencies by using a vanadium standard and normalized to the weight of each sample.

Figure 2

The same data as in Figs. 1 after subtraction of the nonmagnetic background: (a), (b) undoped $\mathrm{Ba}{\left({\mathrm{Zn}}_{1-y}{\mathrm{Mn}}_y\right)}_2$ with $y=0.2$ and 0.15, (c) hole-doped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\left({\mathrm{Zn}}_{1-y}{\mathrm{Mn}}_y\right)}_2$ with $x=0.2$, $y=0.15$. In all panels, the signal from the nonmagnetic reference sample ${\mathrm{BaZn}}_2{\mathrm{As}}_2$ [shown in Fig. 1] has been subtracted to reduce the phonon background and reveal the magnetic signal at low $\left|\mathbf{Q}\right|$, which is now clearly seen around 14 meV. The horizontal features extending to higher $\left|\mathbf{Q}\right|$ are artifacts resulting from imperfect phonon subtraction.

Figure 3

(a) Energy spectra obtained by averaging the first five momentum channels of the INS signals in Figs. 1. (b) The same for the subtracted signals in Figs. 2–2, which contain only the magnetic part of the signal. A clear peak originating from the lowest-energy $\left|\mathrm{\Delta }S\right|=1$ excitation of the nearest-neighbor Mn dimers is seen around 13–14 meV in all three samples. The fitted peak positions are summarized in the table inset.

Figure 4

Energy diagram of a single Mn-Mn dimer in dependence on the double-exchange energy, parametrized here by the $t_{\mathrm{eff}}/J$ ratio.