Excitonic Zeeman effect in the zinc-blende II-VI diluted magnetic semiconductors ${\mathrm{Cd}}_{1-x}{Y}_x\mathrm{Te}$ $(Y=\mathrm{Mn},$ Co, and Fe)

The $sp-d$ exchange constants ${(N}_0\alpha$ and $N_0\beta )$ of the zinc-blende diluted magnetic semiconductors ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te},$ ${\mathrm{Cd}}_{1-x}{\mathrm{Co}}_x\mathrm{Te},$ and ${\mathrm{Cd}}_{1-x}{\mathrm{Fe}}_x\mathrm{Te}$ are deduced from the huge excitonic Zeeman effect observed in wavelength-modulated reflectivity spectra, supplemented with magnetization measurements with a superconducting quantum interference device magnetometer. The Zeeman spectra recorded in magnetic fields $\mathrm{}\left(H\right)\mathrm{}$ up to 60 kG, and temperatures $\mathrm{}\left(T\right)\mathrm{}$ down to 1.8 K clearly reveal the Van Vleck paramagnetism of ${\mathrm{Cd}}_{1-x}{\mathrm{Fe}}_x\mathrm{Te};$ in contrast, ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ and ${\mathrm{Cd}}_{1-x}{\mathrm{Co}}_x\mathrm{Te}$ display a Brillouin-function-like $\mathrm{}(H/T)\mathrm{}$ dependence of their excitonic Zeeman components associated with spin 5/2 and 3/2 ground states of ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Co}}^{2+},$ respectively. The antiferromagnetic d-d interaction between the magnetic ions, displayed in the Zeeman data, is mainly limited to nearest-neighbor ${\mathrm{Mn}}^{2+}$ ions, whereas it is significantly stronger for ${\mathrm{Co}}^{2+}$ than for ${\mathrm{Mn}}^{2+}$ and extends to more distant neighbors.