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We investigated the magnetic properties of(La$_{1-x}$Ba$_{x}$)(Zn$_{1-x}$Mn$_{x}$)AsO with $x$ varying from 0.005 to 0.05at an external magnetic field of 1000 Oe. For doping levels of $x$ $\leq$ 0.01,the system remains paramagnetic down to the lowest measurable temperature of 2K. Only when the doping level increases to $x$ = 0.02 does the ferromagneticordering appear. Our analysis indicates that antiferromagnetic exchangeinteractions dominate for $x$ $\leq$ 0.01, as shown by the negative Weisstemperature fitted from the magnetization data. The Weiss temperature becomespositive, i.e., ferromagnetic coupling starts to dominate, for $x$ $\geq$ 0.02.The Mn-Mn spin interaction parameter $\mid$$2J/k_B$$\mid$ is estimated to be inthe order of 10 K for both $x$ $\leq$ 0.01 (antiferromagnetic ordered state)and $x$ $\geq$ 0.02 (ferromagnetic ordered state). Our results unequivocallydemonstrate the competition between ferromagnetic and antiferromagneticexchange interactions in carrier-mediated ferromagnetic systems.

The Magnetic Properties of 1111-type Diluted Magnetic Semiconductor (La$_{1-x}$Ba$_{x}$)(Zn$_{1-x}$Mn$_{x}$)AsO in the Low Doping Regime