Superexchange induced canted ferromagnetism in dilute magnets

We argue, in contrast to recent studies, that the antiferromagnetic superexchange coupling between nearest neighbor spins does not fully destroy the ferromagnetism in dilute magnets with long-ranged ferromagnetic couplings. Above a critical coupling, we find a canted ferromagnetic phase with unsaturated moment. We have calculated the transition temperature using a simplified local random phase approximation procedure which accounts for the canting. For dilute magnetic semiconductors, such as GaMnAs, using ab initio couplings allows us to predict the existence of a canted phase and provides an explanation for the apparent contradictions observed in experimental measurements. Finally, we compared with previous studies that used Ruderman-Kittel-Kasuya-Yosida couplings and reported nonferromagnetic states when the superexchange is too strong. Even in this case the ferromagnetism should remain essentially stable in the form of a canted phase.

Figure 1

(Color online) Schematic representation of the canted ground state resulting from the competition between the long-range ferromagnetic couplings $J_{ij}$ and the superexchange coupling $J_{AF}$. The spins involved in pairs become canted and the angles ${\theta }_i$ vary from spin to spin.

Figure 2

(Color online) Curie temperature as a function of the superexchange coupling strength. The density of magnetic impurities is set to $x=0.03$ and the coupling range $\lambda$ varies from 0.2 to 0.75. $J_1=J_0{e}^{-a∕\sqrt{2}\lambda }$ denotes the nearest neighbor coupling in the absence of superexchange. The dashed line shows the instability threshold of the simple (noncanted) SCLRPA calculation.

Figure 3

(Color online) Curie temperature (in units of $J_1$) as a function of the magnetic impurity concentration $x$ for different values of the superexchange strength. The range of the couplings, $\lambda$, is fixed to 0.50.

Figure 4

(Color online) Calculated phase diagram (temperature–antisite concentration) for ${\mathrm{Ga}}_{1-x-y}{\mathrm{As}}_y{\mathrm{Mn}}_x\mathrm{As}$ indicating the predicted canted phase. The antisite concentration $y$ allows tuning of the carrier concentration. The density of magnetic impurity $x$ is fixed to 0.05. The transition temperature is calculated with modified LRPA, and compared with Monte Carlo results (from Ref. 23), using the same set of ab initio couplings. $m\left(0\right)$ is the total magnetization per spin at zero temperature.

Figure 5

(Color online) Distribution $P\left(\theta \right)$ of the canting angle of the nearest neighbor pairs in ${\mathrm{Ga}}_{1-x-y}{\mathrm{As}}_y{\mathrm{Mn}}_x\mathrm{As}$ for two different values of the concentration of As antisites, $y$. The density of ${\mathrm{Mn}}^{2+}$ is $x=0.05$.

Figure 6

(Color online) Curie temperature for the RKKY model as a function of $k_F$ for different values of the superexchange coupling $J_{AF}$. The density of impurities is set to $x=0.05$ and the parameter $\lambda =0.50$. The calculations are performed on the fcc lattice.