Magnetism of wurtzite CoO nanoclusters

The possibility that the apparent room-temperature ferromagnetism, often measured in Co-doped ZnO, is due to uncompensated spins at the surface of wurtzite CoO nanoclusters is investigated by means of a combination of density-functional theory and Monte Carlo simulations. We find that the critical temperature extracted from the specific heat systematically drops as the cluster size is reduced, regardless of the particular cluster shape. Furthermore the presence of defects, in the form of missing magnetic sites, further reduces $T_{\text{C}}$. This suggests that even a spinodal decomposed phase is unlikely to sustain room-temperature ferromagnetism in ZnO:Co.

Figure 1

(Color online) Total DFT energy as a function of the angle of the magnetization with respect to the WZ $c$ axis for both CoO and a single Co impurity in a ZnO supercell. Note that in both cases the $c$ axis is a hard axis while the $a\text{−}b$ plane is an easy plane. The anisotropy barrier is about 1.75 meV.

Figure 2

(Color online) Ground-state spin configuration of spherical particles of different radius: $12\text{Å}$ (top) and $18\text{Å}$ (bottom). Note the large degree of compensation in the inner core of the particles and the presence of noncompensated spins at their surfaces.

Figure 3

The specific heat, $C$, as a function of temperature for finite clusters of wurtzite CoO. The curves are for particles of different radii, ranging from $6\text{Å}$ (top) to $30\text{Å}$ (bottom), in increment of $1\text{Å}$

Figure 4

(Color online) Critical temperature as a function of the particle radius $R$ ($\ast$ symbols). The lines are fits to finite-size-scaling theory [Eq. (2)]. The solid red line corresponds to the fit obtained for $R>6\text{Å}$ while the dashed blue curve is for $R>10\text{Å}$.

Figure 5

(Color online) Specific heat as a function of temperature for a representative sample of cylindrical nanoparticles with different radii and lengths.

Figure 6

(Color online) Specific heat against temperature curves for a perforated nanosphere of radius $19\text{Å}$ and various Co concentrations, [Co]. We can clearly observe that by reducing the Co content the peak in $C\left(T\right)$ moves to lower temperature and gets broader. In the inset we show $T_{\text{C}}$ as a function of [Co] as extracted from the specific heat.