Spin reorientation in tetragonally distorted spinel oxide ${\mathrm{NiCo}}_2{\mathrm{O}}_4$ epitaxial films

We experimentally investigated the magnetic properties of ${\mathrm{NiCo}}_2{\mathrm{O}}_4$ epitaxial films known to be conductive oxides with perpendicular magnetic anisotropy (PMA) at room temperature. Both magnetotorque and magnetization measurements at various temperatures provide clear experimental evidence of the spin reorientation transition at which the MA changes from PMA to easy-cone magnetic anisotropy (ECMA) at a certain temperature ($T_{\mathrm{SR}}$). ECMA was commonly observed in films grown by pulsed laser deposition and reactive radio frequency magnetron sputtering, although $T_{\mathrm{SR}}$ is dependent on the growth method as well as the conditions. The cone angles measured from the $c$ axis increased successively at $T_{\mathrm{SR}}$ and approached a maximum of 45–50 degrees at the lowest measurement temperature of 5 K. Calculation with the cluster model suggests that the ${\mathrm{Ni}}^{3+}$ ions occupying the $T_d$ site could be the origin of the ECMA. Both the magnetic properties and the results of the calculation based on the cluster model indicate that the ECMA is attributable to the cation antisite distribution of ${\mathrm{Ni}}^{3+}$, which is possibly formed during the growth process of the thin films.

Figure 1

(a) RSMs around the $\mathrm{NCO}(4,0,8)$ and $\mathrm{MAO}(4,0,8)$ reflections. (b) Temperature dependence of the lattice constant evaluated from the $\mathrm{NCO}(4,0,12)$ Bragg reflection in Sample $S$. The inset shows the temperature dependence of the $c/a$ ratio.

Figure 2

MH loops of NCO film with ${\mu }_{0}H\perp$ film plane of (a) Sample $P_{100}$, (b) Sample $S$, and (c) Sample $P_{10}$. (d) Temperature dependence of the squareness ratio in each sample (inset: MH loops for the three samples at 30 K). (e) Temperature dependence of $M_S$ determined from VSM results. (f) ${\mu }_{0}H\parallel$ film plane of Sample $S$.

Figure 3

Magnetotorque curves of (a) $L_{\theta }$ ($ac$ plane), and (b) $L_{\phi }$ ($ab$ plane) for the three samples at various temperatures.

Figure 4

Temperature dependence (a) of the magnetic anisotropy energy in each sample and (b)–(d) of the cone angles for the two different $\phi$ directions calculated from Eq. (4). The vertical broken lines in (a) roughly indicate the temperatures where $K_{u1}^{\mathrm{eff}}$ change their signs.

Figure 5

Curie temperature for the two respective magnetic anisotropy constants at 5 K of the three samples.

Figure 6

Calculated dependence of the magnetic moment on the angle $\mathrm{\Delta }E\left(\theta \right)$ at (a) $T_d$, and (b) $O_h$ sites. (c) Calculated total anisotropy based on the adapted cation distribution in Table 4.