Temperature dependence of magnetization reversal and angular torque in $\mathrm{Co}∕\mathrm{Co}\mathrm{O}$

The temperature dependence of the magnetization reversal process, reversible and irreversible exchange bias anisotropy, uniaxial anisotropy, and rotational hysteresis of polycrystalline exchange-biased $\mathrm{Co}∕\mathrm{Co}\mathrm{O}$ bilayers have been investigated. A dichotomy in the experimental results is found for thin and thick CoO layers with the boundary near $7\mathrm{nm}$. The uniaxial anisotropy in thin (thick) CoO films is small (large), whereas the rotatable anisotropy is large (small). At low temperatures, the asymmetry in the magnetization reversal is due to instabilities at the antiferromagnet interface. Near the blocking temperature, a different asymmetry is due to a broad distribution of large grains. Near the latter temperature range, the smaller grains dissipate energy as evidenced by an increased rotational anisotropy and training of the hysteresis loop. All features can be understood qualitatively with a distribution of independent antiferromagnetic grains coupled to the ferromagnetic film.

Figure 1

Comparison of the reversible $\left(H_{\mathit{ea}}\right)$ and irreversible interfacial exchange anisotropy energy at $5\mathrm{K}$ varying the thickness of CoO. The hysteresis loop shifts from SQUID measurements $\left(H_{\mathit{eb}}\right)$ show a larger shift in the first loop (L1) compared to the second loop (L2) for CoO thicknesses of $7\mathrm{nm}$ and smaller. The left coercive field of the first hysteresis loop, sum of $H_{\mathit{eb}}$ and coercivity $\left(H_c\right)$, is always smaller than the reversible $H_{\mathit{ea}}$ measurement for all CoO thicknesses, even in exchange-biased films without training. The inset shows the ratio between the reversible $H_{\mathit{ea}}$ and the irreversible $(H_{\mathit{eb}}+H_c)$ exchange anisotropy energy. The lines are guides to the eye.

Figure 2

Interfacial exchange bias shift energy dependence as a function of temperature for two characteristic samples as measured with a SQUID after cooling in $2\mathrm{kOe}$ from $300\mathrm{K}$. The sample with $3\mathrm{nm}$ of CoO shows considerable training in the second loop (open circles). This is in contrast to the sample with $10\mathrm{nm}$ of CoO, where the training (open squares) is minimal and prevalently present near the blocking temperature and at very low temperatures. Lines are guides to the eye.

Figure 3

Calculated temperature dependence of the interfacial exchange bias shift energy for CoO thicknesses of 3.0 and $10.0\mathrm{nm}$. The mean, $L_0$, for the distribution is $8\mathrm{nm}$ $\left(25\mathrm{nm}\right)$ for the thin (thick) CoO layer. The Néel temperature used is $291\mathrm{K}$ and the exchange constant $J=21.8\mathrm{erg}∕{\mathrm{cm}}^2$ appropriate for CoO. The inset shows the lognormal distribution of two grain size distributions with $\sigma =0.3$ as used in the calculation.

Figure 4

(a) Resistance measured in a constant field of $2\mathrm{kOe}$ at $100\mathrm{K}$ for the $3\mathrm{nm}$ thick CoO sample. The film was cooled along the current direction. (b) Torque curve obtained from the resistance data in (a) with fit lines (gray lines) to extract unidirectional, uniaxial, and rotational anisotropies. A large rotational hysteresis is present as the sample is rotated in both directions. The torque does not start at zero, since the sample was cycled before the measurement.

Figure 5

Torque curves evaluated from AMR measurements for a bilayer of $\mathrm{Co}\left(8\mathrm{nm}\right)∕\mathrm{Co}\mathrm{O}\left(10\mathrm{nm}\right)$ at four different temperatures. The closed (open) circles correspond to clockwise (counterclockwise) rotation of the sample in a magnetic field. The dissipated energy is proportional to the enclosed area.

Figure 6

Temperature dependence of the interfacial energies for the (a) $\mathrm{Co}\left(8\mathrm{nm}\right)∕\mathrm{Co}\mathrm{O}\left(10\mathrm{nm}\right)$ and (b) $\mathrm{Co}\left(8\mathrm{nm}\right)∕\mathrm{Co}\mathrm{O}\left(10\mathrm{nm}\right)$ bilayer. The unidirectional anisotropy $\left(K_{\mathit{ud}}\right)$, the uniaxial anisotropy $\left(K_u\right)$, and the rotational anisotropy energy $\left(E_{\mathit{rot}}\right)$ are obtained from fits to the AMR high-field torque measurements. The lines are guides to the eye.

Figure 7

Normalized resistance to the full AMR amplitude for a $10\mathrm{nm}$ CoO film at $T=160$, 237, and $260\mathrm{K}$, and above the blocking temperature at $T=284\mathrm{K}$. The solid lines are the first loop after cooldown; the dotted lines represent the trained second hysteresis loop (not shown for $T=284\mathrm{K}$). Near the blocking temperature $\left(237\mathrm{K}\right)$, the magnetization reversal is asymmetric and shows training.

Figure 8

Normalized resistance to the full AMR amplitude for a $3\mathrm{nm}$ CoO film at $T=4$, 160, 200, and $250\mathrm{K}$. The first (solid) and second (dotted) AMR magnetization reversals are dissimilar at low temperatures. The asymmetry in the reversal at low temperature vanishes after the first loop is taken. Near the blocking temperature $\left(200\mathrm{K}\right)$ the reversal is similar to that of a thicker CoO film and it shows a persistent asymmetry.

Figure 9

Magnetization reversal in the sample with a (a) $3\mathrm{nm}$ and (b) $10\mathrm{nm}$ thick CoO layer as a function of temperature. The resistance is normalized to the full AMR amplitude and the peaks for each temperature are plotted for the left and right hysteresis loop branch. For the thick bilayer, there is little training and only the first loop (L1) is shown. For the thin film, results from the first reversal (L1) and from the trained second reversal (L2) are shown. Values close to the maximum value of 1.0 indicate the magnetization reversal occurs by nucleation, small values near 0.0 suggest a rotation mode, which includes rotation of ferromagnetic domains.