Exchange-Induced Anisotropies at Ferromagnetic-Antiferromagnetic Interfaces above and below the Néel Temperature

The exchange bias and magnetic anisotropies in a Co layer on a single-crystalline ${\mathrm{F}\mathrm{e}\mathrm{F}}_2$ film have been determined between 30 and 300 K. By postulating that the coupling between the ferromagnet and the antiferromagnet persists above the Néel temperature ($T_N$) we develop a model that quantitatively describes the exchange bias and the anisotropies over the whole temperature range, both above and below $T_N$. Using only the measured low temperature exchange bias and a distribution of blocking temperatures we explain (i) the temperature dependence of the bias, (ii) the magnitude of the anisotropies, (iii) the opposite sign of the first and second order anisotropies, (iv) the observed $1/T$ and $1/T^3$ temperature dependencies of the first and second order uniaxial anisotropies above $T_N$, and (v) the decrease of the anisotropies below $T_N$.

Figure 1

Hysteresis loops with the field applied perpendicular (hard axis) and parallel (easy axis) to the ${\mathrm{F}\mathrm{e}\mathrm{F}}_2$ $c$ axis at various temperatures. The lines for the hard-axis data are fits using a coherent rotation model and the energy expression from Eq. (1), while the lines for the easy axis data are just guides to the eye.

Figure 2

Parameters extracted from fitting the hysteresis curves (symbols); $H_E$ (▼), $K_1/M_F$ (●), and $K_2/M_F$ (■). The full lines are the model calculations using Eq. (8). The inset shows the distribution of blocking temperatures used for the calculations.