Evidence for linear dependence of exchange bias on pinned uncompensated spins in an Fe/FeO bilayer

We use a magnetic field to manipulate the pinned spins in an Fe/FeO bilayer at room temperature, observing the behavior of the pinned magnetic moment via magnetometry. Our experiment reveals a linear relationship between the exchange bias field and the pinned magnetic moment. Based on the pinned uncompensated spin density at the interface as a function of the pinned moment, we provide a quantitative description of the exchange bias effect via exchange interaction of ferromagnetic and antiferromagnetic spins.

Figure 1

(a) Under a reset magnetic field, $H_{\text{re}}$, pinned spins at the Fe/FeO interface can be reversed from the cooling field, $H_{\text{cool}}$, direction. (b) Cross-section high-resolution TEM image of the Fe/FeO bilayer. Inset shows the FFT image obtained from the FeO layer. (c) Fe/FeO hysteresis loops measured at room temperature for $H_{\text{re}}$ from $-1$ to $-7$ kOe. Inset shows the magnetic signal of the background [axes are the same as the main figure in panel (c)].

Figure 2

(a) The pinned magnetization, $M_{\text{pin}}$, and the exchange field, $H_{\text{eb}}$, extracted from the Fe/FeO hysteresis loops [Fig. 1], as a function of the maximum negative applied field $H_{\text{re}}$. (b) Coercivity $H_{\text{C}}$ as function of $H_{\text{re}}$. (c) $H_{\text{eb}}$ as a function of $M_{\text{pin}}$.

Figure 3

$H_{\text{eb}}{M}_{\text{FM}}{t}_{\text{FM}}$/$A$ as a function of $p$ for different exchange biased FM/AFM systems. This figure shows our data (blue circles) as well as previous data of other groups obtained from XMCD, MFM, MSHG, and soft x-ray resonant reflectivity [15, 16, 23, 51, 54]. The red dashed line is plotted according to Eq. (2).