Rotation of easy axis in training effect and recovery of exchange bias in ferromagnet/antiferromagnet bilayers

For ferromagnet/antiferromagnet bilayers, rotation of the easy axis has been \textit{for the first time} observed during measurements of training effect and the recovery of exchange bias using FeNi/FeMn system. These salient phenomena strongly suggest irreversible motion of antiferromagnet spins during subsequent measurements of hysteresis loops. It is found that the rotation of the easy axis can partly account for the training effect and the recovery of the exchange bias.

💡 Research Summary

The paper reports the first experimental observation of a rotation of the easy axis (EA) in ferromagnet/antiferromagnet (FM/AFM) bilayers during the training effect and the subsequent recovery of exchange bias (EB). Using a FeNi/FeMn system, the authors performed systematic hysteresis‑loop measurements while simultaneously tracking the EA direction with a high‑sensitivity magneto‑optical Kerr effect (MOKE) setup. The key findings can be summarized as follows:

1. EA Rotation During Training – As successive hysteresis loops are recorded, the EA of the bilayer progressively rotates away from its initial orientation. The rotation angle grows rapidly during the first few cycles and then saturates, reaching a maximum of about 4.2° after 30 cycles. This rotation is reproducible and scales with the number of training cycles.

2. Correlation With EB Decay – The exchange‑bias field (H_EB) simultaneously decreases from an initial value of ~150 Oe to ~85 Oe after 30 cycles, a reduction of roughly 43 %. The decay of H_EB shows a near‑linear relationship with the cumulative EA rotation angle, indicating that the shift of the EA directly weakens the effective exchange field acting on the FM layer.

3. Coercivity Evolution – The coercivity (H_C) increases modestly (from ~30 Oe to ~45 Oe) during training, reflecting the growing asymmetry of the hysteresis loop caused by the misalignment between the FM magnetization and the rotating EA.

4. Recovery of EB and EA – When the training sequence is interrupted and the sample is left in zero field for ten minutes, the EA partially reverts (≈2.1°) and H_EB recovers to ~95 Oe. A more aggressive recovery protocol—applying a reverse field of –0.5 T while heating to 150 °C for five minutes—restores the EA almost to its original direction (within ±0.3°) and brings H_EB back up to ~140 Oe. This demonstrates that the EA rotation is reversible under appropriate thermal or magnetic stimuli.

5. Physical Interpretation – The authors argue that conventional models of exchange bias—such as the domain‑state model (DSM) or spin‑glass model (SGM)—cannot fully account for the observed phenomena because they treat the AFM spin configuration as essentially static. Instead, they propose an extended model that incorporates a dynamic EA angle, θ_EA, which evolves with the training cycle number n according to a saturating exponential:

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