Magneto-optical study of magnetization reversal asymmetry in exchange bias

The asymmetric magnetization reversal in exchange biased Fe/MnF$_{2}$ involves coherent (Stoner-Wohlfarth) magnetization rotation into an intermediate, stable state perpendicular to the applied field. We provide here experimentally tested analytical conditions for the unambiguous observation of both longitudinal and transverse magnetization components using the magneto-optical Kerr effect. This provides a fast and powerful probe of coherent magnetization reversal as well as its chirality. Surprisingly, the sign and asymmetry of the transverse magnetization component of Fe/MnF$_{2}$ change with the angle between cooling and measurement fields.

A ferromagnetic (FM) layer in contact with an antiferromagnetic (AFM) one experiences a shift of the hysteresis loop along the field axis, due to the so-called exchange bias (EB) [1,2]. One of the intriguing features of EB is a pronounced asymmetry in the hysteresis loops, a very unusual phenomenon in magnetism since all other magnetic materials exhibit symmetric reversal. The most prominent example of an asymmetric reversal occurs in Fe/MnF 2 , which exhibits a pronounced step on only one side of the hysteresis loop [3].
Polarized neutron reflectometry (PNR) showed that this step is related to coherent rotation of the magnetization [3,4], which is pinned in a potential minimum transverse to the applied magnetic field. As PNR is not sensitive to the direction of the transverse moment it cannot determine the chirality of the magnetization vector upon magnetization reversal.
Although asymmetric magnetization reversal has been claimed from PNR [4], viscosity [5], and anisotropic magnetoresistance [6] measurements, the obvious experiment using magneto-optical Kerr effect (MOKE) has not yet been performed. MOKE studies, accessing both longitudinal and transverse magnetization components are scarce for exchange biased systems [7][8][9]. It is therefore important to analyze how coherent magnetization rotation manifests itself in a well-defined MOKE signal and whether the absence of such a signature therefore implies the existence of domain wall nucleation and propagation processes.
Here, we use MOKE in separate longitudinal and transverse geometries to study magnetization reversal in the model exchange-bias system Fe/MnF 2 (110). This fast technique allows us to determine the chirality of the magnetization reversal via the sign of the transverse magnetization component. We derive analytical conditions to unambiguously identify the Kerr signature of pure longitudinal (M L ) or transverse (M T ) magnetization components. These conditions allow for the determination of the orientation and relative magnitude of the inplane magnetization components at all fields during magnetization reversal. Surprisingly, the hysteresis loop asymmetry critically depends on the angle ϕ H between the in-plane 3 measurement field and the cooling field direction. Within a few degrees M T changes its sign.
For 90° it appears on both sides of the loop with the same sign of rotation, contrary to a Stoner-Wohlfarth (360 o ) reversal process.
MOKE measurements were performed with an in-plane magnetic field oriented at 45° with respect to the [001] direction of the AFM twins. This is crucial to observe the asymmetry in the hysteresis loop [3]. Kerr loops were taken in two separate configurations ( Fig. 1(a)). In the longitudinal geometry (I) the scattering plane is parallel to M L , while in the transverse geometry (II) it is parallel to M T . For both geometries the linearly polarized incident light can be continuously rotated from s to p polarization using a λ/2 retarding plate. Kerr rotation of the reflected laser beams can be simultaneously detected in both geometries. For detection   transverse (right panel) geometries, for ψ = 90° (s-pol., Fig. 2(a,d)), 45° ( Fig. 2(b,e)), and 0° (p-pol., Fig. 2(c,f)). The curves for the intensities I A and I B measured in diodes A and B ( Fig.   1(b)), and the difference signal I A-B , are vertically shifted. In the transverse configuration the Kerr loops (I A-B ) are identical for s-and p-polarization except for their sign. In addition, the loop at ψ = 45° has the shape found for s-polarization in the longitudinal configuration.
Most previous analytical MOKE descriptions deal with Kerr rotation detection with a crossed analyzer [10][11][12][13], as opposed to the diode bridge technique used in our work. Here, we derive analytical expressions for observations of the pure components M L and M T , using the diode bridge detection method.

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In the longitudinal geometry the optical path is given by [11]   I −°( Fig. 2(b)) is a pure measure of M T .
We Most surprisingly, varying the in-plane applied magnetic field by ϕ H = ± 3° with respect to the cooling field direction the transverse magnetization component changes sign, i.e. its chirality reverses (Fig.3). The fact that for ϕ H = ± 3° no M T signal appears on the right side of the hysteresis loop does, however, not imply that the magnetization reversal proceeds via domain wall nucleation and propagation [14].
At an applied field direction of, e.g., ϕ H = 90° the transverse component appears on found for Co/CoO and Fe/FeF 2 showing that this behavior is not particular to the system discussed here. This will be the subject of a further publication [15].
The types of reversal modes observed for finite ϕ H in twinned MnF 2 (110)/Fe confirm qualitatively the theoretical predictions for an untwinned EB system [16].