Angle and rotational direction dependent horizontal loop shift in epitaxial Co/CoO bilayers on MgO(100)

Systems of exchange-coupled ferromagnetic/antiferromagnetic (FM/AFM) layers can show a horizontal shift of the hysteresis loop, the so-called exchange bias (EB), after cooling the sample through the Néel temperature of the antiferromagnet in a presence of externally applied magnetic field.^1,2

Co/CoO belongs to the well-known EB systems which are often investigated. Opposite to structures like Fe/MnF₂ with its strongly asymmetric hysteresis loops,^3,4 Co/CoO systems usually show a classical EB shift.⁵ In a recent publication about Co nanoparticles with CoO shell of diameter approx. 6 nm, however, asymmetric hysteresis loops described as “hummingbird-like loops” were found and attributed to a soft FM phase related to the early formation of the CoO shells.⁶ While former publications have motivated the existence of such a soft phase in Co/CoO nanoparticles with the existence of a Co₃O₄ phase,⁷ the soft phase in Ref. 6 occurred also well below the Néel temperature of Co₃O₄. Another group attributed the asymmetry found in Co/CoO nanoparticles to the freezing of shell moments parallel to the cooling field orientation and thus introducing an additional anisotropy larger than the Zeeman energy in the other branch of the hysteresis loop.⁸ 

Such asymmetries, however, are only scarcely reported for bilayer systems. Liu et al. found an asymmetric magnetization reversal in CoO/Co epitaxially grown on MgO(001) only for field cooling along the hard axis, while hysteresis loops were symmetric for field cooling along the easy axis.⁹ Here, this effect was attributed to an increased deviation of the average uncompensated AFM magnetization from the cooling field orientation, based on the extended Fulcomer and Charap model.

In a Co/CoO bilayer system with twofold anisotropy, magnetization reversal along the easy axis was dominated by domain wall motion for all temperatures under examination, while along the hard axis, domain wall motion was dominant at low temperatures and domain rotation at high temperatures, resulting in a significant asymmetry in the hysteresis loop around a temperature of 170 K.¹⁰ 

In epitaxially grown Co/CoO systems, the exchange bias fields were shown to be correlated with the FM magnetization direction during field cooling, as expected from usual theoretical descriptions of the exchange bias effect,¹¹ while rotatable contributions, in the meaning of being independent from the cooling field direction, were found experimentally⁵ but not yet quantitatively explained.

Some more general effects are still under investigation in this system. In Co/CoO bilayers with different Co layer thickness, e.g., exchange bias and training effect were shown to be reduced with increasing layer thickness which was correlated with decreasing disorder at the FM-AFM interface. The training effect could be separated into an athermal effect dominating for thinner FM layers, significantly changing the FM domain structure, while a thermal mechanism dominated with increasing layer thickness.¹² Differences between the training effects along hard and easy axes in a Co/CoO bilayer system with biaxial anisotropy were correlated to different motion modes of the antiferromagnetic interface spins, triggered by different reversal modes of the FM layer.¹³ 

In an in-situ experiment, the interface roughness of polycrystalline Co/CoO bilayers could be varied with the annealing time of the sample, allowing for studying an EB decrease with increasing interface roughness in just one sample.¹⁴ 

The purpose of the current paper is to provide more precise explanations of rotatable and directional effects. In order to reach this goal, we report here MOKE (magneto-optical Kerr effect) measurements to detect longitudinal and transverse magnetization components in a Co/CoO thin film system. While longitudinal signals give rise to the coercive fields and allow calculating the EB, the transverse magnetization measurements deliver information about a possible coherent rotation of the magnetization and the rotatable effects.² Opposite to Fe/MnF₂ and Fe/FeF₂ bilayers,² the Co/CoO systems mostly do not show any transverse magnetization components, indicating non-coherent magnetization reversal.¹⁵ 

Thin films were grown by molecular-beam epitaxy (MBE) in the stacking order MgO(100)/Co (8 nm)/CoO (20 nm). Co was grown at a substrate temperature of 300 °C, using a growth rate of 2-3 Å/min. The CoO layer was grown by evaporating Co in an oxygen atmosphere of p = 3.3 · 10^-7 mbar, resulting in CoO with low defect concentration.¹⁶ 

While the Co layer grew in an fcc lattice in (100) orientation, verified by measurements at room temperature revealing a fourfold symmetry and giving rise to the orientation of hard and easy FM axes, RHEED images of the CoO layer showed a twinned (100) pattern,¹⁷ superposing the fourfold symmetry with a second fourfold symmetry with slightly tilted axes.

Field cooling in 0.5 T was performed at 0° and 180° (two of the hard directions of the fourfold FM) as well as 45° (one of the easy directions of the FM, located in the middle between the hard axes) to 215 K which is well below the blocking temperature of the system of 260 K for the sample type under investigation.¹⁷ Fig. 1 depicts the principle of the MOKE measurement in longitudinal orientation together with exemplary results of longitudinal and transverse hysteresis loops. Each change in the magnetization is detected by a rotation of the angle of the linear polarization axis (black arrows in Fig. 1, left panel) and can be translated by an optical setup into measurements of longitudinal and transverse hysteresis loops. For completely de-coherent magnetization reversal processes, the transverse loop does not show any peaks, while completely coherent magnetization rotation often results in broad, rectangular-shaped transverse peaks.⁴ In the system under investigation here, the peaks vary in sign and width, the latter being measured as full-width half-maximum (cf. arrows in Fig. 1, right panel), with the “underground” visible in all transverse loops as deviations from a straight line between both transverse saturation magnetizations defined as the baseline. The transverse peaks correspond to steps in the longitudinal hysteresis loop, as visible in Fig. 1 (right panel).

The longitudinal hysteresis loop in Fig. 1 has a similar shape as the “hummingbird-like loops” depicted in Ref. 6. The angle chosen hear clearly shows an asymmetry of the longitudinal as well as transverse hysteresis loop. The evaluation of the loop shape with the sample angle depends on the cooling field direction. If the width of the transverse peaks vanishes on one side (cf. Figs. 4, 5), the corresponding side of the longitudinal hysteresis loop does not show a peak. To be more exact, an asymmetry is always visible in the longitudinal loop if the peaks in the transverse loop have different widths.

Fig. 2 depicts the horizontal shift for different cooling field orientations at low temperatures. Firstly, this horizontal shift cannot be attributed to an EB since cooling field direction and opposite orientation show the same values. Instead, changing the sample rotation direction shows clearly that here a bias is correlated with a rotatable effect. Importantly, the effect is not supposed to be attributed to erroneously measuring minor loops due to insufficient intensity of saturation field, a problem which is known from several systems in experiment and theory.^18–20 Here, the risk of not reaching a saturated state was eliminated by measuring in fields up to 0.5 T which is nearly ten times higher than average coercive fields detected for this sample.

Field cooling the sample along an easy axis, however, modifies this result, as depicted in Fig. 3. In the directions approximately perpendicular to the cooling field direction (here marked by white areas), the horizontal shifts are similar to the bias from Fig. 2, with the angular region around 135° being identical to measurements during clockwise rotation and the angular region around 315° showing counter-clockwise behavior. Additionally, now a clear unidirectional effect is visible in the grey areas around the cooling field and opposite directions, superimposed by the rotatable effect seen above. The competing anisotropies result in a shift of the sample angle at which the maximum EB is reached from 45° and 225° to 60° and 250°, respectively.

It should be mentioned that no “rotatable training effect” was visible for any of the cooling field directions discussed above, i.e. rotating the sample further after the first complete rotation resulted in identical measurements as during the first 360°. Additionally, zero field cooling led to a repetition of the measurements after the last field cooling process. On the other hand, repeating measurements at the same angle resulted in a training effect which depended on the sample orientation, as described in Refs. 12 and 13.

A small or non-existent training effect is unusual for a Co/CoO system. Here, it can be explained by the difference in the measurement principle. While measuring hysteresis loops in the same orientation is the standard procedure reported in the literature, here we have rotated the sample and measured at always changing angles. Interestingly, this effect was already described by Liu et al.²¹ They found in CoO/Co(100) bilayers – with a significantly thinner AFM than in our sample of only 2-3 nm thickness and a FM of similar thickness, and unfortunately without describing whether CoO was twinned in their samples, too – that the asymmetry of the hysteresis loop did not only survive training, opposite to polycrystalline bilayers, but the reversal asymmetry could even be inverted by applying a perpendicular hysteresis loop. This corresponds exactly to our finding that changing the rotational direction can (partly) invert the horizontal loop shift.

Additionally, the original state without training effect could partially be restored by a perpendicular hysteresis loop from the opposite field direction. Liu et al. attribute this finding the relative orientation of the average uncompensated AFM magnetization with respect to the cooling field. Since the first can be modified by in-plane perpendicular loops, the magnetization reversal asymmetry can be manipulated in this way.

Comparing these findings with our results, it should be mentioned that the experiments of Liu et al. can be regarded as a base for our investigation which broadens the experiments from measuring at single angles to a more complex spectrum. Tests at other temperatures (e.g. 20 K and 120 K) showed that the effects were in principal identical to the results shown here. At lower temperatures, however, the peak widths were significantly increased so that the maximum available external magnetic field (0.5 T) was insufficient for measurements of several sample orientations. This is why here a relatively high temperature was chosen for the detailed study.

Similar effects are visible in the transverse magnetization component measurements. Fig. 4 depicts the peak widths for peaks on the left and on the right side of the transverse curves. The field area in which such peaks occur depict the areas of (partly) coherent magnetization rotation, i.e. the field range in which magnetization reversal occurs.⁴ Here, positive widths indicate the respective peak pointing “down”, as given along the cooling field direction, while negative widths are correlated with transverse peaks pointing “up”, as shown in the insets in Fig. 4(a). Changing the sign of the peak means changing the direction of the coherent magnetization rotation.

Firstly, opposite to typical Co/CoO systems, clear peaks in the transverse magnetization component are visible, for larger widths similar to the rectangular-shaped peaks in Fe/MnF₂.⁴ This is typical for coherent magnetization reversal processes in which a stable intermediate state approx. perpendicular to the external magnetic field is assumed,⁴ with the sign of the transverse peak indicating the magnetization orientation in this state and thus the rotational direction of the complete magnetization reversal process. The effect that these stable intermediate states become broader next to hard axes is well-known from the EB system Fe/MnF₂, too.¹⁵ 

While the longitudinal hysteresis loops measured after field cooling at a hard axis did not reveal any evidence for a significant EB (cf. Fig. 2), the situation is clearer for the transverse magnetization component. In all cases, the first quarter (between 0° and 90°) which is reached from the cooling field direction shows different magnetization reversal processes than the other three angular regions. This means especially that around the angle opposite to the cooling field direction (180°), no special behavior was found. Thus the finding that reversing the rotation direction leads to the same results, being mirrored at the field cooling direction, is not unexpected. For field cooling at 0°, e.g., measuring during counter-clockwise rotation results in special magnetization reversal processes in the angular region between 0° and 270°.

It should be mentioned that rotating the sample further by n·360° leads to the same findings within the measurement accuracy, i.e. no training effect can be found in the transverse signal either; the quarter around the cooling field direction (cooling field angle ± 90°) keeps a different magnetization reversal process even after several rotations. This finding can be explained in the same way as the missing training effect in the longitudinal loops.

A more complex phase diagram becomes visible after field cooling at an easy axis. Fig. 5 depicts the peak widths after field cooling at 45° using transverse magnetization component measurements. In both angular regions around the direction perpendicular to the cooling field direction (marked white), mirror symmetry is visible, comparing the widths of both peaks. The area around 135° shows a similar peak structure and thus magnetization reversal behavior as it was visible around the next easy axis after field cooling along a hard axis (Fig. 4). Near to 315°, a cross-like structure slightly below the x-axis is visible, similar to the peak structures reached after field cooling along a hard axis and rotating by 270°-360°. Opposite to Fig. 4, here both the quarters around the cooling field direction and the opposite direction (marked grey) are influenced by an exchange bias. This unidirectional anisotropy is clearly visible, comparing the angular regions around 45° and around 225°. As already depicted in Fig. 3, Co/CoO(100) shows a superposition of the exchange bias and the before described changes of the relative orientation of the average uncompensated antiferromagnetic magnetization with respect to the cooling field in case of field cooling along an easy axis.

It should be mentioned that experiments with Co/CoO samples grown on MgO(111) or MgO(110) substrates did not reveal similar effects, nor did similar samples on MgO(100) in the reversed stacking order. In the literature, to our knowledge the only similar experimental result was found in a similar sample, grown on the same substrate in the same stacking order.²¹ This emphasizes the importance to further investigate epitaxial Co/CoO samples on MgO(100) and understand in detail which microscopic effects lead to the negligible training effect during a sample rotation and the switching of the transverse peaks’ signs which is identical with a change of the direction of magnetization rotation during reversal processes.

To conclude, in the thin film system MgO(100)/Co/CoO field cooled to temperatures below the Néel temperature of the AFM, magnetization reversal processes can be manipulated by modifying the relative orientation of the average uncompensated AFM magnetization with respect to the cooling field by in-plane perpendicular loops. In this way, the reversal asymmetry of the longitudinal and transverse hysteresis loops can be inverted, and the training effect which is well-known for Co/CoO systems can be suppressed.

Future experiments will concentrate on further combinations of cooling field directions and measurement angles, as well as analysis of irreversible processes and thermomagnetic effects, in order to examine the microscopic origin of the unexpected findings.

Samples were prepared in RWTH Aachen University by A. E. The authors thank G. Güntherodt for ceding the samples to them.