Miguel A. Marioni, Sara Romer, Hans J. Hug1, EMPA, Swiss Federal Institute for Materials Testing and Research, CH-8600 Dübendorf
1 Also at: Institute of Physics, Universität Basel, CH-4056 Basel
Every computer hard-drive and many magnetic sensors contain a thin-film device using the GMR or TMR effect. In it, the resistance from a stack of thin films is made to depend on the relative orientation of different magnetic layers’ magnetization, of which one serves as a reference and retains its direction. Fixing the magnetization is accomplished with exchange-bias. Not surprisingly, the effect has received much attention throughout the history of magnetic recording and sensor design. Perhaps it is a surprise, then, that so much remains unknown about exchange-bias after half a century since its discovery.
Principles of the exchange bias effect
Exchange-biasing manifests macroscopically as a lateral shift of size Hex of the hysteresis loop (Fig. 1 (a); occasionally there is an accompanying vertical shift Mshift as well.). It occurs if a sample with at least one ferromagnet (F) / antiferromagnet (AF) bilayer (e.g. in Fig. 1 (b)) is cooled through the Néel temperature (TN) of the antiferromagnet. It is generally believed that (local) magnetization of the ferromagnet (F) layer (locally) generates pinned uncompensated spins (pUCS) in the AF layer that are coupled to the F layer. An obstacle to understanding the exchange bias effect is that only a subset of the UCS (those pinned, and coupled to the ferromagnet) are responsible for it . The experimental method and preparation may affect these subsets in distinct ways and an interpretation of UCS measurements must take this into account.
Experimental Methods to measure uncompensated pinned spins
Reflectometry experiments using polarized neutrons or circularly polarized X-rays as probes have been used to access UCS sub-systems and to map out their thickness distribution. Both methods fit proposed model descriptions of these distributions to the experimental data. Neutron-based techniques can unambiguously determine the relative orientation of the UCS of the various sub-systems and the F-spins. To accomplish this X-ray-based experiments require, in addition, specifying magneto-optical constants of the atomic species carrying the spin in the AF. Recent results have also stressed the influence on XMLD (X-ray Magnetic Linear Dichroism) signals of the orientation of AF spins relative to the crystallographic axes.
Reflectometry techniques cannot, however, reveal the lateral distribution of UCS. This very important aspect of exchange bias characterizations is accessible with other (complementary) techniques. Among these, photoemission electron microscopy (PEEM) with circular and/or linearly polarized X-rays has revealed a correlation between AF domains and F-domains, the formation of new chemical phases at the AF/F interface with magnetic moments parallel to those of the F, and induced ferromagnetic moments at the AF/F interface. But PEEM microscopes have to-date not attained lateral resolutions on the length scale of grains-sizes of typical polycrystalline AF materials, important for applications. Note that PEEM experiments require the applied magnetic field to be zero or near-zero, and accordingly cannot distinguish pinned from non-pinned UCS of the AF directly. In fact, only a small part of the net moment induced locally by the F in the AF consists of pinned UCS, which are difficult to isolate from the rest with present-day PEEM sensitivities.
In contrast to XMCD-PEEM, XMCD (X-ray Magnetic Circular Dichroism) holography is a lens-less imaging method and hence allows the application of arbitrary magnetic fields. Recently, element-selective soft x-ray holography and spectroscopy measurements have been used to study the evolution of domains in ferromagnetic multilayer of [Pt(1.8nm)Co(0.6nm)]×8 on a Mn80Ir20(5nm) antiferromagnetic layer . Element-specific magnetometry revealed uncompensated AF magnetic moments on the Mn and allowed to estimate that about 10% of these moments are pinned and thus are relevant for the exchange bias effect. However, no magnetic contrast could be observed at the Mn L3 edge, so the imaging of the pattern of uncompensated and pinned uncompensated Mn moments was not achieved.
A different technique to gain access to the UCS of a system is magnetic force microscopy (MFM). Operated in vacuum, MFM typically measures shifts in the resonance frequency of a cantilever outfitted with a magnetic tip. These are proportional to the magnetic field gradients to which the tip is exposed. Therefore an MFM investigation of sample properties requires a sample with suitable domains generating stray field . In a rough approximation, the MFM contrast arising from the stray field of a domain pattern in a ferromagnetic thin film with perpendicular magnetization is proportional to the z-component of the magnetic moment areal density . This allows a first estimate of the contrast expected for a domain pattern of pinned uncompensated spins imprinted by a corresponding pattern of ferromagnetic domains. In our recent work  the MFM contrast measured above an up/down domain pattern in a CoPt ferromagnetic multilayer was 46 Hz (Fig. 2 (a)). From the magnetization of the CoPt-multilayer and its thickness a total magnetic moment areal density of mFz/A= MCoPt tCoPt = 622 kA/m × 22 nm = 1.37 · 10-2 Am2/m2 is found. Likewise an areal moment density of 4.48 · 10-4 Am2/m2, corresponding to a fully uncompensated CoO AF, would thus generate a frequency shift of 1.5 Hz. Our MFM can easily detect ±0.05 Hz in a reasonable measurement bandwidth of 100 Hz, corresponding to a scan speed of about 1s/line in a 256 pixel line. This means that the corresponding ±1.49 · 10-5 Am2/m2 are detectable, and hence also about ±3% of a fully uncompensated monolayer.
Assessing the number of pinned uncompensated spins by MFM
Not only can MFM image fractions of uncompensated AF spins but it can also be used in applied homogeneous fields. These do not generate a force on the magnetic tip and thus do not give rise to MFM contrast. One can therefore study the evolution of the F-domain pattern in external fields as shown Fig. 2 (a) and (b) (In prior work up to 7 T were applied ).
MFM however lacks the element-specificity of XMCD methods, so it cannot distinguish directly between different sources of the stray field, i.e. generated by different atomic species. The contrast observed in the data shown in Fig. 2 (a) and (b) arises predominantly from the stray fields emanating from the up/down domain pattern of the F-layer and a small contribution from the imprinted local uncompensated AF moments. However, magnetic stray fields generated the F-layer roughness, as well as by local variations of its thickness or saturation magnetization, could also generate a small MFM contrast. Topography-induced variations of the van der Waals force occurring when the tip of the MFM scans in a plane parallel to the average slope of the sample provide yet another contribution to the measured contrast. Modeling shows that from these last contributions to contrast only the van der Waals force-mediated topography contribution is relevant. It leads to the grainy appearance of the F-domain contrast (Fig. 2 (a)).
If the F-layer is saturated by applying a sufficiently strong external field, it does no longer generate an MFM contrast. One can easily understand this by noting that the stray fields generated by the magnetic poles of the top and bottom surface compensate. In this situation the only remaining source of contrast is the pattern of pinned uncompensated AF moments. Note that if the other contrast contributions cannot be neglected, the difference of two consecutive MFM measurements performed in positive and negative saturation fields will solely contain the contrast contribution of the pinned UCS moments .
Quantitative MFM on exchange-biased systems
It is now possible to ascertain the exact relation between pinned uncompensated spins and exchange bias by looking at the evolution of ferromagnetic domains over the underlaying pattern of pinned uncompensated spins . For example a film of Pt(2nm)/CoO(1nm)/Co(0.6nm)/ [Pt(0.7nm)Co(0.4nm)]x20/Pt(20nm)/Si (Fig. 1 (b) and (c)) can be seen as the ferromagnetic domains evolve, Fig. 2. Dark areas correspond to parallel tip and sample magnetization; i.e. there is an attractive force and negative frequency shift. Conversely, bright areas correspond to the antiparallel orientation and positive frequency shift. F-domains are clearly visible in Figs. 2 (a) and (b), generating a contrast of several tens of Hz. As expected, the area of the bright domains (magnetization opposite to the applied field) diminishes as fields are applied parallel to the dark domain magnetization, as e.g. Fig. 2(b) for 200 mT. Consistent with the saturation of the ferromagnet the bright domains have disappeared at 300 mT, Fig. 2 (c). At this and larger fields (up to 7 T) the MFM data reveals a rather irregular pattern with contrast of only 4.4 Hz. Cooling the F/AF system with the F in different initial domain states reveals that the shape of the patterns observed after saturation are governed by the structure of the initial F-domains.
In the same way that the saturated F does not produce a stray field, the uncompensated AF spins which rotate with the F-domains will not be imaged at saturation. The main contrast is thus due to pinned UCS . Using the response function of the MFM tip according to quantitative MFM methods  one can obtain the areal moment of pinned uncompensated spins (more specifically the z-component of the areal moment of the pinned UCS projected onto a virtual F/AF interfacial plane) from the Δf pattern (Fig. 2 (c)). The result can be seen in Fig. 3 (a). At the AF-F interface a strikingly inhomogeneous distribution of the pinned UCS is revealed. TEM images of the films (Fig. 1(c)) show columnar grains in the film with sizes of the order of 10 nm, placing the observed pinned UCS variations on the same length scale. This pinned UCS distribution also represents an inhomogeneous distribution of ‘‘pinning’’ centers for F-domain motion, leading to the commonly observed EB-induced increase in coercivity.
Figures 3 (a) and (b) also show the F-domain contours (white lines) at different fields overlaid to the pinned uncompensated AF moment pattern that biases them. From them we see that the pinned UCS in the area initially covered by bright F domains (Fig. 1) is predominantly negative [blue in Figs. 3 (a) and (b)], whereas the area initially covered by dark F domains (Fig. 1) is predominantly positive [yellow in Figs. 3 (a) and (b)]. This local antiparallel alignment between the F magnetization and the pinned UCS suggests antiferromagnetic coupling across the F/AF interface and is consistent with earlier work [2,6,7]. Because the local alignment is antiparallel to the local cooling field, it can only be the result of exchange coupling.
Notice the existence of isolated regions of pinned UCS that do not follow the above trend. They are oriented parallel to the (initial) adjacent F-magnetization, and seem to be circumscribed to areas of the size of single grains of the film (cf. Fig. 1 (c)).
More insight can be gained from a quantitative evaluation of the data just discussed.
One can compute the average pinned UCS density (data from Figs. 3 (a) and (b) for the areas under the F-domains, i.e. delimited by the white contours of the figures, as shown in Figs. 3 (c). Under the initial yellow and blue F-domains the average pinned UCS density is ±21.8% of a fully uncompensated monolayer of AF spins. As a magnetic field is applied parallel to the blue F-domains, they expand at the expense of the yellow F-domains. Over the area covered by the retracted yellow F-domains the average pinned UCS is more negative than before the field was applied. Figure 3 (d) shows the average densities of UCS under each domain type as a function of the applied field. A roughly proportional relation between the applied field and the average pinned UCS density under the surviving yellow F-domains is apparent.
In Figure 3 (c) small regions can be seen with parallel pinned UCS-F domain alignment at zero field (red arrows). The retracting F-domains avoid these regions as they reconfigure in response to the applied field.
In other words, at least in the CoO (and MnIr as shown in ) Co/Pt perpendicular system pinned UCSs coupling antiparallel to the F magnetization stabilize its orientation, i.e. they are biasing, whereas pinned UCSs oriented parallel to the F magnetization have the opposite effect, i.e. they are anti-biasing.
These results are a direct observation of the stabilizing effect of (antiparallel) pinned UCS on F domains, and show that a higher pinned UCS density leads to a stronger F domain pinning, i.e. a higher EB effect.
The density of pinned UCS found by MFM agrees well with work on polycrystalline Py/CoO samples estimating the pinned UCS at about 10% of a 1.1 monolayer-thick layer of interfacial Co2+ spins. A decreasing magnetic moment of the FM layer near the interface may explain the somewhat smaller density of pinned UCS observed there. But the high density of pinned UCS requires that the average coupling strength between the pinned UCS and F-spins be much smaller than previously expected, in order to explain the rather small exchange bias field.
Without an exhaustive theoretical analysis of the pinned UCS coupling strength and possible variations thereof, we point out that the interface between the AF and the F very likely differs from a chemically sharp interface across which the system goes from F to AF, on account of interdiffusion and interface reconstruction. A similar reconstruction ought to be expected in the CoO/Co interfaces discussed here and may lead to a structurally and chemically disordered interfacial phase, explaining the higher density of pinned UCS and their weaker coupling to the F-spins. Furthermore frustration, as found in spin glass systems, may also lead to weak or indirect coupling between AF UCS and the F-layer. Yet a weak coupling may be a necessary condition for the UCS AF moments to remain pinned to the AF-lattice rather than rotate with the F-moments.
Exchange coupling between different AF grains across their grain boundaries could lead to frustration of the magnetic orientation over grain-size areas, giving rise to the observed anti-biasing effect. Further work to address this issue is under way.
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[Released: May 2012]