Depth profile of uncompensated spins in an exchange bias system

eScholarship provides open access, scholarly publishing services to the University of California and delivers a dynamic research platform to scholars worldwide. Abstract: We have used the unique spatial sensitivity of polarized neutron and soft x-ray beams in reflection geometry to measure the depth dependence of magnetization across the interface between a ferromagnet and and antiferromagnet. The new uncompensated magnetization near the interface responds to applied field, while the uncompensated spins in the antiferromagnetic bulk are pinned, thus providing a means to establish exchange bias. The spin structure of an antiferromagnet plays a critically important role in magnetic devices; however, the spin structure at the surface and interior of an antiferromagnetic thin film remains unknown. Here, we have used the unique spatial sensitivity of polarized neutron and soft X-ray beams in reflection geometry to measure the depth dependence of magnetization across the interface between a ferromagnet and an antiferromagnet. The net uncompensated magnetization near the interface responds to applied field, while uncompensated spins in the antiferromagnet bulk are pinned; thus, providing a means to establish a magnetic reference state.

The spin structure of an antiferromagnet plays a critically important role in magnetic devices; however, the spin structure at the surface and interior of an antiferromagnetic thin film remains unknown. Here, we have used the unique spatial sensitivity of polarized neutron and soft X-ray beams in reflection geometry to measure the depth dependence of magnetization across the interface between a ferromagnet and an antiferromagnet. The net uncompensated magnetization near the interface responds to applied field, while uncompensated spins in the antiferromagnet bulk are pinned; thus, providing a means to establish a magnetic reference state. heads or magnetic random access memory, involves understanding the influence of physical confinement of materials (at the nanometer length scale) on magnetic phenomena. 1 An example is exchange bias, 2, , , , 3 4 5 6 which is observed as a shift of the ferromagnetic hysteresis loop along the field axis, observed in ferromagnetic-antiferromagnet (F-AF) systems. The shift is attributed to the exchange coupling between the F and AF across the interface.
Exchange bias serves as a means to establish a magnetic reference in a spin valve.
The dependence of exchange bias 2,3 on environmental variables such as field, 7, , 8 9 temperature 10 and strain 11 is commonly attributed to changes in the AF domain state, 12 or the metastability of the spin structure in the AF film bulk or at the F-AF interface. 13 Indeed, a neutron scattering study of exchange biased Co/LaFeO 3 14 and an X-ray magnetic circular dichroism study of exchange biased Co/Ir 0.8 Mn 0. 2 15 each observed a correlation between exchange bias and pinned magnetization in the antiferromagnet. Yet, detailed information about the depth dependence of the spin structures of AF domains, particularly at the F-AF interface and extending into the AF film bulk is mostly lacking for exchange bias systems.
There is a compelling need to know the distribution of uncompensated magnetization at the F-AF interface and in the AF bulk when in proximity to a ferromagnet, and the response of uncompensated magnetization to magnetic field.
We have used polarized neutron and soft X-ray beams in reflection geometry to measure the depth profile of magnetization across the F-AF interface and inside the AF film with unprecedented sensitivity. Measurement with neutron beams provides the variation of the vector magnetization (in our case its projection onto the sample plane) 16 in absolute units, and measurement with circularly polarized X-ray beams tuned to the L-edges of the magnetic atoms provides the variation of the element specific magnetization projected onto the incident beam axis. 17, , 18 19 For a Co/FeF 2 bilayer-an often studied model exchange biased system-we find that the net uncompensated magnetization in the FeF 2 antiferromagnet as far as 3.5 nm from the Co/FeF 2 interface responds to applied field, and this magnetization is anti-parallel to the Co magnetization. In the remainder of the FeF 2 layer, the uncompensated magnetization is pinned. Our observations motivate an alternative explanation of exchange bias that attributes bias to spins that are pinned in the antiferromagnet bulk, rather than at the F-AF interface.
Exchange bias samples were prepared by sequential electron beam evaporation of comparison of the off-specular X-ray reflectivity to the specular X-ray reflectivity 20 indicates that the roughnesses of the two interfaces were uncorrelated.
In-plane glancing angle X-ray diffraction and transmission electron microscopy confirmed that the AF layer was an untwinned single crystal film with [ ]   21 The ~1.8° widths of in-plane Bragg reflections from the FeF 2 single crystal were about four times broader than the reflections from the MgF 2 substrate. The dislocation density 22 at the FeF 2 /MgF 2 interface corresponds to an average spacing between dislocations of ~55 nm; however, were all the misfit strain in the FeF 2 film relieved, we would expect the spacing to be 21 nm. 23 Therefore, only a fraction of the total misfit strain relieved is relieved in the FeF 2 film. Defects and strain (through piezomagnetism) can produce uncompensated magnetization in an antiferromagnet such as The resonant soft X-ray scattering experiment was performed using a circularly polarized incident X-ray beam (geometry shown in the inset of Figure 1  We performed a second soft X-ray experiment that involved measuring the reflected beam intensity as a function of Q, for one incident X-ray beam polarization for H = ±796 kA/m. This protocol is sensitive to changes in the specular reflectivity due to the reversal of unpinned spins. From the variation of I H+ and I H− with Q ( Figure 2, inset)-here, the subscript refers to H being parallel (+) or anti-parallel (-) to H FC -the depth profiles of the Co and Fe spins can be obtained for each field direction. A theory for reflectometry with resonant X-ray beams based on a generalization of the Distorted Wave Born Approximation was used to analyze the data. ,, We chose to treat the Co magnetization as rotatable, but retained the possibility for having both unpinned Fe spins and Fe spins pinned along the direction of the cooling field. Using this model, the reflectivities for the two directions of H were calculated from the spin density profile shown in Figure 2 to obtain the solid curves (inset) which are those yielding a minimum χ 2 (best fit). 26 The spin profile represents the projection of the net magnetization of Co or Fe along the incident beam axis, which is nearly parallel to H r . 27 We see a change of the Fe spin magnetization from negative to positive values over a distance of ~2 nm below the Co/FeF 2 interface. The changes in the projections of the Co and Fe spins along H r with depth occur over a distance much larger than that corresponding to interdiffusion or chemical roughness across the Co/FeF 2 interface, which could be explained by the presence of magnetic domains at the interface, or the rotation of magnetization away from the field axis.
We undertook a polarized neutron reflectometry 28,29 study of the sample including polarization analysis in order to determine whether the spatial variation of the net   direction-a direction that was perpendicular to the cooling field.
We note that SF reflectivity was not observed when the field during the neutron measurement was applied parallel to the cooling field. Nor, was SF reflectivity observed when the measurement field was applied perpendicular to the cooling field and the temperature of the sample was 108 K-significantly above the ordering temperature T N = 78 K of FeF 2 .
Quantitative information about the locations of unpinned and pinned uncompensated magnetization in the sample was obtained from an analysis of the Q dependence of the neutron reflectivity using the Parratt formalism. 31 The magnetic structure of the model was   Figure 4). 35 The twist of the magnetization across the Co/FeF 2 interface is reminiscent of a domain wall parallel to the interface between soft and hard magnetic materials, as found for example in exchange spring magnets 36,37 or in the computational model proposed by Kiwi et al. 38 to explain exchange bias in Fe/FeF 2 bilayers. The rotation of the uncompensated magnetization close to the Co/FeF 2 interface provides a natural explanation for the experimental observation that an antiferromagnet must exceed a critical thickness, t c (Figure 1), before bias is produced. 39 In a previous study of the influence of crystalline quality of FeF 2 films on exchange bias, 40       32 The magnitude of the Co magnetization, M Co , was obtained from neutron data collected when the sample temperature was 108 K.
33 The magnetic widths of the Co/interface and interface/FeF 2 were determined to be 1.5±0.1 nm.
34 The neutron scattering data are sensitive to the orientation of the FeF 2 magnetization relative to the Co magnetization. The key point is that our data indicate the magnetizations in the two layers move in opposite directions.
35 The tendency for the Co magnetization to oppose the rotation of the FeF 2 magnetization near the Co/FeF 2 interface is not contrived. The starting configuration was one that began with a twist of the same sign