Depth Profile of Uncompensated Spins in an Exchange-Bias System

The phenomenon known as exchange bias at the interface between a ferromagnet and an antiferromagnet is currently a subject of intense research because of its applications in the magnetic recording and read-head industries. An international collaboration headed by researchers from the University of California, San Diego, has used resonant x-ray scattering and polarized-neutron reflectometry to determine the depth-dependent magnetization in an exchange-biased sample. These results provide atomic-level insights into the mechanism of exchange bias, specifically the involvement of mutual interactions between two kinds of uncompensated spins in the antiferromagnet and spins in the ferromagnet.

An In-Depth Profile of Atomic Spin

When it comes to magnetic atoms, such as iron, researchers developing state-of-the-art devices for magnetic reading and writing are finding that location makes just as much difference as it does in real estate. Consider the quantum mechanical spins that make some atoms magnetic. In a ferromagnet, the spins are aligned in parallel but are free to rotate, whereas in an antiferromagnet, the spins are antiparallel. Interactions across the interface between a ferromagnet and an antiferromagnet result in “exchange bias,” which locks the ferromagnet spins, thereby forming a reference layer with a fixed direction of magnetization that is one key to modern magnetic devices.

Despite years of effort, the details of how exchange bias occurs remain incomplete. Roy et al. have combined two experimental techniques, one based on reflection of x rays from an exchange-biased sample consisting of iron difluoride (the antiferromagnet) and cobalt (the ferromagnet) and the other relying on reflection of neutrons to obtain the distribution of spins of both iron and cobalt with distance away from the interface between the ferromagnetic and antiferromagnetic layers. Their spin profiles allowed them to determine the distributions of free and pinned spins and of spin orientation, thereby providing atomic-level insights into the mechanism of exchange bias. Specifically, they concluded that mutual interactions between two kinds of spins in the antiferromagnet and spins in the ferromagnet are responsible for exchange bias.

In modern nanolayer magnetic devices, the shifted hysteresis loop centered on a nonzero magnetic field that characterizes exchange bias makes the ferromagnet an excellent magnetic reference layer because it is difficult to reverse the magnetization. Although exchange bias has been extensively studied over the years, fundamental questions remain unanswered or inadequately answered. For example, photoemission electron microscope (PEEM) images and x-ray circular magnetic dichroism (XMCD) studies have revealed the existence of uncompensated moments (spins in one direction not matched by an opposite spin) at the antiferromagnetic interface. What is the nature of the uncompensated spins? What are their lateral and depth distributions? How do they interact with the spins in the ferromagnet?

Hysteresis loops measured from the difference in the reflectivity for left- and right-circularly polarized x rays (I_p+ – I_p–) at a fixed angle of incidence for cobalt and iron. The inset shows the scattering geometry and the spin model used to fit reflectivity data.

To address these issues, the collaboration used circularly polarized soft x-ray and spin-polarized neutron beams in small-angle reflection geometry with a sample consisting of a trilayer of antiferromagnetic FeF₂, ferromagnetic cobalt, and aluminum epitaxially grown onto a single-crystal MgF₂ substrate. Resonant x-ray measurements at the L edges of the magnetic atoms provided the variation of the element-specific magnetization, while neutron measurements yielded the variation of the vector magnetization. With the two techniques, the group was able to determine, in an element-specific way, the depth dependence of the magnetic density in absolute units.

Depth-dependent magnetic-density profiles of cobalt (blue) and iron (red) as obtained by fitting the reflectivity data (inset). The vertical green lines mark the physical interface between Al/Co and Co/FeF₂, respectively. The two curves correspond to magnetizations when the external field is parallel to the direction of the field in which the sample was cooled; dashed curves represents the field-reversed case.

Soft x-ray resonant magnetic reflectivity at ALS Beamline 4.0.2 was used to measure hysteresis loops at the L₃ edges of cobalt and iron in a 1-tesla field at 20 K. The measurements showed that both elements exhibited hysteresis, indicating that some cobalt and some iron spins were unpinned or free to rotate with the applied field. Both loops were shifted along the positive-field axis, with a similar bias field resulting from the shifted loops. The spin-density profiles obtained from analyzing the reflectivity as a function of wave vector transfer revealed a thin interfacial layer (about 17 Å thick) in FeF₂ with unpinned iron spins that were aligned opposite to cobalt spins in the bulk cobalt. Pinned, uncompensated iron spins were also found throughout the depth of the antiferromagnet.

Polarized neutron reflectivity data (symbols) and fit (continuous line). Inset shows the experimental geometry. The sample was cooled initially in a field of 1 Tesla and then a magnetic field applied at right angles to the original field to distinguish between spins that were frozen and those that were free to rotate as a function of depth.

To probe the depth profile of the pinned magnetization, the group turned to the Manuel Lujan Jr. Neutron Scattering Center at Los Alamos National Laboratory for polarized-neutron reflectometry measurements in a cooled sample in a 0.7-T field. The oscillations of the reflectivity with wave vector transfer indicated the presence of pinned moments in the bulk of the FeF₂ at distances greater than about 3.5 nm from the interface. Further analysis showed that near the Co/FeF₂ interface, the angular dependence of the magnetization relative to the applied field is consistent with an antiferromagnetic coupling across an interface.

Depth dependence magnitude (blue) and phase angle (red) of the vector magnetization. A phase angle of –90º corresponds to magnetization parallel to the original field direction. The inset shows the twist in the magnetization near the Co/FeF₂ interface. Cyan and green dots are magnetization magnitudes and phases obtained from a micromagnetic simulation. The sum of the iron and cobalt spin density profiles from Figure 2 are shown in absolute units (open circles).

From these results, the collaborators concluded that the antiferromagnet has a net magnetization made up of two types of spins: those in a thin (about 2-nm) interfacial layer at the interface, which are strongly coupled to the magnetic spins of the ferromagnetic cobalt (and respond with them to an applied field) and those in the bulk of the FeF₂, which do not respond to an external field. It is the coupling of these spins to the ferromagnetic spins via the interfacial spins that gives rise to the exchange bias.

Research conducted by S. Roy, M. Dorn, Z.-P.Li, I.V. Roshchin, and I.K. Schuller (University of California, San Diego); O. Petracic (UCSD and Universität Duisburg-Essen, Germany); X. Batlle (UCSD and Universitat de Barcelona, Spain); R. Morales (UCSD and Universidad de Olviedo, Spain), K. Chesnel (ALS); J.B. Kortright (Berkeley Lab); S. Park, M.R. Fitzsimmons, A. Mishra, and X. Zhang (Los Alamos National Laboratory); and S.K. Sinha (UCSD and Los Alamos National Laboratory).

Research funding: U.S. Department of Energy, Office of Basic Energy Sciences; National Science Foundation; University of California; Alexander von Humboldt Foundation; Spanish MECD; Fulbright Commission; Catalan Dursi; and Swiss National Science Foundation. Operation of the ALS and of LANSCE is supported by BES.

Publication about this research: S. Roy, M.R. Fitzsimmons, S. Park, M. Dorn, O. Petracic, I.V. Roshchin, Z.-P. Li, X. Batlle, R. Morales, A. Mishra, X. Zhang, K. Chesnel, J.B. Kortright, S.K. Sinha, and I.K. Schuller,, “Depth Profile of Uncompensated Spins in an Exchange Bias System,” Phys. Rev. Lett. 95, 047201 (2005).