Soft X-ray techniques to study mesoscale magnetism

Heterogeneity in magnetization (M) is ubiquitous in modern systems. Even in nominally homogeneous materials, domains or pinning centers typically mediate magnetization reversal. Fundamental lengths determining M structure include the domain wall width and the exchange stiffness length, typically in the 4-400 nm range. Chemical heterogeneity (phase separation, polycrystalline microstructure, lithographic or other patterning, etc.) with length scales from nanometers to microns is often introduced to influence magnetic properties. With 1-2 nm wavelengths {lambda}, soft x-rays in principle can resolve structure down to {lambda}/2, and are well suited to study these mesoscopic length scales [1, 2]. This article highlights recent advances in resonant soft x-ray methods to resolve lateral magnetic structure [3], and discusses some of their relative merits and limitations. Only techniques detecting x-ray photons (rather than photo-electrons) are considered [4], since they are compatible with strong applied fields to probe relatively deeply into samples. The magneto-optical (MO) effects discovered by Faraday and Kerr were observed in the x-ray range over a century later, first at ''hard'' wavelengths in diffraction experiments probing interatomic magnetic structure [5]. In the soft x-ray range, magnetic linear [6] and circular [7] dichroism spectroscopies first developed that average over lateral magnetic structure. These large resonant MO effects enable different approaches to study magnetic structure or heterogeneity that can be categorized as microscopy or scattering [1]. Direct images of magnetic structure result from photo-emission electron microscopes [4, 8] and zone-plate microscopes [9, 10]. Scattering techniques extended into the soft x-ray include familiar specular reflection that laterally averages over structure but can provide depth-resolved information, and diffuse scattering and diffraction that provide direct information about lateral magnetic structure. Scattering techniques are further classified as partially for fully coherent according to the extent of transverse coherence of the incident beam