  The first order reversal curve (FORC) method is a macroscopic measurement
technique which can be used to extract quantitative, microscopic properties of
hysteretic systems. Using magnetic transmission X-ray microscopy (MTXM), local
element-specific FORC measurements are performed on a 20 nm thick film of CoTb.
The FORCs measured with microscopy reveal a step-by-step domain evolution under
the magnetic field cycling protocol, and provide a direct visualization of the
mechanistic interpretation of FORC diagrams. They are compared with
magnetometry FORCs and show good quantitative agreement. Furthermore, the high
spatial resolution and element-specific sensitivity of MTXM provide new
capabilities to measure FORCs on small regions or specific phases within
multicomponent systems, including buried layers in heterostructures. The
ability to perform FORCs on very small features is demonstrated with the
MTXM-FORC measurement of a rectangular microstructure with vortex-like Landau
structures. This work demonstrates the confluence of two uniquely powerful
techniques to achieve quantitative insight into nanoscale magnetic behavior.
