Optical resolution limit
Resolution of the Kerr microscopy is defined by optical resolution limit, which according to Reyleigh criterion is
where λ is a wavelength of the light and NA is numerical apperture of the objective lens, which characterizes the range of angles over which the objective can accept the reflected ligh. It is defined by NA=n sin(θ), where n is the index of refraction of the medium in which the lens is working (1.00 for air and typically 1.52 for immersion oil).
Typical working distances for the obejcetives are ranging from 370 μm (100x Oil lens) to 4.3 mm (10x lens).
Actual resolution limit for magnetic objects
A standard microscope for high-resolution domain imaging is typically equipped with the following objective lenses, which ensure the corresponding resolution limits when blue light (λ=457 nm) is used:
10x – 1400 nm, 20x – 570 nm, 50x – 350 nm, 100x immerse oil – 220 nm
However, despite these resolution limits, independent magnetic objects, such as domain walls or skyrmionic bubbles, with sizes close to the resolution limit can still be observed. Here the domain wall in an amorphous metallic ribbon (315 nm) and a FeSi steel sheet (130 nm) can be clearly seen, even when imaged with a low-resolution lens.
Even if magnetic objects are far below the resolution limit, they can be investigated. Here the magnetic state (direction of saturation or demagnetized state) of the flat nano-wire of with a width of only 50 nm can be clearly observed.
(sample courtesy Jimmy Zhu and Matt Moneck, Carnegie Mellon University, Pittsburgh)
The resolution limit of the Kerr microscopy is addressed in the following paper:
Size analysis of sub-resolution objects by Kerr microscopy
I.V. Soldatov, J. Zehner, K. Leistner, T. Kang, D. Karnaushenko and R. Schäfer, JMMM. 529, 167889 (2021)
A Kerr microscopy method for the quantitative measurement of the size of magnetic objects that are smaller than the resolution limit is proposed. It can be applied to domain walls, bubble domains and magnetic skyrmion-bubble hybrid microstructures.