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In Part I of this diptych, we outlined the theory and an analysis methodologyfor quantitative phase recovery from real-space distortions of Fresnel imagesacquired in the parallel mode of transmission electron microscopy (TEM). Inthat work, the properties of the method, termed TEM-differential phase contrast(TEM-DPC), were highlighted through the use of simulated data. In this work, weexplore the use of the TEM-DPC technique with experimental cryo-TEM images of athin lamella of a low temperature two-dimensional (2-D) ferromagnetic material,K$_2$CuF$_4$, to perform two tasks. First, using images recorded below theordering temperature, we compare the TEM-DPC method to the transport ofintensity one for phase recovery, and discuss the relative advantages theformer has for experimental data. Second, by tracking the induction of thesample as it is driven through a phase transition by heating, we extractestimates for the critical temperature and critical exponent of the orderparameter. The value of the latter is consistent with the 2-D XY class, raisingthe prospect that a Kosterlitz--Thoules transition may have occurred.

Parallel mode differential phase contrast in transmission electron microscopy, II: K$_2$CuF$_4$ phase transition