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