Formations of Narrow Stripes and Vortex–Antivortex Pairs in a Quasi-Two-Dimensional Ferromagnet K₂CuF₄

Abstract

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Parallel Mode Differential Phase Contrast in Transmission Electron Microscopy, II: K2CuF4 Phase Transition

“…For KCuF, this window is at low temperatures (the exact window is discussed in detail later), where a modified Kosterlitz–Thouless (KT) transition was observed through neutron scattering and static magnetization measurements reported almost 40 years ago (Hirakawa, 1982). In our recent work on this material (Togawa et al, 2021), we reported real-space, direct observations of vortex and antivortex structures at a single temperature, consistent with the excitation types expected from the KT transition (Berezinskii, 1971, 1972; Kosterlitz & Thouless, 1973), but possibly modified by anisotropies arising from the finite sample size.…”

“…We note that the nonrigid analysis methodology developed in Part I of this work and used here allowed the inclusion of the entire sample and support structure areas in these analyses. This was not possible in our earlier work (Togawa et al, 2021) on account of the choice of the B-spline basis (Arganda-Carreras et al, 2006; Schindelin et al, 2012) for the distortion field.…”

“…1.Cryo-TEM images of a KCuF sample. In-focus ( a ) and underfocus (44 mm) Fresnel ( b , c ) images at temperatures ( b ) below and ( c ) above the phase transition where the sample is ferromagnetic (FM) and paramagnetic (PM), respectively (versions of ( b ) and ( c ) are also included in Togawa et al, 2021). ( d ) Difference Fresnel image, showing a combination of high-frequency nonmagnetic texture and magnetic induction-induced intensity variations suggestive of the presence of a clockwise vortex at the bottom and an anticlockwise vortex at the top of the sample.…”

Parallel Mode Differential Phase Contrast in Transmission Electron Microscopy, I: Theory and Analysis

“…In Part II of this work (Paterson et al, 2021), we apply the TEM-DPC technique to experimental cryo-TEM Fresnel images of the magnetic phase transition of a thin lamella of KCuF, a material of interest for its quasi 2D ferromagnetism at low temperatures (Hirakawa, 1982; Togawa et al, 2021).…”

Cryogenic Lorentz TEM study of a Berezinskii–Kosterlitz–Thouless phase transition in the quasi-two-dimensional ferromagnet K2CuF4?

“…In this study, using cryogenic Lorentz transmission electron microscopy, we investigate the temperature evolution of magnetic structures in single crystal samples of K2CuF4 with a magnetic phase transition at 6.1 K [2]. This material is one of the candidates for a 2D XY magnet that may exhibit the BKT phase transition.…”