Formations of narrow stripes and vortex-antivortex pairs in a quasi-two-dimensional ferromagnet K₂CuF₄

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. This material is known as one of the candidates for a two-dimensional (2D) XY magnet that may exhibit a Berezinskii-Kosterlitz-Thouless (BKT) phase transition. A fine magnetic stripe pattern was found with a period of about 120 nm in a direction along the c axis below 7.3 K in a thin sample with the c axis in the plane. Magnetic columns of vortices and antivortices with a separation of about three micrometers were observed below 6 K in a c-plane sample approximately 150 nm in thickness. The formation of two different types of magnetic structures at different threshold temperatures is likely to be consistent with a picture of two-step dimensional crossover in spin and real spaces previously derived from magnetization and neutron experiments in K₂CuF₄. These results indicate how the 2D XY character of K₂CuF₄ is incorporated in three-dimensional magnetic structures. Based on the experimental observations, we discuss the lengthscale of film thickness appropriate for expanding the 2D XY regime and generating the robust BKT excitations. We expect our study to be an important step in realizing the BKT phase transition in a real magnetic system.