  Three independent components of critical current density, one for the H//c
axis and the other two for the H//ab plane, have been studied in CaKFe4As4
single crystals. When the magnetic field is applied along the c axis, we
observed fish-tail-like peaks in the M-H hysteresis loop, and the magnetization
at higher temperatures exceeds that at lower temperatures at high fields. When
the field is applied parallel to the ab plane, a dip structure is observed in
the M-H hysteresis loop near the self-field. In addition, for the H//ab plane,
we succeeded in separately evaluating the large and significantly anisotropic
in-plane and out-of-plane Jc. Transmission electron microscopy revealed the
presence of planar defects parallel to the ab plane in CaKFe4As4, which have
not been observed in any other iron-based superconductors. We discuss the
possible relationship between the anomalous Jc behavior and the planar defects.
