Dataset 1: Title: Magnetic phase diagrams of HoCu, ErCu, and TmCu for magnetic field along the [111] axis. Description: Maxima and points of inflection observed in AC magnetic susceptibility data are stored in "HoCu111_1.dat", "HoCu111_2.dat", "HoCu111_3.dat", "HoCu111_4.dat", "ErCu111_FS.dat", "ErCu111_TS.dat", "TmCu111_FS.dat", and "TmCu111_TS.dat". The first and second columns correspond to temperature and field values of these points, respectively. Dataset 2: Title: Magnetization and electrical transport properties of bulk TmCu at T = 2K for magnetic field along [111]. Description: The field dependence of the magnetization, longitudinal electrical resistivity, and transverse electrical resistivity are stored in the files "TmCuMagnetization.dat", "TmCuRhoxx.dat", and "TmCuRhoxy.dat", respectively. Contributions to the transverse resistivity that are associated with the normal Hall effect are stored in "TmCuRhoxynormalHall.dat". Anomalous Hall effect contributions that are linear in the magnetization are stored in "TmCuRhoxyAHE.dat". Dataset 3: Title: Magnetic neutron diffraction intensity as a function of temperature in HoCu at zero magnetic field. Description: Magnetic neutron diffraction intensity, as recorded by means of rocking-scans of the sample at the single-crystal diffractometer HEiDi (FRMII, Garching), centered around the reciprocal-space position Q0 = (1.5, 1.5, 1), are presented in "HoCuNeutronDiffraction_Int.dat" in terms of a 81 times 25 matrix. The presented intensity is normalized to the monitor. The first index enumerates the momentum transfer difference with respect to the reciprocal-space position Q0 and the second index the temperatures. The respective values are stored in "HoCuNeutronDiffraction_Q.dat" and "HoCuNeutronDiffraction_T.dat".