<p indent="0mm">Nuclear collective rotation, which involves coherent contributions from many nucleons, has been well known for a long time. It is ascribed as a consequence of deformation and gives rise to regular rotational bands, which are characterized by strong electric quadrupole (<italic>E</italic>2) transitions. Studies of the rotational bands in nuclei have been in the forefront of nuclear structure physics and have led to many interesting phenomena including the backbending, superdeformed bands, and chiral doublet bands. In 1990s, a new type of rotational-like sequences, which have strong <italic>M</italic>1 transitions and weak or vanishing <italic>E</italic>2 transitions, have been discovered in weakly deformed or near-spherical nuclei and attracted a lot of interests. This new type of rotational structure cannot be understood in terms of conventional rotation of deformed nuclei but has been successfully interpreted in terms of the shears mechanism. In this interpretation, nuclear orientation is specified by the current distribution rather than the deformation. The magnetic dipole vector arises from proton particles (holes) and neutron holes (particles) in high-<italic>j</italic> orbitals, and rotates around the total angular momentum vector. In the subsequent experimental studies, the magnetic rotation phenomenon were found in the <italic>A</italic>~60, <italic>A</italic>~80, <italic>A</italic>~110, <italic>A</italic>~140, and <italic>A</italic>~190 mass regions. Here, we report the studies of magnetic rotation in the <italic>A</italic>~80 and <italic>A</italic>~60 mass regions. The high-spin structures of<sup>75</sup>As, <sup>79</sup>Se and <sup>62</sup>Cu were respectively populated via <sup>70</sup>Zn(<sup>9</sup>Be, 1p3n)<sup>75</sup>As, <sup>82</sup>Se(α, α3n)<sup>79</sup>Se and <sup>54</sup>Cr(<sup>12</sup>C, 1p3n)<sup>62</sup>Cu heavy ion fusion–evaporation reactions. The dipole bands were established for the first time in these three nuclei. The properties of these dipole bands are investigated in terms of the self-consistent tilted axis cranking covariant density functional theory. In the calculation for <sup>75</sup>As, <sup>79</sup>Se and <sup>62</sup>Cu, the valence nucleon configurations of π[(1g<sub>9/2</sub>)<sup>1</sup>(1f<sub>5/2</sub>)<sup>−2</sup>]<x content-type="symbol">Ä</x>υ[(1g<sub>9/2</sub>)<sup>5</sup>(fp)<sup>−3</sup>], <sc>π[(1g<sub>9/2</sub>)<sup>1</sup>(fp)<sup>5</sup>]</sc><x content-type="symbol">Ä</x>υ[(1g<sub>9/2</sub>)<sup>5</sup>] and π[(f<sub>7/2</sub>)<sup>−1</sup>(p<sub>3/2</sub>f<sub>5/2</sub>)<sup>2</sup>]<x content-type="symbol">Ä</x>υ[(g<sub>9/2</sub>)<sup>1</sup>(p<sub>3/2</sub>f<sub>5/2</sub>)<sup>4</sup>] are used, respectively. The calculated energy spectra reasonably reproduce the experimental excitation energies of <sup>75</sup>As, <sup>79</sup>Se, and <sup>62</sup>Cu. The evolutions of deformation parameters <italic>β</italic> and <italic>γ</italic> of these dipole bands driven by increasing rotational frequency are discussed. In contrast to the relatively large triaxial deformation of the dipole bands in <sup>75</sup>As and <sup>62</sup>Cu, the dipole band of <sup>79</sup>Se has a relatively axially symmetric and small prolate deformation. With the increase of rotational frequency, the <italic>β </italic>deformations for <sup>75</sup>As, <sup>79</sup>Se and<sup>62</sup>Cu behave in a similar way, i.e., a smooth decrease in <italic>β</italic>. Meanwhile, both <italic>γ</italic> values of <sup>75</sup>As and <sup>62</sup>Cu show a smoothly increasing tendency. Based on the examination of the composition of the proton and neutron angular momentum vectors <italic>J</italic><sub>π</sub> and <italic>J</italic><sub>υ</sub> as well as the total angular momentum <italic>J</italic><sub>tot</sub>=<italic>J</italic><sub>π</sub>+<italic>J</italic><sub>υ</sub> at both the bandhead and the maximum rotational frequency, the dipole bands in <sup>75</sup>As and <sup>79</sup>Se can be interpreted as novel stapler bands, where the valence nucleons in (1g<sub>9/2</sub>) orbital rather than the collective core are responsible for the closing of the stapler of angular momentum. Although not firmly confirmed in experiments, the dipole structure in <sup>62</sup>Cu may be a candidate of magnetic rotational bands. To unambiguously confirm this, further experimental investigations are strongly desirable.