  We evaluate the feasibility of using magnetic-dipole (M1) transitions in
highly-charged ions as a basis of an optical atomic clockwork of exceptional
accuracy. We consider a range of possibilities, including M1 transitions
between clock levels of the same fine-structure and hyperfine-structure
manifolds. In highly charged ions these transitions lie in the optical part of
the spectra and can be probed with lasers. The most direct advantage of our
proposal comes from the low degeneracy of clock levels and the simplicity of
atomic structure in combination with negligible quadrupolar shift. We
demonstrate that such clocks can have projected fractional accuracies below the
$10^{-20}-10^{-21}$ level for all common systematic effects, such as black-body
radiation, Zeeman, AC-Stark and quadrupolar shifts. Notice that
usually-employed hyperfine clock transitions lie in the microwave spectral
region. Our proposal moves such transitions to the optical domain. As the
hyperfine transition frequencies depend on the fine-structure constant,
electron-to-proton mass ratio, and nuclear magnetic moment, our proposal
expands the range of experimental schemes for probing space and time variations
of fundamental constants.
