  Boron nuclei in cosmic rays (CRs) are believed to be mainly produced by the
fragmentation of heavier nuclei, such as carbon and oxygen, via collisions with
the interstellar matter. Therefore, the boron-to-carbon flux ratio (B/C) and
the boron-to-oxygen flux ratio (B/O) are very essential probes of the CR
propagation. The energy dependence of the B/C ratio from previous balloon-borne
and space-based experiments can be well described by a single power-law up to
about 1 TeV/n within uncertainties. This work reports direct measurements of
B/C and B/O in the energy range from 10 GeV/n to 5.6 TeV/n with 6 years of data
collected by the Dark Matter Particle Explorer, with high statistics and well
controlled systematic uncertainties. The energy dependence of both the B/C and
B/O ratios can be well fitted by a broken power-law model rather than a single
power-law model, suggesting the existence in both flux ratios of a spectral
hardening at about 100 GeV/n. The significance of the break is about
$5.6\sigma$ and $6.9\sigma$ for the GEANT4 simulation, and $4.4\sigma$ and
$6.9\sigma$ for the alternative FLUKA simulation, for B/C and B/O,
respectively. These results deviate from the predictions of conventional
turbulence theories of the interstellar medium, which point toward a change of
turbulence properties of the interstellar medium (ISM) at different scales or
novel propagation effects of CRs, and should be properly incorporated in the
indirect detection of dark matter via anti-matter particles.
