  The mechanism of spin reorientation in Nd$_{2}$Fe$_{14}$B, which is a host
crystal of a well-known neodymium permanent magnet, is studied by combining
first-principles calculations and Monte Carlo simulations. The spin
reorientation is thought to be derived from crystal field effects and gets less
attention because of the undesirable property for hard magnet application.
Dzyaloshinskii-Moriya interactions are usually less attractive or often ignored
in rare-earth bulk systems, including permanent magnets such as
Nd$_{2}$Fe$_{14}$B since people believe that the magnetic anisotropy is more
dominant than the Dzyaloshinskii-Moriya interactions. However, in this study,
we have found, for the first time, that the spin reorientation in
Nd$_{2}$Fe$_{14}$B is attributed to Dzyaloshinskii-Moriya interactions. We have
found, furthermore, the spin reorientation in Nd$_{2}$Fe$_{14}$B yields a great
stage of rotating magnetocaloric effect at practical application level. We have
found that the Dzyaloshinskii-Moriya interactions definitely contributes to the
physical properties as a non-negligible effect in magnetic materials.
