  We have measured temperature and magnetic field dependences of the thermal
conductivity along the c-axis, kc, and that along the [110] direction, k110, of
CuB2O4 single crystals in zero field and magnetic fields along the c-axis and
along the [110] direction. It has been found that the thermal conductivity is
nearly isotropic and very large in zero field and that the thermal conductivity
due to phonons is dominant in CuB2O4. The temperature and field dependences of
kc and k110 have markedly changed at phase boundaries in the magnetic phase
diagram, which has been understood to be due to the change of the mean free
path of phonons caused by the change of the phonon-spin scattering rate at the
phase boundaries. It has been concluded that thermal conductivity measurements
are very effective for detecting magnetic phase boundaries.
