  We report magnetic field spectroscopy measurements in carbon nanotube quantum
dots exhibiting four-fold shell structure in the energy level spectrum. The
magnetic field induces a large splitting between the two orbital states of each
shell, demonstrating their opposite magnetic moment and determining transitions
in the spin and orbital configuration of the quantum dot ground state. We use
inelastic cotunneling spectroscopy to accurately resolve the spin and orbital
contributions to the magnetic moment. A small coupling is found between
orbitals with opposite magnetic moment leading to anticrossing behavior at zero
field.
