  The spin-dependent nature of the nuclear tensor force is studied in details
within the relativistic Hartree-Fock approach. The relativistic formalism for
the tensor force is supplemented with an additional Lorentz-invariant tensor
formalism in $\sigma$-scalar channel, so as to take into account almost fully
the nature of the tensor force brought about by the Fock diagrams in realistic
nuclei. Specifically, the tensor sum rules are tested for the spin and
pseudo-spin partners with/without nodes, to further understand the tensor force
nature within relativistic model. It is shown that the interference between two
components of nucleon spinors brings distinct violations on the tensor sum
rules in realistic nuclei , which is mainly due to the opposite sign on
$\kappa$ quantities of the upper and lower components as well as the nodal
difference. Even though, the sum rules can be precisely reproduced if taking
the same radial wave functions for the spin/pseudo-spin partners in addition to
neglecting the lower/upper components, revealing clearly the nature of tensor
force.
