  Employing a realistic tight-binding model describing the Fermi surface in the
normal state of $Sr_2RuO_4$ we map out magnetic field versus temperature phase
diagrams for $d_{x^2-y^2} (B_{1g})$ and $d_{xz}+id_{yz} (E_g)$ pairing types.
Both produce (i) a similar Knight shift suppression of $\sim\!80\%$ and (ii) a
bicritical point at $T=0.88$K separating low field second order phase
transitions from high field Pauli limiting first order transitions. We find,
however, strikingly different phase behaviour within the high field Pauli
limiting region. For $d_{x^2-y^2}$ pairing symmetry an additional lower
critical line of first order transitions is found (terminating in a critical
point at $T=0.09-0.22$K depending on the choice of Hubbard U parameters) while
for $d_{xz}+id_{yz}$ no such additional high field phase transitions are found
for any choice of Hubbard U. In conjunction with our earlier finding [{\it
Physical Review B} {\bf 102} (23), 235203] for $p$-wave helical pairing of a
still different high field phase structure (a lower critical field line meeting
the upper critical field line exactly at the bicritical point), we suggest high
field Pauli limiting phase structure as a possible route to distinguish pairing
symmetries in this material.
