  We have systematically studied the antiferromagnetic and nematic transitions
in Sr$_{1-x}$Ba$_x$Fe$_{1.97}$Ni$_{0.03}$As$_2$ by magnetic susceptibility and
uniaxial-pressure resistivity measurements, respectively. The derivatives of
the temperature dependence of both magnetic and nematic susceptibilities show
clearly sharp peak when the transitions are first-order. Accordingly, we show
that while both of the magnetic and nematic transitions change from first-order
to second-order with increasing Barium doping level, there is a narrow doping
range where the former becomes second-order but the latter remains first-order,
which has never been realized before in other systems. Moreover, the
antiferromagnetic and nematic transition temperatures become different and the
jump of nematic susceptibility becomes small in this intermediate doping range.
Our results provide key information on the interplay between magnetic and
nematic transitions. Concerning the current debate on the microscopic models
for nematicity in iron-based superconductors, these observations agree with the
magnetic scenario for an itinerant fermionic model in excellent details.
