  A series of Sr(Co$_{1-x}$Ni$_x$)$_2$As$_2$ single crystals was synthesized
allowing a comprehensive phase diagram with respect to field, temperature, and
chemical substitution to be established. Our neutron diffraction experiments
revealed a helimagnetic order with magnetic moments ferromagnetically (FM)
aligned in the $ab$ plane and a helimagnetic wavevector of $q=(0,0,0.56)$ for
$x$ = 0.1. The combination of neutron diffraction and angle-resolved
photoemission spectroscopy (ARPES) measurements show that the tuning of a flat
band with $d_{x^2-y^2}$ orbital character drives the helimagnetism and
indicates the possibility of a quantum order-by-disorder mechanism.
