Interplay of metamagnetic and structural transitions in Ca$_{2-x}$Sr$_x$RuO$_4$

Metamagnetism in layered ruthenates has been interpreted as a novel kind of quantum critical behavior. In an external magnetic field, Ca$_{2-x}$Sr$_x$RuO$_4$ undergoes a metamagnetic transition accompanied by a pronounced magnetostriction effect. In this paper we present a mean-field study for a microscopic model that naturally reproduces the key features of this system. The phase diagram calculated is equivalent to the experimental $T$-$x$ phase diagram. The presented model also gives a good basis to discuss the critical metamagnetic behavior measured in the system.