Dimensional Tuning of the Magnetic-Structural Transition in A(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (A=Sr,Ba)

A phase diagram of superconducting Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$ as a function of doping (x) is determined by a series of thermodynamic and transport measurements on single crystals. On comparison with a similar phase diagram for Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (Co-doped Ba122), we find that the increased dimensionality of Co-doped Sr122 results in a single first-order-like transition where the magnetic and structural transitions coincide, unlike the case of Co-doped Ba122 that exhibits split quasicontinuous magnetic and structural transitions. We relate this dimensionally-tuned splitting in the magnetic and structural transitions to the relative size of superconducting temperatures in these materials.