Nematicity of correlated systems driven by anisotropic chemical phase separation

The origin of nematicity, i.e., in-plane rotational symmetry breaking, and in particular the relative role played by spontaneous unidirectional ordering of spin, orbital, or charge degrees of freedom, is a challenging issue of magnetism, unconventional superconductivity, and quantum Hall effect systems, discussed in the context of doped semiconductor systems, such as Ga$_{1-x}$Mn$_x$As, Cu$_x$Bi$_2$Se$_3$, and Ga(Al)As/Al$_x$Ga$_{1-x}$As quantum wells, respectively. Here, guided by our experimental and theoretical results for In$_{1-x}$Fe$_x$As, we demonstrate that spinodal phase separation at the growth surface (that has a lower symmetry than the bulk) can lead to a quenched nematic order of alloy components, which then governs low temperature magnetic and magnetotransport properties, in particular the magnetoresistance anisotropy whose theory for the $C_{2v}$ symmetry group is advanced here. These findings, together with earlier data for Ga$_{1-x}$Mn$_x$As, show under which conditions anisotropic chemical phase separation accounts for the magnitude of transition temperature to a collective phase or merely breaks its rotational symmetry. We address the question to what extent the directional distribution of impurities or alloy components setting in during the growth may account for the observed nematicity in other classes of correlated systems.