Magnetic order and magneto-transport in spin polarised ferrimagnetic Mn$_y$Ru$_x$Ga thin films.

The ruthenium content of half-metallic Mn$_2$Ru$_x$Ga thin films with a biaxially-strained inverse Heusler structure influences the ferrimagnetism that determines their magnetic and electronic properties. An extensive study of Mn$_y$Ru$_x$Ga films on MgO (100) substrates with $1.8 \leq y \leq 2.6$ and $x$ = 0.5, 0.7 or 0.9, including crystallographic and magnetic order, magneto-transport and spin polarisation is undertaken to map specific composition-dependent properties in this versatile ternary system. A comparison of the experimental densities with calculated X-ray densities for alloys with Mn or Ru vacancies exhibit full site occupancy which indicates the presence of chemical disorder. All compositions studied except $x = 0.5$, $y = 2.2$ exhibit compensation. Increasing the Mn or Ru content raises the compensation temperature but increasing Ru decreases the spin polarisation determined by Andreev reflection. Molecular field theory is used to model the temperature dependence of the net ferrimagnetic moment obtained from magnetisation measurements and three principal exchange coefficients are deduced. Marked differences in the shape of anomalous Hall and net magnetisation hysteresis loops are explained by canting of the net moment relative to the c-axis in zero field, which results from non-collinearity of the Mn$^{4c}$ sublattice moments due to competing intra-sublattice exchange interactions. Consequences of the non-collinearity are reduced spin polarisation and an intrinsic contribution to the anomalous Hall effect. Our systematic investigation of the physical properties as a function of $x$ and $y$ will permit the selection of compositions that best match the requirements of any particular application.