Magnetic order in the two-dimensional compass-Heisenberg model

A Green-function theory for the dynamic spin susceptibility in the square-latticespin-1/2 antiferromagneticcompass-Heisenberg model employing a generalized mean-field approximation is presented.The theory describes magnetic long-range order (LRO) and short-range order (SRO) atarbitrary temperatures. The magnetization, Néel temperature T _N , specific heat, anduniform static spin susceptibility χ are calculated self-consistently. As the mainresult, we obtain LRO at finite temperatures in two dimensions, where the dependence ofT _N on the compass-modelinteraction is studied. We find that T _N is close to theexperimental value for Ba₂IrO₄. The effects of SRO are discussed in relation to thetemperature dependence of χ.