Dilute-magnetic semiconductors (DMS) are promising materials for spintronic applications (electronics that take advantage of spin to carry information). Ga_1-xMn_xAs is the most commonly studied DMS system. The direction of the ferromagnetic ordering in a quantum well model of Ga_1-xMn_xAs with doping x is determined. The magnetic order is perpendicular to the plane for low carrier densities, n < n₁, and becomes parallel within the plane for higher carrier densities, n > n₂. However, it is not known if phase separation occurs between regions having carrier density n₁ and moments pointing perpendicular to the plane, and others having n₂ > n₁ and moments within the plane. Phase separation occurs in the system if the chemical potential at two different fillings is the same.

In this project, the first two wave functions of the carriers in the quantum well were used to calculate the energy of the system as a function of angle and carrier density. The energy was minimized with respect to angle, and the chemical potential was calculated. A Maxwell construction indicated phase separation occurs between n₁ = 3.1% and n₂ = 5.3% for x = 0.35. The complete phase diagram for this system was calculated and distinguished between the phase separated, parallel phase, and perpendicular phase regions for different amounts of dopant. Phase separation of the ferromagnetic phases in a quantum well may imply that some regions may be magnetically ordered up to higher temperatures. This might allow the design of spintronic devices that can operate at room temperature.