We present a theory of optical control of magnetism in a self-assembled quantum dot (SAD) containing magnetic ions. We show that the magnetic state of Mn ions can be controlled by the number of excitons in the dot. For an odd number of excitons the magnetic ions are coupled by the spins of valence holes and electrons. For an even number of excitons we derive the effective RKKY interaction between Mn ions, and show that it is controlled by valence holes. We predict the emission spectra of the

more »

... pled Mn-exciton system and relate them to the magnetic state of ions and the number of excitons in the quantum dot. Advances in magneto-electronics, from magnetic information storage, spintronics, to quantum information processing, rely on developing effective means of controlling magnetism other than an external magnetic field, and on creating distinct magnetic phases of magnetic medium allowing for reversible switching [1] [2] [3] [4] . Several attempts have been made to use electric field, strain, and light for the engineering of magnetism [4] [5] [6] [7] [8] . In contrast to a variety of techniques developed for the control of magnetism, only few magnetic materials can exhibit distinct magnetic phases suitable for the encoding of bits of information [9]. Semi-conductor quantum dots [10] containing magnetic ions and a voltage-controlled number of electrons and/or valence holes offer means for the electrical control of magnetic properties [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] . Here we investigate means for the control of magnetic properties of magnetic ions via optical control of the average population of photo-excited electrons and holes [22] [23] [24] [25] . Unlike in electronic quantum dots where orbital degeneracies lead to spin polarization following Hund's rules, in electron-hole quantum dots "hidden symmetries" guarantee that odd exciton numbers carry spin, and even exciton number complexes have no net spin [26, 27] . We show that the odd exciton complexes form many-exciton-many-Mn polaron complexes where bright and dark excitons are mixed in a non-perturbative fashion. The even exciton complexes induce a RKKY-like interaction among magnetic ions [21] . The interaction is long ranged, is dominated by valence holes, and can be controlled on a time