Spin waves and the anomalous Hall effect in ferromagnetic (Ga,Mn)As

5% Mn and a high hole concentration of 0.35nm −3 . The compounds withsmaller anions have smaller lattice constants, which leads to greater p–dhybridisation, and smaller spin-orbit coupling, which scales with the atomicnumber as Z 4 and (in the simple picture) has a detrimental effect on theCurie temperature. The p-type carriers are chosen for their much strongerexchange coupling with the magnetic centres then that of the s electrons.However, their high concentrations are unlikely in the nitrides and oxides.Although the hole-mediated ferromagnetism in these systems has been observed[71], it is still unclear whether it comes from substitutional Mn ionsin the semiconductor lattice or unwanted precipitates. The nature of ferromagnetismin these systems has been studied extensively by ab initio methods[29, 72], also at our Institute [73, 74].Nowadays, ferromagnetism in semiconductor-based materials remainsthe subject of intense interest in solid state physics. Theoretical treatmentsof carrier-mediated ferromagnetism and experimental investigations towardroom-temperature III–V-based DMS have been pursued by many laboratories,from various points of view and shaping new research directions.They identified (Ga,Mn)As as a prototypical DMS. Although the progressin synthesizing and controlling magnetic properties has been astounding,the highest reported Curie temperatures in this material are around 190 K(and lower in (In,Mn)As) [28]. Until the ferromagnetic phase is achievedat room temperatures, dilute magnetic semiconductors will not realise theirfull potential in practical applications.3.2 Crystal structureAs already mentioned, isomorphic crystals of manganese-doped gallium arsenide,(Ga,Mn)As, are fabricated by randomly substituting a small amountof Mn, typically 2% to 6%, for cation sites of the GaAs semiconductor hostlattice. Hence, they have a zincblende structure similar to that of GaAs, asdepictedinFig.3.1. ItistypicaloftheIII–Vcompounds(exceptfornitrides,which are stable in the wurzite structure), as well as II–VI compounds andgroup IV elements.In GaAs, the outermost s- and p-like atomic orbitals from the neighbouringGa and As atoms (three from the 4s 2 4p 1 orbital configuration ofGa and five from the 4s 2 4p 3 configuration of As) hybridise in the crystal toform covalent bonds. This type of bonds is responsible for the semiconductingproperties of the compound. Additionally, the two shared As electronsforming each Ga–As bond are more attracted toward the atom with largestnucleus, As. Thisgivessomeioniccharactertothebond, whichmayresult—for instance—in piezoelectric properties of the GaAs crystal [75].The crystal structure of GaAs is determined by the spatial arrangementof hybridised sp 3 tetrahedral orbitals around atoms. Each orbital lobe con-26