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

semiconductors. For this reason, dilute magnetic semiconductors are a majorfocus of spintronics research. In particular, manganese-doped galliumarsenide, (Ga,Mn)As, is based on gallium arsenide, a direct gap semiconductorthat hit the market back in the 1970s and nowadays is commonlyused in various electronic and optoelectronic devices. Enhanced with magneticproperties, the material can realise the full potential of spintronics asit offers the integration of magnetic and semiconductor properties, allowingthe combination of data processing and storage in one chip.However, there is a serious obstacle on the way to the commercialisationof DMS-based spintronic devices—their operation temperature. The magneticorder in these materials occurs below the Curie temperature, which—despite long years of research effort—does not exceed 200K in (Ga,Mn)AsandotherIII–VDMS[28]. Theoreticalandexperimentalquesttowardroomtemperatureferromagnetism in these systems is being pursued by manylaboratories, from different points of view and often shaping new researchdirections. For its purposes, (Ga,Mn)As is identified as a prototypical DMSand used as a test bed for various spintronic device concepts and functionalities.In this context, my dissertation work can be seen as a contributionto this application-oriented struggle. For example, the theory of spin wavesit explores is a basis of the mechanism of current-induced domain wall motionemployed in racetrack memories, while the anomalous Hall effect is animportant tool for probing spintronic properties as well as spin generationand manipulation in DMS. Sceptics have raised doubts whether we will eversucceed [29]. Even if they are right, research in the solid-state physics hasvalue of its own as the obstacles we encounter are often catalysts for fundamentalinvestigations. For example, the exclusion of magnetic flux froma superconductor was interpreted by Anderson as generation of mass for agauge boson [30]—the effect popularised by Higgs himself plays a centralrole in the electroweak theory [31]. Statistical Chern-Simons gauge fields infield theory are now commonly used to describe the quantum Hall effect [32],which also started the experimental search for a related phenomenon of theparity anomaly in (2+1)-dimensional electrodynamics in solid bodies [33].The significant development of quantum physics over the 20th century haveresulted from efforts to theoretically describe ensembles of atoms and theirinteraction, leading to fundamental theoretical and numerical methods, likethe Metropolis algorithm for solving of the many-body Schrödinger equation[34]. To these I added two penn’orth predicting the cycloidal spinstructure on the surface of the zincblende DMS structures or formulatingmathematical methods, like the Löwdin variation-perturbational calculusgeneralising the RKKY theory to more complex, realistic energy bands, anexact formula for the sum of states of classical spins, and a general methodused for modelling spin-wave excitations (enforcing the correct constrainton their number). The detailed outline of my work will be provided in thenext chapter.17