Topological Hall Effect and Berry Phase in Magnetic Nanostructures

Abstract

We discuss the anomalous Hall effect in a two-dimensional electron gas subject to a spatially varying magnetization. This topological Hall effect (THE) does not require any spin-orbit coupling, and arises solely from Berry phase acquired by an electron moving in a smoothly varying magnetization. We propose an experiment with a structure containing 2D electrons or holes of diluted magnetic semiconductor subject to the stray field of a lattice of magnetic nanocylinders. The striking behavior predicted for such a system (of which all relevant parameters are well known) allows to observe unambiguously the THE and to distinguish it from other mechanisms. PACS numbers: 73.20.Fz; 72.15.Rn; 72.10.Fk After half a century of theoretical efforts, the Hall effect of ferromagnets (usually called anomalous or extraordinary Hall effect) remains a puzzling and controversial topic. Until recently, it was considered that it originates from the combined effect of exchange and spin-orbit (SO) interactions. Two mechanisms of anomalous Hall effect (AHE) have been identified (the skew scattering [1,2] and side-jump [3]) and studied thoroughly [4]. Recently, a new point of view has been proposed [5], in which the AHE is expressed in terms of a Berry curvature in momentum space. However, one should note that a generally accepted theory treating on an equal footing all the above mentioned contributions to the SO-induced AHE is still missing.Recently, it has been suggested that (in addition to the above mentioned SO-induced mechanism) a new mechanism may give rise to a non-vanishing Hall effect in ferromagnets having a topologically non-trivial (chiral) spin-texture, such as manganites or pyrochlore-type compounds [6]. To distinguish this mechanism from the SObased mechanism, we shall refer to it hereafter as the topological Hall effect (THE).Several theoretical papers have been devoted to the THE. In order to explain the AHE observed in manganites, a model of 3D ferromagnet with thermally excited skyrmion strings (topological dipoles)has been proposed [7], showing that a THE can be induced by the Berry phase [8] related to the spatial variation of magnetization in the vicinity of the string. The case of disordered ferromagnets in the limit of small exchange splitting has been addressed in Ref. 9. In both cases, in order to get a net topological field (or chirality), the SO-coupling must be invoked. Even when the net topological field vanishes, a nonvanishing THE may be obtained, as discussed for a 2D kagomé lattice or a 3D pyrochlore lattice [10].All the above mentioned discussions of the THE concern systems with spin-chirality at the microscopic scale (e.g., pyrochlore lattice) or due to skyrmion-strings. In both cases, quantitative experimental information on the chirality is not easily available. Furthermore, the SOmechanism is usually also present, which makes complicate the quantitative interpretation of the observations.In the present Letter, we propose to investigate the THE in nanostructures, namely in a 2D electron (or hole) ...

Geometric Hall effects in topological insulator heterostructures

“…FET devices were measured in the PPMS with a standard lock-in technique at low frequency (∼7 Hz) and with a low excitation current (10 nA) to suppress heating effects. Low-temperature (<2 K) measurements were performed using the 3 He option of the PPMS. Magnetization measurements for the bare film of 2-nm CBST/5-nm BST were conducted using a magnetic property measurement system (MPMS, Quantum Design).…”

“…As a plausible origin, we propose skyrmion formation from both theoretical and experimental aspects. Under skyrmion spin texture, the moving electrons experience the EEMF, giving rise to an additional Hall component termed the topological Hall effect (THE, note that 'topological' is defined in real space) 3,4 , which is observed in the skyrmion phase of some chiral-lattice magnets 5,6 as well as in frustrated magnets endowed with scalar spin chirality 29,30 . The magnetic-field dependence of THE shows a hysteresis behaviour; the magnetic field showing the maximal THE is observed to shift slightly to lower field as a whole by up to ∼0.02 T with decreasing sweep rate from 2 × 10 −3 T s −1 to 3 × 10 −5 T s −1 (see Supplementary Information for the details).…”

Large topological Hall effect in the non-collinear phase of an antiferromagnet

“…However, in a non-coplanar spin configuration the spin chirality k ¼ P S i Á (S k  S l ) of three magnetic moments spanning a triangle can induce a finite Berry phase and an associated fictitious magnetic field. This field generates an AHE even without spin-orbit interaction l SO , the so-called topological Hall effect (THE) 5,6 .…”

Квантовые поправки к проводимости и аномальный эффект Холла в квантовых ямах InGaAs с пространственно отделенной примесью Mn

“…Вклад асимметричного рассеяния характеризуется линейной параметрической зависимостью (R a x y ∝ ρ x x ), а вклады двух других ме-ханизмов -квадратичной (R a x y ∝ ρ 2 x x ). Кроме того, в данных системах возможно проявление топологического вклада в АЭХ [27][28][29], поскольку отсутствие жесткого ФМ упорядочения допускает возникновение нетриви-альной топологии магнитной подсистемы в основном состоянии при понижении температуры. В данном кон-тексте это соответствует формированию скирмионов (или аналогичных образований) за счет взаимодействия Дзялошинского−Мории.…”

“…В структурах, изученных в [13], в области низких темпе-ратур наблюдался переход к прыжковой проводимости, в условиях которой топологический вклад успешно объяс-няется в рамках адиабатического приближения, т. е. при адиабатическом (обменном) взаимодействии носителей заряда в двумерном канале с киральной текстурой магнитной подсистемы. Однако в случае дрейфовой проводимости в канале, изучаемом в данной статье, по-ведение топологического вклада существенно зависит от выполнения или невыполнения условия адиабатичности взаимодействия двумерных дырок и киральных образо-ваний [27,29]. Поэтому количественное и качественное описание топологического вклада в этом случае затруд-нено отсутствием точной теории.…”