Topological Hall Effect Research Articles

Low-field induced topological Hall effect in chiral cubic Cr0.82Mn0.18Ge alloy

The topological Hall effect (THE) in general arises from the Berry phase acquired by conduction electrons moving in a noncoplanar spin textures such as skyrmions. In this paper, low-field induced THE is realized in a chiral-lattice B20-ordered Cr0.82Mn0.18Ge alloy. The maximum topological Hall resistivity of ρxyT ≈ −0.048 μΩ cm at T = 10 K is achieved under a low magnetic field of about μ0H = 0.04 T, which reaches up to ~20% of the anomalous Hall effect. Dip/peak anomalies are observed in the field dependence of AC-susceptibility, which indicates the field evolution of the topologically protected nontrivial spin textures. The results manifest that the Cr0.82Mn0.18Ge alloy should host skyrmions and pave the way for searching new skyrmions materials.

Topological Hall effect and magnetic states in the Nowotny chimney ladder compound Cr11Ge19

We have investigated the magnetic and charge transport properties of single crystals of Nowotney Chimney Ladder compound Cr$_{11}$Ge$_{19}$ and mapped out a comprehensive phase diagram reflecting the complicated interplay between the Dzyaloshinskii-Moriya (DM) interaction, the dipolar interaction, and the magnetic anisotropy. We have identified a set of interesting magnetic phases and attributed a finite topological Hall effect to the recently discovered bi-skyrmion phase. These data also suggest the existence of an anti-skyrmion state at finite fields for temperatures just below the magnetic ordering temperature, $T_c$, as indicated by a distinct change in sign of the topological Hall effect. Above $T_c$, we discovered a region of enhanced magnetic response corresponding to a disordered phase likely existing near the ferromagnetic critical point under small magnetic fields. Strong spin chirality fluctuations are demonstrated by the large value of the topological Hall resistivity persisting up to 1 T which is most likely due to the existence of the DM interaction. We argue that changes to the topological Hall effect correspond to different topological spin textures that are controlled by magnetic dipolar and DM interactions that vary in importance with temperature.

Geometrical Hall effect and momentum-space Berry curvature from spin-reversed band pairs

When nanometric, noncoplanar spin textures with scalar spin chirality (SSC) are coupled to itinerant electrons, they endow the quasiparticle wavefunctions with a gauge field, termed Berry curvature, in a way that bears analogy to relativistic spin-orbit coupling (SOC). The resulting deflection of moving charge carriers is termed geometrical (or topological) Hall effect. Previous experimental studies modeled this signal as a real-space motion of wavepackets under the influence of a quantum-mechanical phase. In contrast, we here compare the modification of Bloch waves themselves, and of their energy dispersion, due to SOC and SSC. Using the canted pyrochlore ferromagnet Nd$_2$Mo$_2$O$_7$ as a model compound, our transport experiments and first-principle calculations show that SOC impartially mixes electronic bands with equal or opposite spin, while SSC is much more effective for opposite spin band pairs.

Topological Hall effect in magnetic topological insulator films

Geometric Berry phase can be induced either by spin–orbit coupling, giving rise to the anomalous Hall effect in ferromagnetic materials, or by chiral spin texture, such as skyrmions, leading to the topological Hall effect. Recent experiments have revealed that both phenomena can occur in topological insulator films with magnetic doping, thus providing us with an intriguing platform to study the interplay between these two phenomena. In this work, we report on a numerical simulation of the anomalous Hall and topological Hall effects in a four-band model that can properly describe the quantum well states in the magnetic topological insulator films by combining Landauer–Büttiker formula and the iterative Green’s function method. Our numerical results suggest that spin–orbit coupling in this model plays a different role in the quantum transport in the clean and disordered limits. In the clean limit, spin–orbit coupling mainly influences the longitudinal transport but does not have much effect on topological Hall conductance. In the disordered limit, the longitudinal transport is determined by disorder scattering and spin–orbit coupling is found to affect strongly the topological Hall conductance. This sharp contrast unveils a dramatic interplay between spin–orbit coupling and disorder effect in topological Hall effect in magnetic topological insulator systems.

Field-induced topological Hall effect and double-fan spin structure with a c-axis component in the metallic kagome antiferromagnetic compound YMn6Sn6.

Geometric frustration in the kagome lattice makes it a great host for the flat electronic band, nontrivial topological properties, and novel magnetism. Here, we use magnetotransport measurements to map out the field-temperature phase diagram of the centrosymmetric YMn6Sn6 with a Mn kagome lattice and show that the system exhibits the topological Hall effect (THE) with an in-plane applied magnetic field around 240 K. In addition, our neutron diffraction results demonstrate that the observed THE cannot arise from a magnetic skyrmion lattice, but instead from an in-plane field-induced double-fan spin structure with -axis components. This paper provides a platform to understand the influence of a field-induced novel magnetic structure on magnetoelectric response in topological kagome metals.

Anomalous Hall resistivity and possible topological Hall effect in the EuAl4 antiferromagnet

We report the observation of anomalous Hall resistivity in single crystals of EuAl$_4$, a centrosymmetric tetragonal compound, which exhibits coexisting antiferromagnetic (AFM) and charge-density-wave (CDW) orders with onset at $T_\mathrm{N} \sim 15.6$ K and $T_\mathrm{CDW} \sim 140$ K, respectively. In the AFM state, when the magnetic field is applied along the $c$-axis direction, EuAl$_4$ undergoes a series of metamagnetic transitions. Within this field range, we observe a clear hump-like anomaly in the Hall resistivity, representing part of the anomalous Hall resistivity. By considering different scenarios, we conclude that such a hump-like feature is most likely a manifestation of the topological Hall effect, normally occurring in noncentrosymmetric materials known to host nontrivial topological spin textures. In view of this, EuAl$_4$ would represent a rare case where the topological Hall effect not only arises in a centrosymmetric structure, but it also coexists with CDW order.

Origin of the hump anomalies in the Hall resistance loops of ultrathin SrRuO3/SrIrO3 multilayers

The proposal that very small N\'eel skyrmions can form in SrRuO$_3$/SrIrO$_3$ epitaxial bilayers and that the electric field-effect can be used to manipulate these skyrmions in gated devices strongly stimulated the recent research of SrRuO$_3$ heterostructures. A strong interfacial Dzyaloshinskii-Moriya interaction, combined with the breaking of inversion symmetry, was considered as the driving force for the formation of skyrmions in SrRuO$_3$/SrIrO$_3$ bilayers. Here, we investigated nominally symmetric heterostructures in which an ultrathin ferromagnetic SrRuO$_3$ layer is sandwiched between large spin-orbit coupling SrIrO$_3$ layers, for which the conditions are not favorable for the emergence of a net interfacial Dzyaloshinskii-Moriya interaction. Previously the formation of skyrmions in the asymmetric SrRuO$_3$/SrIrO$_3$ bilayers was inferred from anomalous Hall resistance loops showing humplike features that resembled topological Hall effect contributions. Symmetric SrIrO$_3$/SrRuO$_3$/SrIrO$_3$ trilayers do not show hump anomalies in the Hall loops. However, the anomalous Hall resistance loops of symmetric multilayers, in which the trilayer is stacked several times, do exhibit the humplike structures, similar to the asymmetric SrRuO$_3$/SrIrO$_3$ bilayers. The origin of the Hall effect loop anomalies likely resides in unavoidable differences in the electronic and magnetic properties of the individual SrRuO$_3$ layers rather than in the formation of skyrmions.

Topological phase transition driven by magnetic field and topological Hall effect in an antiferromagnetic skyrmion lattice

The topological Hall effect (THE), given by a composite of electric and topologically non-trivial spin texture is commonly observed in magnetic skyrmion crystals. Here we present a study of the THE of electrons coupled to antiferromagnetic Skyrmion lattices (AF-SkX). We show that, in the strong Hund coupling limit, topologically non-trivial phases emerge at specific fillings. Interestingly, at low filling an external field controlling the magnetic texture, drives the system from a conventional insulator phase to a phase exhibiting THE. Such behavior suggests the occurrence of a topological transition which is confirmed by a closing of the bulk-gap that is followed by its reopening, appearing simultaneously with a single pair of helical edge states. This transition is further verified by the calculation of the the Chern numbers and Berry curvature. We also compute a variety of observables in order to quantify the THE, namely: Hall conductivity and the orbital magnetization of electrons moving in the AF-SkX texture.

Chiral-Bubble-Induced Topological Hall Effect in Ferromagnetic Topological Insulator Heterostructures.

We report compelling evidence of an emergent topological Hall effect (THE) from chiral bubbles in a two-dimensional uniaxial ferromagnet, V-doped Sb2Te3 heterostructure. The sign of THE signal is determined by the net curvature of domain walls in different domain configurations, and the strength of THE signal is correlated with the density of nucleation or pinned bubble domains. The experimental results are in good agreement with the integrated linear transport and Monte Carlo simulations, corroborating the emergent gauge field at chiral magnetic bubbles. Our findings not only reveal a general mechanism of THE in two-dimensional ferromagnets but also pave the way for the creation and manipulation of topological spin textures for spintronic applications.

Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

The hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, is known to be realized in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Here, we demonstrate by means of Monte Carlo simulations that the hedgehog lattice is induced by not the DM interaction but frustration in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, the breathing bond-alternation is characterized by the ratio of the nearest-neighbor (NN) antiferromagnetic exchange interaction for large tetrahedra to that for small ones, J1'/J1. A quadruple-q state with the ordering vector of q=(\pm 1/2,\pm 1/2,\pm 1/2), which is realized for a large third NN antiferromagnetic interaction along the bond direction J3, turns out to become the hedgehog-lattice state in the breathing case of J1'/J1 <1, while in the uniform case of J1'/J1 =1, it is a collinear state favored by thermal fluctuations. It is also found that in a magnetic field, the structure of the (1/2,1/2,1/2) hedgehog lattice is changed from cubic to tetragonal, resulting in a nonzero net spin chirality which in a metalic system, should yield a characteristic topological Hall effect.

Evolution of diverse Hall effects during the successive magnetic phase transitions in Mn2.5Fe0.6Sn0.9 Kagome-lattice alloy

Evolution of diverse Hall effects due to successive magnetic transitions has been observed in Mn2.5Fe0.6Sn0.9 by suitable chemical substitution of Fe in Mn3.1Sn0.9. This noncollinear antiferromagnetic alloy exhibits a Neel temperature of 325 K. Upon cooling from 325 K, a magnetic phase transition from noncollinear antiferromagnetism to ferromagnetism occurs at 168 K due to the tilting of magnetization towards c axis. Above this temperature, anomalous Hall resistivity ranged from 0.6 to 1.3 μΩ cm has been observed in noncollinear antiferromagnetic state. Below this temperature, a topological Hall effect (THE) starts to appear due to the non-vanishing scalar spin chirality arising from the noncoplanar spin structure. Further decreasing temperature to 132 K, another magnetic transition happens, resulting in the coexistence of ferromagnetism and antiferromagnetism, so that a Hall plateau with large hysteresis below 70 K is yielded. A hysteresis as high as ∼80 kOe is obtained in ρ xy -H at 15 K. However, the Hall plateau disappears and only anomalous Hall effect (AHE) persists when further decreasing the temperature to 5 K. The present study provides a picture of diverse magneto-transport properties correlated to the variable spin structures driven by magnetic phase transitions.

Topological Hall Effect in a Topological Insulator Interfaced with a Magnetic Insulator.

A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI heterostructures may result in an AHE-associated response that resembles a THE but in fact is not. This Letter reports a genuine THE in a TI/MI structure that has only one magnetic phase. The structure shows a THE in the temperature range of T = 2-3 K and an AHE at T = 80-300 K. Over T = 3-80 K, the two effects coexist but show opposite temperature dependencies. Control measurements, calculations, and simulations together suggest that the observed THE originates from skyrmions, rather than the coexistence of two AHE responses. The skyrmions are formed due to a Dzyaloshinskii-Moriya interaction (DMI) at the interface; the DMI strength estimated is substantially higher than that in heavy metal-based systems.

Topological phase transitions driven by topological number change and next-nearest-neighbor hopping in skyrmion crystals

By considering the topological Hall conductivity and the nanoribbon edge states, i.e., the bulk-boundary correspondence of the skyrmion crystal (SkX), this work focused on the relation of the topological properties to the next-nearest-neighbor (nnn) hopping (t′), the exchange coupling strength (J), and the topological number of the skyrmion (Qsk). When the nnn hopping of the electrons coexists with the nearest-neighbor hopping, the flux pattern of the emergent magnetic field traversing the SkX is reshaped giving rise to different topological Hall effect. By increasing t′ from 0 to t, we found the Chern numbers of the electronic bands change from unity to indefinite values demonstrating a phase transition. By continually increasing Qsk from 1 to 2, we found topological phase transitions occur at Qsk=1.3 and 1.7. We also considered the effect of finite J and found the results obtained in the adiabatic limit (J≫t) hold to around J=t.

Topological Hall effect in the Shastry-Sutherland lattice

We study the classical Heisenberg model on the geometrically frustrated Shastry-Sutherland (SS) lattice with additional Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We show that several noncollinear and noncoplanar magnetic phases, such as the flux, all-in/all-out, 3-in--1-out/3-out--1-in, and canted-flux phases are stabilized over wide ranges of parameters in the presence of the DM interaction. We discuss the role of DM interaction in stabilizing these complex magnetic phases. When coupled to these noncoplanar magnetic phases, itinerant electrons experience a finite Berry phase, which manifests in the form of topological Hall effect, whereby a nonzero transverse conductivity is observed even in the absence of a magnetic field. We study this anomalous magnetotransport by calculating the electron band structure and transverse conductivity for a wide range of parameter values, and demonstrate the existence of topological Hall effect in the SS lattice. We explore the role of the strength of itinerant electron-local moment coupling on electron transport and show that the topological Hall features evolve significantly from strong to intermediate values of the coupling strength, and are accompanied by the appearance of a finite spin Hall conductivity.

Competing magnetic phases and fluctuation-driven scalar spin chirality in the kagome metal YMn6Sn6.

Identification, understanding, and manipulation of novel magnetic textures are essential for the discovery of new quantum materials for future spin-based electronic devices. In particular, materials that manifest a large response to external stimuli such as a magnetic field are subject to intense investigation. Here, we study the kagome-net magnet YMn6Sn6 by magnetometry, transport, and neutron diffraction measurements combined with first-principles calculations. We identify a number of nontrivial magnetic phases, explain their microscopic nature, and demonstrate that one of them hosts a large topological Hall effect (THE). We propose a previously unidentified fluctuation-driven mechanism, which leads to the THE at elevated temperatures. This interesting physics comes from parametrically frustrated interplanar exchange interactions that trigger strong magnetic fluctuations. Our results pave a path to chiral spin textures, promising for novel spintronics.

Berry phase manipulation in ultrathin SrRuO3 films

A notion of the Berry phase is a powerful means to unravel the non-trivial role of topology in various novel phenomena observed in chiral magnetic materials and structures. A celebrated example is the intrinsic anomalous Hall effect (AHE) driven by the non-vanishing Berry phase in the momentum space. As the AHE is highly dependent on details of the band structure near the Fermi edge, the Berry phase and AHE can be altered in thin films whose chemical potential is tunable by dimensionality and disorder. Here, we demonstrate that in ultrathin SrRuO$_3$ films the Berry phase can be effectively manipulated by the effects of disorder on the intrinsic Berry phase contribution to the AHE, which is corroborated by our numerically exact calculations. In addition, our findings provide ample experimental evidence for the superficial nature of the topological Hall effect attribution to the protected spin texture and instead lend strong support to the multi-channel AHE scenario in ultrathin SrRuO$_3$.

Topological Hall Effect: Emergent Topological Hall Effect at a Charge‐Transfer Interface (Small 50/2020)

Topological Hall Effect: Emergent Topological Hall Effect at a Charge‐Transfer Interface (Small 50/2020)

Emergent Topological Hall Effect at a Charge-Transfer Interface.

Exploring exotic interface magnetism due to charge transfer and strong spin-orbit coupling has profound application in the future development of spintronic memory. Here, the emergence and tuning of topological Hall effect (THE) from a CaMnO3 /CaIrO3 /CaMnO3 trilayer structure are studied in detail, which suggests the presence of magnetic Skyrmion-like bubbles. First, by tilting the magnetic field direction, the evolution of the Hall signal suggests a transformation of Skyrmions into topologically-trivial stripe domains, consistent with behaviors predicted by micromagnetic simulations. Second, by varying the thickness of CaMnO3 , the optimal thicknesses for the THE signal emergence are found, which allow identification of the source of Dzyaloshinskii-Moriya interaction (DMI) and its competition with antiferromagnetic superexchange. Employing high-resolution transmission electron microscopy, randomly distributed stacking faults are identified only at the bottom interface and may avoid mutual cancellation of DMI. Last, a spin-transfer torque experiment also reveals a low threshold current density of ≈109 A m-2 for initiating the bubbles' motion. This discovery sheds light on a possible strategy for integrating Skyrmions with antiferromagnetic spintronics.

Spontaneous (Anti)meron Chains in the Domain Walls of van der Waals Ferromagnetic Fe5- x GeTe2.

The promise of topologically vortex-like magnetic spin textures hinges on the intriguing physical properties and theories in fundamental research and their distinguished roles as high-efficiency information units in future spintronics. The exploration of such magnetic states with unique spin configurations has never ceased. In this study, the emergence of unconventional (anti)meron chains from a domain wall pair is directly observed at zero field in 2D ferromagnetic Fe5- x GeTe2 , closely correlated with significant enhancement of the in-plane magnetization and weak van der Waals interactions. The simultaneous appearance of a large topological Hall effect is observed at the same temperature range as that of the abnormal magnetic transition. Moreover, the distinctive features of the (anti)meron chains and their collective dynamic behavior under external fields may provide concrete experimental evidence for the recent theoretical prediction of the magnetic-domain-wall topology and endorse a broader range of possibilities for electronics, spintronics, condensed matter physics, etc.

Inhomogeneous ferromagnetism mimics signatures of the topological Hall effect in SrRuO3 films

Topological transport phenomena in magnetic materials are a major topic of current condensed matter research. One of the most widely studied phenomena is the ``topological Hall effect'' (THE), which is generated via spin-orbit interactions between conduction electrons and topological spin textures such as skyrmions. We report a comprehensive set of Hall effect and magnetization measurements on epitaxial films of the prototypical ferromagnetic metal SrRuO$_3$ the magnetic and transport properties of which were systematically modulated by varying the concentration of Ru vacancies. We observe Hall effect anomalies that closely resemble signatures of the THE, but a quantitative analysis demonstrates that they result from inhomogeneities in the ferromagnetic magnetization caused by a non-random distribution of Ru vacancies. As such inhomogeneities are difficult to avoid and are rarely characterized independently, our results call into question the identification of topological spin textures in numerous prior transport studies of quantum materials, heterostructures, and devices. Firm conclusions regarding the presence of such textures must meet stringent conditions such as probes that couple directly to the non-collinear magnetization on the atomic scale.