We measure the anomalous Hall effect (AHE) resistivity $ρ_{xy}$ in thin films of the itinerant ferromagnet SrRuO$_{3}$. At low temperatures, the AHE coefficient $R_{s}$ varies with $ρ_{xx}^2$, and at higher temperatures, $R_{s}$ reaches a peak and then changes sign just below $T_{c}$. We find that for all films studied $R_{s}$ scales with resistivity in the entire ferromagnetic phase. We attribute the observed behavior to the contribution of the extrinsic side jumps mechanism and the intrinsic Karplus-Luttinger (Berry phase) mechanism including the effect of finite scattering rates.
The magnon dispersion of ferromagnetic SrRuO$_3$ was studied by inelastic neutron scattering experiments on single crystals as function of temperature. Even at low temperature the magnon modes exhibit substantial broadening pointing to strong interaction with charge carriers. We find an anomalous temperature dependence of both the magnon gap and the magnon stiffness, which soften upon cooling in the ferromagnetic phase. Both effects trace the temperature dependence of the anomalous Hall effect. We argue that these results show that Weyl points and the anomalous Hall effect can directly influen…
SrRuO$_3$ heterostructures grown in the (111) direction are a rare example of thin film ferromagnets. By means of density functional theory plus dynamical mean field theory we show that the half-metallic ferromagnetic state with an ordered magnetic moment of 2$μ_{B}$/Ru survives the ultimate dimensional confinement down to a bilayer, even at elevated temperatures of 500$\,$K. In the minority channel, the spin-orbit coupling opens a gap at the linear band crossing corresponding to $\frac34$ filling of the $t_{2g}$ shell. We demonstrate that the respective state is Haldane's quantum anomalous Ha…
We observed a hump-like feature in Hall effects of SrRuO$_3$ ultrathin films, and systematically investigated it with controlling thicknesses, temperatures and magnetic fields. The hump-like feature is extremely stable, even surviving as a magnetic field is tilted by as much as 85$^\circ$. Based on the atomic-level structural analysis of a SrRuO$_3$ ultrathin film with a theoretical calculation, we reveal that atomic rumplings at the thin-film surface enhance Dzyaloshinskii-Moriya interaction, which can generate stable chiral spin textures and a hump-like Hall effect. Moreover, temperature dep…
Investigating the effects of the complex magnetic interactions on the formation of nontrivial magnetic phases enables a better understanding of magnetic materials. Moreover, an effective method to systematically control those interactions and phases could be extensively utilized in spintronic devices. SrRuO3 heterostructures function as a suitable material system to investigate the complex magnetic interactions and the resultant formation of topological magnetic phases, as the heterostructuring approach provides an accessible controllability to modulate the magnetic interactions. In this study…
The Hall effect in SrRuO$_3$ thin-films near the thickness limit for ferromagnetism shows an extra peak in addition to the ordinary and anomalous Hall effects. This extra peak has been attributed to a topological Hall effect due to two-dimensional skyrmions in the film around the coercive field; however, the sign of the anomalous Hall effect in SrRuO$_3$ can change as a function of saturation magnetization. Here we report Hall peaks in SrRuO$_3$ in which volumetric magnetometry measurements and magnetic force microscopy indicate that the peaks result from the superposition of two anomalous Hal…
Ionic substitution forms an essential pathway to manipulate the carrier density and crystalline symmetry of materials via ion-lattice-electron coupling, leading to a rich spectrum of electronic states in strongly correlated systems. Using the ferromagnetic metal SrRuO3 as a model system, we demonstrate an efficient and reversible control of both carrier density and crystalline symmetry through the ionic liquid gating induced protonation. The insertion of protons electron-dopes SrRuO3, leading to an exotic ferromagnetic to paramagnetic phase transition along with the increase of proton concentr…
A controversy arose over the interpretation of the recently observed hump features in Hall resistivity $ρ_{xy}$ from ultra-thin SrRuO$_3$ (SRO) film; it was initially interpreted to be due to topological Hall effect but was later proposed to be from existence of regions with different anomalous Hall effect (AHE). In order to settle down the issue, we performed Hall effect as well as magneto-optic Kerr-effect measurements on 4 unit cell SRO films grown on SrTiO$_3$ (001) substrates. Clear hump features are observed in the measured $ρ_{xy}$, whereas neither hump feature nor double hysteresis loo…
In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for determining and understanding topological properties. A prominent example is Hall anomalies observed in SrRuO3 films, which were interpreted in terms of either magnetic skyrmion-induced topological Hall effect (THE) or inhomogeneous anomalous Hall effect (AHE). To clarify this ambiguity, we systematically investigated the AHE of SrRuO3 ultrathin films with controllable inhomogeneities in film thickness (tSRO). By harnessing the st…
We study the magneto-optical Kerr effect (MOKE) in SrRuO$_3$ thin films, uncovering wide regimes of wavelength, temperature, and magnetic field where the Kerr rotation is not simply proportional to the magnetization but instead displays two-component behavior. One component of the MOKE signal tracks the average magnetization, while the second "anomalous" component bears a resemblance to anomalies in the Hall resistivity which have been previously reported in skyrmion materials. We present a theory showing that the MOKE anomalies arise from the non-monotonic relation between the Kerr angle and …
In this work, the BiFeO3 (BFO)/SrRuO3 (SRO) heterostructure was fabricated and the anomalous Hall effect (AHE) was investigated the in BFO/SRO. It is found the nonmonotonic anomalous Hall resistivity behavior in BFO/SRO is originated from the inhomogeneous SRO layer instead of the topological Hall effect. It is surprised that the AHE in BFO/SRO structure can be manipulated by ferroelectric polarization of BFO. Moreover, an inhomogeneous phenomenological model has been applied on those structure. Furthermore, the modification of band structure in SRO under ferroelectric polarization was discuss…
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 ma…
Electron transport coupled with magnetism has attracted attention over the years as exemplified in anomalous Hall effect due to a Berry phase in momentum space. Another type of unconventional Hall effect -- topological Hall effect, originating from the real-space Berry phase, has recently become of great importance in the context of magnetic skyrmions. We have observed topological Hall effect in bilayers consisting of ferromagnetic SrRuO$_3$ and paramagnetic SrIrO$_3$ over a wide region of both temperature and magnetic field. The topological term rapidly decreases with the thickness of SrRuO$_…
Perovskite SrRuO$_3$ is a prototypical itinerant ferromagnet which allows interface engineering of its electronic and magnetic properties. We report synthesis and investigation of atomically flat artificial multilayers of SrRuO$_3$ with the spin-orbit semimetal SrIrO$_3$ in combination with band-structure calculations with a Hubbard $U$ term and topological analysis. They reveal an electronic reconstruction and emergence of flat Ru-4d$_{xz}$ bands near the interface, ferromagnetic interlayer coupling and negative Berry-curvature contribution to the anomalous Hall effect. We analyze the Hall ef…
Ferromagnetism and exotic topological structures in SrRuO$_3$ (SRO) induce sign-changing anomalous Hall effect (AHE). Recently, hump structures have been reported in the Hall resistivity of SRO thin films, especially in the ultra-thin regime. We investigate the AHE and hump structure in the Hall resistivity of SRO ultra-thin films with an SrTiO$_3$ (STO) capping layer and ionic liquid gating. STO capping results in sign changes in the AHE and modulation of the hump structure. In particular, the hump structure in the Hall resistivity is strongly modulated and even vanishes in STO-capped 4 unit …
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 Hal…
Topological spin textures in an itinerant ferromagnet, SrRuO$_3$ is studied combining Hall transport measurements and numerical simulations. We observe characteristic signatures of the Topological Hall Effect associated with skyrmions. A relatively large thickness of our films and absence of heavy metal layers make the interfacial Dzyaloshinskii-Moriya interaction an unlikely source of these topological spin textures. Additionally, the transport anomalies exhibit an unprecedented robustness to magnetic field tilting and temperature. Our numerical simulations suggest that this unconventional be…
Magneto-ionic control of topological transport in SrRuO3 via band topology engineering
Key Laboratory of Magnetic Molecules and Magnetic Information Materials of Ministry of Education & School of Materials Science and Engineering, Shanxi Normal University（山西师范大学材料科学与工程学院）；Research Institute of Materials Science, Shanxi Key Laboratory of Advanced Magnetic Materials and Devices, Shanxi Normal University（山西师范大学材料科学研究所）
One of the key technologies in spintronics is to tame spin-orbit coupling (SOC) that links spin and motion of electrons, giving rise to intriguing magneto-transport properties in itinerant magnets. Prominent examples of such SOC-based phenomena are anomalous and topological Hall effects. However, controlling them by electric field has remained unachieved since electric field tends to be screened in itinerant magnets. Here we demonstrate that both anomalous and topological Hall effects can be modulated by electric field in oxide heterostructures consisting of ferromagnetic SrRuO$_{3}$ and nonma…
It is well established that the anomalous Hall effect that a ferromagnet displays scales with its magnetization. Therefore, an antiferromagnet that has no net magnetization should exhibit no anomalous Hall effect. Here we show that the non-collinear triangular antiferromagnet Mn3Ge exhibits a large anomalous Hall effect comparable to that of ferromagnetic metals; the magnitude of the anomalous conductivity is 500 per ohm per cm at 2 K and 50 per ohm per cm at room temperature. The angular dependence of the anomalous Hall effect measurements confirm that the small residual in-plane magnetic mom…
Analytic Formulas for the Anomalous Hall Effect in Itinerant Magnets
French American Center for Theoretical Science, CNRS（法美理论科学中心，法国国家科学研究中心）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（卡弗里理论物理研究所，加州大学圣塔芭芭拉分校）；École Normale Supérieure de Lyon, CNRS, Laboratoire de physique（里昂高等师范学校，法国国家科学研究中心，物理实验室）
We demonstrate an electric field control of anomalous Hall effect emerging in CaIrO$_3$/CaMnO$_3$ heterostructures. We fabricate both electron-type and hole-type carrier samples by tuning epitaxial strain and then control the carrier density in CaIrO$_3$ layer via electric double layer gating technique. As the Fermi energy of CaIrO$_3$ is tuned close to the Dirac line node, anomalous Hall conductivity is enlarged in both carrier-type samples. This result reveals that the anomalous Hall effect comes from the intrinsic origin reflecting the Dirac like dispersion in CaIrO$_3$. We propose that ban…
Motived by time-reversal symmetry breaking and giant anomalous Hall effect in kagome superconductor \textit{A}V$_3$Sb$_5$ (\textit{A} = Cs, K, Rb), we carried out the thermal transport measurements on CsV$_3$Sb$_5$. In addition to the anomalous Hall effect, the anomalous Nernst effect and the anomalous thermal Hall effect emerge. Interestingly, the longitudinal thermal conductivity $κ_{xx}$ largely deviates from the electronic contribution obtained from the longitudinal conductivity $σ_{xx}$ by the Wiedemann-Franz law. In contrast, the thermal Hall conductivity $κ_{xy}$ is roughly consistent w…
It is known that the Shubnikov--de Haas oscillations can be observed in the Hall resistivity, although their amplitude is much weaker than the amplitude of the diagonal resistivity oscillations. Employing a model of two-dimensional massive Dirac fermions that exhibits anomalous Hall effect, we demonstrate that the amplitude of the Shubnikov--de Haas oscillations of the anomalous Hall conductivity is the same as that of the diagonal conductivity. We argue that the oscillations of the anomalous Hall conductivity can be observed by studying the valley Hall effect in graphene superlattices and the…
Normal and intrinsic anomalous Hall effect in Nb1-yFe2+y
本文研究了Nb_（1-y）Fe_（2 +y）系列样品的霍尔效应。正常和异常的贡献，观察到正正常霍尔效应在高温下占主导地位。一致的异常贡献的分析是唯一可能的富铁Nb 0.985 Fe 2.015具有铁磁基态。在这里，一个积极的正常霍尔系数被发现在所有的温度与适度的最大值在自旋密度波过渡。反常的霍尔效应与本征（贝里相）贡献一致，本征贡献在有序温度TC以下是恒定的，在TC以上连续消失。对于化学计量的NbFe 2和富Nb的Nb 1.01 Fe 1.99-都具有自旋密度波基态-霍尔电阻率的额外贡献阻碍了完整的分析，并表明需要更复杂的模型的异常霍尔效应在巡回反铁磁体。
Topological phases typically encode topology at the level of the single particle band structure. But a remarkable class of models shows that quantum anomalous Hall effects can be driven exclusively by interactions, while the parent non-interacting band structure is topologically trivial. Unfortunately, these models have so far relied on interactions that do not spatially decay and are therefore unphysical. We study a model of spinless fermions on a decorated honeycomb lattice. Using complementary methods, mean-field theory and exact diagonalization, we find a robust quantum anomalous Hall phas…
Observation of anomalous thermal Hall effect in altermagnets
Fudan University（复旦大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究与创新中心）；ShanghaiTech University（上海科技大学）；Hefei National Laboratory（合肥国家实验室）；Collaborative Innovation Center of Advanced Microstructures（先进微结构协同创新中心）
Orthorhombic CuMnAs has been proposed as an antiferromagnetic semimetal hosting nodal line and Dirac points around the Fermi level. We investigate relations between the topological bands and transport phenomena, i.e. spin Hall effect and anomalous Hall effect, in orthorhombic CuMnAs with first-principles calculations combined with symmetry analysis of magnetic structures and of (spin) Berry curvature. We show the nodal line gapped with spin-orbit coupling in CuMnAs dominantly generates large spin Hall conductivity in the ground state. Although the magnetic symmetry in the ground state of CuMnA…
Ab initio prediction of anomalous Hall effect in antiferromagnetic CaCrO$_3$
Institute of Scientific and Industrial Research, Osaka University（大阪大学科学工业研究所）；Department of Precision Engineering, Graduate School of Engineering, Osaka University（大阪大学大学院工学研究科精密工程专攻）
In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$-dimensional topological insulator. The dual description enables a new characterizat…
