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 the magnetization, when we average over magnetic domains which proliferate near the coercive field. Our results suggest that inhomogeneous domain formation, rather than skyrmions, may provide a common origin for the observed MOKE and Hall resistivity anomalies.
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 $ρ_{xx}^2$ in agreement with side jumps and Berry phase models. 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. SrRuO$_{3}$ films with very low residual resistivity exhibit field induced sign changes of the AHE at low temperatures, suggesting an $ω_c τ$ related crossover.
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…
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…
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…
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.
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…
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…
Ultrathin films of the itinerant ferromagnet SrRuO$_3$ were studied using transport and magnto-optic polar Kerr effect. We find that below 4 monolayers the films become insulating and their magnetic character changes as they loose their simple ferromagnetic behavior. We observe a strong reduction in the magnetic moment which for 3 monolayers and below lies in the plane of the film. Exchange-bias behavior is observed below the critical thickness, and may point to induced antiferromagnetism in contact with ferromagnetic regions.
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…
The origin of the Hall effect in many itinerant ferromagnets is still not resolved, with an anomalous contribution from the sample magnetization that can exhibit extrinsic or intrinsic behavior. We report the first mid-infared (MIR) measurements of the complex Hall ($θ_H$), Faraday ($θ_F$), and Kerr ($θ_K$) angles, as well as the Hall conductivity ($σ_{xy}$) in a SrRuO$_3$ film in the 115-1400 meV energy range. The magnetic field, temperature, and frequency dependence of the Hall effect is explored. The MIR magneto-optical response shows very strong frequency dependence, including sign changes…
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 …
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…
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$_…
A notion of the Berry phase is a powerful means to unravel the non-trivial role of topology in various novel phenomena observed in chiral magnetic materials and structures. A celebrated example is the intrinsic anomalous Hall effect (AHE) driven by the non-vanishing Berry phase in the momentum space. As the AHE is highly dependent on details of the band structure near the Fermi edge, the Berry phase and AHE can be altered in thin films whose chemical potential is tunable by dimensionality and disorder. Here, we demonstrate that in ultrathin SrRuO$_3$ films the Berry phase can be effectively ma…
Thin films of the ferromagnetic metal SrRuO3 (SRO) show a varying easy magnetization axis depending on the epitaxial strain and undergo a metal-to-insulator transition with decreasing film thickness. We have investigated the magnetic properties of SRO thin films with varying thicknesses fabricated on SrTiO3(001) substrates by soft x-ray magnetic circular dichroism (XMCD) at the Ru M2,3 edge. Results have shown that, with decreasing film thickness, the film changes from ferromagnetic to non-magnetic around 3monolayer thickness, consistent with previous magnetization and magneto-optical Kerr eff…
We argue that the scaling of the anomalous Hall effect (AHE) by Mathieu et al. [Phys. Rev. Lett. 93, 016602 (2004)] does not provide support to the interpretation of the AHE in SrRuO3 as an intrinsic effect due to Berry phase monopoles in k-space.
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…
We present measurement and analysis techniques that allow the complete complex magneto-conductivity tensor to be determined from mid-infrared (11-1.6 micron; 100-800 meV) measurements of the complex Faraday (theta_F) and Kerr (theta_K) angles. Since this approach involves measurement of the geometry (orientation axis and ellipticity of the polarization) of transmitted and reflected light, no absolute transmittance or reflectance measurements are required. Thick film transmission and reflection equations are used to convert the complex theta_F and theta_K into the complex longitudinal conductiv…
We have performed magneto-optical Kerr spectroscopy measurements on intercalated transition-metal dichalcogenide Fe$_{0.25}$TaS$_{2}$ in the polar Kerr geometry as a function of temperature, magnetic field, and wavelength. The Kerr angle exhibits pronounced peaks at $\sim$775 nm (1.6 eV) and $\sim$515 nm (2.4 eV), which we attribute to spin-dependent interband optical transitions arising from states in the vicinity of the Fermi energy. Below the ferromagnetic transition temperature (165 K), we observe strongly wavelength- and magnetic-field-dependent Kerr signal. At a fixed wavelength, the mag…
Efforts to find the magnetic monopole in real space have been made in cosmic rays and in accelerators, but up to now there is no firm evidence for its existence due to the very heavy mass $\sim 10^{16}$GeV. However, we show that the magnetic monopole can appear in the crystal-momentum space of solids in the accessible low energy region ($\sim0.1-1$eV) in the context of the anomalous Hall effect. We report experimental results together with first-principles calculations on the ferromagnetic crystal SrRuO$_3$ that provide evidence for the magnetic monopole in the crystal-momentum space.
A direct correlation is seen between the coercive field (HC) and the magnetic-field-dependent resistivity (MR) in SrMnO3/SrRuO3 superlattices of perpendicular magnetic anisotropy. The magnetoresistance shows a sharp jump at Hc for in-plane current and the out-of-plane magnetic field. Both HC and high-field MR also oscillate with the thickness of the SrMnO3 spacer layers separating the metallic ruthenate. Since the spacer in these superlattices has no mobile carriers to facilitate an oscillatory coupling, we attribute the observed behavior to the spin-polarized quantum tunneling of electrons be…
Magnetism and spin-orbit coupling (SOC) are two quintessential ingredients underlying novel topological transport phenomena in itinerant ferromagnets. When spin-polarized bands support nodal points/lines with band degeneracy that can be lifted by SOC, the nodal structures become a source of Berry curvature; this leads to a large anomalous Hall effect (AHE). Contrary to three-dimensional systems that naturally host nodal points/lines, two-dimensional (2D) systems can possess stable nodal structures only when proper crystalline symmetry exists. Here we show that 2D spin-polarized band structures…
The unique sensitivity of optical response to different types of symmetry breaking can be used to detect and identify spontaneously ordered many-body states in bilayer graphene. We predict a strong response at optical frequencies, sensitive to electronic phenomena at low energies, which arises because of nonzero inter-band matrix elements of the electric current operator. In particular, the polar Kerr rotation and reflection anisotropy provide fingerprints of the quantum anomalous Hall state and the nematic state, characterized by spontaneously broken time reversal symmetry and lattice rotatio…
We carry out a first-principles investigation on magnetism, electronic structure, magneto-optical effects and topological property of newly grown cubic double perovskite Ba2NiOsO6 and its (111) (Ba2NiOsO6)/(BaTiO3)10 superlattice, based on the density functional theory with the generalized gradient approximation (GGA) plus onsite Couloumb interactions. Interestingly, we find that both structures are rare ferromagnetic (FM) semiconductors with estimated Curie temperatures of ~150 and 70 K, respectively. The calculated near-neighbor exchange coupling parameters reveal that the ferromagnetism is …
The anomalous charge transport observed in some strongly correlated metals raises questions as to the universal applicability of Landau Fermi liquid theory. The coherence temperature $T_{FL}$ for normal metals is usually taken to be the temperature below which $T^2$ is observed in the resistivity. Below this temperature, a Fermi liquid with well-defined quasiparticles is expected. However, metallic ruthenates in the Ruddlesden-Popper family, frequently show non-Drude low-energy optical conductivity and unusual $ω/T$ scaling, despite the frequent observation of $T^2$ dc resistivity. Herein we r…
Interfacial control of magnetism and electron transport in nonisostructural SrRuO$_3$/SrCuO$_2$ heterostructure
Institute of Physics（印度物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立大学）；Department of Physics, Indian Institute of Technology Kanpur（坎普尔印度理工学院物理系）；Department of Physics, Indian Institute of Science（班加罗尔印度科学研究所物理系）；School of Physical Sciences, National Institute of Science Education and Research (NISER)（布巴内斯瓦尔国家科学教育研究中心物理科学学院）
Temperature-invariant magneto-optical Kerr effect in a noncollinear antiferromagnet
University of California, Irvine（加州大学尔湾分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Irvine Materials Research Institute, University of California, Irvine（加州大学尔湾分校欧文材料研究所）；Colorado State University（科罗拉多州立大学）
We show that a finite Hall effect in zero applied magnetic field occurs for partially filled bands in certain time-reversal violating states with zero net flux per unit-cell. These states are the Magneto-chiral states with parameters in the effective one-particle Hamiltonian such that they do not satisfy the Haldane-type constraints for topological electronic states. The results extend an earlier discussion of the Kerr effect observed in the cuprates but may be applicable to other experimental situations.
We study the anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted bilayer graphene (TBG) aligned with hexagonal boron nitride (hBN) substrate as well as twisted double bilayer graphene systems. We show that non-vanishing valley polarizations in twisted graphene systems would give rise to anomalous Hall effect which can be tuned by in-plane magnetic fields. The valley polarized states are also associated with giant Faraday/Kerr rotations in the terahertz frequency regime. Moreover, both hBN-aligned TBG and TDBG exhibit colossal nonlinear optical respons…
We show that the breakdown of time-reversal invariance, confirmed by the recent polar Kerr effect measurements in the cuprates, implies the existence of an anomalous Nernst effect in the pseudogap phase of underdoped cuprate superconductors. Modeling the time-reversal-breaking ordered state by the chiral d-density-wave state, we find that the magnitude of the Nernst effect can be sizable even at temperatures much higher than the superconducting transition temperature. These results imply that the experimentally found Nernst effect at the pseudogap temperatures may be due to the chiral d-densit…
We propose a first-principles scheme for the description of the magneto-optical kerr effect within density functional theory (DFT). Though the computation of Kerr parameters is often done within DFT, starting from the conductivity or the dielectric tensor, there is no formal justification to this choice. As a first steps, using as reference materials iron, cobalt and nickel we show that pseudo-potential based calculations give accurate predictions. Then we derive a formal expression for the full dielectric tensor in terms of the density-density correlation function. The derived equation is exa…
We analyze the polar Kerr effect in an itinerant electron system on a square lattice in the presence of a composite charge order proposed for the pseudogap state in underdoped cuprates. This composite charge order preserves discrete translational symmetries, and is "chiral-nematic" in the sense that it breaks time-reversal symmetry, mirror symmetries in $x$ and $y$ directions, and $C_4$ lattice rotation symmetry. The Kerr angle $θ_K$ in $C_4$-symmetric system is proportional to the antisymmetric component of the anomalous Hall conductivity $σ_{xy}-σ_{yx}$. We show that this result holds when $…
We identify an intrinsic mechanism of the anomalous Hall effect for non-symmorphic chiral superconductors. This mechanism relies on both a nontrivial multi-band chiral superconducting order parameter, which is a mixture of pairings of even and odd angular momentum channels, and a complex normal state inter-sublattice hopping, both of which are consequences of the nonsymmorphic group symmetry of the underlying lattice. We apply this mechanism to the putative chiral superconducting phase of the heavy-fermion superconductor $\mathrm{UPt_3}$ and calculate the anomalous ac Hall conductivity in a si…
Giant spontaneous Kerr effect and its self-doping dependence in altermagnetic MnTe
University of California, Irvine（加州大学尔湾分校）；Pohang University of Science and Technology（浦项科技大学）；U.S. Naval Research Laboratory（美国海军研究实验室）；Rutgers University（罗格斯大学）；National TsingHua University（国立清华大学）
We theoretically propose a mechanism for the anomalous Hall effect (AHE) in an antiferrromagnetic (AFM) state of $κ$-type organic conductors. We incorporate the spin-orbit coupling in the effective Hubbard model on the $κ$-type lattice structure taking into account the orientation of the molecules and their arrangement with dimerization. Treating this model by means of the Hartree-Fock approximation and the linear response theory, we find that an intrinsic contribution to the Hall conductivity becomes nonzero in the electron-doped AFM metallic phase with a small canted ferromagnetic moment. We…
The presence of optical polarization anisotropies, such as Faraday/Kerr effects, linear birefringence, and magnetoelectric birefringence are evidence for broken symmetry states of matter. The recent discovery of a Kerr effect using near-IR light in the pseudogap phase of the cuprates can be regarded as a strong evidence for a spontaneous symmetry breaking and the existence of an anomalous long-range ordered state. In this work we present a high precision study of the polarimetry properties of the cuprates in the THz regime. While no Faraday effect was found in this frequency range to the limit…
