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The coupling of conduction electrons and magnetic textures leads to quantum transport phenomena described by the language of emergent electromagnetic fields [1-3]. For magnetic skyrmions, spin-swirling particle-like objects, an emergent magnetic field is produced by their topological winding [4-6], resulting in the conduction electrons exhibiting the topological Hall effect (THE) [7]. When the skyrmion lattice (SkL) acquires a drift velocity under conduction electron flow, an emergent electric field is also generated [8,9]. The resulting emergent electrodynamics dictate the magnitude of the THE via the relative motion of SkL and conduction electrons. Here, we report the emergent electrodynamics induced by SkL motion in Gd$_2$PdSi$_3$, facilitated by its giant THE [10,11]. With increasing current excitation, we observe the dynamic transition of the SkL motion from the pinned to creep regime and finally to the flow regime, where the THE is totally suppressed. We argue that the Galilean relativity required for the total cancellation of the THE can be generically recovered in the flow regime, even in complex multiband systems such as the present compound. Moreover, the observed THE voltages are large enough to enable real-time measurement of the SkL velocity-current profile, which reveals the inertial-like motion of the SkL in the creep regime, appearing as current-hysteretic behavior of the skyrmion velocity.

The cubic $\beta$-Mn-type alloy Co$_8$Zn$_8$Mn$_4$ is a chiral helimagnet that exhibits a peculiar temperature-dependent behavior in the spiral pitch, which decreases from 130 nm at room temperature to 70 nm below 20 K. Notably, this shortening is also accompanied by a structural transition of the metastable skyrmion texture, transforming from a hexagonal lattice to a square lattice of elongated skyrmions. The underlying mechanism of these transformations remain unknown, with interactions potentially involved including temperature-dependent Dzyaloshinskii-Moriya interaction, magnetocrystalline anisotropy, and exchange anisotropy. Here, x-ray resonant magnetic small-angle scattering in vectorial magnetic fields was employed to investigate the temperature dependence of the anisotropic properties of the helical phase in Co$_8$Zn$_8$Mn$_4$. Our results reveal quantitatively that the magnitude of the anisotropic exchange interaction increases by a factor of 4 on cooling from room temperature to 20 K, leading to a 5% variation in the helical pitch within the (001) plane at 20 K. While anisotropic exchange interaction contributes to the shortening of the spiral pitch, its magnitude is insufficient to explain the variation in the spiral periodicity from room to low temperatures. Finally, we demonstrate that magnetocrystalline and exchange anisotropies compete, favoring different orientations of the helical vector in the ground state., Comment: 8 pages, 4 figures

The thermoelectric Nernst effect of solids converts heat flow to beneficial electronic voltages. Here, using a correlated topological semimetal with high carrier mobility $\mu$ in presence of magnetic fluctuations, we demonstrate an enhancement of the Nernst effect close to a magnetic phase transition. A magnetic instability in NdAlSi modifies the carrier relaxation time on 'hotspots' in momentum space, causing a strong band filling dependence of $\mu$. We quantitatively derive electronic band parameters from a novel two-band analysis of the Nernst effect $S_{xy}$, in good agreement with quantum oscillation measurements and band calculations. While the Nernst response of NdAlSi behaves much like conventional semimetals at high temperatures, an additional contribution $\Delta S_{xy}$ from electronic correlations appears just above the magnetic transition. Our work demonstrates the engineering of the relaxation time, or the momentum-dependent self energy, to generate a large Nernst response independent of a material's carrier density, i.e. for metals, semimetals, and semiconductors with large $\mu$.

Skyrmion lattices (SkL) in centrosymmetric materials typically have a magnetic period on the nanometer-scale, so that the coupling between magnetic superstructures and the underlying crystal lattice cannot be neglected. Here, we reveal the commensurate locking of a SkL to the atomic lattice in Gd$_3$Ru$_4$Al$_{12}$ via high-resolution resonant elastic x-ray scattering (REXS). Weak easy-plane magnetic anisotropy, demonstrated here by a combination of ferromagnetic resonance and REXS, penalizes placing a skyrmion core on a site of the atomic lattice. Under these conditions, a commensurate SkL, locked to the crystal lattice, is stable at finite temperatures -- but gives way to a competing incommensurate ground state upon cooling. We discuss the role of Umklapp-terms in the Hamiltonian for the formation of this lattice-locked state, its magnetic space group, the role of slight discommensurations, or (line) defects in the magnetic texture, and contrast our findings with the case of SkLs in noncentrosymmetric material platforms., Comment: 17 pages, 4 figures, additional SI included (19 pages, 11 figures, 1 table)

Zintl phase EuIn$_{2}$As$_{2}$ has garnered growing attention as an axion insulator candidate, triggered by the identification of a commensurate double-${\mathbf Q}$ broken-helix state in previous studies, however, its periodicity and symmetry remain subjects of debate. Here, we perform resonant x-ray scattering experiments on EuIn$_{2}$As$_{2}$, revealing an incommensurate nature of the broken-helix state, where both the wave number and the amplitude of the helical modulation exhibit systematic sample dependence. Furthermore, the application of an in-plane magnetic field brings about a broken-fanlike state preserving the double-${\mathbf Q}$ nature, which could be attributed to multiple-spin interactions in momentum space. We propose that the itinerant character of EuIn$_{2}$As$_{2}$, possibly induced by Eu deficiency, gives rise to the helical modulation and impedes the realization of a theoretically-predicted axion state with the collinear antiferromagnetic order., Comment: 6 pages, 5 figures, SM: 9 pages, 6 figures

Imaging antiferromagnetic 180{\deg} domains with actively controlled visibility is vital for both fundamental science and sophisticated applications. While optical second-harmonic generation (SHG) is a well-known technique for distinguishing such domains in non-centrosymmetric antiferromagnets, a general material-based strategy to control domain contrast remains elusive. Using van der Waals antiferromagnet MnPS$_3$ as a proof of concept, we demonstrate the tuning of nonreciprocity-induced domain contrast in SHG through applying an in-plane electric field that transforms the magnetic point group to its unitary subgroup. The interference among intrinsic electric-dipole, magnetic-dipole, and field-induced electric-dipole transitions, each carrying distinct characters under space-inversion ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) operations, enables large tuning of domain contrast and nonreciprocity in a broad spectral range. This strategy, generically applicable to systems characterized by $\mathcal{PT}$-symmetric magnetic groups with a polar unitary subgroup, offers a path to fast electrical modulation of nonlinear nonreciprocal photonic behaviors using antiferromagnets.

The theoretically observable limit of electron density distribution by single-crystal X-ray diffraction is discussed. When F_{orb} and {\delta}F are defined as, respectively, the partial structure factor for an orbital and the deviation of the observed F from the true F, the accuracy of electron density attributable to F_{orb} is chiefly determined by the number of reflections satisfying the condition F_{orb}/F > {\delta}F/F. Since F_{orb}/F, which is generally small for crystals with large F(0,0,0), is constant under a given set of experimental conditions, {\delta}F/F must be reduced to increase the number of reflections satisfying F_{orb}/F > {\delta}F/F. The present paper demonstrates how to reduce {\delta}F mathematically and experimentally, and the following topics are covered: the Poisson statistics, accumulation of errors in the data collection and reduction procedure, multiple diffraction, conversion error from F^2 to F in refinement programs, which is unavoidable when the input quantities have different dimension from F, weighting of reflections, and tips. For demonstration, observation of the electron density of the Ti-3d^1 orbital in YTiO_3 by synchrotron single-crystal X-ray diffraction is presented., Comment: 68 pages, 20 figures

Manipulating carrier density through gate effects, both in electrostatic charge storage and electrochemical intercalation mode, offers powerful control over material properties, although commonly restricted to ultra-thin films or van der Waals materials. Here we demonstrate the application of gate-driven carrier modulation in the microdevice of magnetic Weyl semimetal Co3Sn2S2, fabricated from a bulk single crystal via focused ion beam (FIB). We discovered a Li-intercalated phase LixCo3Sn2S2 featuring electron doping exceeding 5*1021 cm-3, resulting in the Fermi energy shift of 200 meV. The carrier density dependent anomalous Hall conductivity shows fair agreement with density functional theory (DFT) calculation, which also predicts intercalated Li+ ion stabilization within the anion layer while maintaining the kagome-lattice intact. This likely explains the observed rigid band behavior and constant Curie temperature, contrasting with magnetic site substitution experiments. Our findings suggest ionic gating on FIB devices broadens the scope of gate-tuning in quantum materials.

Engineering heterostructures with various types of quantum materials can provide an intriguing playground for studying exotic physics induced by the proximity effect. Here, we report the successful synthesis of iron-based superconductor FeSe$_{x}$Te$_{1-x}$ (FST) thin films across the entire composition range of $0 \leq x \leq 1$ and its heterostructure with a magnetic topological insulator by using molecular beam epitaxy. Superconductivity is observed in the FST films with an optimal superconducting transition temperature $T_c$ $\sim$ 12 K at around x = 0.1. We found that superconductivity survives in the very Te-rich films ($x \leq 0.05$), showing stark contrast to bulk crystals with suppression of superconductivity due to an appearance of bicollinear antiferromagnetism accompanied by a monoclinic structural transition. By examining thickness $t$ dependence of magnetic susceptibility and electrical transport properties, we observed a trend where anomalies associated with the first order structural transition broaden in films with below $t \sim$ 100 nm. We infer this observation suggests a suppression of the structural instability near substrates. Furthermore, we fabricated an all chalcogenide-based heterointerface between FST and a magnetic topological insulator (Cr,Bi,Sb)$_{2}$Te$_{3}$ for the first time, observing both superconductivity and a large anomalous Hall conductivity. The anomalous Hall conductivity increases with decreasing temperature, approaching the quantized value of $e^2/h$ down to the measurable minimum temperature at $T_c$. The result suggests coexistence of magnetic and superconducting gaps at low temperatures opening at the top and bottom surfaces, respectively. Our novel magnetic topological insulator/superconductor heterostructure could be an ideal platform to explore chiral Majorana edge mode.

Surface states of a topological insulator demonstrate interesting quantum phenomena, such as the quantum anomalous Hall (QAH) effect and the quantum magnetoelectric effect. Fermi energy tuning plays a role in inducing phase transitions and developing future device functions. Here, we report on controlling the topological phases in a dual-gate field-effect transistor of a semi-magnetic topological insulator heterostructure. The heterostructure consists of magnetized one-surface and non-magnetic other-surface. By tuning the Fermi energy to the energy gap of the magnetized surface, the Hall conductivity $\sigma_{xy}$ becomes close to the half-integer quantized Hall conductivity $e^2/2h$, exemplifying parity anomaly. The dual-gate control enables the band structure alignment to the two quantum Hall states with $\sigma_{xy} = e^2/h$ and 0 under a strong magnetic field. These states are topologically equivalent to the QAH and axion insulator states, respectively. Precise and independent control of the band alignment of the top and bottom surfaces successively induces various topological phase transitions among the QAH, axion insulator, and parity anomaly states in magnetic topological insulators., Comment: 20 pages, 4 figures

The magnetization and electric polarization of a polar antiferromagnet Fe$_2$Mo$_3$O$_8$ are studied up to 66 T for spin-saturation magnetic fields applied along the polar axis. The magnetization process at 1.4 K exhibited multistep structures below the saturation field of 65 T. The electric polarization along the polar axis exhibits a similar multistep behavior with a total change of 1.2 $\rm{\mu}C/cm^{2}$. A combined triangular-lattice antiferromagnetic model with strong Ising-type spin anisotropy reproduces this multistep magnetoelectric (ME) effect. The exchange striction mechanism explains the remarkable ME response in the two sub-lattice type-I multiferroic materials. These results and interpretation demonstrate a method for realizing multistage magnetoelectric effects in hybrid spin systems., Comment: 10 pages, 5 figures

Hysteretic behaviour accompanies any first-order phase transition, forming a basis for many applications. However, its quantitative understanding remains challenging, and even a qualitative understanding of pronounced hysteresis broadening at low temperature, which is often observed in magnetic-field-induced first-order phase transition materials, is unclear. Here, we show that such pronounced hysteresis broadening emerges if the phase-front velocity during the first-order phase transition exhibits an activated behaviour as a function of both temperature and magnetic field. This is demonstrated by using real-space magnetic imaging techniques, for the magnetic-field-induced first-order phase transition between antiferromagnetic and ferrimagnetic phases in (Fe$_{0.95}$Zn$_{0.05}$)$_{2}$Mo$_{3}$O$_{8}$. When combined with the Kolmogorov-Avrami-Ishibashi model, the observed activated temperature- and field-dependences of the growth velocity of the emerging antiferromagnetic domain quantitatively reproduce the pronounced hysteresis broadening. Furthermore, the same approach also reproduces the field-sweep-rate dependence of the transition field observed in the experiment. Our findings thus provide a quantitative and comprehensive understanding of pronounced hysteresis broadening from the microscopic perspective of domain growth., Comment: 32 pages, 8 figures

Topological magnetic (anti)skrymions are robust string-like objects heralded as potential components in next-generation topological spintronics devices due to their manipulability via low-energy stimuli such as magnetic fields, heat, and electric/thermal current. While these two-dimensional (2D) topological objects are widely studied, intrinsically three-dimensional (3D) electron-spin real-space topology remains less explored despite its prevalence in bulky magnets. Here, we capture the 3D structure of antiskyrmions in a single-crystal, precision-doped (Fe_{0.63}Ni_{0.3}Pd_{0.07})_{3}P lamellae using holographic vector field electron tomography at room temperature and zero field. Our measurements reveal hybrid string-like solitons composed of skyrmions with topological number W = -1 on the lamellae's surfaces and an antiskyrmion (W = +1) connecting them. High resolution images uncover a Bloch point (BP) quadrupole (four magnetic (anti)monopoles) positioned along the rectangular antiskyrmion's four corners (Bloch lines), which enable the observed lengthwise topological transitions. Furthermore, we calculate and compare the energy densities of hybrid strings with ideal (anti)skyrmion strings using micromagnetic simulations, which suggest that this composite (anti)BP structure stabilizes via the subtle interplay between the magnetostatic interaction and anisotropic Dzyaloshinskii-Moriya interaction. The discovery of these hybrid spin textures enables topological tunabilty, a tunable topological Hall effect, and the suppression of skyrmion Hall motion, disrupting existing paradigms within spintronics., Comment: 11 pages, 4 main figures, 7 extended data figures, 1 extended data table

Ultrafast and coherent generation of magnons is of great significance for high-speed antiferromagnetic spintronics. One possible route is by exciton-magnon pairwise optical excitation. To date, such exciton-magnon transitions have been studied mostly by linear optical means in a limited number of conventional three-dimensional antiferromagnets. Here we investigate this correlated transition in van der Waals antiferromagnet MnPS$_3$ by using resonant second-harmonic generation spectroscopy, a nonlinear optical probe sensitive to the symmetry of electronic and magnetic excitations. Two exciton-magnon peaks are observed, in line with the exciton-induced splitting of magnon density of states predicted by a Koster-Slater type theory, indicating significant exciton-magnon interactions. In addition, a large linear magnetoelectric effect of excitons is observed. These findings provide renewed understandings on the correlation effects in two-dimensional magnets with enhanced quasiparticle scattering cross-sections, and point to potential coherent control among charge, spin and orbital degrees of freedom in two-dimensional magnets by optical means.

With the introduction of x-ray free electron laser sources around the world, new scientific approaches for visualizing matter at fundamental length and time-scales have become possible. As it relates to magnetism and "magnetic-type" systems, advanced methods are being developed for studying ultrafast magnetic responses on the time-scales at which they occur. We describe three capabilities which have the potential to seed new directions in this area and present original results from each: pump-probe x-ray scattering with low energy excitation, x-ray photon fluctuation spectroscopy, and ultrafast diffuse x-ray scattering. By combining these experimental techniques with advanced modeling together with machine learning, we describe how the combination of these domains allows for a new understanding in the field of magnetism. Finally, we give an outlook for future areas of investigation and the newly developed instruments which will take us there.

The helimagnetic compounds MnSi$_{1-x}$Ge$_{x}$ show the three-dimensional multiple-$q$ order as referred to as spin-hedgehog-anti-hedgehog (SHAH) lattice. Two representative forms of SHAH are cubic-3$q$ lattice with $q \| \langle100\rangle$ and tetrahedral-4$q$ lattice with $q \| \langle111\rangle$, which show up typically for $x=1.0-~0.8$ and for $x=0.6$, respectively. Here, we have investigated the spin fluctuations in the MnSi$_{1-x}$Ge$_{x}$ polycrystalline samples with $x=0.6$ and $0.8$ by using the time-of-flight (TOF) neutron inelastic scattering and MIEZE-type neutron spin echo techniques to elucidate the microscopic origin of the unconventional Hall effect in the SHAH lattice states. This research is motivated by the observation of a sign change in the unconventional Hall resistivity as a function of temperature [Y. Fujishiro et al., Nat. Comm. $\textbf{10}$, 1059 (2019)]. The present results reveal the correspondences between the temperature ranges where the positive Hall resistivity and spin fluctuations are observed. These results agree well with the theoretical model of the conduction electrons scattered by the fluctuating spin clusters with a non-zero average of sign-biased scalar spin chirality as a mechanism of the positive Hall resistivity [H. Ishizuka and N. Nagaosa, Sci. Adv. $\textbf{4}$, eaap9962 (2018)]., Comment: 10 pages, 8 figures

Microwave impedance microscopy (MIM) has been utilized to directly visualize topological edge states in many quantum materials, from quantum Hall systems to topological insulators, across the GHz regime. While the microwave response for conventional metals and insulators can be accurately quantified using simple lumped-element circuits, the applicability of these classical models to more exotic quantum systems remains limited. In this work, we present a general theoretical framework of the MIM response of arbitrary quantum materials within linear response theory. As a special case, we model the microwave response of topological edge states in a Chern insulator and predict an enhanced MIM response at the crystal boundaries due to collective edge magnetoplasmon (EMP) excitations. The resonance frequency of these plasmonic modes should depend quantitatively on the topological invariant of the Chern insulator state and on the sample's circumference, which highlights their non-local, topological nature. To benchmark our analytical predictions, we experimentally probe the MIM response of quantum anomalous Hall edge states in a Cr-doped (Bi,Sb)2Te3 topological insulator and perform numerical simulations using a classical formulation of the EMP modes based on this realistic tip-sample geometry, both of which yield results consistent with our theoretical picture. We also show how the technique of MIM can be used to quantitatively extract the topological invariant of a Chern insulator, disentangle the signatures of topological versus trivial edge states, and shed light on the microscopic nature of dissipation along the crystal boundaries., Comment: 8 pages, 4 figures

Phase diagrams form the basis for the study of material science, and the profiles of phase-transition lines separating different thermodynamic phases include comprehensive information about thermodynamic quantities, such as latent heat. However, in some materials exhibiting field-induced first-order transitions (FOTs), the equilibrium phase-transition line is hidden by the hysteresis region associated with the FOT; thus, it cannot be directly determined from measurements of resistivity, magnetization, etc. Here, we demonstrate a thermodynamics-based method for determining the hidden equilibrium FOT line. This method is verified for the FOT between antiferromagnetic and ferrimagnetic states in magneto-electric compounds (Fe$_{0.95}$Zn$_{0.05}$)$_{2}$Mo$_{3}$O$_{8}$. The equilibrium FOT line determined based on the Clausius-Clapeyron equation exhibits a reasonable profile in terms of the third law of thermodynamics, and it shows marked differences from the midpoints of the hysteresis region. Our findings highlight that care should be taken for referring to the hysteresis midpoint line when discussing field-induced latent heat or magnetocaloric effects., Comment: 22 pages, 7 figures

Ac current-driven motions of spiral spin textures can give rise to emergent electric fields acting on conduction electrons. This in turn leads to the emergent electromagnetic induction effect which may realize quantum inductor elements of micrometer size. ${\rm YMn}_{6}{\rm Sn}_{6}$ is a helimagnet with a short helical period (2-3 nm) that shows this type of emergent inductance beyond room temperature. To identify the optimized materials conditions for ${\rm YMn}_{6}{\rm Sn}_{6}$-type room-temperature emergent inductors, we have investigated emergent electromagnetic inductance (EEMI) as the magnetism is modified through systematic partial substitution of Y by Tb. By small angle neutron scattering and inductance measurements, we have revealed that the pinning effect on the spin-helix translational mode by Tb doping selectively and largely suppresses the negative component of EEMI, while sustaining the positive inductance arising from the spin tilting mode. We also find that in addition to the spin helix, even the spin-collinear antiferromagnetic structure can host the positive EEMI due to thermally enhanced spin fluctuations. The present study highlights the facile control of both the magnitude and sign of EEMI beyond room temperature, and thus suggests a route to expand the range of emergent inductor candidate materials., Comment: 20 pages, 13 figures

Orbital degrees of freedom mediating an interaction between spin and lattice were predicted to raise strong magnetoelectric effect, i.e. realize an efficient coupling between magnetic and ferroelectric orders. However, the effect of orbital fluctuations have been considered only in a few magnetoelectric materials, as orbital degeneracy driven Jahn-Teller effect rarely couples to polarization. Here, we explore the spin-lattice coupling in multiferroic Swedenborgites with mixed valence and Jahn-Teller active transition metal ions on a stacked triangular/Kagome lattice using infrared and dielectric spectroscopy. On one hand, in CaBa$M_4$O$_7$ ($M$ = Co, Fe), we observe strong magnetic order induced shift in the phonon frequencies and a corresponding large change in the dielectric response. Remarkably, as an unusual manifestation of the spin-phonon coupling, the spin-fluctuations reduce the phonon life-time by an order of magnitude at the magnetic phase transitions. On the other hand, lattice vibrations, dielectric response, and electric polarization show no variation at the N\'eel temperature of CaBaFe$_2$Co$_2$O$_7$, which is built up by orbital singlet ions. Our results provide a showcase for orbital degrees of freedom enhanced magnetoelectric coupling via the example of Swedenborgites., Comment: Supplementary included, 7 + 8 pages, 4 + 9 figures, Accepted version

Intermetallic Pd-doped (Fe,Ni)$_3$P, that crystalizes in a non-centrosymmetric tetragonal structure with $S_4$ symmetry, has recently been discovered to host magnetic antiskyrmions, antivortex-like topological spin textures. In this material, uniaxial magnetic anisotropy and dipolar interactions play a significant role, giving rise to finely branched magnetic domain patterns near the surface of bulk crystals, as revealed by a previous magnetic force microscopy (MFM) measurement. However, small-angle neutron scattering (SANS) is a more suitable method for characterizing bulk properties and fractal structures at the mesoscopic length scale. In this study, using SANS and MFM, we quantitatively investigate the magnetic domain structure in bulk single crystals of (Fe$_{0.63}$Ni$_{0.30}$Pd$_{0.07}$)$_3$P. The SANS results demonstrate that the magnetic domain structure exhibits anisotropic fractal character on the length scale down to the width of the magnetic domain walls. The fractal features are gradually lost in magnetic fields, and different field dependences are observed at 300 K and 2 K due to a temperature-dependent anisotropy. This study quantifies the fractality of the highly anisotropic magnetic domain structures in an antiskyrmion material, and highlights the versatility of SANS for the study of fractal structures in magnetic systems., Comment: This is a post-peer-review, pre-copyedit version of an article published in Journal of Applied Crystallography (2022). The final authenticated version is available online at: https://doi.org/10.1107/S1600576722008561

Reservoir computing is a neuromorphic architecture that potentially offers viable solutions to the growing energy costs of machine learning. In software-based machine learning, neural network properties and performance can be readily reconfigured to suit different computational tasks by changing hyperparameters. This critical functionality is missing in ``physical" reservoir computing schemes that exploit nonlinear and history-dependent memory responses of physical systems for data processing. Here, we experimentally present a `task-adaptive' approach to physical reservoir computing, capable of reconfiguring key reservoir properties (nonlinearity, memory-capacity and complexity) to optimise computational performance across a broad range of tasks. As a model case of this, we use the temperature and magnetic-field controlled spin-wave response of Cu$_2$OSeO$_3$ that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to a host of different physical reservoir responses. We quantify phase-tunable reservoir performance, characterise their properties and discuss the correlation between these in physical reservoirs. This task-adaptive approach overcomes key prior limitations of physical reservoirs, opening opportunities to apply thermodynamically stable and metastable phase control across a wide variety of physical reservoir systems, as we show its transferable nature using above(near)-room-temperature demonstration with Co$_{8.5}$Zn$_{8.5}$Mn$_{3}$ (FeGe)., Comment: Main manuscript: 14 pages, 5 figures. Supplementary materials: 13 pages, 10 figures

In a $\beta$-Mn-type chiral magnet Co$_9$Zn$_9$Mn$_2$, we demonstrate that the magnetic field-driven collapse of a room temperature metastable topological skyrmion lattice passes through a regime described by a partial topological charge inversion. Using Lorentz transmission electron microscopy, the magnetization distribution was observed directly as the magnetic field was swept antiparallel to the original skyrmion core magnetization, i.e. negative magnetic fields. Due to the topological stability of skyrmions, a direct transition of the metastable skyrmion lattice to the equilibrium helical state is avoided for increasingly negative fields. Instead, the metastable skyrmion lattice gradually transforms into giant magnetic bubbles separated by $2\pi$ domain walls. Eventually these large structures give way to form a near-homogeneously magnetized medium that unexpectedly hosts a low density of isolated skyrmions with inverted core magnetization, and thus a total topological charge of reduced size and opposite sign compared with the initial state. A similar phenomenon has been observed previously in systems hosting ordered lattices of magnetic bubbles stabilized by the dipolar interaction and called "topological melting". With support from numerical calculations, we argue that the observed regime of partial topological charge inversion has its origin in the topological protection of the starting metastable skyrmion state., Comment: 9 pages, 4 figures

We have investigated magnetic structures of the centrosymmetrric skyrmion material Gd2PdSi3 by means of polarized neutron scattering near zero field with an isotope-160Gd-enriched single crystal. In a previous study, magnetic structures in Gd2PdSi3 at low temperatures were studied by resonant X-ray scattering measurements [T. Kurumaji et al. Science 365, 914 (2019)]. The present polarized neutron results confirm that the magnetic structure in zero field has elliptic screw-type magnetic modulation with a propagation vector of (q, 0, 0) with q ~ 0.14 and its equivalents. As the temperature increases, the system undergoes a magnetic phase transition while keeping the incommensurate q-vector of (q,0,0). We found that the thermally-induced phase has sinusoidal magnetic modulations with magnetic moments perpendicular both to the c axis and to the q-vector. We also investigate the spin-helicity degree of freedom in the ground state by polarized neutrons, revealing that the system contains equal fractions of the left-handed and right-handed screw-type orders as expected from the centrosymmetric crystal structure., Comment: 6 pages, 4 figures

Magnetic materials with tilted electron spins often exhibit conducting behavior that cannot be explained from semiclassical theories without invoking fictitious (emergent) electromagnetic fields. Quantum-mechanical models explaining such phenomena are rooted in the concept of a moving quasiparticle's Berry phase, driven by a chiral (left- or right-handed) spin-habit. Dynamical and nearly random spin fluctuations, with a slight bent towards left- or right-handed chirality, represent a promising route to realizing Berry-phase phenomena at elevated temperatures, but little is known about the effect of crystal lattice geometry on the resulting macroscopic observables. Here, we report thermoelectric and electric transport experiments on two metals with large magnetic moments on a triangular and on a slightly distorted kagom\'e lattice, respectively. We show that the impact of chiral spin fluctuations is strongly enhanced for the kagom\'e lattice. Both these spiral magnets have similar magnetic phase diagrams including a periodic array of magnetic skyrmions. However, our modelling shows that the geometry of the kagom\'e lattice, with corner-sharing spin-trimers, helps to avoid cancellation of Berry-phase contributions; spin fluctuations are endowed with a net chiral habit already in the thermally disordered (paramagnetic) state. Hence, our observations for the kagom\,e material contrast with theoretical models treating magnetization as a continuous field, and emphasize the role of lattice geometry on emergent electrodynamic phenomena., Comment: 16 pages, 4 figures

When a conduction electron couples with a non-coplanar localized magnetic moment, the realspace Berry curvature is exerted to cause the geometrical Hall effect, which is not simply proportional to the magnetization. So far, it has been identified in the case mostly where the non-coplanar magnetic order is present on the sublattice of conduction electrons. Here, we demonstrate that the geometrical Hall effect shows up even without long-range magnetic order of conduction electrons, as induced by non-coplanar exchange fields from the localized magnetic moments, in hole-doped phyrochlore molybdates. We find that the geometrical Hall effect is markedly anisotropic with respect to the applied magnetic field direction, which is in good accordance with the field-dependent magnitude and sign change of the real-space scalar spin chirality of local Tb moments. These results may facilitate the understanding of emergent electromagnetic responses induced by the Kondo-like coupling between conduction electrons and local spins in a broad material class., Comment: 9 pages, 7 figures

We have investigated the nonreciprocal electrical transport, that is a nonlinear resistance effect depending on the current direction, in multiferroic Rashba semiconductor (Ge,Mn)Te. Due to coexistence of ferromagnetic and ferroelectric orders, (Ge,Mn)Te provides a unique platform for exploring the nonreciprocal electrical transport in a bulk form. (Ge,Mn)Te thin films shows a large nonreciprocal resistance compared to GeTe, the nonmagnetic counterpart with the same crystal structure. The magnetic-field-angle dependence of the nonreciprocal resistance is maximized when magnetic field is orthogonal to both current and electric polarization, in accord with the symmetry argument. From the analysis of temperature and magnetic field dependence, we deduce that inelastic scatterings of electrons mediated by magnons dominantly contribute to the observed nonreciprocal response. Furthermore, the nonreciprocal resistance is significantly enhanced by lowering hole density. The Fermi level dependence is attributed to the deformation of the Rashba band in which the spin-momentum locked single Fermi surface appears by exchange field from the in-plane magnetization. The present study provides a key insight to the mechanisms of novel transport phenomena caused by the interplay of ferroelectric and ferromagnetic orders in a semiconductor.

Using small angle neutron scattering, we have investigated higher-order peaks in the skyrmion-lattice phase of Cu$_2$OSeO$_3$, in which two different skyrmion lattices, SkX1 and SkX2, are known to form. For each skyrmion-lattice phase, we observed two sets of symmetrically inequivalent peaks at the higher-order-reflection positions with the indices $(110)$ and $(200)$. Under the condition where the SkX1 and SkX2 coexist, we confirmed the absence of the scattering at $\mathbf{Q}$ positions combining reflections from the two phases, indicating a significantly weak double-scattering component. Detailed analysis of the peak profile, as well as the temperature and magnetic-field dependence of the peak intensity, also supports the intrinsic higher-order modulation rather than the parasitic double scattering. The two higher-order modulations show contrasting magnetic-field dependence; the former $(110)$ increases as the field is increased, whereas the latter $(200)$ decreases. This indicates that, in Cu$_2$OSeO$_3$, skyrmions are weakly distorted, and the distortion is field-dependent in a way that the dominant higher-order modulation switches from $(110)$ to $(200)$ under field. Monte Carlo simulations under sweeping external magnetic field qualitatively reproduce the observed magnetic-field dependence, and suggests that the higher-order modulations correspond to the superlattices of weak swirlings appearing in the middle of the original triangular-latticed skyrmions., Comment: 13 pages, 14 figures

We report experimental signatures of topological transitions among the Weyl semimetal states of pyrochlore Pr2Ir2O7, where the Kondo coupling between the Ir topological electrons and the spin-ice like orders of Pr moments plays a decisive role. The magnetic-field dependence of resistivity and the Hall conductivity exhibits a plateau and a sharp jump associated with a magnetic-field hysteresis, similar to a liquid-gas-like transition in dipolar spin ice system. Furthermore, the Kondo coupling is controlled by the hydrostatic pressure, revealing that the field-induced displacement of Weyl points in the momentum space strongly depends on the respective electronic state as well as on the Kondo coupling strength. These observations pave a route toward the engineering of band topology in hybrid quantum materials with relativistic conduction electrons and localized magnetic moments.

Magnetic skyrmions, vortex-like topological spin textures, have attracted much interest in a wide range of research fields from fundamental physics to spintronics applications. Recently, growing attention has also been paid to antiskyrmions emerging in opposite topological charge in non-centrosymmetric magnets with $D_{2\mathrm{d}}$ or $S_4$ symmetry. In these magnets, complex interplay among anisotropic Dzyaloshinskii-Moriya interaction, uniaxial magnetic anisotropy, and magnetic dipolar interactions generates a variety of magnetic structures. However, the relation between the stability of antiskyrmions and these magnetic interactions remains to be elucidated. In this work, we control the uniaxial magnetic anisotropy of schreibersite (Fe,Ni)$_3$P with $S_4$ symmetry by doping and investigate its impact on the stability of antiskyrmions. Our magnetometry study, supported by ferromagnetic resonance spectroscopy, shows that the variation of the Ni content and slight doping with 4$d$ transition metals considerably change the magnetic anisotropy. In particular, doping with Pd induces easy-axis anisotropy, giving rise to formation of antiskyrmions, while a temperature-induced spin reorientation is observed in a Rh-doped compound. In combination with Lorentz transmission electron microscopy and micromagnetic simulations, we quantitatively analyze the stability of antiskyrmion as functions of uniaxial anisotropy and demagnetization energy, and demonstrate that subtle balance between them is necessary to stabilize the antiskyrmions., Comment: This is a post-peer-review, pre-copyedit version of an article published in Advanced Materials (2022). The final authenticated version is available online at: https://onlinelibrary.wiley.com/doi/full/10.1002/adma.202108770

Photodetection is an indispensable function of optoelectronic devices in modern communication and sensing systems. Contrary to the near-infrared/visible regions, the fast and sensitive photodetectors operated at room temperature for the far-infrared/terahertz regions are not well developed despite a possibly vast range of applications. The bulk photovoltaic effect (BPVE) in single-phase noncentrosymmetric materials based on the shift current mechanism enables less-dissipative energy conversion endowed with instantaneous responsivity owing to the quantum-mechanical geometric phase of electronic states. Nevertheless, the small-band-gap material for the low-energy BPVE inevitably suffers from the thermal noise due to the intrinsically high conductivity. Here, we demonstrate the shift current induced by soft-phonon excitations without creation of electron-hole pairs in the archetypal ferroelectric BaTiO3 by using the terahertz light, whose energy scale is three orders of magnitude smaller than the electronic band gap. At and above room temperature, we observe appreciable photocurrents caused by the soft-phonon excitation as large as that for electronic excitation and their strong phonon-mode dependence. The observed phonon-driven BPVE can be well accounted for by the shift current model considering the electron-phonon coupling in the displacement-type ferroelectrics as supported by the first-principles calculation. Our findings establish the efficient quantum BPVE arising from low-energy elementary excitations, suggesting the novel principle for the high-performance terahertz photodetectors., Comment: 25 pages, 8 figures

The linear magnetoelectric (ME) effect allows for the selection or switching between two antiferromagnetic (AFM) states via the application of large electric ($E$) and magnetic ($H$) fields. Once an AFM state is selected, it is preserved by an energy barrier, even when the fields are removed. Using a simple phenomenological model, we find that this energy barrier, needed to switch the AFM state, is proportional to the product of the $E$ and $H$ coercive fields $(EH)_{\rm C}$. We measured the field and temperature dependence of $(EH)_{\rm C}$ in LiCoPO$_4$ for two different field configurations, and the data show the temperature variation of $(EH)_{\rm C}\sim(T_{\rm N}-T)^{3/2}$ in good agreement with the model. We also investigated the dynamics of the AFM domain switching using pulsed $E$-field measurements. It was found that the coercive field $(EH)_{\rm C}$ follows a power-law frequency dependence and is well described in the framework of Ishibashi-Orihara model, implying 1-dimensional character of domain wall propagation., Comment: main + supplementary, 9+5 pages, 7+4 figures

Topologically protected nanoscale spin textures, known as magnetic skyrmions, possess particle-like properties and feature emergent magnetism effects. In bulk cubic heli-magnets, distinct skyrmion resonant modes are already identified using a technique like ferromagnetic resonance in spintronics. However, direct light-matter coupling between microwave photons and skyrmion resonance modes has not been demonstrated yet. Utilising two distinct cavity systems, we realise to observe a direct interaction between the cavity resonant mode and two resonant skyrmion modes, the counter-clockwise gyration and breathing modes, in bulk Cu$_2$OSeO$_3$. For both resonant modes, we find the largest coupling strength at 57 K indicated by an enhancement of the cavity linewidth at the degeneracy point. We study the effective coupling strength as a function of temperature within the expected skyrmion phase. We attribute the maximum in effective coupling strength to the presence of a large number of skyrmions, and correspondingly to a completely stable skyrmion lattice. Our experimental findings indicate that the coupling between photons and resonant modes of magnetic skyrmions depends on the relative density of these topological particles instead of the pure spin number in the system., Comment: 11 pages, main text: page 1-8 with 4 figures, supplementary material: page 9-11 with 6 figures

The quest for nonmagnetic Weyl semimetals with high tunability of phase has remained a demanding challenge. As the symmetry breaking control parameter, the ferroelectric order can be steered to turn on/off the Weyl semimetals phase, adjust the band structures around the Fermi level, and enlarge/shrink the momentum separation of Weyl nodes which generate the Berry curvature as the emergent magnetic field. Here, we report the realization of a ferroelectric nonmagnetic Weyl semimetal based on indium doped Pb1 xSnxTe alloy where the underlying inversion symmetry as well as mirror symmetry is broken with the strength of ferroelectricity adjustable via tuning indium doping level and Sn/Pb ratio. The transverse thermoelectric effect, i.e., Nernst effect both for out of plane and in plane magnetic field geometry, is exploited as a Berry curvature sensitive experimental probe to manifest the generation of Berry curvature via the redistribution of Weyl nodes under magnetic fields. The results demonstrate a clean non-magnetic Weyl semimetal coupled with highly tunable ferroelectric order, providing an ideal platform for manipulating the Weyl fermions in nonmagnetic system., Comment: 20 pages, 4 figures

A chiral compound FeSi is a nonmagnetic narrow-gap insulator, exhibiting peculiar charge and spin dynamics beyond a simple band-structure picture. Those unusual features have been attracting renewed attention from topological aspects. Although a signature of surface conduction was indicated according to size-dependent resistivity in bulk crystals, its existence and topological properties remain elusive. Here we demonstrate an inherent surface ferromagnetic-metal state of FeSi thin films and its strong spin-orbit-coupling (SOC) properties through multiple characterizations of the two-dimensional (2D) conductance, magnetization and spintronic functionality. Terminated covalent-bonding orbitals constitute the polar surface state with momentum-dependent spin textures due to Rashba-type spin splitting, as corroborated by unidirectional magnetoresistance measurements and first-principles calculations. As a consequence of the spin-momentum locking, non-equilibrium spin accumulation causes magnetization switching. These surface properties are closely related to the Zak phase of the bulk band topology. Our findings propose another route to explore noble-metal-free materials for SOC-based spin manipulation., Comment: 22 pages, 6 figures, supplementary materials

Nonreciprocal resistance, depending on both directions of current ($j$) and magnetic-field ($H$) or magnetization ($M$), is generally expected to emerge in a chiral conductor, and be maximized for $j$ $\parallel$ $H$($M$). This phenomenon, electrical magnetochiral effect (eMChE), is empirically known to increase with $H$ in a paramagnetic or fully ferromagnetic state on chiral lattice or to depend on fluctuation properties of a helimagnetic state. We report here the eMChE over a wide temperature range in the chiral-lattice magnet MnGe in which the spin hedgehog lattice (HL) forms with the triple spin-helix modulation vectors. The magnitude of nonreciprocal resistivity is sharply enhanced in the course of the field-induced structural transition of HL from cubic to rhombohedral form. This is attributed to the enhanced asymmetric electron scatterings by vector spin chirality in association with the large thermal fluctuations of spin hedgehogs., Comment: 8 pages, 7 figures

Epitaxial thin films of (Sn$_{x}$Pb$_{1-x}$)$_{1-y}$In$_{y}$Te were successfully grown by molecular-beam-epitaxy (MBE) in a broad range of compositions (0 $\leq$ x $\leq$ 1, 0 $\leq$ y $\leq$ 0.23). We investigated electronic phases of the films by the measurements of electrical transport and optical second harmonic generation. In this system, one can control the inversion of band gap, the electric polarization that breaks the inversion symmetry, and the Fermi level position by tuning the Pb/Sn ratio and In composition. A plethora of topological electronic phases are expected to emerge, such as topological crystalline insulator, topological semimetal, and superconductivity. For the samples with large Sn compositions (x > 0.5), hole density increases with In composition (y), which results in the appearance of superconductivity. On the other hand, for those with small Sn compositions (x < 0.5), increase in In composition reduces the hole density and changes the carrier type from p-type to n-type. In a narrow region centered at (x, y) = (0.16, 0.07) where the n-type carriers are slightly doped, charge transport with high mobility exceeding 5,000 cm$^{2}$V$^{-1}$s$^{-1}$ shows up, representing the possible semimetal states. In those samples, the optical second harmonic generation measurement shows the breaking of inversion symmetry along the out-of-plane [111] direction, which ensures the presence of polar semimetal state. The thin films of (Sn$_{x}$Pb$_{1-x}$)$_{1-y}$In$_{y}$Te materials systems with a variety of electronic states would become a promising materials platform for the exploration of novel quantum phenomena.

Topologically non-trivial spin textures, such as skyrmions and dislocations, display emergent electrodynamics and can be moved by spin currents over macroscopic distances. These unique properties and their nanoscale size make them excellent candidates for the development of next-generation logic gates, race-track memory, and artificial synapses for neuromorphic computing. A major challenge for these applications - and the investigation of nanoscale magnetic structures in general - is the realization of detection schemes that provide high resolution and sensitivity. We study the local magnetic properties of disclinations, dislocations, and domain walls in FeGe, and reveal a pronounced response that distinguishes the individual spin textures from the helimagnetic background. Combination of magnetic force microscopy and micromagnetic simulations links the non-linear response to the local magnetic susceptibility. Based on the findings, we propose a read-out scheme using superconducting micro-coils, representing an innovative approach for detecting topologically non-trivial spin textures and domain walls in device-relevant geometries.

In the metallic pyrochlore Nd$_2$Mo$_2$O$_7$, the conducting Molybdenum sublattice adopts canted, yet nearly collinear ferromagnetic order with nonzero scalar spin chirality. The chemical potential may be controlled by replacing Nd$^{3+}$ with Ca$^{2+}$, while introducing only minimal additional disorder to the conducting states. Here, we demonstrate the stability of the canted ferromagnetic state, including the tilting angle of Molybdenum spins, in (Nd$_{1-x}$Ca$_{x}$)$_2$Mo$_2$O$_7$ (NCMO) with $x\le 0.15$ using magnetic susceptibility measurements. Mo-Mo and Mo-Nd magnetic couplings both change sign above $x=0.22$, where the canted ferromagnetic state gives way to a spin-glass metallic region. Contributions to the Curie-Weiss law from two magnetic sublattices are separated systematically., Comment: 22 pages, 9 figures

Carrier doping to the Mott insulator is essential to produce highly correlated metals with emergent properties. Pyrochlore ruthenates, Pr$_{2}$Ru$_{2}$O$_{7}$ (Ru-$4d$ electron number, $n=4$) and Ca$_{2}$Ru$_{2}$O$_{7}$ ($n=3$), are a Mott insulator and a magnetic bad metal, respectively, due to the strong electron correlation. We investigate magneto-transport properties of (Pr$_{1-x}$Ca$_{x}$)$_{2}$Ru$_{2}$O$_{7}$ in a whole band-filling range, $0

Emergent electromagnetic induction based on electrodynamics of noncollinear spin states may enable dramatic miniaturization of inductor elements widely used in electric circuits, yet many issues are to be solved toward application. One such problem is how to increase working temperature. We report the large emergent electromagnetic induction achieved around and above room temperature based on short-period ($\leq$ 3 nm) spin-spiral states of a metallic helimagnet ${\rm YMn}_{6}{\rm Sn}_{6}$. The observed inductance value $L$ and its sign are observed to vary to a large extent, depending not only on the spin helix structure controlled by temperature and magnetic field but also on the current density. The present finding on room-temperature operation and possible sign control of $L$ may provide a new step toward realizing microscale quantum inductors., Comment: 19 pages, 6 figures

We have studied spin excitations in a single-domain crystal of antiferromagnetic LiCoPO4 by THz absorption spectroscopy. By analyzing the selection rules and comparing the strengths of the absorption peaks in the different antiferromagnetic domains, we found electromagnons and magnetoelectric spin resonances besides conventional magnetic-dipole active spin-wave excitations. Using the sum rule for the magnetoelectric susceptibility we determined the contribution of the spin excitations to all the different off-diagonal elements of the static magnetoelectric susceptibility tensor in zero as well as in finite magnetic fields. We conclude that the magnetoelectric spin resonances are responsible for the static magnetoelectric response of the bulk when the magnetic field is along the x-axis, and the symmetric part of the magnetoelectric tensor with zero diagonal elements dominates over the antisymmetric components., Comment: Editors' suggestion, Final version, 15 pages with Supplementary, 6 + 3 figures

Magneto-optical effects have been investigated over the infrared{visible spectral range in ACr2O4 (A = Fe, Co) spinel oxides with non-collinear spin orders in their ground states. We found large magneto-optical Kerr rotation and ellipticity at the on-site d-d transitions of the A2+ ions located within the charge gap. The magneto-optical Kerr rotation of 12 deg observed in CoCr2O4 is unprecedentedly large among magnetic semiconductors and points towards the uniqueness of tetrahedrally coordinated Co2+ ions in generating a strong magneto-optical response. Criteria of strong magneto-optical effects emerging at on-site d-d transitions of transition metal ions are discussed., Comment: Final version, 9 pages, 6 figures