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Distinguishing surface and bulk electromagnetism via their dynamics in an intrinsic magnetic topological insulator

The indirect exchange interaction between local magnetic moments via surface electrons has been long predicted to bolster the surface ferromagnetism in magnetic topological insulators (MTIs), which facilitates the quantum anomalous Hall effect. This unconventional effect is critical to determining the operating temperatures of future topotronic devices. However, the experimental confirmation of this mechanism remains elusive, especially in intrinsic MTIs. Here, we combine time-resolved photoemission spectroscopy with time-resolved magneto-optical Kerr effect measurements to elucidate the unique electromagnetism at the surface of an intrinsic MTI MnBi 2 Te 4 . Theoretical modeling based on 2D Ruderman-Kittel-Kasuya-Yosida interactions captures the initial quenching of a surface-rooted exchange gap within a factor of two but overestimates the bulk demagnetization by one order of magnitude. This mechanism directly explains the sizable gap in the quasi-2D electronic state and the nonzero residual magnetization in even-layer MnBi 2 Te 4 . Furthermore, it leads to efficient light-induced demagnetization comparable to state-of-the-art magnetophotonic crystals, promising an effective manipulation of magnetism and topological orders for future topotronics.

74 ATOMIC AND MOLECULAR PHYSICS↗

The 2022 magneto-optics roadmap

Abstract Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton–Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light–matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17). Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ultrafast Light-Induced Magnetoelectric Effect in van der Waals Magnetic Semiconductor Heterostructures

Atomic-scale heterostructures of van der Waals (vdW) magnets and semiconductors provide a unique environment for exploring magnetic dynamics. In contrast to typical photothermal excitation of precessional magnetization dynamics by a pump laser pulse, we find that ultrafast optical excitation of a WS2/CrGeTe3 (CGT) bilayer produces an opposite sign of magnetic torque compared to an isolated CGT film. Experimental observations by time-resolved magneto-optic Kerr effect (TR-MOKE) and theoretical analysis by density functional theory (DFT) and Landau-Lifshitz-Gilbert (LLG) simulations support a mechanism in which charge transfer of photoexcited carriers across the interface alters the perpendicular magnetic anisotropy, which in turn generates a torque on the magnetic layer to trigger precessional magnetization dynamics. These results provide new avenues for ultrafast manipulation of magnetization in vdW heterostructures with type-II band alignments. Lastly, we show that optically-generated spin currents from WS2 into CGT can also trigger precessional dynamics via angular momentum transfer.

Zhou, Wenyi [The Ohio State University]↗

Optical and magneto-optical properties of ferromagnetic monolayer CrBr 3 : A first-principles G W and G W plus Bethe-Salpeter equation study

The discovery of atomically thin two-dimensional (2D) magnetic semiconductors has triggered enormous research interest recently. In this paper, we use first-principles many-body perturbation theory to study a prototypical 2D ferromagnetic semiconductor, monolayer chromium tribromide (CrBr 3 ). With broken time-reversal symmetry, spin-orbit coupling, and excitonic effects included through the full-spinor GW and GW plus Bethe-Salpeter equation (GW-BSE) methods, we compute the frequency-dependent layer polarizability tensor and dielectric function tensor that govern the optical and magneto-optical (MO) properties. In addition, we provide a detailed theoretical formalism for simulating magnetic circular dichroism, MO Kerr effect, and Faraday effect, demonstrating the approach with monolayer CrBr 3 . Due to reduced dielectric screening in 2D and the localized nature of the Cr d orbitals, we find strong self-energy effects on the quasiparticle band structure of monolayer CrBr 3 that give a 3.8 eV indirect bandgap. Also, excitonic effects dominate the low-energy optical and MO responses in monolayer CrBr 3 where a large exciton binding energy of 2.3 eV is found for the lowest bright exciton state with excitation energy at 1.5 eV. We further find that the MO signals demonstrate strong dependence on the excitation frequency and substrate refractive index. Furthermore, our theoretical framework for modeling optical and MO effects could serve as a powerful theoretical tool for future study of optoelectronic and spintronics devices consisting of van der Waals 2D magnets.

36 MATERIALS SCIENCE↗

Ultrafast measurements of the interfacial spin Seebeck effect in Au and rare-earth iron-garnet bilayers

We investigate picosecond spin-currents across Au/iron-garnet interfaces in response to ultrafast laser heating of the electrons in the Au film. In the picoseconds after optical heating, interfacial spin currents occur due to an interfacial temperature difference between electrons in the metal and magnons in the insulator. We report measurements of this interfacial longitudinal spin Seebeck effect between Au and rare-earth iron-garnet insulators, i.e. RE 3 Fe 5 O 12 , where RE is Y, Eu, Tb, Tm. By systematically varying the rare-earth element, we modify the total magnetic moment of the iron-garnet. We use time domain thermoreflectance (TDTR) measurements to characterize the thermal response of the bilayer to ultrafast optical heating. We use time-resolved magneto-optic Kerr effect (TR-MOKE) measurements of the Au layer to measure the time-evolution of spin accumulation in the Au film. Replacing Y with other rare-earths enhances the electron-magnon conductance G e-m at the Au iron-garnet interface by as much as a factor of three. The electron-magnon conductance does not follow the trend of either the total magnetization of the iron garnet or the magnetic moment of the rare-earth.

36 MATERIALS SCIENCE↗

Van der Waals heterostructure Pt 2 HgSe 3 / CrI 3 for topological valleytronics

We identify a valley-polarized Chern insulator in a van der Waals heterostructure, monolayer Pt 2 HgSe 3 /monolayer CrI 3 , for potential applications with interplay between electric, magnetic, optical, and mechanical effects. The interlayer proximity magnetic coupling nearly closes the band gap of monolayer Pt 2 HgSe 3 , and the strong intralayer spin-orbit coupling further lifts the valley degeneracy by over 100 meV, leading to positive and negative band gaps at opposite valleys. In the valley with negative gap, the interfacial Rashba spin-orbit coupling opens a topological band gap of 17.8 meV, which is enlarged to 30.8 meV by adding a hexagonal boron nitride (h-BN) layer. We find large orbital magnetization in the Pt 2 HgSe 3 layer that is much larger than spin, which can induce a measurable optical Kerr effect. Additionally, the valley polarization and Chern number are coupled to the magnetic order of the nearest-neighbor CrI3 layer, which is switchable by electric, magnetic, and mechanical means in experiments. The presence of h-BN protects the topological phase, allowing the construction of superlattices with valley, spin, and layer degrees of freedom.

36 MATERIALS SCIENCE↗

Magnetic state switching in FeGa microstructures

This work demonstrates that magnetoelectric composite heterostructures can be designed at the length scale of 10µms that can be switched from a magnetized state to a vortex state, effectively switching the magnetization off, using electric field induced strain. This was accomplished using thin film magnetoelectric heterostructures of Fe 81.4 Ga 18.6 on a single crystal (011) [Pb(Mg 1/3 Nb 2/3 )O 3 ] 0.68 -[PbTiO 3 ] 0.32 (PMN-32PT) ferroelectric substrate. Here, the heterostructures were tripped from a multi-domain magnetized state to a flux closure vortex state using voltage induced strain in a piezoelectric substrate. FeGa heterostructures were deposited on a Si-substrate for superconducting quantum interference device magnetometry characterization of the magnetic properties. The magnetoelectric coupling of a FeGa continuous film on PMN-32PT was characterized using a magneto optical Kerr effect magnetometer with bi-axial strain gauges, and magnetic multi-domain heterostructures were imaged using x-ray magnetic circular dichroism—photoemission electron microscopy during the transition to the vortex state. The domain structures were modelled using MuMax 3 , a micromagnetics code, and compared with observations. The results provide considerable insight into designing magnetoelectric heterostructures that can be switched from an ‘on’ state to an ‘off’ state using electric field induced strain.

36 MATERIALS SCIENCE↗

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗

Unusual Ferromagnetic Band Evolution and High Curie Temperature in Monolayer 1T‐CrTe2 on Bilayer Graphene

2D van der Waals ferromagnets hold immense promise for spintronic applications due to their controllability and versatility. Despite their significance, the realization and in-depth characterization of ferromagnetic materials in atomically thin single layers, close to the true 2D limit, has been scarce. Here, a successful synthesis of monolayer (ML) 1T-CrTe2 is reported on a bilayer graphene (BLG) substrate via molecular beam epitaxy. Using angle-resolved photoemission spectroscopy and magneto-optical Kerr effect measurements, that the ferromagnetic transition is observed at the Curie temperature (TC) of 150 K in ML 1T-CrTe2 on BLG, accompanied by unconventional temperature-dependent band evolutions. The spectroscopic analysis and first-principle calculations reveal that the ferromagnetism may arise from Goodenough-Kanamori super-exchange and double-exchange interactions, enhanced by the lattice distortion and the electron doping from the BLG substrate. These findings provide pivotal insight into the fundamental understanding of mechanisms governing 2D ferromagnetism and offer a pathway for engineering higher TC in 2D materials for future spintronic devices.

Park, Kyoungree↗

Magnetic anisotropy in permalloy antidot square lattice

Here, magnetic anisotropy of Permalloy (Py) antidot square lattice was investigated by torquemetry method using Rotation Magneto-Optic Kerr Effect (ROTMOKE). We find that there exists a field-dependent 4-fold magnetic anisotropy with the easy magnetization axis along the axis of the antidot square lattice. In addition, there also exists an artifact of a uniaxial magnetic anisotropy in ROTMOKE result. We show that both results are due to the period wiggling of the magnetization in space which was confirmed by magnetic imaging using magnetic transmission soft x-ray microscopy (MTXM). Micromagnetic simulation from MuMax3 supports the wiggling structure of the magnetization, as well as reproduces ROTMOKE result. A simplified model was developed based on the periodic wiggling of the magnetization and successfully explored the physical origin of the field-dependent 4-fold anisotropy and the artifact of the uniaxial anisotropy.

36 MATERIALS SCIENCE↗

Anisotropic optical and magnetic response in self-assembled TiN–CoFe 2 nanocomposites

Transition metal nitrides (e.g., TiN) have shown tremendous promise in optical metamaterials for nanophotonic devices due to their plasmonic properties comparable to noble metals and superior high temperature stability. Vertically aligned nanocomposites (VANs) offer a great platform for combining two dissimilar functional materials with a one-step deposition technique toward multifunctionality integration and strong structural/property anisotropy. Here, we report a two-phase nanocomposite design combining ferromagnetic CoFe 2 nanosheets in the plasmonic TiN matrix as a new hybrid plasmonic metamaterial. The hybrid metamaterials exhibit anisotropic optical and magnetic responses, as well as a pronounced magneto-optical coupling response evidenced by Magneto-optic Kerr Effect measurement, owing to the novel vertically aligned structure. This work demonstrates a new TiN-based metamaterial with anisotropic properties and multifunctionality toward light polarization modulation, optical switching, and integrated optics.

36 MATERIALS SCIENCE↗

Interplay between Ultrafast Electronic and Librational Dynamics in Liquid Nitrobenzene Probed with Two-Color Four-Wave Mixing

Here, we present an experimental and theoretical study of the interplay between ultrafast electron dynamics and librational dynamics in liquid nitrobenzene. A femtosecond ultraviolet pulse and two femtosecond near-infrared pulses interact with nitrobenzene molecules, generating a four-wave mixing nonlinear signal measured in the Optical Kerr Effect geometry. The signal is measured to be nonzero only at negative time delays, corresponding to the near-infrared pulses arriving before the ultraviolet pulse. We perform time-dependent Quantum Master Equation calculations with classical libration to simulate the experiment. The simulations support the conclusion that the near-infrared pulses launch librational motion while creating electronic coherences resulting in a libration-modulated electronic nonlinear response. The analysis of the phase-matched four-wave mixing signals suggests a nonparametric process leaving the molecules in an excited electronic state, providing new insight into ultrafast nonlinear optical interactions in liquids and advancing toward probing ultrafast electronic coherences in complex molecular liquids.

Shivaram, Niranjan [Lawrence Berkeley National Lab↗

Picosecond Ultrasonics in Magnetic Topological Insulator MnBi 2 Te 4

MnBi 2 Te 4 is a magnetic topological insulator with layered A-type antiferromagnetic order. It exhibits a rich layer- and magnetic-state dependent topological phase diagram; however, much about the coupling between spin, charge, and lattice remains to be explored. Here, in this work, we report that MnBi 2 Te 4 is an excellent acoustic phonon cavity by realizing phonon frequency combs using picosecond ultrasonics. With the generated acoustic phonon wavepackets, we demonstrate that the timing and phase of acoustic echoes can be used to detect the presence of stacking faults between van der Waals layers buried deep within the crystal. Furthermore, by implementing this nondestructive ultrafast optical measurement in conjunction with time-resolved magneto-optical Kerr effect experiments, we uncover that out-of-plane vibrations in MnBi 2 Te 4 do not couple to the magnetic order, i.e. there is no appreciable magnetostriction. Our work points out how a well-developed technique can probe the structural defects and phonon pulse engineering in layered topological insulators.

36 MATERIALS SCIENCE↗

Two-Dimensional Ferroelectric Altermagnets: From Model to Material Realization

Multiferroic altermagnets offer new opportunities for magnetoelectric coupling and electrically tunable spintronics. However, due to intrinsic symmetry conflicts between altermagnetism and ferroelectricity, achieving their coexistence, known as ferroelectric altermagnets (FEAM), remains an outstanding challenge, especially in two-dimensional (2D) systems. Here, we propose a universal, symmetry-based design principle for 2D FEAM, supported by tight-binding models and first-principles calculations. We show that lattice distortions can break spin equivalence and introduce the necessary rotation-related symmetry, enabling altermagnetism with electrically reversible spin splitting. Guided by this framework, we identify a family of 2D vanadium oxyhalides and sulfide halides as promising FEAM candidates. In these compounds, pseudo Jahn-Teller distortions and Peierls-like dimerization cooperatively establish the required symmetry conditions. Here, we further propose the magneto-optical Kerr effect as an experimental probe to confirm FEAM and its electric spin reversal. Furthermore, our findings provide a practical framework for 2D FEAM and advancing electrically controlled spintronic devices.

2D materials↗

Unusual Magnetic Hysteresis and Transition between Vortex and Double Pole States Arising from Interlayer Coupling in Diamond-Shaped Nanostructures

Controlling the magnetic ground states at the nanoscale is a long-standing basic research problem and an important issue in magnetic storage technologies. Here, we designed a nanostructured material that exhibits very unusual hysteresis loops due to a transition between vortex and double pole states. Arrays of 700 nm diamond-shaped nanodots consisting of Py(30 nm)/Ru(t Ru )/Py(30 nm) (Py, permalloy (Ni 80 Fe 20 )) trilayers were fabricated by interference lithography and e-beam evaporation. We show that varying the Ru interlayer spacer thickness (t Ru ) governs the interaction between the Py layers. We found this interaction mainly mediated by two mechanisms: magnetostatic interaction that favors antiparallel (antiferromagnetic, AFM) alignment of the Py layers and exchange interaction that oscillates between ferromagnetic (FM) and AFM couplings. For a certain range of Ru thicknesses, FM coupling dominates and forms magnetic vortices in the upper and lower Py layers. For Ru thicknesses at which AFM coupling dominates, the magnetic state in remanence is a double pole structure. Our results showed that the interlayer exchange coupling interaction remains finite even at 4 nm Ru thickness. Furthermore, the magnetic states in remanence, observed by magnetic force microscopy (MFM), are in good agreement with corresponding hysteresis loops obtained by the magneto-optic Kerr effect (MOKE) and micromagnetic simulations.

interlayer exchange interaction↗

Density Functional Theory Study of Controllable Optical Absorptions and Magneto-Optical Properties of Magnetic CrI 3 Nanoribbons: Implications for Compact 2D Magnetic Devices

A chromium triiodide (CrI 3 ) monolayer has an interesting ferromagnetic ground-state. In this work, we calculate band structures and magnetic moments of tensile-strained and bent zigzag CrI 3 nanoribbons with density functional theory. The edge iodine atoms form flat low-lying conduction bands and couple with chromium atoms ferromagnetically, while the non-edge iodine atoms weakly couple antiferromagnetically. Narrow CrI 3 nanoribbons have two locally stable magnetic moment orientations, namely out-of-plane and in-plane (along the nanoribbon periodic direction) configurations. This enables four magnetization states in CrI 3 nanoribbons, including two out-of-plane ones (up and down) and two in-plane ones (forward and backward along the nanoribbon periodical direction), increasing the operating controllability. Based on the one-dimensional Ising spin chain model, the spin correlation length of the narrow CrI 3 nanoribbon is estimated as about 10 Å at its estimated Curie temperature of 27 Kelvin, which is lower than the measured 45 Kelvin of the monolayer CrI 3 . The optical absorption and magneto-optical properties of CrI 3 nanoribbons are investigated with many-body perturbation GW-BSE (Bethe-Salpeter equation), including magnetic dichroism, Faraday and magneto-optical Kerr effects. Here, the low-energy dark excitons are mainly from transitions between electrons and holes with unlike spins and are non-Frenkel-like, while the bright excitons have mixed spin configurations. The intrinsic lifetime of excitons can be over one nanosecond, suitable for quantum information processes. Tensile strains and bending manifestly modulate the absorption spectra and magneto-optical properties of CrI 3 nanoribbons within a technologically important photon energy-range of ~1.0-2.0 eV. The CrI 3 nanoribbons can be used in 1D or 2D magnetic storage nanodevices, tunable magnetic optoelectronics, and spin-based quantum information controls.

36 MATERIALS SCIENCE↗

Tunable room-temperature ferromagnetism in Co-doped two-dimensional van der Waals ZnO

The recent discovery of ferromagnetism in two-dimensional van der Waals crystals has provoked a surge of interest in the exploration of fundamental spin interaction in reduced dimensions. However, existing material candidates have several limitations, notably lacking intrinsic room-temperature ferromagnetic order and air stability. Here, motivated by the anomalously high Curie temperature observed in bulk diluted magnetic oxides, we demonstrate room-temperature ferromagnetism in Co-doped graphene-like Zinc Oxide, a chemically stable layered material in air, down to single atom thickness. Through the magneto-optic Kerr effect, superconducting quantum interference device and X-ray magnetic circular dichroism measurements, we observe clear evidences of spontaneous magnetization in such exotic material systems at room temperature and above. Transmission electron microscopy and atomic force microscopy results explicitly exclude the existence of metallic Co or cobalt oxides clusters. X-ray characterizations reveal that the substitutional Co atoms form Co 2+ states in the graphitic lattice of ZnO. By varying the Co doping level, we observe transitions between paramagnetic, ferromagnetic and less ordered phases due to the interplay between impurity-band-exchange and super-exchange interactions. Our discovery opens another path to 2D ferromagnetism at room temperature with the advantage of exceptional tunability and robustness.

36 MATERIALS SCIENCE↗

Observation of a phase transition within the domain walls of ferromagnetic Co3Sn2S2

Abstract The ferromagnetic phase of Co 3 Sn 2 S 2 is widely considered to be a topological Weyl semimetal, with evidence for momentum-space monopoles of Berry curvature from transport and spectroscopic probes. As the bandstructure is highly sensitive to the magnetic order, attention has focused on anomalies in magnetization, susceptibility and transport measurements that are seen well below the Curie temperature, leading to speculation that a “hidden” phase coexists with ferromagnetism. Here we report spatially-resolved measurements by Kerr effect microscopy that identify this phase. We find that the anomalies coincide with a deep minimum in domain wall (DW) mobility, indicating a crossover between two regimes of DW propagation. We demonstrate that this crossover is a manifestation of a 2D phase transition that occurs within the DW, in which the magnetization texture changes from continuous rotation to unidirectional variation. We propose that the existence of this 2D transition deep within the ferromagnetic state of the bulk is a consequence of a giant quality factor for magnetocrystalline anisotropy unique to this compound. This work broadens the horizon of the conventional binary classification of DWs into Bloch and Néel walls, and suggests new strategies for manipulation of domain walls and their role in electron and spin transport.

36 MATERIALS SCIENCE↗