Scaling, rotation, and channeling behavior of helical and skyrmion spin textures in thin films of Te-doped Cu2OSeO3

Hysteretic Responses of Skyrmion Lattices to Electric Fields in Magnetoelectric Cu2OSeO3

Electric field control of topologically nontrivial magnetic textures, such as skyrmions, provides a paradigm shift for future spintronics beyond the current silicon-based technology. While significant progress has been made by X-ray and neutron scattering studies, direct observation of such nanoscale spin structures and their dynamics driven by external electric fields remains a challenge in understanding the underlying mechanisms and harness functionalities. Here, using Lorentz transmission electron microscopy combined with in situ electric and magnetic fields at liquid helium temperatures, we report the crystallographic orientation-dependent skyrmion responses to electric fields in thin slabs of magnetoelectric Cu2OSeO3. We show that electric fields not only stabilize the hexagonally packed skyrmion lattices in the entire sample in a hysteretic manner but also induce the rotation of their reciprocal vector discretely by 30°. The nonvolatile and energy-efficient skyrmion lattice control by electric fields demonstrated in this work provides an important foundation for designing skyrmion-based qubits and memory devices.

Hexagonal Close-Packed Polar-Skyrmion Lattice in Ultrathin Ferroelectric PbTiO_{3} Films

Polar skyrmions are topologically stable, swirling polarization textures with particlelike characteristics, which hold promise for next-generation, nanoscale logic and memory. However, the understanding of how to create ordered polar skyrmion lattice structures and how such structures respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO_{3} films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel's law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.

Controllable Topological Magnetic Transformations in the Thickness-Tunable van der Waals Ferromagnet Fe5GeTe2

Recent observations of topological meron textures in two-dimensional (2D) van der Waals (vdW) magnetic materials have attracted considerable research interest for both fundamental physics and spintronic applications. However, manipulating the meron textures and realizing the topological transformations, which allow for exploring emergent electromagnetic behaviors, remain largely unexplored in 2D magnets. In this work, utilizing real-space imaging and micromagnetic simulations, we reveal temperature- and thickness-dependent topological magnetic transformations among domain walls, meron textures, and stripe domain in Fe₅GeTe₂ (FGT) lamellae. The key mechanism of the magnetic transformations can be attributed to the temperature-induced change of exchange stiffness constant within layers and uniaxial magnetic anisotropy, while the magnetic dipole interaction as governed by sample thickness is crucial to affect the critical transformation temperature and stripe period. Our findings provide reliable insights into the origin and manipulation of topological spin textures in 2D vdW ferromagnets.

A theory of skyrmion crystal formation

A generic theory about skyrmion crystal (SkX) formation in chiral magnetic thin films and its fascinating thermodynamic behaviours is presented. A chiral magnetic film can have many metastable states with an arbitrary skyrmion density up to a maximal value when the parameter κ, which measures the relative Dzyaloshinskii-Moriya interaction (DMI) strength, is large enough. The lowest energy state of an infinite film is a long zig-zag ramified stripe skyrmion occupying the whole film in the absence of a magnetic field. Under an intermediate field perpendicular to the film, the lowest energy state has a finite skyrmion density. This is why a chiral magnetic film is often in a stripy state at a low field and a SkX only around an optimal field when κ is above a critical value. The lowest energy state is still a stripy helical state no matter with or without a field when κ is below the critical value. The multi-metastable states explain the thermodynamic path dependences of the various metastable states of a film. The decrease of the κ value with the temperature explains why SkXs become metastable at low temperatures in many skyrmion systems. These findings open a new avenue for SkX manipulation and skyrmion-based applications.

Spin and Orbital Effects on Asymmetric Exchange Interaction in Polar Magnets: M(IO3)2 (M = Cu and Mn)

Magnetic polar materials feature an astonishing range of physical properties, such as magnetoelectric coupling, chiral spin textures, and related new spin topology physics. This is primarily attributable to their lack of space inversion symmetry in conjunction with unpaired electrons, potentially facilitating an asymmetric Dzyaloshinskii-Moriya (DM) exchange interaction supported by spin-orbital and electron-lattice coupling. However, engineering the appropriate ensemble of coupled degrees of freedom necessary for enhanced DM exchange has remained elusive for polar magnets. Here, we study how spin and orbital components influence the capability of promoting the magnetic interaction by studying two magnetic polar materials, α-Cu(IO₃)₂ (²D) and Mn(IO₃)₂ (⁶S), and connecting their electronic and magnetic properties with their structures. The chemically controlled low-temperature synthesis of these complexes resulted in pure polycrystalline samples, providing a viable pathway to prepare bulk forms of transition-metal iodates. Rietveld refinements of the powder synchrotron X-ray diffraction data reveal that these materials exhibit different crystal structures but crystallize in the same polar and chiral P2₁ space group, giving rise to an electric polarization along the b-axis direction. The presence and absence of an evident phase transition to a possible topologically distinct state observed in α-Cu(IO₃)₂ and Mn(IO₃)₂, respectively, imply the important role of spin-orbit coupling. Neutron diffraction experiments reveal helpful insights into the magnetic ground state of these materials. While the long-wavelength incommensurability of α-Cu(IO₃)₂ is in harmony with sizable asymmetric DM interaction and low dimensionality of the electronic structure, the commensurate stripe AFM ground state of Mn(IO₃)₂ is attributed to negligible DM exchange and isotropic orbital overlapping. The work demonstrates connections between combined spin and orbital effects, magnetic coupling dimensionality, and DM exchange, providing a worthwhile approach for tuning asymmetric interaction, which promotes evolution of topologically distinct spin phases.

Cryogenic Electron Microscopy on Strongly Correlated Quantum Materials

ConspectusQuantum materials refers to a class of materials with exotic properties that arise from the quantum mechanical nature of their constituent electrons, exhibiting, for example, high-temperature superconductivity, colossal magnetoresistivity, multiferroicity, and topological behavior. Quantum materials often have incompletely filled d- or f-electron shells with narrow energy bands, and the conduct of their electrons is strongly correlated. One distinct characteristic of the materials is that their electronic states are often spatially inhomogeneous and thus well suited for study using a spatially resolved electron beam with its great scattering power and sensitivity to atomic ionicity. Furthermore, most of these exotic properties only manifest at very low temperatures, posing a challenge to modern electron microscopy. It requires extraordinarily instrument stabilities at cryogenic temperatures with critical spatial, temporal, and energy resolutions in both static and dynamic manner to probe these materials. On the other hand, the ability to directly visualize the atomic, electronic and spin structures and inhomogeneities of quantum materials and correlate them to their functionalities creates enormous opportunities. At the most elementary levels of condensed matter physics, understanding the competing order of electron, spin, orbital, and lattice and their degrees of freedom, the impacts of defects and interfaces, and the site-specific quantum phenomena and phase transitions that give rise to the emergent behaviors allows us to discover and control novel materials for quantum information science and technologies.In this Account, several of our research examples are selected to highlight the use of cryogenic electron microscopy (cryo-EM) to study strongly correlated quantum materials. We focus on the critical roles of heterogeneity, interfaces, defects, and disorder in crystal structure, magnetic structure, and electronic structure to understand the physical properties of the materials that cryo-EM enables. We show how electron crystallography coupled with Bragg diffraction and diffuse scattering analysis empowers us to reveal the nature of structural modulations, lattice distortion, and phonons and how quantitative electron diffraction can be used to map the distributions of the valence electrons that bond atoms together. We exploit transformative advances in imaging capabilities including the use of femtosecond laser and ultrafast electron diffraction to probe electron-lattice interactions and photoinduced transitions beyond equilibrium of matter. We review our Lorentz phase microscopy studies to illustrate the intriguing transformations among various topological chiral spin states under applied magnetic field at various cryogenic temperatures. Finally, we show that atomically resolved imaging and electron energy-loss spectroscopy at 10 K can be used to understand interface-enhanced superconductivity. The wide range of research and progress on quantum materials at low temperature reported here may inspire and attract more researchers in this ever-expanding field of cryo-EM.

Effect of chemical substitution on the skyrmion phase in Cu2OSeO3

Magnetic skyrmions have been the focus of intense research due to their unique qualities which result from their topological protections. Previous work on Cu2OSeO3, the only known insulating multiferroic skyrmion material, has shown that chemical substitution alters the skyrmion phase. We chemically substitute Zn, Ag, and S into powdered Cu2OSeO3 to study the effect on the magnetic phase diagram. In both the Ag and the S substitutions, we find that the skyrmion phase is stabilized over a larger temperature range, as determined via magnetometry and small-angle neutron scattering (SANS). Meanwhile, while previous magnetometry characterization suggests two high temperature skyrmion phases in the Zn-substituted sample, SANS reveals the high temperature phase to be skyrmionic while we are unable to distinguish the other from helical order. Overall, chemical substitution weakens helical and skyrmion order as inferred from neutron scattering of the q ≈ 0.01 Å - 1 magnetic peak.

Anomalous helimagnetic domain shrinkage due to the weakening of the Dzyaloshinskii-Moriya interaction in CrAs

CrAs is a well-known helimagnet with the double-helix structure originating from the competition between the Dzyaloshinskii-Moriya interaction (DMI) and antiferromagnetic exchange interaction J. By resonant soft-x-ray scattering, we observe the magnetic peak (0 0 q m ) that emerges at the helical transition with T S ≈ 267.5 K. Intriguingly, the helimagnetic domains significantly shrink on cooling below ~255 K, opposite to the conventional thermal effect. The weakening of DMI on cooling is found to play a critical role here. It causes the helical wave vector to vary, ordered spins to rotate, and extra helimagnetic domain boundaries to form at local defects, thus leading to the anomalous shrinkage of helimagnetic domains. Our results indicate that the size of magnetic helical domains can be controlled by tuning DMI in certain helimagnets.