Topological spin textures emerging in magnetic materials usually appear in crystalline states. A long-standing dilemma is whether we should understand these emergent crystals as gathering particles or coupling waves, the answer of which affects almost every aspect of our understanding on the subject. Here we prove that 2-D emergent crystals with long-range order in helimagnets, such as skyrmion crystals and dipole skyrmion crystals, have a wave nature. We systematically study their equilibrium properties, metastability, and phase transition path when unstable. We show that the robustness of a skyrmion crystal derives from its metastability, and that its phase transition dynamics at low (high) magnetic field is mediated by a soft mode which breaks (maintains) its hexagonal symmetry. Different from ordinary crystals which are formed by. and breaks into atoms, emergent crystals have a new formation (destruction) mechanism: they appear from (turn to) single-Q spin-density-wave states through nonlinear mode-mode interactions.
We report simultaneous quasi-dc magnetotransport and high frequency surface acoustic wave measurements on bilayer two-dimensional electron systems in GaAs. Near strong integer quantized Hall states a strong magnetic field sweep hysteresis in the velocity of the acoustic waves is observed at low temperatures. This hysteresis indicates the presence of a metastable state with anomalously high conductivity in the interior of the sample. This non-equilibrium state is not revealed by conventional low frequency transport measurements which are dominated by dissipationless transport at the edge of the…
We report detailed magnetic measurements on history and metastability effects in the intermediate state of mesoscopic cylinders of type I superconducting Indium. This includes the observation of topological hysteresis with the signature occurrence of different critical fields during flux entry and flux exit. We show the existence of a plethora of metastable configuration and recipes to access them. We also demonstrate the manifestation of superheating and supercooling of superconducting and normal states, respectively across the superconductivity transition.
Magnetic emergent crystals are periodic alignment of "particle-like" spin textures that emerge in magnets. Instead of focusing on an individual spin or a macroscopic magnetization field, we analyze the dynamical behaviors of these novel states by taking a solid-state point of view. Based on variational principles, the basic equations for lattice dynamics of any emergent crystalline states appearing in magnetic materials is established. For small amplitude emergent elastic waves propagating in emergent crystals, the basic equations reduce to an eigenvalue problem, from which the dispersion rela…
Higher-order exchange interactions and quantum effects are widely known to play an important role in describing the properties of low-dimensional magnetic compounds. Here we identify the recently discovered two-dimensional (2D) van der Waals (vdW) CrI3 as a quantum non-Heisenberg material with properties far beyond an Ising magnet as initially assumed. We find that biquadratic exchange interactions are essential to quantitatively describe the magnetism of CrI3 but requiring quantum rescaling corrections to reproduce its thermal properties. The quantum nature of the heat bath represented by dis…
The three-dimensional emergent magnetic field $\textbf{B}^e$ of a magnetic hopfion gives rise to emergent magneto-multipoles in a similar manner to the multipoles of classical electromagnetic field. Here, we show that the nonlinear responses of a hopfion are characterized by its emergent magnetic toroidal moment ${T}^e_z = \frac{1}{2}\int (\textbf{r}\times \textbf{B}^e)_z dV$ and emergent magnetic octupole component ${\it Γ}^e =\int [(x^2+y^2)B^e_z - xz B^e_x - y z B^e_y] dV$. The hopfion exhibits nonreciprocal dynamics (nonlinear hopfion Hall effect) under an ac driving current applied along …
Here we derive the linear constitutive equations governing the emergent elastic behavior of skX under applied mechanical forces as well as other effective fields. The linear coefficients appearing in the equations are expressed analytically in terms of the thermodynamic parameters describing the magnetoelastic interaction of the underlying chiral magnet. Through the deduction of equations, we clarify that two types of coupled deformation may occur for skX, that is the internal deformation, described by variation of the Fourier magnitudes, and the lattice deformation, described by the emergent …
Emergent electromagnetism in magnets originates from the strong coupling between conduction electron spins and those of noncollinear ordered moments and the consequent Berry phase. This offers possibilities to develop new functions of quantum transport and optical responses. The emergent inductance in spiral magnets is an example recently proposed and experimentally demonstrated, used the emergent electric field induced by alternating currents. However, the microscopic theory of this phenomenon is missing, which should reveal the factors to determine the magnitude, sign, frequency dependence, …
Skyrmion crystals (SkX) are periodic alignment of magnetic skyrmions, i.e., a type of topologically protected spin textures. Compared with ordinary crystals, they can be drastically deformed under anisotropic effects because they are composed of field patterns whose deformation does not cause any bond-breaking. This exotic ductility of SkX bring about great tunability of its collective excitations called emergent phonons, which are vital for magnonics application. The question is how to quantitatively determine the emergent phonons of distorted SkX. Here we systematically study the long wavele…
The transport properties of a twisted bilayer graphene barrier are investigated for various twist angles. Remarkably, for small twist angles around the magic angle $θ_m \sim 1.05^{\circ}$, the local currents around the AA-stacked regions are strongly enhanced compared to the injected electron rate. Furthermore, the total and counterflow (magnetic) current patterns show high correlations in these regions, given rise to well-defined magnetic moments that form a magnetic Moiré superlattice. The orientation and magnitude of these magnetic moments changes as function of the gate voltage and possibl…
We demonstrate directional dependence of the self-modification of internal mesospin textures in magnetic metamaterials, arising from the coupling of the atomic- and mesoscopic length-scales. Dressing the mesospins in different directions enables the quantification of the degree of texture in the internal magnetization and its impact on the interaction energy of the mesospins. The emerging anisotropy is manifested in a directional dependence of the remanent magnetization with temperature.
Spin-orbit (SO) interactions in two dimensional systems split the Fermi surface, and allow for the spatial separation of spin-states via transverse magnetic focusing (TMF). In this work, we consider the case of combined Rashba and Zeeman interactions, which leads to a Fermi surface without cylindrical symmetry. While the classical trajectories are effectively unchanged, we predict an additional contribution to the phase, linear in the applied in-plane magnetic field. We show that this term is unique to TMF, and vanishes for magnetic (Shubnikov de Haas) oscillations. Finally we propose some exp…
Magnetic analogue of an isolated free electric charge, i.e., a magnet with a single north or south pole, is a long sought-after particle which remains elusive so far. In magnetically frustrated pyrochlore solids, a classical analogue of monopole was observed as a result of excitation of spin ice vertices. Direct visualization of such excitations were proposed and later confirmed in analogous artificial spin ice (ASI) systems of square as well as Kagome geometries. However, such charged vertices are randomly created as they are thermally driven and are always associated with corresponding emerg…
It is a fundamental paradigm that the physical effects induced by electric fields are qualitatively different from those induced by magnetic fields. Here we show that electrons at a Dirac point in bilayer graphene experience an unusual type of electromagnetism where magnetic and electric fields are virtually equivalent: every coupling of an electron's degrees of freedom to a magnetic field is matched by an analogous coupling of the same degrees of freedom to an electric field. This counter-intuitive duality of matter-field interactions enables novel ways to create and manipulate spin and pseud…
When electrons are driven through unconventional magnetic structures, such as skyrmions, they experience emergent electromagnetic fields that originate several Hall effects. Independently, ground state emergent magnetic fields can also lead to orbital magnetism, even without the spin-orbit interaction. The close parallel between the geometric theories of the Hall effects and of the orbital magnetization raises the question: does a skyrmion display topological orbital magnetism? Here we first address the smallest systems with nonvanishing emergent magnetic field, trimers, characterizing the orb…
The effect of the size of the system, aspect ratio and impurities concentration on the dynamic of emergent magnetic monopoles in artificial spin ice systems
Facultad de Ingeniería, Universidad Diego Portales（迭戈帕拉莱斯大学工程学院）
The fundamental idea that the constituents of interacting many body systems in complex quantum materials may self-organise into long range order under highly non-equilibrium conditions leads to the notion that entirely new and unexpected functionalities might be artificially created. However, demonstrating new emergent order in highly non-equilibrium transitions has proven surprisingly difficult. In spite of huge recent advances in experimental ultrafast time-resolved techniques, methods that average over successive transition outcomes have so far proved incapable of elucidating the emerging s…
Two hundred years ago, André-Marie Ampère discovered that electric loops in which currents of electrons are generated by a penetrating magnetic field can interact with each other. Here we show that Ampère's observation can be transferred to the quantum realm of interactions between triangular plaquettes of spins on a lattice, where the electrical currents at the atomic scale are associated with a peculiar type of the orbital motion of electrons in response to the non-coplanarity of neighbouring spins playing the role of a magnetic field. The resulting topological orbital moment underlies the r…
A fundamental fact in solids is that the frequencies of elastic waves vanish as the wave number approaches zero\cite{6}. Here we theoretically show that this fact is overturned when studying the lattice vibration of skyrmion crystals (SkX), i.e., periodic alignment of topologically nontrivial spin solitons called magnetic skyrmions. As emergent crystals, SkX possess collective excitations called "emergent phonons", which describe dynamics of SkX caused by lattice vibration (resembling acoustical branches of ordinary phonons) and in-lattice vibration (resembling optical branches of ordinary pho…
When an electron moves in a smoothly varying non-collinear magnetic structure, its spin-orientation adapts constantly, thereby inducing forces that act on both the magnetic structure and the electron. These forces may be described by electric and magnetic fields of an emergent electrodynamics. The topologically quantized winding number of so-called skyrmions, i.e., certain magnetic whirls, discovered recently in chiral magnets are theoretically predicted to induce exactly one quantum of emergent magnetic flux per skyrmion. A moving skyrmion is therefore expected to induce an emergent electric …
In this letter we present emergent screening of magnetic monopole and dipole by the presence of 20nm aluminum cover layer. Our results were obtained in base of magnetic atomic force measurements, performed after external magnetic field steps application. We show that the evolution of magnetization and monopole population is affected by the aluminum presence and attribute that phenomena to the proximity effect, which is responsible for the magnetization vanish of the firstatomic layers at the interface. Using experimental values to estimate the decrease in the nano-magnetic dipole value used in…
Magnetic multilayers are promising tuneable systems for hosting magnetic skyrmions at/above room temperature. Revealing their intriguing switching mechanisms and associated inherent electrical responses are prerequisites for developing skyrmionic devices. In this work, we theoretically demonstrate the annihilation of single skyrmions occurring through a multilayer structure, which is mediated by hopping dynamics of topological hedgehog singularities known as Bloch points. The emerging intralayer dynamics of Bloch points are dominated by the Dzyaloshinskii-Moriya interaction, and their propagat…
Whirling topological textures play a key role in exotic phases of magnetic materials and offer promise for logic and memory applications. In antiferromagnets, these textures exhibit enhanced stability and faster dynamics with respect to ferromagnetic counterparts, but they are also difficult to study due to their vanishing net magnetic moment. One technique that meets the demand of highly sensitive vectorial magnetic field sensing with negligible backaction is diamond quantum magnetometry. Here, we show that the archetypal antiferromagnet, hematite, hosts a rich tapestry of monopolar, dipolar …
We apply the general conception of non-Abelian gauge fields for description of magnetic soliton excitations. We show that the component of the gauge field along the soliton local magnetization (Abelian part of the gauge potential) determines dynamics of spin fluctuations over the soliton background in a ferromagnet. Assumption that the gauge field is a pure gauge allows calculating the gauge field components and finding simple expressions for the emergent electromagnet fields related to the soliton motion. The gauge field results in soliton-magnon interaction leading to renormalization of the …
We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only throug…
Advanced vector imaging techniques provide us with 3D maps of magnetization fields in which topological concepts can be directly applied to describe real-space experimental textures in non-ideal geometries. Here, the 3D magnetization of a low symmetry permalloy microstructure is obtained by X-ray vector magnetic tomography and analysed in detail in terms of topological charges and emergent fields. A central asymmetric domain wall with a complex 3D structure is observed in which magnetization chirality transitions are mediated by Bloch points arranged in several dipoles and a triplet. The ideal…
Altermagnetic spin textures: Emergent electrodynamics, quantum geometry, and probes
Hearne Institute of Theoretical Physics, Department of Physics & Astronomy, Louisiana State University（路易斯安那州立大学物理与天文学系希恩理论物理研究所）；Institute for Theoretical Physics III, University of Stuttgart（斯图加特大学理论物理第三研究所）
We consider the recently discovered Dirac semimetals with two Dirac points $\pm{\bf K}$. In the presence of elastic deformations each fermion propagates in a curved space, whose metric is defined by the expansion of the effective Hamiltonian near the Dirac point. Besides, there is the emergent electromagnetic field that is defined by the shift of the Dirac point. We consider the case, when the deformations are caused by the dislocations. The dislocation carries singular torsion and the quantized flux of emergent magnetic field. Both torsion singularity and emergent magnetic flux may be observe…
Neutron reflectometry (NR) has emerged as a unique technique for the investigation of structure and magnetism of thin films of both biologically relevant and magnetic materials. The advantage of NR with respect to many other surface-sensitive techniques is its sub-nanometer resolution that enables structural characterizations at the molecular level. While in the case of bio-relevant samples, NR can be used to probe thin films at buried interfaces, non-destructively, even adopting a complex sample environment. Whereas the polarized version of NR is best suited for revealing the interface magnet…
In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and …
Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into…
