We investigate the spin transport across the magnetic phase diagram of a frustrated antiferromagnetic insulator and uncover a drastic modification of the transport regime from spin diffusion to spin superfluidity. Adopting a triangular lattice accounting for both nearest neighbor and next-nearest neighbor exchange interactions with easy-plane anisotropy, we perform atomistic spin simulations on a two-terminal configuration across the full magnetic phase diagram. We found that as long as the ground state magnetic moments remain in-plane, irrespective of whether the magnetic configuration is ferromagnetic, collinear or non-collinear antiferromagnetic, the system exhibits spin superfluid behavior with a device output that is independent on the value of the exchange interactions. When the magnetic frustration is large enough to compete with the easy-plane anisotropy and cant the magnetic moments out of the plane, the spin transport progressively evolves towards the diffusive regime. The robustness of spin superfluidity close to magnetic phase boundaries is investigated and we uncover the possibility for {\em proximate} spin superfluidity close to the ferromagnetic transition.
We present a theoretical investigation of magnetostatic interaction effects in geometrically frustrated arrays of anisotropic multilayer ferromagnetic nanoparticles arranged in different spatially configured systems with triangular symmetry. We show that the interlayer magnetostatic interaction significantly expands the opportunities to create magnetically frustrated systems. The effects of the magnetostatic interaction in magnetization reversal processes and the possibility to control the ferromagnetic resonance spectrum in such systems are discussed.
We study the onset of spin superfluidity, namely coherent spin transport mediated by a topological spin texture, in frustrated exchange-dominated magnetic systems, engendered by an external magnetic field. We show that for typical device geometries used in nonlocal magnetotransport experiments, the magnetic field stabilizes a spin superflow against fluctuations, up to a critical current. For a given current, the critical field depends on the precessional frequency of the texture, which can be separately controlled. We contrast such dynamic stabilization of a spin superfluid to the conventional…
Magnetic skyrmions are particle-like topological excitations recently discovered in chiral magnets. Their small size, topological protection and the ease with which they can be manipulated by electric currents generated much interest in using skyrmions for information storage and processing. Recently, it was suggested that skyrmions with additional degrees of freedom can exist in magnetically frustrated materials. Here, we show that dynamics of skyrmions and antiskyrmions in nanostripes of frustrated magnets is strongly affected by complex spin states formed at the stripe edges. These states c…
Patterning nanomagnets in three-dimensions presents a new paradigm in condensed matter physics and allows access to a plethora of fundamental phenomena including robust spin textures, magnetic metamaterials that are home to defects carrying magnetic charge and ultrahigh density devices that store information in three-dimensions. However, the nanostructuring of functional magnetic materials into complex three-dimensional geometries has thus far proven to be a formidable challenge. Here we show magnetic nanowires can be arranged into 3D frustrated magnetic nanowire lattices by using a combinatio…
We study the nucleation and collective dynamics of Shankar skyrmions [R. Shankar, Journal de Physique 38, 1405 (1977)] in the class of frustrated magnetic systems described by an SO(3) order parameter, including multi-lattice antiferromagnets and amorphous magnets. We infer the expression for the spin-transfer torque that injects skyrmion charge into the system and the Onsager-reciprocal pumping force that enables its detection by electrical means. The thermally-assisted flow of topological charge gives rise to an algebraically decaying drag signal in nonlocal transport measurements. We contra…
Non-trivial topology in a two-dimensional frustrated spin system with the Dzyaloshinskii-Moriya (DM) interaction was investigated by Monto Carlo simulations. At finite temperatures, thermally driven topology was discovered and was found to be dominant at low magnetic field. This topological charge has a quadratic relation with the DM interaction and linear realtions with the external magnetic field or the uniaxial magnetic anisotropy. We also proposed a real frustrated system, the Mn-Bi mono-layer film with exceedingly large DM interaction, to enable thermally driven topology. Other topologica…
Magnetic skyrmionium can be used as a nanometer-scale non-volatile information carrier, which shows no skyrmion Hall effect due to its special structure carrying zero topological charge. Here, we report the static and dynamic properties of an isolated nanoscale skyrmionium in a frustrated magnetic monolayer, where the skyrmionium is stabilized by competing interactions. The frustrated skyrmionium has a size of about $10$ nm, which can be further reduced by tuning perpendicular magnetic anisotropy or magnetic field. It is found that the nanoscale skyrmionium driven by the damping-like spin-orbi…
Frustrated lattices1-3, characterized by minor breakdown in local order in an otherwise periodic lattice, lead to simultaneous possibilities of several ground states which can trigger unique physical properties, in condensed matter systems. In magnetic materials with atomic spins, frustration takes another shape with added possibilities to construct various topological arrangements of spins, whereby magnetic order is disturbed2,4. We have achieved a new approach to introduce positional atomic disorder inside a Fe nanoparticle lattice, forming domains without boundaries to study magnetic dynami…
Magnetic skyrmions are particle-like topological excitations that recently generated much interest as candidates for future spintronic devices based on skyrmion small size, enhanced topological stability, and/or mutual interaction. Here we examine the properties of isolated skyrmions in a frustrated chiral magnet with competing Dzyaloshinskii-Moriya and frustrated exchange interactions. We show that the skyrmion size drastically decreases even for small values of competing stabilization mechanisms. Skyrmion mutual interaction remains attracting as is inherent for frustrated skyrmions, but the …
The interplay between topology and energy-hierarchy plays a vital role in the collective magnetic order in artificial ferroic systems. Here we investigate, experimentally, the effect of having one or two activation energies of interacting Ising-like magnetic islands -- mesospins -- in thermalized, vertex-frustrated lattices. The thermally arrested magnetic states of the elements were determined using synchrotron-based magnetic microscopy after cooling the samples from temperatures above the Curie temperature of the material. Statistical analysis of the correlations between mesospins across sev…
We study the electron dynamics in magnetic conductors with frustrated interactions dominated by isotropic exchange. We present a transport theory for itinerant carriers built upon the (single-band) doped Hubbard model and the slave-boson formalism, which incorporates the spin-exchange with the magnetically frustrated background into the representation of electron operators in a clear and controllable way. We also formulate hydrodynamic equations for the itinerant charge and spin degrees of freedom, whose currents contain new contributions that depend on the spatiotemporal variations of the ord…
Frustrated magnets are known to support two-dimensional topological solitons, called skyrmions. A continuum model for frustrated magnets has recently been shown to support both two-dimensional skyrmions and three-dimensional knotted solitons (hopfions). In this note we derive lower bounds for the energies of these solitons expressed in terms of their topological invariants. The bounds are linear in the degree in the case of skyrmions and scale as the Hopf degree to the power 3/4 in the case of hopfions.
We clarify the conditions for the emergence of multiple-${\bf Q}$ structures out of lattice and easy-axis spin anisotropy in frustrated magnets. By considering magnets whose exchange interaction has multiple global minima in momentum space, we find that both types of anisotropy stabilize triple-${\bf Q}$ orderings. Moderate anisotropy leads to a magnetic field-induced skyrmion crystal, which evolves into a bubble crystal for increasing spatial or spin anisotropy. The bubble crystal exhibits a quasi-continuous (devil's staircase) temperature dependent ordering wave-vector, characteristic of the…
Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh-Benard convection, Faraday waves, liquid crystals, domain patterns in ferromagnetic films and skyrmion crystals recently observed in chiral magnets. Here we study a simple model of an anisotropic frustrated magnet and show that its zero-temperature phase diagram contains numerous multi-q states including the skyrmion crystal. We clarify the mechanism for stabilization of these states, discuss their multiferroic properties and formulate rules for finding new skyrmion materials. In addition to skyrmion c…
Under certain experimental conditions, the deposition of C60 molecules onto an atomically flat copper surface gives rise to the formation of corrugated islands. This corrugation, which reflects a molecular displacement perpendicular to the surface plane, presents an astonishing pattern: it is well described by a frustrated Ising spin Hamiltonian whose thermodynamics is compatible with a spin liquid about to transit towards an ordered zigzag state. Here we study the statistical properties of such a molecular corrugation using tools generally employed in frustrated magnetism. More specifically, …
We study the transport properties of frustrated itinerant magnets comprising localized {\it classical} moments, which interact via exchange with the conduction electrons. Strong frustration stabilizes a liquidlike spin state, which extends down to temperatures well below the effective Ruderman-Kittel-Kasuya-Yosida interaction scale. The crossover into this state is characterized by spin structure factor enhancement at wave vectors smaller than twice the Fermi wave vector magnitude. The corresponding enhancement of electron scattering generates a resistivity upturn at decreasing temperatures.
We study the impact of geometry on magnetostatically frustrated single-domain nanomagnet arrays. We examine square and hexagonal lattice arrays, as well as a brickwork geometry that combines the anisotropy of the square lattice and the topology of the hexagonal lattice. We find that the more highly frustrated hexagonal lattice allows for the most thorough minimization of the magnetostatic energy, and that the pair-wise correlations between moments differ qualitatively between hexagonal and brickwork lattices, although they share the same lattice topology. The results indicate that the symmetry…
Helicity indicates the in-plane magnetic-moment swirling direction of a skyrmionic configuration. The ability to reverse the helicity of a skyrmionic bubble via purely electrical means has been predicted in frustrated magnetic systems, however its experimental observation has remained challenging. Here, we experimentally demonstrate the current-driven helicity reversal of the skyrmionic bubble in a nanostructured frustrated Fe3Sn2 magnet. The critical current density required to trigger the helicity reversal is 109 - 1010 A/m2, with a corresponding pulse-width varying from 1 μs to 100 ns. Comp…
Magnetism in single-side hydrogenated (C$_2$H) and fluorinated (C$_2$F) graphene is analyzed in terms of the Heisenberg model with parameters determined from first principles. We predict a frustrated ground state for both systems, which means the instability of collinear spin structures and sheds light on the absence of a conventional magnetic ordering in defective graphene demonstrated in recent experiments. Moreover, our findings suggest a highly correlated magnetic behavior at low temperatures offering the possibility of a spin-liquid state.
The skyrmions generated by frustration in centrosymmetric structures host extra internal degrees of freedom: vorticity and helicity, resulting in distinctive properties and potential functionality, which are not shared by the skyrmions stemming from the Dzyaloshinskii-Moriya interaction in noncentrosymmetric structures. The present work indicates that the magnetism-driven electric polarization carried by skyrmions provides a direct handle for tuning helicity. Especially for the in-plane magnetized skyrmions, the helicity can be continuously rotated and exactly picked by applying an external el…
A magnetic Skyrmion is a stable two-dimensional nanoparticle describing a localized winding of the magnetization in certain magnetic materials. Skyrmions are the subject of intense experimental and theoretical investigation and have potential technological spintronic applications. Here we show that numerical computations of frustrated magnets predict that Skyrmions can be tied into knots to form new stable three-dimensional nanoparticles. These stable equilibria of twisted loops of Skyrmion strings have an integer-valued topological charge, known as the Hopf charge, that counts the number of p…
