Real-Space Observation of Short-Period Cubic Lattice of Skyrmions in MnGe

Abstract

Emergent phenomena and functions arising from topological electron-spin textures in real space or momentum space are attracting growing interest for new concept of states of matter as well as for possible applications to spintronics 1-5 . One such example is a magnetic skyrmion 3-5 , a topologically stable nanoscale spin vortex structure characterized by a topological index. Real-space regular arrays of skyrmions are described by combination of multi-directional spin helixes. Nanoscale configurations and characteristics of the two-dimensional skyrmion hexagonal-lattice have been revealed extensively by real-space observations 6-8 . Other three-dimensional forms of skyrmion lattices, such as a cubic-lattice of skyrmions, are also anticipated to exist 9,10 , yet their direct observations remain elusive. Here we report real-space observations of spin configurations of the skyrmion cubic-lattice in MnGe with a very short period (~3 nm) and hence endowed with the largest skyrmion number density. The skyrmion lattices parallel to the {100} atomic lattices are directly observed using Lorentz transmission electron microscopes (Lorentz TEMs). It enables the first simultaneous observation of magnetic skyrmions and underlying atomic-lattice fringes. These results indicate the emergence of skyrmion-antiskyrmion lattice in MnGe, which is a source of emergent electromagnetic responses 9,11 and will open a possibility of controlling few-nanometer scale skyrmion lattices through atomic lattice modulations.The discovery of giant magnetoresistance 12,13 in magnetic multilayers opened a new field, i.e., spintronics, of controlling motions of electrons using structures of spin ensemble 14 . In solids, spins interact with electron orbits at specific atomic sites. This spin-orbit (or spin-orbital) interaction is the origin of emergent states and phenomena,

Topological–chiral magnetic interactions driven by emergent orbital magnetism

“…Next, we substantiate the importance of the topological-chiral interactions taking the intensively scrutinized B20 magnet MnGe as one specific example. In contrast to FeGe that forms wellunderstood two-dimensional skyrmions with a radius of 70 nm, for MnGe puzzling three-dimensional skyrmion lattices with lattice constants of a few nanometers were observed experimentally 13,18 , but could not be reproduced by any theoretical calculation so far 36,37 . Employing electronic-structure theory (see Methods), we show below that while the chiral-chiral and spin-chiral interactions are suppressed in FeGe, where chiral physics is dominated by the Dzyaloshinskii-Moriya interaction (DMI) 15,16 , the topological-chiral interactions are very prominent in MnGe.…”

Helical magnetic structure and the anomalous and topological Hall effects in epitaxial B20 Fe1−yCoyGe films

“…Here, A is the spin-stiffness parameter that stems from the isotropic and nonrelativistic exchange parameter J ij from the Heisenberg model. Parameter D stands for the strength of the DMI, whose contribution to the energy is linear and antisymmetric around q = 0 with respect to D. We converged the spin-spiral calculations starting from collinear calculations to 24 3 k points in the full Brillouin zone for small values of the reciprocal spin-spiral vector and including the ferromagnetic state q = 0 for the Fe 1−y Co y Ge systems. The spin-spiral vector q = (q,q,q) is chosen along the [111] direction and due to symmetry the DMI vector points parallel or antiparallel to the chosen q vector.…”

“…MnSi was the first B20 compound shown to display a stable skyrmion crystal [15] below the magnetic transition temperature of 29 K. Experimental measurements of MnGe show the largest THE for any skyrmionic lattice [23], which is due to the small skyrmion size of 3-6 nm. Furthermore, the THE does not depend on the chirality of Bloch skyrmions but changes sign and magnitude as a function of external field and as a function of temperature, suggesting a change in the skyrmion lattice [24] or shape [25]. The chirality of the skyrmion in the simplest case is determined by the sign of the DMI, where substituting Fe into MnGe caused a change in sign of the skyrmion at a critical concentration of x = 0.8 and the skyrmion's texture becomes a trivial ferromagnet [26][27][28][29].…”

Formation of a topological monopole lattice and its dynamics in three-dimensional chiral magnets

“…13. Several recent Hall and Nernst effect experiments on MnGe crystal have boosted our confidence that such three-dimensional topological phase has already been realized in nature even at ambient pressure [14,15], while a more direct visual confirmation, analogous to the Lorentz microscopy imaging of the the two-dimensional Skyrmion lattice, may still be forthcoming [16]. A pressing issue for theory at this stage would be whether a simple magnetic model Hamiltonian supporting the MAM crystal phase can be written down, and used to address various aspects of the monopole dynamics.…”