Skyrmions represent topologically stable field configurations with particle-like properties. We used neutron scattering to observe the spontaneous formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortex, in the chiral itinerant-electron magnet MnSi. The skyrmion lattice stabilizes at the border between paramagnetism and long-range helimagnetic order perpendicular to a small applied magnetic field regardless of the direction of the magnetic field relative to the atomic lattice. Our study experimentally establishes magnetic materials lacking inversion symmetry as an arena for new forms of crystalline order composed of topologically stable spin states.

Skyrmion Lattice in a Chiral Magnet

Magnetic skyrmions are particle-like nanometre-sized spin textures of topological origin found in several magnetic materials, and are characterized by a long lifetime. Skyrmions have been observed both by means of neutron scattering in momentum space and microscopy techniques in real space, and their properties include novel Hall effects, current-driven motion with ultralow current density and multiferroic behaviour. These properties can be understood from a unified viewpoint, namely the emergent electromagnetism associated with the non-coplanar spin structure of skyrmions. From this description, potential applications of skyrmions as information carriers in magnetic information storage and processing devices are envisaged.

Topological properties and dynamics of magnetic skyrmions

Crystal order is not restricted to the periodic atomic array, but can also be found in electronic systems such as the Wigner crystal or in the form of orbital order, stripe order and magnetic order. In the case of magnetic order, spins align parallel to each other in ferromagnets and antiparallel in antiferromagnets. In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures. Among them is the unusual, topologically stable skyrmion spin texture, in which the spins point in all the directions wrapping a sphere. The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin-electronic phenomena such as the topological Hall effect. The crystallization of skyrmions as driven by thermal fluctuations has recently been confirmed in a narrow region of the temperature/magnetic field (T-B) phase diagram in neutron scattering studies of the three-dimensional helical magnets MnSi (ref. 17) and Fe(1-x)Co(x)Si (ref. 22). Here we report real-space imaging of a two-dimensional skyrmion lattice in a thin film of Fe(0.5)Co(0.5)Si using Lorentz transmission electron microscopy. With a magnetic field of 50-70 mT applied normal to the film, we observe skyrmions in the form of a hexagonal arrangement of swirling spin textures, with a lattice spacing of 90 nm. The related T-B phase diagram is found to be in good agreement with Monte Carlo simulations. In this two-dimensional case, the skyrmion crystal seems very stable and appears over a wide range of the phase diagram, including near zero temperature. Such a controlled nanometre-scale spin topology in a thin film may be useful in observing unconventional magneto-transport effects.

Real-space observation of a two-dimensional skyrmion crystal

The d1 layer metals TaS2, TaSe2, NbSe2, in all their various polytypic modifications, acquire, below some appropriate temperature, phase conditions that their electromagnetic properties have previously revealed as ‘anomalous’. Our present electron-microscope studies indicate that this anomalous behaviour usually includes the adoption, at some stage, of a superlattice. The size of superlattice adopted often is forecast in the pattern of satellite spotting and strong diffuse scattering found above the transition. Our conclusions are that charge-density waves and their concomitant periodic structural distortions occur in all these 4d1/5d1 dichalcogenides. We have related the observed periodicities of these CDW states to the theoretical form of the parent Fermi surfaces. Particularly for the 1T octahedrally coordinated polytypes the Fermi surface is very simple and markedly two-dimensional in character, with large near-parallel walls. Such a situation is known theoretically to favour the formation of...

Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

Helical spin structure in manganese silicide MnSi

The magnetic phase diagram of γ Fe-Mn alloys has been investigated in the whole range of composition by neutron diffraction and other techniques. The f.c.c. phase of Fe-Mn alloys with less than 40 at. % iron and more than 85 at. % iron was stabilized by addition of small amounts of copper and carbon respectively in the alloys. An antiferromagnetic long range order was detected in the whole range composition. The antiferromagnetism of this alloy system Fe x -Mn 1- x was found to be classified into three distinct groups according to the composition. They are 1) 0≤ x ≤0.3, 2) 0.4≤ x ≤0.8, and 3) 0.8≤ x ≤1. The magnetic phase of the second group is markedly different from other two groups. The results agree qualitatively with the prediction based on the band theory.

Antiferromagnetism of γ Iron Manganes Alloys

An intercalated 2H-type layer compound, Cr 1/3 NbS 2 , was investigated by magnetic and neutron diffraction measurements. It was found that this compound is a helimagnet with a very long period along the c -axis and with the spins in the c -plane. The magnetic behavior is similar to that of an easy-plane type ferromagnet except for the magnetization curve in the c -plane. The Curie temperature is 127 K. The saturation magnetization corresponds to 2.9 µ B /Cr. The uniaxial anisotropy constant, K 1 , is -1.46×10 6 ergs/cc at 4.2 K. The magnetizatiom curve in the c -plane shows a metamagnetic behavior, the critical field of which is as low as 1.5 kOe except near T c . Small angle scattering measurements showed a helical structure with Q =0.013 A -1 (480 A period). The helical spin structure and the metamagnetism is explained as due to the antisymmetric exchange interaction.

Magnetic Properties of Cr1/3NbS2

Paramagnetic spin fluctuations in the weak itinerant-electron ferromagnet MnSi have been measured by using both unpolarized and polarized neutron scattering, and the scattering intensity was put on an absolute value by the simultaneous measurements of phonon cross sections. The magnetic excitation spectra over the whole Brillouin zone, for a wide energy range from 0 to 20 meV (\ensuremath{\Elzxh}\ensuremath{\omega}/${\mathrm{kT}}_{c}$=7.9) and up to temperatures (T/${T}_{c}$=10) well above ${T}_{c}$, follow closely the Moriya-Kawabata self-consistent-renormalization theory for the weak itinerant-electron ferromagnet. Based on these experimental results, the origin of the increase in the amplitude of the local magnetic moment 〈${M}_{L}^{2}$〉 above ${T}_{c}$ is attributed to the thermal excitations of the high-energy spin fluctuations in the Stoner continuum.

Paramagnetic spin fluctuations in the weak itinerant-electron ferromagnet MnSi

The magnetic interactions in Heusler alloys Pd 2 MnSn and Ni 2 MnSn have been investigated using neutron spin wave scattering. The spin wave dispersion relations along the [00ζ], [ζζ0] and [ζζζ] directions have been observed across the whole magnetic Brillouin zone. The results have been analyzed using a Heisenberg Hamiltonian where only Mn atoms have a localized moment. It has been found that the interactions between more than 6th neighbors should be taken into account to reproduce the observation. The exchange constants at large distances have an oscillatory character which can be interpreted by the s - d type interactions based on the nearly free electron model. However, the n . n . and n . n . n . interactions have signs opposite to those expected from the simple s - d model. The n . n . and n . n . n . exchange constants in Ni 2 MnSn ( T C =344 K) are larger than those in Pd 2 MnSn ( T C =189 K), although the oscillatory parts have nearly the same values for both alloys.

Yoshikazu Ishikawa

Papers

Helical spin structure in manganese silicide MnSi

Antiferromagnetism of γ Iron Manganes Alloys

Magnetic Properties of Cr1/3NbS2

Paramagnetic spin fluctuations in the weak itinerant-electron ferromagnet MnSi

Spin Waves in Heusler Alloys Pd2MnSn and Ni2MnSn