Blue quantum fog: chiral condensation in quantum helimagnets

The influence of antiferromagnetic spin cantings on the magnetic helix pitch in cubic helimagnets

In cubic helimagnets MnSi and Cu2OSeO3with their nearly isotropic magnetic properties, the magnetic structure undergoes helical deformation, which is almost completely determined by the helicoid wavenumberk=D/J, where magnetization field stiffnessJis associated with isotropic spin exchange, andDis a pseudoscalar value characterizing the antisymmetric Dzyaloshinskii-Moriya (DM) interaction. Another magnetic feature of these crystals, also caused by the DM interactions, are antiferromagnetic spin cantings, similar to the ferromagnetic cantings responsible for the phenomenon of weak ferromagnetism. Here we show that cantings can strongly influence the helical order through the value of the parameterD. Changing the cantings in a strong magnetic field is predicted to affect the magnon spectrum of the crystals.

Giant Topological Hall Effect in van der Waals Heterostructures of CrTe2/Bi2Te3

Discoveries of the interfacial topological Hall effect (THE) provide an ideal platform for exploring the physics arising from the interplay between topology and magnetism. The interfacial topological Hall effect is closely related to the Dzyaloshinskii-Moriya interaction (DMI) at an interface and topological spin textures. However, it is difficult to achieve a sizable THE in heterostructures due to the stringent constraints on the constituents of THE heterostructures, such as strong spin-orbit coupling (SOC). Here, we report the observation of a giant THE signal of 1.39 μΩ·cm in the van der Waals heterostructures of CrTe₂/Bi₂Te₃ fabricated by molecular beam epitaxy, a prototype of two-dimensional (2D) ferromagnet (FM)/topological insulator (TI). This large magnitude of THE is attributed to an optimized combination of 2D ferromagnetism in CrTe₂, strong SOC in Bi₂Te₃, and an atomically sharp interface. Our work reveals CrTe₂/Bi₂Te₃ as a convenient platform for achieving large interfacial THE in hybrid systems, which could be utilized to develop quantum science and high-density information storage devices.

Magnetic Skyrmion Materials

Skyrmion, a concept originally proposed in particle physics half a century ago, can now find the most fertile field for its applicability, that is, the magnetic skyrmion realized in helimagnetic materials. The spin swirling vortex-like texture of the magnetic skyrmion can define the particle nature by topology; that is, all the constituent spin moments within the two-dimensional sheet wrap the sphere just one time. Such a topological nature of the magnetic skyrmion can lead to extraordinary metastability via topological protection and the driven motion with low electric-current excitation, which may promise future application to spintronics. The skyrmions in the magnetic materials frequently show up as the crystal lattice form, e.g., hexagonal lattice, but sometimes as isolated or independent particles. These skyrmions in magnets were initially found in acentric magnets, such as chiral, polar, and bilayered magnets endowed with antisymmetric spin exchange interaction, while the skyrmion host materials have been explored in a broader family of compounds including centrosymmetric magnets. This review describes the materials science and materials chemistry of magnetic skyrmions using the classification scheme of the skyrmion forming microscopic mechanisms. The emergent phenomena and functions mediated by skyrmions are described, including the generation of emergent magnetic and electric field by statics and dynamics of skrymions and the inherent magnetoelectric effect. The other important magnetic topological defects in two or three dimensions, such as biskyrmions, antiskyrmions, merons, and hedgehogs, are also reviewed in light of their interplay with the skyrmions.

Bulk and surface topological indices for a skyrmion string: current-driven dynamics of skyrmion string in stepped samples

The magnetic skyrmion is a topological magnetic vortex, and its topological nature is characterized by an index called skyrmion number which is a mapping of the magnetic moments defined on a two-dimensional space to a unit sphere. In three-dimensions, a skyrmion, i.e., a vortex penetrating though the magnet naturally forms a string, which terminates at the surfaces of the magnet or in the bulk. For such a string, the topological indices, which control its topological stability are less trivial. Here, we study theoretically, in terms of numerical simulation, the dynamics of current-driven motion of a skyrmion string in a film sample with the step edges on the surface. In particular, skyrmion–antiskyrmion pair is generated by driving a skyrmion string through the side step with an enough height. We find that the topological indices relevant to the stability are the followings; (1) skyrmion number along the developed surface, and (2) the monopole charge in the bulk defined as the integral over the surface enclosing a singular magnetic configuration. As long as the magnetic configuration is slowly varying, the former is conserved while its changes is associated with nonzero monopole charge. The skyrmion number and the monoplole charge offer a coherent understanding of the stability of the topological magnetic texture and the nontrivial dynamics of skyrmion strings.

Dynamics of active nematic defects on the surface of a sphere

A nematic liquid crystal confined to the surface of a sphere exhibits topological defects of total charge +2 due to the topological constraint. In equilibrium, the nematic field forms four +1/2 defects, located at the corners of a regular tetrahedron inscribed within the sphere, since this minimizes the Frank elastic energy. If additionally the individual nematogens exhibit self-driven directional motion, the resulting active system creates large-scale flow that drives it out of equilibrium. In particular, the defects now follow complex dynamic trajectories which, depending on the strength of the active forcing, can be periodic (for weak forcing) or chaotic (for strong forcing). In this paper we derive an effective particle theory for this system, in which the topological defects are the degrees of freedom, whose exact equations of motion we subsequently determine. Numerical solutions of these equations confirm previously observed characteristics of their dynamics and clarify the role played by the time dependence of their global rotation. We also show that Onsager's variational principle offers an exceptionally transparent way to derive these dynamical equations, and we explain the defect mobility at the hydrodynamics level.

Skyrmions and Hall transport

We review recent progresses towards an understanding of the skyrmion Hall transport in insulating as well as conducting materials. First, we consider a theoretical breakthrough based on the quantum field theory ward identity, a first principle analysis, relying on symmetries and conservation laws. Broken parity (inversion) symmetry plays a crucial role in skyrmion Hall transport. In addition to the well known thermal and electric Hall conductivities, our analysis has led us to the discovery of a new and unforeseen physical quantity, Hall viscosity-an anti-symmetric part of the viscosity tensor. We propose a simple way to confirm the existence of Hall viscosity in the measurements of Hall conductivity as a function of momentum. We provide various background materials to assist the readers to understand the quantum field theory ward identity. In the second part, we review recent theoretical and experimental advancements of the skyrmion Hall effects and the topological (magnon) Hall effects for conducting (insulting) magnets. For this purpose, we consider two enveloping themes: spin torque and thermo-electromagnetic effect. First, we overview various spin torques, such as spin transfer torque, spin-orbit torque, and spin Hall torque, and generalized Landau-Lifshitz-Gilbert equations and Thiele equations using a phenomenological approach. Second, we consider irreversible thermodynamics to survey possible thermo-electromagnetic effects, such as Seebeck, Peltier and Thompson effects in the presence of the electric currents, along with the Hall effects in the presence of a background magnetic field. Recently developed spin Seebeck effects are also a significant part of the survey. We also accommodate extensive background materials to make this review self-contained. Finally, we revisit the skyrmion Hall transport from the ward identity view point.

Dynamics of skyrmion in disordered chiral magnet of thin film form

Magnetic skyrmion is a topological spin texture characterized by the mapping from the two dimensional real space to the unit sphere. It is realized in chiral magnets under an external magnetic field in the plane perpendicular to it. In thin film samples, which are most relevant to the applications, the thickness of the system parallel to the magnetic field is finite, and a skyrmion turns into a skyrmion string, which is often assumed to be a straight rod. There are phenomena related to the internal degrees of freedom along the string, e.g., the monopole and anti-monopole creation/annihilation, corresponding to the change in the skyrmion number. However, the role of this finite thickness in the topological stability and dynamics has not been explored yet. Here we study theoretically the current-driven dynamics of a skyrmion string under disorder potential by systematically changing the thickness of the sample to reveal the dynamical phase diagram in the plane of current density and thickness. We found the three regions, i.e., (i) pinned skyrmion string, (ii) moving depinned skyrmion string, and (iii) annihilation of skyrmion string, for thin and thick limits while (iii) is missing in the intermediate case. This indicates that there is the optimal range of thickness for the topological stability of skyrmion string enhanced compared with a two-dimensional skyrmion. This result provides a way to design and control skyrmions in thin films and interfaces of finite thickness.

Theory of current-driven skyrmions in disordered magnets

An emergent topological particle in magnets, skyrmion, has several unique features distinct from the other magnetic textures such as domain wall, helical structure, and vortex. It is characterized by a topological integer called skyrmion number N_sk, which counts how many times the directions of the magnetic moments wrap the unit sphere. This N_sk gives the chiral nature of the skyrmion dynamics, and leads to the extremely small critical current density j_c for the current-driven motion in terms of spin transfer torque effect. The finite j_c indicates the pinning effect due to the disorder such as impurities and defects, and the behaviors of skyrmions under disorder have not been explored well theoretically although it is always relevant in real systems. Here we reveal by a numerical simulation of Landau-Lifshitz-Gilbert equation that there are four different skyrmion phases with the strong disorder, i.e., (A) pinned state, (B) depinned state, (C) skyrmion multiplication/annihilation, and (D) segregation of skyrmions, as the current density increases, while only two phases (A) and (B) appear in the weak disorder case. The microscopic mechanisms of the new phases (C) and (D) are analyzed theoretically. These results offer a coherent understanding of the skyrmion dynamics under current with disorder.

Spin chirality induced skew scattering and anomalous Hall effect in chiral magnets

Noncoplanar magnetic orders in magnetic metals give rise to an anomalous Hall effect of unconventional origin, which, by the spin Berry phase effect, is known as the topological Hall effect. This effect is pronounced in the low-temperature limit, where the fluctuation of spins is suppressed. In contrast, we here discuss that the fluctuating but locally correlated spins close to the phase boundary give rise to another anomalous Hall effect, that with the opposite sign to the topological Hall effect. Using the Born approximation, we show that the anomalous Hall effect is attributed to the skew scattering induced by the local correlation of spins. The relation of the scalar spin chirality to the skew scattering amplitude is given, and the explicit formula for the Hall conductivity is derived using a semiclassical Boltzmann transport theory. Our theory potentially accounts for the sign change of the anomalous Hall effect observed in chiral magnets in the vicinity of the phase boundary.

Electron nematic effect induced by magnetic field in antiferroquadrupole phase of CeB 6

Spatial anisotropy generated spontaneously in the translationally invariant metallic phase, i.e. electron nematic effect, addresses a great challenge for both experimentalists and theoreticians. An interesting option for the realization of the electron nematic phase is provided by the system with orbital ordering, as long as both orbitally ordered states and electron nematic phases possess broken spatial symmetry. Here we report the detailed study of the angular dependences of the magnetoresistance in the orbitally ordered antiferroquadrupole (AFQ) phase of CeB₆. Our data allowed revealing the electron nematic effect, which develops when magnetic field exceeds a critical value of 0.3–0.5T. As a result, new transition inside the AFQ phase corresponding to the change of the symmetry of magnetic scattering on spin fluctuations in CeB₆ is discovered.

Skyrmion lattice structural transition in MnSi

Magnetic skyrmions exhibit particle-like properties owing to the topology of their swirling spin texture, providing opportunities to study crystallization of topological particles. However, they mostly end up with a triangular lattice, and thus, the packing degree of freedom in the skyrmion particles has been overlooked so far. We report a structural transition of the skyrmion lattice in MnSi. By use of small-angle neutron scattering, we explore a metastable skyrmion state spreading over a wide temperature and magnetic field region, after thermal quenching. The quenched skyrmions undergo a triangular-to-square lattice transition with decreasing magnetic field at low temperatures. Our study suggests that various skyrmion lattices can emerge at low temperatures, where the skyrmions exhibit distinct topological nature and high sensitivity to the local magnetic anisotropy arising from the underlying chemical lattice.

Theory of skyrmions in bilayer systems

Skyrmion is an emergent particle consisting of many spins in magnets, and has many nontrivial features such as (i) nano-scale size, (ii) topological stability, (iii) gyrodynamics, and (iv) highly efficient spin transfer torque, which make skyrmions the promising candidate for the magnetic devices. Earlier works were focusing on the bulk or thin film of Dzyaloshinskii-Moriya (DM) magnets, while recent advances are focusing on the skyrmions induced by the interfaces. Therefore, the superstructures naturally leads to the interacting skyrmions on different interfaces, which has unique dynamics compared with those on the same interface. Here we theoretically study the two skyrmions on bilayer systems employing micromagnetic simulations as well as the analysis based on Thiele equation, revealing the reaction between them such as the collision and bound state formation. The dynamics depends sensitively on the sign of DM interactions, i.e., helicities, and skyrmion numbers of two skyrmions, which can be well described by Thiele equation. Furthermore, we have found the colossal spin-transfer-torque effect of bound skyrmion pair on antiferromagnetically coupled bilayer systems.

Skyrmions and Hall Transport

We derive a generalized set of Ward identities that captures the effects of topological charge on Hall transport. The Ward identities follow from the (2+1)-dimensional momentum algebra, which includes a central extension proportional to the topological charge density. In the presence of topological objects like Skyrmions, we observe that the central term leads to a direct relation between the thermal Hall conductivity and the topological charge density. We extend this relation to incorporate the effects of a magnetic field and an electric current. The topological charge density produces a distinct signature in the electric Hall conductivity, which is identified in existing experimental data and yields further novel predictions. For insulating materials with translation invariance, the Hall viscosity can be directly determined from the Skyrmion density and the thermal Hall conductivity to be measured as a function of momentum.

Theory of antiskyrmions in magnets

Skyrmions and antiskyrmions are swirling topological magnetic textures realized as emergent particles in magnets. A skyrmion is stabilized by the Dzyaloshinskii–Moriya interaction in chiral magnets and/or a dipolar interaction in thin film magnets, which prefer the twist of the magnetic moments. Here we show by a numerical simulation of the Landau–Lifshitz–Gilbert equation that pairs of skyrmions and antiskyrmions are created from the helix state as the magnetic field is increased. Antiskyrmions are unstable and disappear immediately in chiral magnets, whereas they are metastable and survive in dipolar magnets. The collision between a skyrmion and an antiskyrmion in a dipolar magnet is also studied. It is found that the collision depends on their relative direction, and the pair annihilation occurs in some cases and only the antiskyrmion is destroyed in the other cases. These results indicate that the antiskyrmion offers a unique opportunity to study particles and antiparticles in condensed-matter systems.

Skyrmions are swirling topological magnetic textures that behave as if they were particles. Here, the authors present numerical simulations that describe the creation and destruction of these spin vortices in both chiral and dipolar magnets, and show what happens when skyrmions and antiskyrmions collide.

Scrutinizing Hall Effect in Mn_{1-x}Fe_{x}Si: Fermi Surface Evolution and Hidden Quantum Criticality

Separating between the ordinary Hall effect and anomalous Hall effect in the paramagnetic phase of Mn_{1-x}Fe_{x}Si reveals an ordinary Hall effect sign inversion associated with the hidden quantum critical (QC) point x^{*}∼0.11. The effective hole doping at intermediate Fe content leads to verifiable predictions in the field of fermiology, magnetic interactions, and QC phenomena in Mn_{1-x}Fe_{x}Si. The change of electron and hole concentrations is considered as a "driving force" for tuning the QC regime in Mn_{1-x}Fe_{x}Si via modifying the Ruderman-Kittel-Kasuya-Yosida exchange interaction within the Heisenberg model of magnetism.

Noncommuting momenta of topological solitons

We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

Topological properties and dynamics of magnetic skyrmions

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.

Weak antiferromagnetic ordering induced by Dzyaloshinskii-Moriya interaction and pure magnetic reflections in MnSi-type crystals

A symmetry analysis of the Dzyaloshinskii-Moriya (DM) interaction in MnSi-type crystals reveals a nontrivial antiferromagnetic pattern of tilted Mn moments remaining even after an unwinding of the ground-state helix by a strong magnetic field. The remaining tilts are caused by that component of the DM vector which is perpendicular to the component responsible for helical spiraling; both components are evaluated and related to the atomic structure using a simple model. It is shown that the tilting should induce pure magnetic reflections 00ℓ(ℓ=2n+1) in neutron or x-ray magnetic scattering. In addition, the DM-induced antiferromagnetic ordering is important for the core structure of intrinsic defects, for the spectra of magnetic resonances, and generally for a better understanding of spin-orbit interaction in this type of magnetics.

Quantum order-by-disorder near criticality and the secret of partial order in MnSi

The vicinity of quantum phase transitions has proven fertile ground in the search for new quantum phases. We propose a physically motivated and unifying description of phase reconstruction near metallic quantum-critical points using the idea of quantum order by disorder. Certain deformations of the Fermi surface associated with the onset of competing order enhance the phase space available for low-energy, particle-hole fluctuations and self-consistently lower the free energy. Applying the notion of quantum order by disorder to the itinerant helimagnet MnSi, we show that, near the quantum critical point, fluctuations lead to an increase of the spiral ordering wave vector and a reorientation away from the lattice-favored directions. The magnetic ordering pattern in this fluctuation-driven phase is found to be in excellent agreement with the neutron-scattering data in the partially ordered phase of MnSi.

Stabilization of blue phases by the variation of elastic constants

We study theoretically the effect of the variation of the elastic constants on the stability of cholesteric blue phases (BPs). We demonstrate that the stability of BPs is greatly enhanced when the bend elastic constant K(33) is smaller, in agreement with recent experimental findings. Larger splay (K(11)) and twist (K(22)) elastic constants also stabilize BPs. Our argument sheds light on the subtle effect of the variation of the elastic constants on the stability of BPs, and could guide the synthesis of liquid crystals with a wider temperature range of stable BPs.

Proximity of iron pnictide superconductors to a quantum tricritical point

In several materials, unconventional superconductivity appears nearby a quantum phase transition where long-range magnetic order vanishes as a function of a control parameter like charge doping, pressure or magnetic field. The nature of the quantum phase transition is of key relevance, because continuous transitions are expected to favour superconductivity, due to strong fluctuations. Discontinuous transitions, on the other hand, are not expected to have a similar role. Here we determine the nature of the magnetic quantum phase transition, which occurs as a function of doping, in the iron-based superconductor LaFeAsO(1-x)F(x). We use constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The outcome is intriguing, as this material turns out to be remarkably close to a quantum tricritical point, where the transition changes from continuous to discontinuous, and several susceptibilities diverge simultaneously. We discuss the consequences for superconductivity and the phase diagram.

Magnetic blue phase in the chiral itinerant magnet MnSi

Chiral nematic liquid crystals sometimes form blue phases characterized by spirals twisting in different directions. By combining model calculations with neutron-scattering experiments, we show that the magnetic analogue of blue phases does form in the chiral itinerant magnet MnSi in a large part of the phase diagram. The properties of this blue phase explain a number of previously reported puzzling features of MnSi such as partial magnetic order and a two-component specific-heat and thermal-expansion anomaly at the magnetic transition.

Columnar fluctuations as a source of non-Fermi-liquid behavior in weak metallic magnets

It is shown that columnar fluctuations, in conjunction with weak quenched disorder, lead to a T{3/2} temperature dependence of the electrical resistivity. This is proposed as an explanation of the observed non-Fermi-liquid behavior in the helimagnet MnSi, with one possible realization of the columnar fluctuations provided by Skyrmion lines that have independently been proposed to be present in this material.

Skyrmion lattices in metallic and semiconducting B20 transition metal compounds

High pressure studies in MnSi suggest the existence of a non-Fermi liquid state without quantum criticality. The observation of partial magnetic order in a small pocket of the pressure versus temperature phase diagram of MnSi has additionally inspired several proposals of complex spin textures in chiral magnets. We used neutron scattering to observe the formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortices, under applied magnetic fields in metallic and semiconducting B20 compounds. In strongly disordered systems the skyrmion lattice is hysteretic and extends over a large temperature range. Our study experimentally establishes magnetic materials lacking inversion symmetry as an arena for new forms of spin order composed of topologically stable spin textures.

Chiral paramagnetic skyrmion-like phase in MnSi

We present a comprehensive study of chiral fluctuations in the reference helimagnet MnSi by polarized neutron scattering and neutron spin echo spectroscopy, which reveals the existence of a completely left-handed and dynamically disordered phase. This phase may be identified as a spontaneous Skyrmion phase: it appears in a limited temperature range just above the helical transition T_{C} and coexists with the helical phase at T_{C}.

Ultrasonic studies of the magnetic phase transition in MnSi

Measurements of the sound velocities in a single crystal of MnSi were performed in the temperature range 4-150 K. Elastic constants, controlling propagation of longitudinal waves, reveal significant softening at a temperature of about 29.6 K and small discontinuities at ∼28.8 K, which corresponds to the magnetic phase transition in MnSi. In contrast, the shear elastic moduli do not show any softening at all, reacting only to the small volume deformation caused by the magneto-volume effect. The current ultrasonic study exposes an important fact that the magnetic phase transition in MnSi, occurring at 28.8 K, is just a minor feature of the global transformation marked by the rounded maxima or minima of heat capacity, thermal expansion coefficient, sound velocities and absorption, and the temperature derivative of resistivity.

Unusual Hall effect anomaly in MnSi under pressure

We report the observation of a highly unusual Hall current in the helical magnet MnSi in an applied pressure P=6-12 kbars. The Hall conductivity displays a distinctive stepwise field profile quite unlike any other Hall response observed in solids. We identify the origin of this Hall current with the effective real-space magnetic field due to chiral spin textures, which may be a precursor of the partial-order state at P>14.6 kbar. We discuss evidence favoring the chiral spin mechanism for the origin of the observed Hall anomaly.

Quantum order in the chiral magnet MnSi

Systems lacking inversion symmetry, such as selected three-dimensional compounds, multilayers and surfaces support Dzyaloshinsky-Moriya (DM) spin-orbit interactions. In recent years DM interactions have attracted great interest, because they may stabilize magnetic structures with a unique chirality and non-trivial topology. The inherent coupling between the various properties provided by DM interactions is potentially relevant for a variety of applications including, for instance, multiferroic and spintronic devices. The, perhaps, most extensively studied material in which DM interactions are important is the cubic B20 compound MnSi. We review the magnetic field and pressure dependence of the magnetic properties of MnSi. At ambient pressure this material displays helical order. Under hydrostatic pressure a non-Fermi liquid state emerges, where a partial magnetic order, reminiscent of liquid crystals, is observed in a small pocket. Recent experiments strongly suggest that the non-Fermi liquid state is not due to quantum criticality. Instead it may be the signature of spin textures and spin excitations with a non-trivial topology.

Magneto-elastic interaction in cubic helimagnets with B20 structure

The magneto-elastic interaction in cubic helimagnets with B 20 symmetry is considered. It is shown that this interaction is responsible for a negative contribution to the square of the spin-wave gap Δ and it alone appears to disrupt the assumed helical structure. It is suggested that competition between the positive part of Δ(I)(2), which stems from magnon-magnon interaction, and its negative magneto-elastic part leads to the quantum phase transition observed at high pressure in MnSi and FeGe. This transition has to occur when [Formula: see text]. For MnSi it was shown using rough estimations that at ambient pressure both parts Δ(I) and |Δ(ME)| are comparable with the experimentally observed gap. The magneto-elastic interaction is responsible for 2k modulation of the lattice where k is the helix wavevector and contributes to the magnetic anisotropy. Properties of the magnetic state above the quantum phase transition are also discussed. Experimental observation of the lattice modulation by x-ray and neutron scattering allows the determination of the strength of the anisotropic part of the magneto-elastic interaction responsible for the above phenomena and the lattice helicity.

Two-step magnetic ordering in quasi-one-dimensional helimagnets: possible experimental validation of villain's conjecture about a chiral spin liquid phase

Low-temperature specific heat, magnetic susceptibility, and zero-field muon spin resonance (microSR) measurements have been performed in the quasi-one-dimensional molecular helimagnetic compound Gd(hfac)3NITEt. The specific heat presents two anomalies at T(0)=2.19+/-0.02 K and T(N)=1.88+/-0.02 K, which both disappear upon the application of a weak magnetic field. Conversely, magnetic susceptibility and muSR data show the divergence of two-spin correlation functions only at T(N)=1.88+/-0.02 K. These results suggest an experimental validation of Villain's conjecture of a two-step magnetic ordering in quasi-one-dimensional XY helimagnets; i.e., the paramagnetic phase and the helical spin solid phase are separated by a chiral spin liquid phase, where translational invariance is broken without violation of rotational invariance.

Magnetic field and pressure dependence of small angle neutron scattering in MnSi

We report small angle neutron scattering of spontaneous and magnetic field aligned components of the helical spin polarization in MnSi for temperatures T down to 0.35 K, at pressures p up to 21 kbar, and magnetic field B up to 0.7 T. The parameter range of our study spans the first order transition between helical order and partial magnetic order at p{c}=14.6 kbar, which coincides with the onset of an extended regime of non-Fermi liquid resistivity. Our study suggests that MnSi above p{c} is not dominated by the remnants of the first order transition at p{c}, but that an unidentified mechanism favors stabilization of a new ground state other than helical order.

Non-Fermi Liquid Metal Without Quantum Criticality

A key question in condensed matter physics concerns whether pure three-dimensional metals can always be described as Fermi liquids. Using neutron Larmor diffraction to overcome the traditional resolution limit of diffraction experiments, we studied the lattice constants of the cubic itinerant-electron magnet manganese silicide (MnSi) at low temperatures and high pressures. We were able to resolve the nature of the phase diagram of MnSi and to establish that a stable, extended non-Fermi liquid state emerges under applied pressure without quantum criticality. This suggests that new forms of quantum order may be expected even far from quantum phase transitions.

Spontaneous skyrmion ground states in magnetic metals

Since the 1950s, Heisenberg and others have addressed the problem of how to explain the appearance of countable particles in continuous fields. Stable localized field configurations were searched for an ingredient for a general field theory of elementary particles, but the majority of nonlinear field models were unable to predict them. As an exception, Skyrme succeeded in describing nuclear particles as localized states, so-called 'skyrmions'. Skyrmions are a characteristic of nonlinear continuum models ranging from microscopic to cosmological scales. Skyrmionic states have been found under non-equilibrium conditions, or when stabilized by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids, spin textures in quantum Hall magnets, or the blue phases in liquid crystals. However, it has generally been assumed that skyrmions cannot form spontaneous ground states, such as ferromagnetic or antiferromagnetic order, in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed-matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model based on a few material-specific parameters that can be determined experimentally. Our model has a condition not considered before: we allow for softened amplitude variations of the magnetization, characteristic of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist generally in a large number of materials, notably at surfaces and in thin films, as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.

Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi

MnSi is an itinerant magnet which at low temperatures develops a helical spin-density wave. Under pressure it undergoes a transition into an unusual partially ordered state whose nature is debated. Here we propose that the helical spin crystal (the magnetic analog of a solid) is a useful starting point to understand partial order in MnSi. We consider different helical spin crystals and determine conditions under which they may be energetically favored. The most promising candidate has bcc structure and is reminiscent of the blue phase of liquid crystals in that it has line nodes of magnetization protected by symmetry. We introduce a Landau theory to study the properties of these states, in particular, the effect of crystal anisotropy, magnetic field, and disorder. These results compare favorably with existing data on MnSi from neutron scattering and magnetic field studies. Future experiments to test this scenario are also proposed.