Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet.

Cubic chiral magnets, such as Cu_{2}OSeO_{3}, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

Ultrasmall Moment Incommensurate Spin Density Wave Order Masking a Ferromagnetic Quantum Critical Point in NbFe_{2}.

In the metallic magnet Nb_{1-y}Fe_{2+y}, the low temperature threshold of ferromagnetism can be investigated by varying the Fe excess y within a narrow homogeneity range. We use elastic neutron scattering to track the evolution of magnetic order from Fe-rich, ferromagnetic Nb_{0.981}Fe_{2.019} to approximately stoichiometric NbFe_{2}, in which we can, for the first time, characterize a long-wavelength spin density wave state burying a ferromagnetic quantum critical point. The associated ordering wave vector q_{SDW}=(0,0,l_{SDW}) is found to depend significantly on y and T, staying finite but decreasing as the ferromagnetic state is approached. The phase diagram follows a two-order-parameter Landau theory, for which all of the coefficients can now be determined. Our findings suggest that the emergence of spin density wave order cannot be attributed to band structure effects alone. They indicate a common microscopic origin of both types of magnetic order and provide strong constraints on related theoretical scenarios based on, e.g., quantum order by disorder.

Unique Crystal Structure of Ca_{2}RuO_{4} in the Current Stabilized Semimetallic State.

The electric-current stabilized semimetallic state in the quasi-two-dimensional Mott insulator Ca_{2}RuO_{4} exhibits an exceptionally strong diamagnetism. Through a comprehensive study using neutron and x-ray diffraction, we show that this nonequilibrium phase assumes a crystal structure distinct from those of equilibrium metallic phases realized in the ruthenates by chemical doping, high pressure, and epitaxial strain, which in turn leads to a distinct electronic band structure. Dynamical mean field theory calculations based on the crystallographically refined atomic coordinates and realistic Coulomb repulsion parameters indicate a semimetallic state with partially gapped Fermi surface. Our neutron diffraction data show that the nonequilibrium behavior is homogeneous, with antiferromagnetic long-range order completely suppressed. These results provide a new basis for theoretical work on the origin of the unusual nonequilibrium diamagnetism in Ca_{2}RuO_{4}.

Formation of a topological non-Fermi liquid in MnSi.

Fermi liquid theory provides a remarkably powerful framework for the description of the conduction electrons in metals and their ordering phenomena, such as superconductivity, ferromagnetism, and spin- and charge-density-wave order. A different class of ordering phenomena of great interest concerns spin configurations that are topologically protected, that is, their topology can be destroyed only by forcing the average magnetization locally to zero. Examples of such configurations are hedgehogs (points at which all spins are either pointing inwards or outwards) and vortices. A central question concerns the nature of the metallic state in the presence of such topologically distinct spin textures. Here we report a high-pressure study of the metallic state at the border of the skyrmion lattice in MnSi, which represents a new form of magnetic order composed of topologically non-trivial vortices. When long-range magnetic order is suppressed under pressure, the key characteristic of the skyrmion lattice--that is, the topological Hall signal due to the emergent magnetic flux associated with the topological winding--is unaffected in sign or magnitude and becomes an important characteristic of the metallic state. The regime of the topological Hall signal in temperature, pressure and magnetic field coincides thereby with the exceptionally extended regime of a pronounced non-Fermi-liquid resistivity. The observation of this topological Hall signal in the regime of the NFL resistivity suggests empirically that spin correlations with non-trivial topological character may drive a breakdown of Fermi liquid theory in pure metals.

Response of the Skyrmion Lattice in MnSi to Cubic Magnetocrystalline Anisotropies.

We report high-precision small-angle neutron scattering of the orientation of the Skyrmion lattice in a spherical sample of MnSi under systematic changes of the magnetic field direction. For all field directions the Skyrmion lattice may be accurately described as a triple-Q[over →] state, where the modulus |Q[over →]| is constant and the wave vectors enclose rigid angles of 120°. Along a great circle across ⟨100⟩, ⟨110⟩, and ⟨111⟩ the normal to the Skyrmion-lattice plane varies systematically by ±3° with respect to the field direction, while the in-plane alignment displays a reorientation by 15° for magnetic field along ⟨100⟩. Our observations are qualitatively and quantitatively in excellent agreement with an effective potential, which is determined by the symmetries of the tetrahedral point group T and includes contributions up to sixth order in spin-orbit coupling, providing a full account of the effect of cubic magnetocrystalline anisotropies on the Skyrmion lattice in MnSi.

Reentrant Phase Diagram of Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ Magnetic Field.

We present a magnetic phase diagram of rare-earth pyrochlore Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ magnetic field. Using heat capacity, magnetization, and neutron scattering data, we show an unusual field dependence of a first-order phase boundary, wherein a small applied field increases the ordering temperature. The zero-field ground state has ferromagnetic domains, while the spins polarize along ⟨111⟩ above 0.65 T. A classical Monte Carlo analysis of published Hamiltonians does account for the critical field in the low T limit. However, this analysis fails to account for the large bulge in the reentrant phase diagram, suggesting that either long-range interactions or quantum fluctuations govern low field properties.

Dynamical Defects in Rotating Magnetic Skyrmion Lattices.

The chiral magnet Cu_{2}OSeO_{3} hosts a Skyrmion lattice that may be equivalently described as a superposition of plane waves or a lattice of particlelike topological objects. A thermal gradient may break up the Skyrmion lattice and induce rotating domains, raising the question of which of these scenarios better describes the violent dynamics at the domain boundaries. Here, we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz transmission electron microscope different parts of the Skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence, we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D Monte Carlo simulations. Fluctuations of boundaries show a surgelike rearrangement of Skyrmion clusters driven by defect rearrangement consistent with simulations treating Skyrmions as point particles. Our findings underline the particle character of the Skyrmion.

Multidomain Skyrmion Lattice State in Cu2OSeO3.

Magnetic skyrmions in chiral magnets are nanoscale, topologically protected magnetization swirls that are promising candidates for spintronics memory carriers. Therefore, observing and manipulating the skyrmion state on the surface level of the materials are of great importance for future applications. Here, we report a controlled way of creating a multidomain skyrmion state near the surface of a Cu2OSeO3 single crystal, observed by soft resonant elastic X-ray scattering. This technique is an ideal tool to probe the magnetic order at the L3 edge of 3d metal compounds giving an average depth sensitivity of ∼50 nm. The single-domain 6-fold-symmetric skyrmion lattice can be broken up into domains, overcoming the propagation directions imposed by the cubic anisotropy by applying the magnetic field in directions deviating from the major cubic axes. Our findings open the door to a new way to manipulate and engineer the skyrmion state locally on the surface or on the level of individual skyrmions, which will enable applications in the future.

Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets.

Nearly seven decades of research on microwave excitations of magnetic materials have led to a wide range of applications in electronics. The recent discovery of topological spin solitons in chiral magnets, so-called skyrmions, promises high-frequency devices that exploit the exceptional emergent electrodynamics of these compounds. Therefore, an accurate and unified quantitative account of their resonant response is key. Here, we report all-electrical spectroscopy of the collective spin excitations in the metallic, semiconducting and insulating chiral magnets MnSi, Fe1-xCoxSi and Cu2OSeO3, respectively, using broadband coplanar waveguides. By taking into account dipolar interactions, we achieve a precise quantitative modelling across the entire magnetic phase diagrams using two material-specific parameters that quantify the chiral and the critical field energy. The universal behaviour sets the stage for purpose-designed applications based on the resonant response of chiral magnets with tailored electric conductivity and an unprecedented freedom for an integration with electronics.

Uniaxial Pressure Dependence of Magnetic Order in MnSi.

We report comprehensive small angle neutron scattering measurements complemented by ac susceptibility data of the helical order, conical phase, and Skyrmion lattice phase (SLP) in MnSi under uniaxial pressures. For all crystallographic orientations uniaxial pressure favors the phase for which a spatial modulation of the magnetization is closest to the pressure axis. Uniaxial pressures as low as 1 kbar applied perpendicular to the magnetic field axis enhance the Skyrmion lattice phase substantially, whereas the Skyrmion lattice phase is suppressed for pressure parallel to the field. Taken together we present quantitative microscopic information on how strain couples to magnetic order in the chiral magnet MnSi.

Band Structure of Helimagnons in MnSi Resolved by Inelastic Neutron Scattering.

A magnetic helix realizes a one-dimensional magnetic crystal with a period given by the pitch length λh. Its spin-wave excitations-the helimagnons-experience Bragg scattering off this periodicity, leading to gaps in the spectrum that inhibit their propagation along the pitch direction. Using high-resolution inelastic neutron scattering, the resulting band structure of helimagnons was resolved by preparing a single crystal of MnSi in a single magnetic-helix domain. At least five helimagnon bands could be identified that cover the crossover from flat bands at low energies with helimagnons basically localized along the pitch direction to dispersing bands at higher energies. In the low-energy limit, we find the helimagnon spectrum to be determined by a universal, parameter-free theory. Taking into account corrections to this low-energy theory, quantitative agreement is obtained in the entire energy range studied with the help of a single fitting parameter.

Real-space and reciprocal-space Berry phases in the Hall effect of Mn(1-x)Fe(x)Si.

We report an experimental and computational study of the Hall effect in Mn(1-x)Fe(x)Si, as complemented by measurements in Mn(1-x)Co(x)Si, when helimagnetic order is suppressed under substitutional doping. For small x the anomalous Hall effect (AHE) and the topological Hall effect (THE) change sign. Under larger doping the AHE remains small and consistent with the magnetization, while the THE grows by over a factor of 10. Both the sign and the magnitude of the AHE and the THE are in excellent agreement with calculations based on density functional theory. Our study provides the long-sought material-specific microscopic justification that, while the AHE is due to the reciprocal-space Berry curvature, the THE originates in real-space Berry phases.

Topological aspects of multi-kantiferromagnetism in cubic rare-earth compounds.

We advertise rare-earth intermetallics with high-symmetry crystal structures and competing interactions as a possible materials platform hosting spin structures with non-trivial topological properties. Focusing on the series of cubicRCu compounds, whereR= Ho, Er, Tm, the bulk properties of these systems display exceptionally rich magnetic phase diagrams hosting an abundance of different phase pockets characteristic of antiferromagnetic order in the presence of delicately balanced interactions. The electrical transport properties exhibit large anomalous contributions suggestive of topologically non-trivial winding in the electronic and magnetic structures. Neutron diffraction identifies spontaneous long-range magnetic order in terms of commensurate and incommensurate variations of(ππ0)antiferromagnetism with the possibility for various multi-kconfigurations. Motivated by general trends in these materials, we discuss the possible existence of topologically non-trivial winding in real and reciprocal space in the class ofRCu compounds including antiferromagnetic skyrmion lattices. Putatively bringing together different limits of non-trivial topological winding in the same material, the combination of properties inRCu systems promises access to advanced functionalities.

Specific heat of the Skyrmion lattice phase and field-induced tricritical point in MnSi.

We report high-precision measurements of the temperature and magnetic field dependence of the specific heat, C(T,H), across the magnetic phase diagram of MnSi. Clear anomalies establish the Skyrmion lattice unambiguously as a thermodynamic phase. The evolution of the specific heat anomalies, the field dependence of the entropy released at the phase transitions, and the temperature versus field dependence of crossover lines provide striking evidence of a tricritical point at µ0H(TCP)(int) = 340 mT and T(TCP) = 28.5 K. The existence of this tricritical point represents strong support of a helimagnetic Brazovskii transition, i.e., a fluctuation-induced first-order transition at H = 0.

Long-wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3.

We report a long-wavelength helimagnetic superstructure in bulk samples of the ferrimagnetic insulator Cu2OSeO3. The magnetic phase diagram associated with the helimagnetic modulation inferred from small-angle neutron scattering and magnetization measurements includes a skyrmion lattice phase and is strongly reminiscent of MnSi, FeGe, and Fe(1-x)Co(x)Si, i.e., binary isostructural siblings of Cu2OSeO3 that order helimagnetically. The temperature dependence of the specific heat of Cu2OSeO3 is characteristic of nearly critical spin fluctuations at the helimagnetic transition. This provides putative evidence for effective spin currents as the origin of enhancements of the magnetodielectric response instead of atomic displacements considered so far.

First order metamagnetic transition in Ho2Ti2O7 observed by vibrating coil magnetometry at Milli-Kelvin temperatures.

We report vibrating coil magnetometry of the spin-ice system Ho(2)Ti(2)O(7) down to ~0.04 K for magnetic fields up to 5 T applied parallel to the [111] axis. History-dependent behavior emerges below T(0)(*) ~ 0.6 K near zero magnetic field, in common with other spin-ice compounds. In large magnetic fields, we observe a magnetization plateau followed by a hysteretic metamagnetic transition. The temperature dependence of the coercive fields as well as the susceptibility calculated from the magnetization identify the metamagnetic transition as a line of first order transitions terminating in a critical end point at T(m)(*) 0.37 ~/= K, B(m) ~/= 1.5 T. The metamagnetic transition in Ho(2)Ti(2)O(7) is strongly reminiscent of that observed in Dy(2)Ti(2)O(7), suggestive of a general feature of the spin ices.

Vibrating-coil magnetometry of the spin liquid properties of Tb2Ti2O7.

We have explored the spin liquid state in Tb(2)Ti(2)O(7) with vibrating-coil magnetometry down to ~0.04 K under magnetic fields up to 5 T. We observe magnetic history dependence below T*~0.2 K reminiscent of the classical spin ice systems Ho(2)Ti(2)O(7) and Dy(2)TiTi(2)O(7). The magnetic phase diagram inferred from the magnetization is essentially isotropic, without evidence of magnetization plateaus as anticipated for so-called quantum spin ice, predicted theoretically for [111] when quantum fluctuations renormalize the interactions. Instead, the magnetization for T≪T* agrees semiquantitatively with the predictions of "all-in-all-out" (AIAO) antiferromagnetism. Taken together, this suggests that the spin liquid state in Tb(2)Ti(2)O(7) is akin to an incipient AIAO antiferromagnet.

Observation of coherent helimagnons and gilbert damping in an itinerant magnet.

We study the magnetic excitations of itinerant helimagnets by applying time-resolved optical spectroscopy to Fe(0.8)Co(0.2)Si. Optically excited oscillations of the magnetization in the helical state are found to disperse to lower frequency as the applied magnetic field is increased; the fingerprint of collective modes unique to helimagnets, known as helimagnons. The use of time-resolved spectroscopy allows us to address the fundamental magnetic relaxation processes by directly measuring the Gilbert damping, revealing the versatility of spin dynamics in chiral magnets.

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.

Optimized signal deduction procedure for the MIEZE spectroscopy technique.

A method is reported to determine the phase and amplitude of sinusoidally modulated event rates, binned into four bins per oscillation, based on data generated at the resonant neutron spin-echo spectrometer RESEDA at FRM-II. The presented algorithm relies on a reconstruction of the unknown parameters. It omits a calculation-intensive fitting procedure and avoids contrast reduction due to averaging effects. It allows the current data acquisition bottleneck at RESEDA to be relaxed by a factor of four and thus increases the potential time resolution of the detector by the same factor. The approach is explained in detail and compared with the established fitting procedures of time series having four and 16 time bins per oscillation. In addition the empirical estimates of the errors of the three methods are presented and compared with each other. The reconstruction is shown to be unbiased, asymptotic and efficient for estimating the phase. Reconstructing the contrast increases the error bars by roughly 10% as compared with fitting 16 time-binned oscillations. Finally, the paper gives heuristic, analytical equations to estimate the error for phase and contrast as a function of their initial values and counting statistics.