Christian Pfleiderer

We report near-surface small-angle neutron scattering (NS-SANS) and complementary off-specular neutron reflectometry (OSR) of the magnetic order in a single-crystalline epitaxial MnSi film grown on Si(111) in the thick-film limit. Providing a means of direct reciprocal space mapping, NS-SANS and OSR reveal one-dimensional magnetic modulations perpendicular to the film surface under magnetic fields parallel and perpendicular to the film surface, where additional polarized neutron reflectometry (PNR) and magnetization measurements are in excellent agreement with the literature. Regardless of the field orientation, our data do not suggest the presence of more complex spin textures, notably the formation of skyrmions. This observation establishes a distinct contrast to bulk MnSi thinned to similar nanoscale thicknesses, in which a skyrmion lattice dominates the phase diagram under perpendicular fields. Extended x-ray absorption fine structure measurements suggest that small shifts of the Si positions within the unstrained unit cell of the film control the magnetic state, representing the main structural difference between epitaxial and thinned bulk MnSi.

In the metallic magnet NbFe 2 , the low temperature threshold of ferromagnetism can be investigated by varying the Fe concentration within a narrow homogeneity range. NbFe 2 is one of a number of compounds where modulated order is found to mask the ferromagnetic quantum critical point. However, here we report the rare case where the masking modulated magnetic order has been fully refined. Spherical neutron polarimetry and high-intensity single-crystal neutron diffraction reveal the first case of a longitudinal spin-density wave masking the ferromagnetic quantum critical point. The spin-density wave is characterized by a large-wavelength incommensurate modulation of its low average moment. It is formed from ferrimagnetic building blocks with antiparallel ferromagnetic sheets. The existence of ferromagnetic sheets and compensation of the magnetization only over mesoscopic length scales show local similarity between the spin-density wave and the ferromagnetic parent phase and indicate the spin-density wave's unconventional nature as emerging from underlying ferromagnetic quantum criticality.

Spin textures are magnetic configurations that vary smoothly in space, momentum, or time. This review explores the topology, geometry, dynamics, and imaging of these complex, often noncollinear configurations in magnetic and multiferroic systems, providing a framework for investigating the interplay between local spatial patterns and their global physical properties. A central theme is the role of Berry phases and quantum geometry, which provide a common framework linking topological textures, emergent electrodynamics, charge transport, and magnetically induced ferroelectricity. Spin textures can manifest as stable topological particles, coupling to electrons or magnons via emergent electromagnetic fields. Advanced real-space imaging techniques resolve the internal structure and dynamics of topological textures like magnetic skyrmions or multiferroic domains, enabling the direct observation of their nucleation, motion, and annihilation in both two and three dimensions. In multiferroic systems, spin textures can induce ferroelectricity, and nonlinear optical techniques, such as second-harmonic generation, can resolve the coexisting order parameters in such systems. Last, we examine emergent functionalities of spin textures and multiferroics, such as nonreciprocal transport, and provide an outlook on the technological potential of magnetic textures and their role in exploring the link between topology and magnetism.

Magnetic skyrmions are spin textures with nontrivial topology that form two-dimensional hexagonal lattices (SkX) in chiral magnets. Element-specific reciprocal-space characterization of skyrmion lattices with soft x-rays commonly relies on transmission geometries, which require thinning of bulk crystals and can modify their magnetic properties. Here, we show that resonant elastic x-ray scattering in a grazing-incidence geometry (GIREXS) provides a nondestructive and geometrically flexible probe of skyrmion lattices in bulk materials. Using MnSi as a model system, GIREXS resolves the helical, conical, and skyrmion-lattice states through their characteristic magnetic satellite peaks and yields the skyrmion wave vector. By operating just above the critical angle ( α c ≈ 1.6 ° in MnSi at the Mn L 3 edge), the method achieves a probing depth of approximately 3 nm , tunable up to approximately 20 nm via the incidence angle, while maintaining full reciprocal-space access to the in-plane magnetic correlations. The grazing-incidence approach circumvents the structural Bragg-peak constraints that limit conventional reflection resonant elastic x-ray scattering (REXS) at fixed soft-x-ray energies. Our measurements establish GIREXS as a practical method for studying magnetic superstructures in bulk crystals, providing direct reciprocal-space access to magnetic satellite reflections and a basis for future depth-controlled, element-selective investigations of complex spin textures.

We present a temperature-modulated de Haas–van Alphen measurement technique that allows selective addressing of quantum oscillations with different effective masses m∗ using a non-monotonic amplitude evolution with temperature and magnetic field, governed by the temperature derivative of the Lifshitz–Kosevich factor. The technique relies on harmonic modulation of the sample temperature and phase-sensitive detection of quantum oscillations in the voltage induced in a pickup coil. We use a set of frequencies with strong Zeeman-driven harmonic content in the compensated topological semimetal MoSi2 as a natural linear mass comb ranging from 1 m∗ to 13 m∗ to demonstrate the tunability of the mass-dependent quantum oscillation amplitudes experimentally. The technique allows us to reliably isolate weak contributions of heavy orbits that are inaccessible in conventional de Haas–van Alphen frequency spectra because their frequency peaks overlap with much stronger frequency peaks of lighter orbits.

We developed an optically detected magnetic resonance setup designed for compatibility with a widely used, commercially available helium bath cryostat equipped with a variable temperature insert. The optical path extends nearly 2 m, spanning the full length of the cryostat insert, enabling excitation of the nitrogen-vacancy (NV) centers and detection of the resulting fluorescence from outside the cryostat. The setup preserves optical alignment and beam quality along this extended path, allowing integration into existing cryogenic systems without significant modifications. We demonstrate the setup’s performance by measuring the temperature dependence of the resonance signal and its behavior under small applied magnetic fields, as well as the magnetic transition of a SrRuO3 sample, thereby showcasing the feasibility of NV magnetometry on a sample in constrained cryogenic environments.

The magnetic excitations of the skyrmion lattice in MnSi comprise a multitude of individual modes, which are non-reciprocal and thereby propagate unidirectionally. We report inelastic neutron scattering experiments for temperatures near and above the skyrmion–paramagnetic phase transition in the chiral magnet MnSi, tracking the evolution from the skyrmion lattice towards the high-temperature paramagnetic state. Within the resolution of the triple-axis measurements the excitations vary smoothly across the skyrmion–paramagnetic boundary, and the quasi-elastic paramagnetic signal under applied field retains the non-reciprocal character seen in the skyrmion phase even far above the critical temperature. Using a resolution convolution, our results are consistent with linear spin-wave theory.

In three-dimensional chiral magnets, skyrmions are line-like objects oriented parallel to the applied magnetic field. The efficient coupling of magnetic skyrmion lattices to spin currents and magnetic fields permits their dynamical manipulation. Here, we explore the dynamics of skyrmion lattices when slowly oscillating the field direction by up to a few degrees on millisecond timescales while simultaneously pushing the skyrmion lattice by electric currents. The field oscillations induce a shaking of the orientation of the skyrmion lines, leading to a phase where the critical depinning current for translational motion vanishes. We measure the transverse susceptibility of MnSi to track various depinning phase transitions induced by currents, oscillating fields, or combinations thereof. An effective slip–stick model for the bending and motion of the skyrmion lines in the presence of disorder explains main features of the experiment and predicts the existence of several dynamical skyrmion lattice phases under shaking and pushing representing phases of matter far from thermal equilibrium.