We present a comprehensive investigation of the evolution of helimagnetic correlations in Mn1−xFexSi with increasing doping. By combining polarized neutron scattering and high resolution neutron spin echo spectroscopy we investigate three samples with x = 0.09, 0.11, and 0.14, i.e., with compositions on both sides of the concentration x∗∼0.11 where the helimagnetic Bragg peaks disappear and between x∗ and the quantum critical concentration xC∼0.17, where TC vanishes. We find that the abrupt disappearance of the long range helical periodicity at x∗ does not affect the precursor fluctuating correlations. These build up with decreasing temperature in a similar way as for the parent compound MnSi. Also the dynamics bears strong similarities to MnSi. The analysis of our results indicates that frustration, possibly due to achiral Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, increases with increasing Fe doping. We argue that this effect explains both the expansion of the precursor phase with increasing x and the abrupt disappearance of long range helimagnetic periodicity at x∗.@en

This chapter is mainly devoted to the distinctive properties of spiral and skyrmion states accounted by the cubic anisotropy in bulk cubic helimagnets such as MnSi and Cu2OSeO3. We start by systematizing the main features of the universal phase diagrams at the critical fields Hc1 and Hc2. We first discuss the influence of cubic anisotropy on the reversible, or irreversible, alignment of oblique spiral states into the conical phase at Hc1. We then address the phase transition between the conical and field-polarized state at Hc2, which may be of both first order and second order depending on the orientation of the applied magnetic field with respect to easy anisotropy axes. We show that the effect of cubic anisotropy is more subtle than assumed so far, as it may induce new elliptically distorted spiral states and phase transitions between them. Finally, we show how this distortion of the spiral states by cubic anisotropy opens up the way to skyrmion stabilization.@en

We discuss distinctive features of spiral states in bulk chiral magnets such as MnSi and Cu2OSeO3 that stem from the effect of the cubic magnetocrystalline anisotropy. First of all, at both the helical-to-conical and theconical-to-ferromagnetic transitions, taking place at Hc1 and Hc2, respectively, the cubic anisotropy leads to reversible or irreversible jumplike reorientations of the spiral wave vectors. The subtle interplay between the easy and hard anisotropy axes gives rise to a phase transition between elliptically distorted conical states almost without any detectable change in the period. We show that the competition between on-site cubic and exchange anisotropy terms can also lead to oblique spiral states. Our work gives clear directions for further experimental studies to reveal theoretically predicted spiral states in cubic helimagnets beyond the aforementioned well-
established states and thus it can help to understand the magnetic phase diagram of these archetypal skyrmion hosts. In addition, we show that properties of isolated skyrmions such as interskyrmion attraction, orientation, and/or nucleation are also rooted in the properties of host spiral states, in which skyrmions are stabilized@en

Recent experimental findings in the bulk cubic helimagnet and Mott insulator Cu2OSeO3 highlight the paramount role of cubic anisotropy in stabilizing novel chiral and skyrmion phases. It was indeed found that if a magnetic field is applied along the easy 001 crystallographic direction, competing cubic and
exchange anisotropies tilt the wave vector of the conical spiral away from the magnetic field [Qian et al., Sci. Adv. 4, eaat7323 (2018)]. Furthermore, in this configuration skyrmions have been observed in a broad range of temperatures and magnetic fields [Chacon et al., Nat. Phys. 14, 936 (2018)]. Starting from these
experimental observations and on the basis of a phenomenological Dzyaloshinskii theory, we investigate additional implications of the cubic anisotropy for this specified field direction. By including cubic anisotropy we show that the phase transition between the conical and field-polarized or homogeneous states becomes first order. Furthermore, we show that this transition is accompanied by the formation of conical droplets—domains of the conical phase in the homogeneous state. We investigate the internal structure of these droplets, which at their boundaries encompass alternating regions of positive and negative energy densities with respect to
the homogeneous state. We thus deduce that these droplets may be zipped and unzipped in phase during the first-order phase transition that occurs by either increasing or decreasing the magnetic field. On the other hand, we show that in the conical phase skyrmions may form clusters due to their attractive mutual interaction. However, in
the homogeneous state, the skyrmion-skyrmion interaction becomes repulsive, and the skyrmion clusters expand and disperse isolated skyrmions. This mutual skyrmion repulsion prevents the stabilization of skyrmion clusters even if the energy of isolated skyrmions is lower than that of the homogeneous state. Yet this skyrmion dispersal
may be prevented if skyrmions are surrounded by the circular spiral state and form skyrmion bags. Such a scenario could explain the existence of skyrmions in the field-polarized state reported experimentally.@en

Magnetic skyrmions are topologically protected nanoscale spin textures with particle-like properties. In bulk cubic helimagnets, they appear under applied magnetic fields and condense spontaneously into a lattice in a narrow region of the phase diagram just below the magnetic ordering temperature, the so-called A-phase. Theory, however, predicts skyrmions to be locally stable in a wide range of magnetic fields and temperatures. Our neutron diffraction measurements reveal the formation of skyrmion states in large areas of the magnetic phase diagram, from the lowest temperatures up to the A-phase. We show that nascent and disappearing spiral states near critical lines catalyze topological charge changing processes, leading to the formation and destruction of skyrmionic states at low temperatures, which are thermodynamically stable or metastable depending on the orientation and strength of the magnetic field. Skyrmions are surprisingly resilient to high magnetic fields: the memory of skyrmion lattice states persists in the field polarized state, even when the skyrmion lattice signal has disappeared. These findings highlight the paramount role of magnetic anisotropies in stabilizing skyrmionic states and open up new routes for manipulating these quasi-particles towards energy-efficient spintronics applications.@en