Abstract
Since the late 1970s, MnSi has played a major role in developing the theory of helical magnets in non-centrosymmetric materials showing the Dzyaloshinsky-Moriya interaction (DMI). With a long helimagnetic pitch of 175 Å as compared to the lattice d-spacing of 4.55 Å, it was ideal for performing neutron studies, especially as large single crystals could be grown. A (B-T)-phase diagram was measured, and in these studies, under the application of a field of about 180 mT perpendicular to the scattering vector Q, a so-called A-phase in the B-T phase diagram was found and first interpreted as a re-orientation of the magnetic helix. After the surprising discovery of the skyrmion lattice in the A-phase in 2009, much interest arose due to the rigidity of the skyrmionic lattice, which is only loosely bound to the crystal lattice, and therefore only relatively small current densities can already induce a motion of this lattice. A very interesting approach to even better understand the complex structures in the phase diagram is to measure and model the spin excitations in MnSi. As the helimagnetic state is characterized by a long pitch of about 175 Å, the associated characteristic excitations form a band structure due to Umklapp scattering and can only be observed at very small Q with energies below 1 meV. Similarly, the excitations of the skyrmion lattice are very soft and low-energetic. We investigated the magnons in MnSi in the whole (B,T)-phase diagram starting in the single-k helimagnetic state by applying a small magnetic field, B = 100 mT. This way, the complexity of the magnon spectrum is significantly reduced, allowing for a detailed comparison of the data with theory, resulting in a full theoretical understanding of the spin system of MnSi in all its different magnetic phases.
Highlights
Helical magnets are currently of high interest because they serve as model systems for complex magnetic ordering, yielding interesting properties such as multiferroicity and the appearance of stable magnetic vortices, to name a few
We investigated the magnons in MnSi in the whole (B,T)-phase diagram starting in the single-k helimagnetic state by applying a small magnetic field, B = 100 mT
Theoretical explanations were based on the early theory of Bak and Jensen [6], who proposed an explanation of the phase diagram of MnSi based on the Dzyaloshinsky-Moriya interaction (DMI) originating from non-centrosymmetry
Summary
Helical magnets are currently of high interest because they serve as model systems for complex magnetic ordering, yielding interesting properties such as multiferroicity and the appearance of stable magnetic vortices (i.e. skyrmions), to name a few. The interplay of the various energy scales often leads to magnetic ordering, exhibiting a periodicity that is incommensurate with the lattice and to magnetic Brillouin zones that are much smaller than the chemical ones. A prominent example showing incommensurate helical ordering is MnSi, which is a non-centrosymmetric itinerant magnet with a P213 structure and a lattice spacing of a = 4.55 Å. The (B-T)-phase diagram is shown on the left of Figure 1. It exhibits a large variety of different phases, such as single-handed helical and conical ordering, a field-polarized and paramagnetic state, as well as a non-trivial topological spin state (A-phase), i.e., a skyrmion phase. Together with a mean-field theory of the dynamics in MnSi, this leads to a very detailed understanding of the experimentally observed spectra
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