Nonlinear magnetic responses at the phase boundaries around helimagnetic and skyrmion lattice phases in MnSi: Evaluation of robustness of noncollinear spin texture

Abstract

The phase diagram of a cubic chiral magnet MnSi with multiple Dzyaloshinskii-Moriya (DM) vectors as a function of temperature T and dc magnetic field H dc was investigated using intensity mapping of the odd-harmonic responses of ac magnetization (M 1ω and M 3ω ), and the responses at phase boundaries were evaluated according to a prescription [J. Phys. Soc. Jpn. 84, 104707 (2015)]. By evaluating M 3ω /M 1ω appearing at phase boundaries, the robustness of noncollinear spin texture in both the helimagnetic (HM) and the skyrmion lattice (SkL) phases of MnSi was discussed. The robustness of vortices-type solitonic texture SkL in MnSi is smaller than those of both the single DM HM and chiral soliton lattice phases of a monoaxial chiral magnet Cr 1/3 NbS 2 , and furthermore the robustness of the multiple DM HM phase in MnSi is smaller than that of its SkL. Through magnetic diagnostics over the wide T -H dc range, we found a new paramagnetic (PM) region with ac magnetic hysteresis, where spin fluctuations have been observed via electrical magnetochiral effect. The anomalies observed in the previous ultrasonic attenuation measurement correspond to the peak positions of out-of-phase M 1ω . The appearance of a new PM region occurs at a characteristic magnetic field, above which indeed the SkL phase appears. It has us suppose that the new PM region could be a phase with spin fluctuation like the skyrmion gas phase.

A.C. susceptibility as a probe of low-frequency magnetic dynamics

“…Moreover, more complicated expressions can be derived if a d.c. magnetic field is also applied [39]. Measuring the nonlinear susceptibility has been used to differentiate between different types of slow magnetic relaxation [38] due to the divergence in χ (3) near the critical temperature [8,37,41] and can be very sensitive to the presence of some magnetic phases which are undetected in linear a.c. susceptibility [36,42,43,44,45]. A different treatment of nonlinear effects is used in studies of superconductors, as will be described in section 4.6.…”

Chiral Magnetism: Coupling Static and Dynamic Chirality

“…Incidentally, this huge third-order nonlinear magnetic susceptibility is also found in the system of Skyrmion, which is a non-uniaxial chiral magnet. 17…”

Nonlinearity and harmonics of the magnetic susceptibility of a Co-=SUP=-2+-=/SUP=- single-ion magnet in the paramagnetic region above the magnetic ordering temperature

“…A lot of relatively recent work has been devoted to nonlinear magnetic susceptibility in ferromagnets, where the low-frequency dynamics of domain walls leads to a resonant response to an external alternating magnetic field and makes it possible to obtain data on the mobility of domain boundaries [1][2][3][4][5]. The presence of second, third and higher-order harmonics in the study of ferromagnets does not seem unusual because the domain walls themselves are solitons, and their dynamics are always significantly nonlinear.…”