Evolution of magnetocrystalline anisotropies in Mn1−xFexSi and Mn1−x

Abstract

We report a comprehensive small-angle neutron scattering (SANS) study of magnetic correlations in Mn 1−x Fe x Si at zero magnetic field. To delineate changes of magnetocrystalline anisotropies (MCAs) from effects due to defects and disorder, we recorded complementary susceptibility and high-resolution specific heat data and investigated selected compositions of Mn 1−x Co x Si. For all systems studied, the helimagnetic transition temperature and magnetic phase diagrams evolve monotonically with composition consistent with literature. The SANS intensity patterns of the spontaneous magnetic order recorded under zero-field cooling, which were systematically tracked over forty angular positions, display strong changes of the directions of the intensity maxima and smeared out intensity distributions as a function of composition. We show that cubic MCAs account for the complex evolution of the SANS patterns, where for increasing x the character of the MCAs shifts from terms that are fourth order to terms that are sixth order in spin-orbit coupling. The magnetic field dependence of the susceptibility and SANS establishes that the helix reorientation as a function of magnetic field for Fe-or Co-doped MnSi is dominated by pinning due to defects and disorder. The presence of well-defined thermodynamic anomalies of the specific heat at the phase boundaries of the skyrmion lattice phase in the doped samples and properties observed in Mn 1−x Co x Si establishes that the pinning due to defects and disorder remains, however, weak and comparable to the field scale of the helix reorientation. The observation that MCAs, which are sixth order in spin-orbit coupling, play an important role for the spontaneous order in Mn 1−x Fe x Si and Mn 1−x Co x Si offers a fresh perspective for a wide range of topics in cubic chiral magnets such as the generic magnetic phase diagram, the morphology of topological spin textures, the paramagnetic-to-helical transition, and quantum phase transitions.

Compositional Studies of Metals with Complex Order by means of the Optical Floating-Zone Technique

“…The samples MF1 and MF2 were measured in magnetic fields of 110 mT and 180 mT, respectively [46]. Consistent with the literature, no magnetic peaks were observed in Mn 1−x Fe x Si for iron concentrations x > 0.1 [47,45].…”

“…Prior to the measurements, the samples FC1 and FC2 were high-field cooled in a vertical magnetic field of 180 mT, before the field was reduced to 5 mT. In a doped chiral magnet such as Fe 1−x Co x Si, such a field and temperature history yields a single-domain state oriented along the field direction [38,43,37,44,45]. The samples MF1 and MF2 were measured in magnetic fields of 110 mT and 180 mT, respectively [46].…”

Cubic B20 helimagnets with quenched disorder in magnetic field

“…We found a remarkable electrostatic analogy in this problem: the distortion of the spiral ordering by a single defect is given by a Poisson equation for an electric dipole. The electrostatic analogy allowed us to find that a small concentration c of impurities leads to a correction to the spiral vector proportional to c as it was recently observed 12,13 in Mn 1−x Fe x Si at small x.…”

“…This lies in agreement with recent experimental findings of Refs. 12,13 in Mn 1−x Fe x Si at small x. The sign of the correction can be either positive, negative or zero, depending on the model parameters.…”

“…Such a linear in dopant concentration correction to the spiral vector was observed recently experimentally in Mn 1−x Fe x Si. 12,13 It should be pointed out that solution (27) lies in contradiction with the requirement |ρ R | √ S at large enough R. It happens because the finite concentration of defects changes the spiral vector. As a result, orientation of some spins differs significantly from their orientation in the pure system.…”