Evolution of magneto-crystalline anisotropies in Mn$_{1-x}$Fe$_x$Si and Mn$_{1-x}$Co$_x$Si as inferred from small-angle neutron scattering and bulk properties

Abstract

We report a comprehensive small-angle neutron scattering (SANS) study of magnetic correlations in Mn1−xFexSi at zero magnetic field. To delineate changes of magneto-crystalline anisotropies (MCAs) from effects due to defects and disorder, we recorded complementarysusceptibility and highresolution specific heat data, and investigated selected compositions of Mn1−xCoxSi. 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 under doping 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 Mn1−xCoxSi establishes that the pinning due to defects and disorder remains, however, comparatively weak. The observation that MCAs, that are sixth order in spin-orbit coupling, play an important role for the spontaneous order in Mn1−xFexSi and Mn1−xCoxSi offer 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.

Unpinning the skyrmion lattice in MnSi: Effect of substitutional disorder

“…Note Added: It was brought to our attention that there are at least 3 related recent manuscripts that address the effect of disorder on the SKL and helical states of B20 structured materials. This includes SANS exploration of nominally pure MnSi with a rotation of the sample with respect the beam and magnetic field [47] and two papers exploring the effect of Fe and Co substitution in Mn 1-x Fe x Si and Mn 1-x Co x Si [48,49].…”

Physical properties of (Mn1−xFex)Si at x ≃0.15

“…Indeed, it became known that doping MnSi with Fe and Co decreases a temperature of the magnetic phase transitions and finally completely suppress the transitions at some critical concentrations of the dopants. In case of Fe doping a critical concentration consist about 15% (actually different estimates vary from 0.10 to 0.19) 10,11,13 .…”

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.…”

“…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.…”

“…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.…”