No Arabic abstract
We present a comprehensive and systematic magnetization and ac susceptibility study of Mn$_{1-x}$Fe$_{x}$Si over an extensive range of ten Fe concentrations between $x$ = 0 - 0.32. With increasing Fe substitution, the critical temperature decreases but the magnetic phase diagrams remain qualitatively unaltered for $x$ $leq$ $x^*$ $approx$ 0.11 with clear boundaries between the helical, conical, and skyrmion lattice phase as well as an enhanced precursor phase. A notably different behavior sets in for $x$ $=$ 0.11, 0.13 and 0.14, where certain characteristics of helimagnetic correlations persist, but without clear phase boundaries. Although a qualitative change already sets in at $x^*$, the transition temperature and spontaneous magnetization vanish only at $x_C$ = 0.17 where also the average magnetic interactions change sign. Although the Curie-Weiss temperature reaches -12~K for $x$ = 0.32, no signature of long-range magnetic order is found down to the lowest temperature, indicating a possible significant role for quantum fluctuations in these systems.
We present a systematic study of the ac susceptibility of the chiral magnet Fe$_{1-x}$Co$_x$Si with $x$ = 0.30 covering four orders of magnitude in frequencies from 0.1 Hz to 1 kHz, with particular emphasis to the pronounced history dependence. Characteristic relaxation times ranging from a few milliseconds to tens of seconds are observed around the skyrmion lattice A-phase, the helical-to-conical transition and in a region above $T_C$. The distribution of relaxation frequencies around the A-phase is broad, asymmetric and originates from multiple coexisting relaxation processes. The pronounced dependence of the magnetic phase diagram on the magnetic history and cooling rates as well as the asymmetric frequency dependence and slow dynamics suggest more complicated physical phenomena in Fe$_{0.7}$Co$_{0.3}$Si than in other chiral magnets.
We present a comprehensive small angle neutron scattering study of the doping dependence of the helimagnetic correlations in Mn$_{1-x}$Fe$_{x}$Si. The long-range helimagnetic order in Mn$_{1-x}$Fe$_x$Si is suppressed with increasing Fe content and disappears for $x$ $>$ $x^*$ $approx$ 0.11, i.e. well before $x_C$ $approx$ 0.17 where the transition temperature vanishes. For $x$ $>$ $x^*$, only finite isotropic helimagnetic correlations persist which bear similarities with the magnetic correlations found in the precursor phase of MnSi. Magnetic fields gradually suppress and partly align these short-ranged helimagnetic correlations along their direction through a complex magnetization process.
Small angle neutron scattering measurements on a bulk single crystal of the doped chiral magnet Fe$_{1-x}$Co$_x$Si with $x$=0.3 reveal a pronounced effect of the magnetic history and cooling rates on the magnetic phase diagram. The extracted phase diagrams are qualitatively different for zero and field cooling and reveal a metastable skyrmion lattice phase outside the A-phase for the latter case. These thermodynamically metastable skyrmion lattice correlations coexist with the conical phase and can be enhanced by increasing the cooling rate. They appear in a wide region of the phase diagram at temperatures below the $A$-phase but also at fields considerably smaller or higher than the fields required to stabilize the A-phase.
We present a comprehensive Small Angle Neutron Scattering (SANS) and Neutron Spin Echo Spectroscopy (NSE) study of the structural and dynamical aspects of the helimagnetic transition in Fe$_{1-x}$Co$_x$Si with $x$ = 0.30. In contrast to the sharp transition observed in the archetype chiral magnet MnSi, the transition in Fe$_{1-x}$Co$_x$Si is gradual and long-range helimagnetic ordering coexists with short-range correlations over a wide temperature range. The dynamics are more complex than in MnSi and involve long relaxation times with a stretched exponential relaxation which persists even under magnetic field. These results in conjunction with an analysis of the hierarchy of the relevant length scales show that the helimagnetic transition in Fe$_{1-x}$Co$_x$Si differs substantially from the transition in MnSi and question the validity of a universal approach to the helimagnetic transition in chiral magnets.
A comprehensive ellipsometric study was performed on Fe$_{1-x}$Co$_{x}$Si single crystals in the spectral range from 0.01 eV to 6.2 eV. Direct and indirect band gaps of 73 meV and 10 meV, respectively, were observed in FeSi at 7 K. One of four infrared-active phonons that is energetically close to the direct absorption edge is coupled both to the electrons and to the low-energy phonon. This is evident from asymmetry in the phonon line shape and a reduction of its frequency when the absorption edge shifts across the phonon energy due to the temperature dependence of the direct band gap. As the temperature increases, the indirect gap changes sign, which manifests as a transition from a semiconductor to a semimetal. The corresponding gain of the spectral weight at low energies was recovered within an energy range of several eV. The present findings strongly support the model indicating that Fe$_{1-x}$Co$_{x}$Si can be well described in an itinerant picture, taking into account self-energy corrections.