Crossover behavior of critical helix fluctuations in MnSi

Abstract

The critical helix fluctuations in the cubic noncentrosymmetric helimagnet MnSi have been studied by means of neutron small angle scattering and spin echo spectroscopy. To interpret the data, analytical formulas for the susceptibility in real space were obtained for the first time. The calculations presented here are based on the theory introduced in S. V. Grigoriev et al., Phys. Rev. B 72, 134420 (2005). According to this theory the temperature in the critical region can be divided into three parts with different types of chiral fluctuations: (i) ferromagnetic like; (ii) isotropic helical; and (iii) anisotropic helical ones. The fluctuations increase in amplitude with a randomly oriented but left-skewed pitch $\mathbf{k}$ upon approaching ${T}_{c}=29\text{ }\text{K}$. The scaling law of the inverse correlation length $\ensuremath{\kappa}$ exhibits a crossover at $\ensuremath{\kappa}\ensuremath{\approx}k$. The value of the critical exponent $\ensuremath{\nu}$ is changed from ${\ensuremath{\nu}}_{1}=0.40(6)$ in the vicinity of ${T}_{c}$ to ${\ensuremath{\nu}}_{2}=0.68(1)$ at high temperatures. The critical behavior of the relaxation rate $\ensuremath{\Gamma}$ along the easy direction obeys the dynamical scaling $\ensuremath{\Gamma}\ensuremath{\sim}{\ensuremath{\kappa}}^{Z}\ensuremath{\sim}{\ensuremath{\tau}}^{Z\ensuremath{\nu}}$ with a crossover at the temperature where $\ensuremath{\kappa}\ensuremath{\approx}k$ with ${Z}_{1}=2.5(1)$ for the high temperatures and ${Z}_{2}=1.10(3)$ close to ${T}_{c}$. Fluctuations become 100% left handed at the crossover point. The observed crossover is associated with the dominating influence of the Dzyaloshinskii-Moria interaction near ${T}_{c}$, responsible for the chiral ordering.