Critical behavior of the single-crystal helimagnet MnSi

Abstract

The critical behavior of the single-crystal helimagnet MnSi is investigated by means of bulk dc magnetization at the boundary between the conical state and paramagnetic phase. We obtain the critical exponents $(\ensuremath{\beta}=0.242\ifmmode\pm\else\textpm\fi{}0.006,\ensuremath{\gamma}=0.915\ifmmode\pm\else\textpm\fi{}0.003$, and $\ensuremath{\delta}=4.734\ifmmode\pm\else\textpm\fi{}0.006)$, where the self-consistency and reliability are verified by the Widom scaling law and the scaling equation. The critical exponents of MnSi belong to the universality class of tricritical mean-field theory, which unambiguously indicates a tricritical phenomenon at the boundary between the first-order phase transition and the second-order one induced by the external magnetic field. The tricritical point (TCP) is determined as ${H}_{\mathrm{TCP}}\ensuremath{\approx}3200$ Oe at the critical temperature, consistent with the previous report [A. Bauer, M. Garst, and C. Pfleiderer, Phys. Rev. Lett. 110, 177207 (2013)]. The critical behavior suggests a long-range magnetic coupling with the exchange distance decaying as $J(r)\ensuremath{\approx}{r}^{\ensuremath{-}4.3}$ in MnSi.