Thermal expansion and magnetovolume studies of the itinerant helical magnet MnSi

Thermal expansion and forced magnetostriction of MnSi were measured as a function of temperature down to 5 K and magnetic field to 3 T. The small length (volume) discontinuity at the magnetic phase transition in MnSi decreases with application of magnetic field to a value $\mathrm{\Delta }L/L\sim {10}^{-7}$, and then suddenly the discontinuity seemingly jumps to zero. Thermal expansivity peaks strongly deteriorate with magnetic fields. No specific features identifying a tricritical point were observed. We propose that the Frenkel concept of heterophase fluctuations may be relevant in the current case. Therefore, we suggest that the magnetic phase transition in MnSi always remains first order at any temperature and magnetic field, but the transition is progressively smoothed by heterophase fluctuations. These results question the applicability of a model of a fluctuation-induced first-order phase transition for MnSi. Probably a model of coupling of an order parameter with other degrees of freedom is more appropriate.

Figure 1

Linear thermal expansion of MnSi along [110] as a function of temperature and magnetic field. The magnetic field is directed along [100] (data shown with offsets for better viewing), with field increasing from zero (bottom curve) to 0.43 T (top curve). Insets show enlarged views of corresponding curves near the phase-transition region. Temperature scale division is 0.3 K for both insets, $\mathrm{\Delta }L/L_0$ scale division is $1\times {10}^{-6}$ and $2\times {10}^{-6}$ for upper and lower insets respectively.

Figure 2

Longitudinal (a) and transverse magnetostriction (b) of MnSi along [110]. A low-field anomaly $H^{*}$ [seen in panel (a) and in Fig. 3] corresponds to the helical-conical transition. A change of slope at $H_c$ is the result of a transformation from the conical phase to a field-induced ferromagnetic phase. This effect becomes less pronounced at low temperatures in the longitudinal configuration (see also Ref. [5]).

Figure 3

Detailed view of longitudinal (a) and transverse magnetostriction (b) of MnSi along [110] in a restricted range of temperatures and magnetic fields. The low-field anomaly at $H^{*}$ corresponds to a helical-conical transition. A higher field change of slope occurs due to a transition of the conical phase to a field-induced ferromagnet state. This transition is associated with tiny dips in $\mathrm{\Delta }L/L_0$ that can be seen in panel (b). These dips can be viewed as continuations of the smoothed first-order phase transitions observed at lower magnetic fields. So-called hills (a) and canyons (b) in the range of $\sim 0.12–0.23$ T characterize the skyrmion phase.

Figure 4

Dependence of $\mathrm{\Delta }L/L_0\left(T\right)$, after subtracting a linear function that describes $\mathrm{\Delta }L/L_0$ in the paramagnetic phase of MnSi in the vicinity of the phase transition (see text). Numbers on the plot are values of applied magnetic field in Tesla. At $\sim 0.26$ Tesla the form of the thermal expansion curves suddenly changes. Quasidiscontinuities are replaced by increasingly smoother anomalies. The inset illustrates how the discontinuity was determined.

Figure 5

Temperature dependence of linear thermal expansivity $1/L(dL/dT)$ along [110] for the applied magnetic field along [100]. Deterioration of the peaks with magnetic field can be clearly seen. A peak in thermal expansivity, corresponding to the skyrmion phase, is apparent at 0.145 T.

Figure 6

Dependence on magnetic field of the quasidiscontinuity of sample length $\delta$ and height of peaks of expansivity at the phase transition. The discontinuity curves are terminated at 0.26 T, where the discontinuities virtually disappeared. The expansivity peaks can be still observed at least to 0.43 T. A plateau in the range $\sim 0.12–0.2$ T (a) and a local maximum at $\sim 0.14–0.23$ T (b) are related to the existence of the skyrmion $A$ phase (see Fig. 3).