Magnetic phase diagram of MnSi in the high-field region

The high-field region of the magnetic phase diagram of MnSi is probed by magnetization, resistivity, and magnetoresistance measurements carried out in the temperature range 1.8–300 K for magnetic fields up to 8 T. It is shown that the phase boundary between the paramagnetic (PM) phase and the spin-polarized (SP) phase has no positive slope as was suggested previously, and appears to be practically vertical at the transition temperature $T_c\sim$ 30 K. We argue that the broad maxima of the resistivity and magnetization derivative, which develop in the range $T>T_c$, are determined by the specific form of functional dependences of these quantities in the PM phase and do not correspond to any “diffuse” SP-PM transition. A universal relation between magnetoresistance and magnetization $\Delta \rho /\rho =-a_0{M}^2$ found in the PM phase of MnSi is shown to hold in a wide temperature and magnetic field range where magnetoresistance varies by more than two orders of magnitude. The analysis of the transport and magnetic resonance data favors the explanation of the magnetic properties of MnSi by Heisenberg-type localized magnetic moments rather than within the magnetism of itinerant electrons. A low-temperature anomaly at $T\sim$ 15 K corresponding to the features of magnetoresistance and $g$ factor is reported.

Figure 1

Temperature dependences of zero-field resistivity (a) and the derivatives $\partial \rho /\partial T$ calculated from the experimental data in various magnetic fields (b) for MnSi. The dashed line in panel (a) denotes the approximation used in simulations (Sec. 5). The inset shows the jump in resisitivity in the vicinity of $T_{c0}$.

Figure 2

Magnetization $M$ in ${\mu }_B$ per Mn ion (a) and derivatives $\partial M/\partial B$ (b) of MnSi. Numbers on the curves correspond to temperature in K in panel (a) and to magnetic field in T in panel (b). In panel (a) open circles for $T⩾35$ K correspond to experimental data, while black lines are approximations used in numerical simulations (Sec. 5). Experimental $M\left(B\right)$ data for $T⩽30$ K are denoted by solid lines. In panel (b) arrows mark positions of the $\partial M/\partial B$ maxima.

Figure 3

Field (a) and temperature (b) dependences of magnetoresistance in MnSi. In panel (b) numbers near curves correspond to magnetic field in T. Arrows mark the magnetoresistance minima and the dashed line indicates the position of the low-temperature anomaly.

Figure 4

The magnetic phase diagram of MnSi restored from the experimental data. The hatched area marks helical phase, conical phase, and $A$ phase, with the corresponding phase boundaries taken from the literature.[2, 14] Points with error bars denote experimental positions of the $\partial \rho /\partial T$, $\partial M/\partial B$, and $\Delta \rho /\rho$ extrema; diamonds show result of simulations of $\partial \rho /\partial T$ with the help of experimental magnetization and resistivity data using Eq. (3). Dashed lines are the results of calculations with the help of the analytical model described in Sec. 5. The dash-dotted line marks the position of the low-temperature anomaly.

Figure 5

The absolute values of negative magnetoresistance versus the squared magnetization taken in ${\mu }_B$ per Mn ion: (a) the universal relation in PM phase $(T>T_c)$ and (b) nonuniversal behavior in the SP phase ($T<T_c$). The straight line is the best fit for $T>T_c$.

Figure 6

Static magnetization (open circles) and dynamic magnetization (filled circles) in ${\mu }_B$ per Mn ion, and $g$ factor (open triangles) in MnSi. Lines are guides to the eye.