Complex magnetic phase diagram of metamagnetic MnPtSi

The magnetic, thermal, and transport properties as well as electronic band structure of MnPtSi are reported. MnPtSi is a metal that undergoes a ferromagnetic transition at $T_{\mathrm{C}}=340$(1) K and a spin-reorientation transition at $T_{\mathrm{N}}=326$(1) K to an antiferromagnetic phase. First-principles electronic structure calculations indicate a not-fully polarized spin state of Mn in a $d^5$ electron configuration with $J=S=3$/2, in agreement with the saturation magnetization of 3 ${\mu }_{\mathrm{B}}$ in the ordered state and the observed paramagnetic effective moment. A sizable anomalous Hall effect in the antiferromagnetic phase alongside the computational study suggests that the antiferromagnetic structure is noncollinear. Based on thermodynamic and resistivity data we construct a magnetic phase diagram. Magnetization curves $M(H$) at low temperatures reveal a metamagnetic transition of spin-flop type. The spin-flopped phase terminates at a critical point with $T_{\mathrm{cr}}\approx 300$ K and $H_{\mathrm{cr}}\approx 10$ kOe, near which a peak of the magnetocaloric entropy change is observed. Using Arrott plot analysis and magnetoresistivity data we argue that the metamagnetic transition is of a first-order type, whereas the strong field dependence of $T_{\mathrm{N}}$ and the linear relationship of the $T_{\mathrm{N}}$ with $M^2$ hint at its magnetoelastic nature.

Figure 1

(a) Magnetization per f.u. as a function of temperature in selected magnetic fields. (b) $\partial (\chi ·T$)/$\partial T$ versus $T$ estimated from the $M\left(T\right)$ data and scaled to allow visual comparisons of curves for different fields. Arrows indicate magnetic transitions.

Figure 2

(a) Isothermal magnetization curves (per f.u.) measured at selected temperatures. The inset shows $M(H$) data recorded at 2 K in pulsed magnetic fields up to 600 kOe. (b) Field dependencies of $\partial M$/$\partial H$. Arrows indicate positions of peaks in the $\partial M$/$\partial H$ versus $H$ curves that are used as estimates for $H_{\mathrm{t}}$ and $H_{\mathrm{c}}$ at different temperatures.

Figure 3

(a) Standard Arrott plot with corrected $M\left(H\right)$ curves (per f.u.) measured at selected temperatures. Points corresponding to magnetic fields $H_{\mathrm{t}}$ and $H_{\mathrm{c}}$ at different temperatures are indicated by open and filled arrows, respectively. (b) Modified Arrott plot with critical exponents $\beta =0$.25 and $\gamma =1$.33 applied to get straight lines in the high-field range.

Figure 4

High-temperature magnetic susceptibility versus temperature measured in selected magnetic fields. Inset shows ${\chi }^{-1}(T$), together with the fit using Eq. (1).

Figure 5

Specific heat of MnPtSi. Magnetic phase transitions are indicated. The brown area represents the magnetic specific heat estimated as described in the text. Insets: (a) Specific heat in selected external magnetic fields. The values of $H$ (kOe) are given above the arrows indicating the transition temperatures; (b) $C_{\mathrm{p}}/T$ plotted versus $T^2$. The red dashed line represents the fit to the experimental data using Eq. (2); (c) Magnetic entropy.

Figure 6

Resistivity of MnPtSi measured on cooling in $H=0$ (black dots) and in $H=90$ kOe (red dots), with fits to $\rho \left(T\right)={\rho }_0+A{T}^2$ in the temperature range of 25–60 K (dashed lines). Insets: (a) Exponents obtained from fits of $\rho (T$) in different magnetic fields for $T<20$ K using a power law; (b) $\rho (T$) near the magnetic transitions measured in $H=0$ and in selected fields. The curves were shifted along the vertical axis to enable their comparison. Transition temperatures $T_{\mathrm{N}}$ and $T_{\mathrm{C}}$ are indicated by filled arrows. Open arrows show the directions of measurements.

Figure 7

Magnetoresistance ratio as a function of magnetic field at selected temperatures. The $\mathrm{MR}(H$) curves were shifted along the vertical axis to enable their visual comparison. Arrows indicate phase boundaries $H_{\mathrm{t}}$ and $H_{\mathrm{c}}$ estimated from the magnetization data (Sec. 3a).

Figure 8

Hall resistivity of MnPtSi as a function of magnetic field at selected temperatures. Dashed blue lines represent fits using Eq. (3) to the measured data (black dots). The ordinary ($R_0{\mu }_{0}H$) and anomalous ($R_{\mathrm{S}}{\mu }_{0}M$) contributions are shown as black dashed and red solid lines, respectively. The ${\rho }_{xy}(H$) and $R_{\mathrm{S}}{\mu }_{0}M$) curves were shifted along the vertical axis to enable their visual comparison. Arrows indicate the AFM-SF phase boundary estimated from the magnetization data (Sec. 3a). Yellow areas visualize the additional contribution attributed to THE.

Figure 9

Crystal structure of MnPtSi. Red, black, and green balls represent Mn, Pt, and Si, respectively. Different couplings between magnetic moments of neighboring Mn species along $d_1$, $d_2$, $d_3$, and $d_4$ are indicated.

Figure 10

The total and atomic resolved DOSs for MnPtSi calculated assuming the FM state. The majority (minority) spin is plotted upward (downward).

Figure 11

Magnetic phase diagram for MnPtSi. Black dot denotes the critical point at which the SF phase terminates. Dashed lines separating different magnetic phases are guided to the eye.

Figure 12

(a) Magnetocaloric entropy change calculated from the $M(T$) curves and the $d{T}_{\mathrm{N}}$/$dH$ data using Clausius-Clapeyron relation. (b) $M^2$ versus $T_{\mathrm{N}}$ plot obtained based on the $M(T$) curves. Dashed lines are guides to the eye.