Short-range magnetic correlations and spin dynamics in the paramagnetic regime of $(\text{Mn},\text{Fe}){}_2(\text{P},\text{Si})$

The spatial and temporal correlations of magnetic moments in the paramagnetic regime of ${\left(\mathrm{Mn},\mathrm{Fe}\right)}_2\left(\mathrm{P},\mathrm{Si}\right)$ have been investigated by means of polarized neutron diffraction and muon-spin relaxation techniques. Short-range magnetic correlations are present at temperatures far above the ferromagnetic transition temperature $\left(T_C\right)$. This leads to deviations of paramagnetic susceptibility from Curie-Weiss behavior. These short-range magnetic correlations extend in space, slow down with decreasing temperature, and finally develop into long-range magnetic order at $T_C$.

Figure 1

Schematic representation of the crystal and magnetic structure for ${\left(\mathrm{Mn},\mathrm{Fe}\right)}_2\left(\mathrm{P},\mathrm{Si}\right)$.

Figure 2

Bulk magnetic susceptibility (unitless) for ${\mathrm{Mn}}_{1.00}{\mathrm{Fe}}_{0.95}{\mathrm{P}}_{0.67}{\mathrm{Si}}_{0.33}$ (a) and ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$ (b). The corresponding inverse susceptibility is shown in (c) and (d), respectively.

Figure 3

Contour plots of the x-ray diffraction patterns measured on cooling for ${\mathrm{Mn}}_{1.00}{\mathrm{Fe}}_{0.95}{\mathrm{P}}_{0.67}{\mathrm{Si}}_{0.33}$ (a) and ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$ (b). The color bar on the right represents the normalized intensity scale.

Figure 4

Lattice parameters derived from x-ray diffraction for ${\mathrm{Mn}}_{1.00}{\mathrm{Fe}}_{0.95}{\mathrm{P}}_{0.67}{\mathrm{Si}}_{0.33}$ (a),(b) and ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$ (c),(d).

Figure 5

Magnetic and nuclear scattering cross section for ${\mathrm{Mn}}_{1.00}{\mathrm{Fe}}_{0.95}{\mathrm{P}}_{0.67}{\mathrm{Si}}_{0.33}$ measured at 500 K (a) and 175 K (b).

Figure 6

Magnetic scattering cross section as a function of temperature for ${\mathrm{Mn}}_{1.00}{\mathrm{Fe}}_{0.95}{\mathrm{P}}_{0.67}{\mathrm{Si}}_{0.33}$.

Figure 7

Magnetic and nuclear scattering cross section for ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$ measured at 500 K (a) and 180 K (b).

Figure 8

Magnetic scattering cross section (a) and the derived magnetic correlation length (b) as a function of temperature for ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$. The solid lines in (a) represent fits to the data.

Figure 9

Zero-field $\mu \mathrm{SR}$ spectra for ${\mathrm{Mn}}_{1.00}{\mathrm{Fe}}_{0.95}{\mathrm{P}}_{0.67}{\mathrm{Si}}_{0.33}$. The solid lines represent fits to the data.

Figure 10

Temperature dependence of initial asymmetry $A_0$ (a) and muon-spin relaxation rate $\lambda$ (b) for ${\mathrm{Mn}}_{1.00}{\mathrm{Fe}}_{0.95}{\mathrm{P}}_{0.67}{\mathrm{Si}}_{0.33}$.

Figure 11

Zero-field $\mu \mathrm{SR}$ spectra for ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$. The solid lines represent fits to the data.

Figure 12

Temperature dependence of initial asymmetry $A_0$ (a) and muon-spin relaxation rate $\lambda$ (b) for ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$.

Figure 13

Temperature dependence of the magnetic relaxation rate for ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$.

Figure 14

Relation between the correlation time and correlation length for ${\mathrm{Mn}}_{1.70}{\mathrm{Fe}}_{0.25}{\mathrm{P}}_{0.50}{\mathrm{Si}}_{0.50}$. The solid line represents a fit to the data.