Kinetic-arrest-induced phase coexistence and metastability in ${\left(\mathrm{Mn},\mathrm{Fe}\right)}_2\left(\mathrm{P},\mathrm{Si}\right)$

Neutron diffraction, Mössbauer spectroscopy, magnetometry, and in-field x-ray diffraction are employed to investigate the magnetoelastic phase transition in hexagonal ${\left(\mathrm{Mn},\mathrm{Fe}\right)}_2\left(\mathrm{P},\mathrm{Si}\right)$ compounds. ${\left(\mathrm{Mn},\mathrm{Fe}\right)}_2\left(\mathrm{P},\mathrm{Si}\right)$ compounds undergo for certain compositions a second-order paramagnetic (PM) to a spin-density-wave (SDW) phase transition before further transforming into a ferromagnetic (FM) phase via a first-order phase transition. The SDW-FM transition can be kinetically arrested, causing the coexistence of FM and untransformed SDW phases at low temperatures. Our in-field x-ray diffraction and magnetic relaxation measurements clearly reveal the metastability of the untransformed SDW phase. This unusual magnetic configuration originates from the strong magnetoelastic coupling and the mixed magnetism in hexagonal ${\left(\mathrm{Mn},\mathrm{Fe}\right)}_2\left(\mathrm{P},\mathrm{Si}\right)$ compounds.

Figure 1

$M-T$ and $M-H$ plots for S0 (a) and (b) and S1 (c) and (d).

Figure 2

$M-T$ and $M-H$ plots for the as-prepared S2 (a) and (b), and S3 (c) and (d).

Figure 3

(a) Contour plot of the neutron diffraction patterns collected at WISH (detector bank 5 with $\langle 2\theta \rangle \approx 152.{83}^{\circ }$) for S1. The intensity is on a logarithmic scale. (b) The (0.355 0 0) magnetic reflection of the SDW phase at different temperatures recorded at WISH (detector bank 1 with $\langle 2\theta \rangle \approx 27.{08}^{\circ }$).

Figure 4

(a) Fitted powder neutron diffraction pattern for S1 collected at 1.5 K at WISH (detector bank 3 with $\langle 2\theta \rangle \approx {90}^{\circ }$). Vertical lines indicate the peak positions (from top to bottom) for the nuclear structure of the SDW phase, magnetic structure of the SDW phase, nuclear structure of the FM phase, magnetic structure of the FM phase, and the impurity ${\left(\mathrm{Mn},\mathrm{Fe}\right)}_3\mathrm{Si}$ phase, respectively. (b) Schematic representation ($4\times 4$) of magnetic configuration in the basal $ab$ plane for the SDW phase. ${\mathit{a}}^{*}$ and ${\mathit{b}}^{*}$ are the primitive vectors of the reciprocal lattice. The propagation vector $\mathit{k}$ is along ${\mathit{a}}^{*}$. Both the Mn and Fe moments lie within the basal $ab$ plane. The Mn moment is aligned parallel to $\mathit{k}$ and the Fe moment is perpendicular to $\mathit{k}$.

Figure 5

(a) Peak width of the (0.355 0 0) magnetic reflection. (b) Temperature-dependent inverse susceptibility. (c) Weight fraction of the FM phase and integrated intensity of the (0.355 0 0) magnetic reflection at different temperatures. (d) Temperature dependence of the normalized intensity of the (0.355 0 0) magnetic reflection.

Figure 6

Lattice parameters as a function of temperature derived from neutron diffraction for S1.

Figure 7

Thermal evolution of interatomic distances extracted from neutron diffraction for S1.

Figure 8

Mössbauer spectra collected at 300 K for the as-prepared S0 (a), S1 (b), S2 (c), and S3 (d). The black and red solid lines are individual binomial PM components and their sum, respectively.

Figure 9

Mössbauer spectra obtained at 4.2 K for the as-prepared S0 (a), S1 (b), S2 (c), and S3 (d). The black, blue, and red lines are individual binomial FM components, the SDW component, and their sum, respectively.

Figure 10

XRD patterns measured at 300 and 10 K in different magnetic field for the as-prepared S0 (a), S1 (b) and (c), and S3 (d) and (e).

Figure 11

(a) Isothermal $M-H$ curves for the as-prepared S1 cooled in different magnetic fields. Open symbols indicate the magnetization process, and the solid line shows the demagnetization process. The demagnetization curve is the same for all four conditions. (b) Derived $f_{\text{FM}}-H$ at 5 K after cooling in different magnetic fields.

Figure 12

(a) Temperature-dependent magnetization of S1 measured during warming after being cooled in different magnetic fields. (b) Magnetization versus time measured at 5 K after zero-field cooling. The temperature dependence of the characteristic relaxation time is shown in the inset.