Muon-spin relaxation and heat capacity measurements on the magnetoelectric and multiferroic pyroxenes ${\text{LiFeSi}}_2{\text{O}}_6$ and ${\text{NaFeSi}}_2{\text{O}}_6$

We present the results of muon-spin relaxation and heat capacity measurements on ${\text{LiFeSi}}_2{\text{O}}_6$ and ${\text{NaFeSi}}_2{\text{O}}_6$. In synthetic samples of both compounds we see a single muon oscillation frequency consistent with commensurate magnetic structures below $T_{\text{N}}$. In contrast, for a specimen of naturally occurring ${\text{NaFeSi}}_2{\text{O}}_6$, in which multiferroicity has been observed, a rapid Gaussian depolarization of the muon polarization is observed instead, showing that the magnetic structure in this case is more complex. Heat capacity measurements reproduce the phase diagrams previously derived from other techniques and demonstrate that the main contribution to the magnetic entropy is associated with the buildup of correlations in the quasi-one-dimensional ${\text{Fe}}^{3+}$ chains.

Figure 1

(Color online) Structure of ${\text{LiFeSi}}_2{\text{O}}_6$ showing the ${\text{Fe}}^{3+}$ chains running along the $c$ axis linked by ${\text{SiO}}_4$ tetrahedra. The structural data come from Ref. 16.

Figure 2

(Color online) Heat capacity measurements on (a) ${\text{LiFeSi}}_2{\text{O}}_6$, (b) synthetic ${\text{NaFeSi}}_2{\text{O}}_6$, and (c) natural ${\text{NaFeSi}}_2{\text{O}}_6$. The lines in the main panels show the fitted lattice terms described in the text and the insets show the variation with applied magnetic field close to the magnetic ordering transitions described in the text.

Figure 3

(Color online) Muon asymmetry data above and below the magnetic transitions for (a) ${\text{LiFeSi}}_2{\text{O}}_6$, (b) synthetic ${\text{NaFeSi}}_2{\text{O}}_6$, and (c) natural ${\text{NaFeSi}}_2{\text{O}}_6$. Below $T_{\text{N}}$ we fit with Eq. (1) for (a) and (b), and Eq. (2) for (c). Above $T_{\text{N}}$ the relaxation is exponential. The widths of the time bins in the asymmetry histograms have been increased for clarity. For the synthetic ${\text{NaFeSi}}_2{\text{O}}_6$, measurements were done with the initial muon spin rotated differently relative to the detectors, leading to the lower asymmetry values.

Figure 4

(Color online) (a) Muon oscillation frequencies, $\nu$ [Eq. (1)], for ${\text{LiFeSi}}_2{\text{O}}_6$ and the synthetic sample of ${\text{NaFeSi}}_2{\text{O}}_6$ with fits described in the text. (Inset) The oscillation frequencies plotted against reduced temperature, $t=\left(T_{\text{N}}-T\right)/T_{\text{N}}$, showing the similarity of the trends approaching $T_{\text{N}}$. (b) The Gaussian relaxation rate, $\sigma$ [Eq. (2)], for the natural ${\text{NaFeSi}}_2{\text{O}}_6$ and the linewidth ${\lambda }_1$ for the synthetic ${\text{NaFeSi}}_2{\text{O}}_6$.