Canonical spin glass and cluster glass behavior in the polymorphs of $\mathrm{LiFeSn}{\mathrm{O}}_4$

We report a comprehensive and comparative study of structural, static, dynamic, and nonequilibrium magnetic properties on the polymorphs of $\mathrm{LiFeSn}{\mathrm{O}}_4$. It exhibits two polymorphs: (i) orthorhombic phase (HT) stabilized at high temperature and (ii) hexagonal phase (LT) obtained at lower synthetic temperature. The HT phase crystallizes in the orthorhombic structure (space group: Pmcn) and exhibits a site disordered, nonfrustrated zig-zag network of ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Sn}}^{4+}$ ions. On the other hand, the LT phase shows a disordered frustrated kagome network of ${\mathrm{Li}}^{1+}, {\mathrm{Fe}}^{3+}$, and ${\mathrm{Sn}}^{4+}$ ions crystallizing in the hexagonal structure (space group: $P{6}_{3}mc$). The low-temperature thermo-magnetic irreversibility and the absence of heat capacity anomaly in both polymorphs indicate the absence of long-range magnetic ordering and a possible glassy state. Zero-field-cooled and field-cooled magnetic memory effect and spin relaxation measurements stipulate the spin glass nature of the polymorphs. Further, spin glass behavior is confirmed by the AC susceptibility measurements. Interestingly, these polymorphs reveal different classes of spin glass states. The site disordered HT phase exhibits a single spin-flip time ${\tau }_0\sim 3\times {10}^{-13}$ sec, indicating a canonical spin glass state. In contrast, LT phase, which is disordered and geometrically frustrated, shows the spin-flip time of ${\tau }_0\sim 9\times {10}^{-10}$ sec, suggesting a cluster spin glass state. In addition, the exchange bias effect was observed due to magnetic inhomogeneity in both polymorphs.

Figure 1

Rietveld refinement of XRD data for (a) HT phase, and (b) the LT phase. The crystal structures for (c) HT and (d) the LT phases. (e) The zig-zag Fe/Sn disordered network of the HT phase. (f) Distorted kagome lattice of the LT phase for Li/Fe/Sn disorder.

Figure 2

Temperature dependent ZFC and FC magnetization at 100 Oe for (a) HT and (b) the LT phase. ZFC and FC magnetization under different magnetic fields for (c) HT and (d) the LT phase. The de Almeida-Thouless (AT) line fitting for (e) HT and (f) the LT polymorphs.

Figure 3

Isothermal magnetization at different temperatures for (a) HT and (b) the LT polymorphs. (c) and (d) Temperature-dependent specific heat capacity with fittings shown in insets for both phases, respectively. Curie- Weiss fitting for (e) HT and (f) the LT polymorphs.

Figure 4

The magnetic relaxation at different temperatures for (a) HT and (b) the LT phases.

Figure 5

Zero-field-cooled (ZFC) memory effect at different temperatures for (a) HT and (b) the LT phase. (c) and (d) Field-cooled memory effect (FC memory) interrupted at temperatures 10 and 5 K by magnetic field 100 Oe with a time delay of 3600 sec.

Figure 6

(a) and (b) Frequency-dependent ac magnetic susceptibility and relative shift of spin freezing temperature $T_f$. (c) and (d) Power law fitting of the shift of $T_f$ with $\upsilon$. (e) and (f) VF fitting for HT and the LT polymorphs, respectively.

Figure 7

(a) and (b) Shifting of coercive field under different cooling field $\left(H_{CF}\right)$. (c) The variation of exchange bias field for HT and the LT phases.