Coexistence of ferromagnetism and unconventional spin-glass freezing in the site-disordered kagome ferrite $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$

Single-crystal x-ray diffraction refinements indicate $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ crystallizes in the hexagonal $R$-type ferrite structure with noncentrosymmetric space group $P{6}_{3}mc$ and lattice parameters $a=5.9541\left(2\right)\AA , c=13.5761\left(5\right)\AA , Z=2$ ($R\left(F\right)=0.034$). Octahedrally coordinated $2a$ [$M$(1) and $M$(1a)] and $6c$ sites $\left[M\right(2\left)\right]$ have random, mixed occupation by Sn and Fe; whereas the tetrahedrally coordinated $2b$ sites [Fe(3) and Fe(3a)] are exclusively occupied by Fe, whose displacement from the ideal position with trigonal-bipyramidal coordination causes the loss of inversion symmetry. Our dc and ac magnetization data indicate $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystals undergo a ferro- or ferri-magnetic transition below a temperature $T_C=630\mathrm{K}$ with very low coercive fields ${\mu }_{\mathrm{o}}{H}_{c\perp }=0.27\mathrm{Oe}$ and ${\mu }_{\mathrm{o}}{H}_{c\parallel }=1.5\mathrm{Oe}$ at 300 K, for applied field perpendicular and parallel to the $\mathit{c}$ axis, respectively. The value for $T_C$ is exceptionally high, and the coercive fields exceptionally low, among the known R-type ferrites. Time-dependent dc magnetization and frequency-dependent ac magnetization data indicate the onset of short-range, spin-glass freezing below $T_f=35.8\mathrm{K}$, which results from crystallographic disorder of magnetic $\mathrm{F}{\mathrm{e}}^{3+}$ and nonmagnetic $\mathrm{S}{\mathrm{n}}^{4+}$ ions on a frustrated Kagome sublattice. Anomalous ac susceptibility and thermomagnetic relaxation behavior in the short-range-ordered state differs from that of conventional spin glasses. Optical measurements in the ultraviolet to visible frequency range in a diffuse reflectance geometry indicate an overall optical band gap of 0.8 eV, consistent with observed semiconducting properties.

Figure 1

Crystal structure of $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$. The unit cell shown is extended by the oxide coordination of the metal atoms. Dark ellipsoids represent Sr. Small, dark ellipsoids represent mixed occupation by Fe/Sn in octahedral coordination, or Fe in tetrahedral coordination. Light spheres represent O. Atoms are depicted with displacement ellipsoids with $90\%$ probability.

Figure 2

Section of the crystal structure of $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$. Sr is coordinated by twelve oxygen atoms that define a nearly ideal anti-cuboctahedrom. Face-sharing octahedral sites have mixed occupation by Sn/Fe atoms with different ratios ($M\left(1\right)$ by $86\%$ Sn, $M$(1a) by $54\%$ Sn). Face-sharing tetrahedra are occupied to a different extent: Fe(3) to $19\%$, Fe(3a) to $81\%$, which corresponds to a shift of the Fe(3a) atoms by about 0.2 Å off the ideal center position along [001] in the trigonal bipyramidal void. Atoms are depicted with displacement ellipsoids with $90\%$ probability.

Figure 3

Temperature dependence of the FC dc magnetic susceptibility $\chi \left(T\right)$ of a $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystal for $\mathit{H}\perp \mathit{c}$ and $\mathit{H}\parallel \mathit{c}$ in applied magnetic field ${\mu }_{\mathrm{o}}H=0.1\mathrm{T}$. Arrows designate the high-temperature onset of long-range magnetic order, and the much lower onset temperature of spin-glass order at $T_f=35.8\mathrm{K}$.

Figure 4

Coercive field $H_{C\perp }$ for dc field applied perpendicular to the c-axis, versus temperature $T$ for a $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystal. The dashed line is a fit to Eq. (1) (see text for details) using parameters $H_{C\mathrm{O}}=5.06\mathrm{Oe}, T_1=4.60\mathrm{K}, H_{C1}=391\mathrm{Oe}, T_2=37.9\mathrm{K}$, and $H_{C2}=58.1\mathrm{Oe}$. Inset: The low-temperature dependence of the ZFC and FC dc magnetic moment of a $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystal for applied field $H$ parallel and perpendicular to the c-axis. Arrow designates the spin-glass transition temperature $T_f=35.8\mathrm{K}$.

Figure 5

Magnetic moment $m$ vs. applied field $\mathit{H}\perp \mathit{c}$ for temperatures $T=300\mathrm{K}$ (solid line) and $T=4.5\mathrm{K}$ (dashed lines) for a $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystal. Note the lack of saturation for $T=4.5\mathrm{K}$, and the very small hysteresis for dc applied field swept back and forth between $\pm 5\mathrm{T}$. Note also the very similar behavior of these data and those of Fig. 6 for $\mathit{H}\parallel \mathit{c}$.

Figure 6

Magnetic moment $m$ vs. applied field $\mathit{H}\parallel \mathit{c}$ for temperatures $T=300\mathrm{K}$ (solid line) and $T=4.5\mathrm{K}$ (dashed lines) for a $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystal. Note the lack of saturation for $T=4.5\mathrm{K}$, and the very small hysteresis for dc applied field swept back and forth between $\pm 5\mathrm{T}$. Note also the very similar behavior of these data and those of Fig. 5 for $\mathit{H}\perp \mathit{c}$.

Figure 7

Temperature and frequency dependences of the (a) real, ${\chi }^{\prime }$, and (b) imaginary, ${\chi }^{\prime \prime }$, parts of the ac susceptibility of a $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystal for applied ac magnetic field $\mathit{h}\perp \mathit{c}$, with RMS magnitude 5.0 Oe. The vertical dashed line in (a) indicates the frequency-independent temperature $T_k$ of a kink in ${\chi }^{\prime }$, which corresponds well with the proposed freezing temperature, $T_f=35.8\mathrm{K}$ (see Fig. 3).

Figure 8

Dependence of the anomaly temperatures $T_k, T_p$, and $T_i$ on the ac measuring frequency $f$ from the ac moment data of Fig. 7.

Figure 9

Logarithm (base-10) of the measuring frequency $logf$ versus the inverse of the peak temperature in ${\chi }^{\prime \prime }\left(T\right), 1/T_p$ [see Fig. 7], for a $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystal. The solid line is a fit of the data to the Arrhenius law [Eq. (3)] with $E_{\mathrm{a}}/k_{\mathrm{B}}=138\mathrm{K}$ and $log\left(f_0\right)=6.7134$, corresponding to $f_0=5.169\times {10}^6\mathrm{Hz}$. Note the appreciable deviations from the fit below 20 K.

Figure 10

Frequency dependence of the imaginary part of the ac susceptibility, ${\chi }^{\prime \prime }\left(f\right)$, at different temperatures (see online for color key).

Figure 11

Time dependence of the magnetic moment $m$ of a $\mathrm{SrS}{\mathrm{n}}_2\mathrm{F}{\mathrm{e}}_4{\mathrm{O}}_{11}$ single crystal at $T=25\mathrm{K}$ (see text for experimental protocol). Dotted line corresponds to power law fit [Eq. (6)] with parameters: $M_0=6.8\times {10}^{-3}\mathrm{emu}/\mathrm{mol}, \gamma =0.18$. Dashed line corresponds to stretched exponential fit [Eq. (4)] with parameters: $M_0=2.6\times {10}^{-2}\mathrm{emu}/\mathrm{mol}, \tau =255\mathrm{s}, n=0.1$. Solid line corresponds to Eq. (7) with parameters $M_0=6.8\times {10}^{-3}\mathrm{emu}/\mathrm{mol}, \gamma =0.18, M_1=2.6\times {10}^{-2}\mathrm{emu}/\mathrm{mol}, \tau =255\mathrm{s}$, and $n=0.1$.

Figure 12

Plot of the Kubelka-Munk function $(\alpha /\mathrm{S})$ against energy. The absorption edge energies are derived from the individual intersection point of the base lines drawn along the energy axis and the extrapolated lines of the linear parts of the threshold.