Low-field anomalous magnetic phase in the kagome-lattice shandite $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$

The magnetization process of single crystals of the metallic kagome ferromagnet $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ was carefully measured via magnetization and ac susceptibility. Field-dependent anomalous transitions observed in low fields indicate the presence of an unconventional magnetic phase just below the Curie temperature, $T_{\mathrm{C}}$. The magnetic phase diagrams in low magnetic fields along different crystallographic directions were determined for the first time. The magnetic relaxation measurements at various frequencies covering five orders of magnitude from 0.01 to 1000 Hz indicate markedly slow spin dynamics only in the anomalous phase with characteristic relaxation times longer than 10 s.

Figure 1

Crystal structure projection in (001) plane, drawn using VESTA software [43], shows a Co kagome sublattice in $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$.

Figure 2

Typical temperature dependences of ZFC (open) and FC (closed) magnetizations, $M(T,H)$, of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ measured at the indicated low magnetic fields applied (a) along and (b) perpendicular to the $c$ axis. Vertical arrows indicate the transition temperature, $T_{\mathrm{A}}$, and the broad dip (see text). The inset of (b) shows a magnification of the ZFC $M_{ab}\left(T\right)$ measured at very low fields.

Figure 3

Temperature dependences of ZFC ${\chi }^{\prime }$ (at $f=1\mathrm{Hz}$, on left axis) and $M$ (on right axis) of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ at 150 Oe applied along the $c$ axis. Vertical dotted lines indicate $T_{\mathrm{A}}$ (see text) and $T_{\mathrm{C}}$.

Figure 4

Thermal variation of ZFC and FC ${\chi }^{\prime }$ and ${\chi }^{\prime \prime }$ of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ measured at different frequencies from 1 to 1000 Hz and for magnetic fields of (a, b) 0 Oe, (c, d) 150 Oe, and (e, f) 600 Oe applied along the $c$ axis. Arrows indicate $T_{\mathrm{C}}$ and $T_{\mathrm{A}}$ (see text). For clarity, the data with frequencies of 1, 10, and 100 Hz have been shifted vertically with respect to the baseline by multiplying their data by the numbers indicated as in (a) and (b).

Figure 5

Magnetic $H-T$ phase diagrams of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ for fields applied (a) along and (b) perpendicular to the $c$ axis. Dashed and solid curves are a guide for the eye.

Figure 6

Frequency dependences of ZFC-${\chi }^{\prime }$ and ${\chi }^{\prime \prime }$ of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ at (a, b) $T=50-160\mathrm{K}$ and at (c, d) $T=170-172\mathrm{K}$ (close to $T_{\mathrm{C}}$), under a magnetic field of 150 Oe applied along the $c$ axis. (e, f) ZFC-${\chi }^{\prime }$ and ${\chi }^{\prime \prime }$ at $T_{\mathrm{C}}\approx 172\mathrm{K}$ for different fields up to 250 Oe applied along the $c$ axis. Solid lines in (c)–(f) represent fittings to Eqs. (2) and (3). Insets of (d) and (f) show the fitting parameters, $\alpha$ and $f_0$, as functions of temperature at $H=150\mathrm{Oe}$ and as functions of applied field at $T=172\mathrm{K}$, respectively.