Magnetic anisotropy and spin dynamics in the kagome magnet ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$: NMR and magnetic susceptibility study on oriented powder

${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$ hosts an undistorted kagome lattice of ${\mathrm{Fe}}^{2+}$ ($3d^6, S=2$) ions. We present results of bulk magnetization and Sn nuclear magnetic resonance (NMR) measurements on an oriented ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$ powder sample oriented in geometries parallel ($\parallel$) and perpendicular ($\perp$) to the external applied magnetic field used for orienting the powder ($B_{\text{ori}}$). The bulk susceptibility $\chi$ shows a broad peak at $T_N\sim 3$ K associated with antiferromagnetic ordering. NMR spectra indicate the presence of planar anisotropy in the kagome planes. From an analysis of the static NMR shift ($K$) and dynamic spin-lattice relaxation rate ($1/T_1$) we conclude the presence of dominant magnetic fluctuations in the kagome planes. For the $\parallel$ orientation, $K$ scales linearly with the bulk susceptibility for temperatures down to $\sim 4$ K, while in the $\perp$ orientation $K$ starts to deviate strongly below $T\sim 30$ K. We associate this deviation with the onset of spin-tilting towards the kagome planes. These correlations are also reflected in the $1/T_1$ data for the $\parallel$ orientation, which starts to decrease below $T\sim 30$ K. In this correlated regime, $T_N<T< \sim 30$ K, we discuss the formation of positive chiral spin correlations in the kagome planes.

Figure 1

(a) Crystal structure of ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$ with the kagome layer made up of ${\mathrm{FeO}}_6$ (Fe1, O1, O3) and ${\mathrm{SnO}}_6$ (Sn1, O1, O3) octahedra. Kagome layers are separated by a nonmagnetic layer of ${\mathrm{FeSn}}_6$ octahedra (Fe2, Sn2). The unit cell is shown by dashed lines. (b) Two Sn sites (Sn1, gray; Sn2, brown) in the crystal. Sn1 is located at the center of the kagome rings formed by Fe1 (blue). Sn2 are located equally above and below the kagome layer. There are six times more Sn2 sites than Sn1 sites. (c) Hyperfine pathways between Fe1 and Sn (Sn1, Sn2) via connecting O3.

Figure 2

Schematic of the expected orientation of a polycrystalline sample with respect to the applied field $B_{\text{ori}}$. For an ideal case and a hexagonal system, the alignment of $\mathit{xy}$ planes in the case of (a) global easy-plane and (b) global easy-axis anisotropy, respectively.

Figure 3

ZFC magnetic susceptibilities ($\chi$) for unoriented (black) and oriented (red, olive green) samples vs temperature measured in a field of 100 mT. Inset: Low-temperature data. The dashed black line represents the broad AFM transition at $T_N\sim 3\mathrm{K}$. The dashed gray line represents the estimated ${\chi }_{\text{unoriented}}^m$ per Eq. (5).

Figure 4

Temperature dependence of ${}^{119/117}\mathrm{Sn}$ spectra measured at 54 MHz in an unoriented powder sample. At 150 K, the green- and red-shaded regions show similar signals coming from two isotopes of ${}^{119}\mathrm{Sn}$ and ${}^{117}\mathrm{Sn}$, respectively. The dashed black and red lines represent the peak positions for the diamagnetic ${}^{119}\mathrm{Sn}$ and ${}^{117}\mathrm{Sn}$ isotopes, respectively. Filled squares show the peak positions on the right side of the individual ${}^{119/117}\mathrm{Sn}$ spectra.

Figure 5

${}^{119}\mathrm{Sn}$ spectrum measured at $B_0=3.4$ T (54 MHz) for unoriented (filled black squares) and oriented ($\parallel$, filled red triangles; $\perp$, filled olive-green diamonds) samples. Open black squares show the one-tenth intensities from the unoriented sample and confirm a high degree of orientation, $\sim 79$%, of the oriented powdered sample (see the text). Red planes on the left and right show the expected geometry of kagome planes with respect to $B_{\text{ext}}$ for the $B_{\perp }$ and $B_{\parallel }$ orientations, respectively.

Figure 6

Temperature variation of the measured spectrum at $B_0=3.4$ T (54 MHz) for (a) the $\perp$ and (b) the $\parallel$ orientations. Note that the $x$-axis scales are different for both orientations. For $B_{\parallel }$ we see well-separated intensities belonging to ${}^{119}\mathrm{Sn}$ and ${}^{117}\mathrm{Sn}$, while for the $\perp$ orientation we focus on the ${}^{119}\mathrm{Sn}$ signal. For both orientations, purple stars indicate the positions of the peak maxima of the ${}^{119}\mathrm{Sn}$ signal. In the spectrum at 120 K, for $B_{\perp }$, the vertical green shading and sharp blue line represent the expected line positions and broadening for the $\parallel$ and $\perp$ orientations, respectively. These line shapes are estimated from dipole-dipole interactions as discussed in the text.

Figure 7

Temperature dependence of the measured $\chi$ and corresponding $K$ for (a) the $\parallel$ and (b) the $\perp$ orientations. The dashed pink line in the right-hand panel shows the estimated ${\chi }_{\perp }^i$ for $\alpha =0.79$ as discussed in the text.

Figure 8

NMR shift versus macroscopic susceptibility (Clogston-Jaccario plots) for (a) the $B_{\parallel }$ and (b) the $B_{\perp }$ orientations. For $B_{\perp }$, we performed a comparison by estimating ${\chi }_{\perp }^i$ and ${\chi }_{\perp }^i$ at the respective $B_{\text{ext}}$ (2, 3.5, and 5 T) with $\alpha$ = 0.79. All dashed lines are guides for the eye. The Clogston-Jaccario plot shows a linear relationship down to 4 K for $B_{\parallel }$. For $\perp$, this linear relationship starts to deviate below $T\sim 30$ K. (c) The deviation from linear behavior is plotted as a function of the temperature and shows a tendency to increase as the temperature decreases. We ascribe this increase in the shift to the tilting of the polarized moments toward the kagome planes. These polarized moments are shown as brown arrows in the bottom panel.

Figure 9

Temperature dependence of $1/T_1$ measured at $B_0=2.64$ T (42 MHz), 3.4 T (54 MHz), and 5.28 T (84 MHz) in (a) the $\parallel$ and (b) the $\perp$ orientation, respectively. For the $\parallel$ orientation, $1/T_1$ starts to decrease at $\sim 30$ K. Insets: In both orientations for $B_0$ = 2.64 and 3.4 T a small peak is observed around 2–3 K, related to the slowing-down of spin fluctuations near the AFM transition. This peak is enhanced in the $\perp$ orientation. (c) Temperature dependence of the ratio ${(1/T_1)}_{\parallel }/{(1/T_1)}_{\perp }$. All dashed lines are guides for the eye.

Figure 10

q = (0, 0, 0) magnetic ordering with (a) positive and (b) negative chirality. $J_1, J_2$, and $J_d$ show interactions between NN and corresponding further NN interactions, respectively. (c) $\mathbf{q}=(0,1/2,0)$ magnetic structure, which is similar to the magnetic structure for ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$ proposed by Ling et al. [15], with 2/3 ordered moments and 1/3 disordered moments without AFM ordering along the $z$ axis. Magnetic atoms are shown as blue spheres and arrows represent the magnetic spin on the corresponding atom. Magnetic atoms with disordered moments are represented without a spin vector.