Magnetic interactions in the tripod kagome antiferromagnet ${\mathrm{Mg}}_2{\mathrm{Gd}}_3{\mathrm{Sb}}_3{\mathrm{O}}_{14}$ probed by static magnetometry and high-field ESR spectroscopy

We report an experimental study of the static magnetization $M(H,T)$ and high-field electron spin resonance (ESR) of polycrystalline ${\text{Mg}}_2{\text{Gd}}_3{\text{Sb}}_3{\text{O}}_{14}$, a representative member of the newly discovered class of the so-called tripod kagome antiferromagnets where the isotropic ${\mathrm{Gd}}^{3+}$ spins $(S=7/2)$ form a two-dimensional kagome spin-frustrated lattice. It follows from the analysis of the low-$TM\left(H\right)$ curves that the ${\mathrm{Gd}}^{3+}$ spins are coupled by a small isotropic antiferromagnetic (AFM) exchange interaction, $\left|J\right|\approx 0.3$ K. The $M(H,T)$ dependences measured down to 0.5 K evidence a long-range AFM order at $T_N=1.7\mathrm{K}$ and its rapid suppression at higher fields, $\ge 4$ T. ESR spectra measured in fields up to 15 T are analyzed considering possible effects of demagnetizing fields, single-ion anisotropy, and spin-spin correlations. While the demagnetization effects due to a large sample magnetization in high fields and its shape anisotropy become relevant at low temperatures, the broadening of the ESR line commencing already at $T\lesssim 30\mathrm{K}$ may indicate the onset of the spin-spin correlations far above the ordering temperature due to the geometrical spin frustration in this compound.

Figure 1

(a) Side view of the principal ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Gd}}^{3+}$ ions which constitute the pyrochlore lattice. (b) View along the $c$ direction of ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Gd}}^{3+}$ ions, with the kagome plane shown as red triangles. (c) Complete unit cell of ${\text{Mg}}_2{\text{Gd}}_3{\text{Sb}}_3{\text{O}}_{14}$.

Figure 2

(a) Field dependence of the magnetization at $T=2\mathrm{K}$ (black squares), its derivative $dM/dH$ (solid line), the Brillouin function corresponding to noninteracting ${\mathrm{Gd}}^{3+}$ ions with $J=S=7/2$ (dashed line, scaled to the observed saturation moment), and the modeled $M\left(H\right)$ dependence (green stars), which takes into account dipolar and exchange interactions between the ${\mathrm{Gd}}^{3+}$ spins (for details see the text). (b) Temperature dependence of the static susceptibility $\chi \left(T\right)$ (black squares) and $1/\chi \left(T\right)$ (purple circles) at a field of ${\mu }_{0}H=20\mathrm{mT}$ together with the Curie-Weiss fit (dashed line). The AFM transition at $T_{\mathrm{N}}=1.7\mathrm{K}$ is indicated by the dashed vertical line. Inset: The derivative of $1/\chi \left(T\right)$ (symbols). The solid horizontal line corresponds to the derivative of the high-temperature Curie-Weiss fit. The shaded rectangle centered around $T_{\mathrm{a}}\approx 15\pm 5\mathrm{K}$ indicates the region where the $\chi \left(T\right)$ dependence begins to gradually deviate from the Curie-Weiss law.

Figure 3

Zero-field-cooled (ZFC; red squares) vs field-cooled (FC; blue circles) susceptibility at low temperatures measured at a field ${\mu }_{0}H=20\mathrm{mT}$.

Figure 4

Temperature dependence of the static susceptibility $\chi \left(T\right)$ in the low-$T$ range at different applied magnetic fields. Curves are shifted with respect to each other in order to improve visibility. The dashed gray line marks the position of the broad maximum (called $T^{\max }$ in the text) of the $\chi \left(T\right)$ curves. The arrow shows the sharp peak on top of the broad maximum.

Figure 5

(a) Temperature dependence of the ESR spectrum of ${\text{Mg}}_2{\text{Gd}}_3{\text{Sb}}_3{\text{O}}_{14}$ at $\nu =222\mathrm{GHz}$. The dashed vertical line indicates the high-temperature resonance field. Note the development of the shoulder on the high-field side of the spectrum with decreasing $T$. Dashed gray lines show the temperature trend of the main peak and the shoulder; (b) frequency dependence of the ESR spectrum at $T=3\mathrm{K}$. Arrows indicate the shoulder in the spectra. Inset: Symbols denote the microwave frequency $\nu$ vs the position of the main peak $H_{\mathrm{res}}$. The solid line shows the fit of the data to the resonance condition $h\nu =g{\mu }_{\mathrm{B}}{H}_{\mathrm{res}}$ yielding the $g$ factor $g=1.987$.

Figure 6

Calculated (black line) and observed (red circles) XRD patterns and the difference thereof (green line) of the Rietveld refinement for ${\text{Mg}}_2{\text{Gd}}_3{\text{Sb}}_3{\text{O}}_{14}$ ($\lambda =1.5460$ Å, Bragg R factor = 5.61%; Rf factor = 7.17%; Bragg R factor = $\mathrm{\Sigma }|I_{k\text{−}\mathrm{obs}}-I_{k\text{−}\mathrm{calc}}|/\mathrm{\Sigma }|I_{k\text{−}\mathrm{obs}}|$; Rf factor = ${[(N-P)/\mathrm{\Sigma }{w}_i{y}_{i\text{−}\mathrm{obs}}^2]}^{1/2}$). Blue lines indicate the Bragg reflections. Inset: An optical image of a typical white polycrystalline sample of ${\text{Mg}}_2{\text{Gd}}_3{\text{Sb}}_3{\text{O}}_{14}$.

Figure 7

$M\left(H\right)$ at different temperatures with the exchange parameter $a_{\text{ex}}$ kept fixed. Red squares represent experimental data; blue circles, model data.

Figure 8

Simulated field dependence of the magnetization with only dipolar interactions in the $x$, $y$, and $z$ directions together with the experimental $M\left(H\right)$ curve and the Brillouin function of noninteracting spins $S=7/2$, at $T=2\mathrm{K}$.

Figure 9

Results of the demagnetization model [14, 15] for the ESR powder spectra. The solid black line shows the experimental data; the dashed red and dash-dotted pink lines, the model with a Lorentzian line as the basic lineshape; and the dotted blue line, the model with a Gaussian line as the basic lineshape. The dashed red line represents the Lorentzian with optimal parameters.

Figure 10

Simulated Gaussian spectra for different mixing angles $\varphi =0–60{}^{\circ }$ in Eq. (A3).

Figure 11

Sketch of the field geometries. The internal field ${\mathit{H}}_{\text{int}}$ makes an angle $\theta$ with the external field ${\mathit{H}}_{\text{ext}}$, resulting in an effective total field ${\mathit{H}}_{\text{tot}}$ according to Eq. (2).

Figure 12

(a) Integrals of the recorded absorption derivative curves $dP\left(u\right)/dH$ at 10 GHz (X band) and different temperatures. (b) The $g$-factor fit at $T=40\mathrm{K}$.

Figure 13

Exemplary fitting plots of selected ESR spectra for the internal field model (red lines) in comparison with the experimental data (black symbols) for $\nu =109\mathrm{GHz}$ at $T=3\mathrm{K}$ and $\nu =222\mathrm{GHz}$ at $T=5$ and 40 K. For details see the text.