Magnetic excitations in the geometrically frustrated pyrochlore antiferromagnet ${\text{Gd}}_2{\text{Sn}}_2{\text{O}}_7$ studied by electron spin resonance

The spin dynamics in the geometrically frustrated pyrochlore antiferromagnet ${\text{Gd}}_2{\text{Sn}}_2{\text{O}}_7$ is studied by means of the electron spin resonance. In the ordered phase $\left(T_N=1\text{K}\right)$, we have detected three gapped resonance modes. Their values agree well with the developed spin-wave theory which takes into account the Heisenberg nearest-neighbor exchange, the single-ion anisotropy, and the long-range dipolar interactions. The theory also predicts a fourth lowest-frequency gap, which lies beyond the experimental range of frequencies, but determines the exponential decrease in the specific heat at low temperature.

Figure 1

(Color online) Thermal variation in the specific heat divided by temperature in ${\text{Gd}}_2{\text{Sn}}_2{\text{O}}_7$ measured with different heating rates (● and ○ are faster and slower scans, respectively); ◻ and △ are previous data from Refs. 4, 11; the dashed line is a linear approximation to the high-temperature part of the data, the fit by a solid line is described in the text, and the arrow marks the low-temperature limit of data reliability.

Figure 2

Evolution of the magnetic-resonance absorption spectra in a powder sample of ${\text{Gd}}_2{\text{Sn}}_2{\text{O}}_7$ on cooling from above the ordering transition to $T=0.45\text{K}$ recorded in a perpendicular polarization of the microwave field with respect to the external field ${\mathbf{h}}_{\text{mw}}\perp \mathbf{H}$ (left panel) and in a tilted polarization (right panel); the recorded lines are shifted upwards for clarity.

Figure 3

(Color online) The magnetic-resonance absorption spectra in a powder sample of ${\text{Gd}}_2{\text{Sn}}_2{\text{O}}_7$ recorded at $T=0.45\text{K}$ for various frequencies with ${\mathbf{h}}_{\text{mw}}\perp \mathbf{H}$ (upper panel) and in a tilted direction of ${\mathbf{h}}_{\text{mw}}$ (lower panel); dashed lines are guide for the eyes in tracing the field evolution of different resonance lines labeled by letters A–E; the inset in the lower panel expands the in-frame part of the absorption record at $\nu =62.0\text{GHz}$ including spectral lines D and E. The second-order transition at $H_s=53\text{kOe}$ is marked by a vertical line.

Figure 4

(Color online) Frequency-field diagram of the resonance spectrum observed on a powder sample of ${\text{Gd}}_2{\text{Sn}}_2{\text{O}}_7$ at $T=0.45\text{K}$; ○ and $\oplus$ correspond to the modes excited at ${\mathbf{h}}_{\text{mw}}\perp \mathbf{H}$ and ${\mathbf{h}}_{\text{mw}}\angle \mathbf{H}$, respectively; ◼ mark the gap values calculated by the SWT; the solid lines represent the solution of Eq. (20) for a doublet mode with $H\parallel \left[001\right]$, the dashed lines are linear fits to the two components of spectral line E with $g=2$, and the dash-dotted line corresponds to a $g=2$ paramagnet. The transition to a spin-polarized phase at $H_s=53.0\text{kOe}$ is marked by a vertical line. The unreachable low-frequency range $\nu <25\text{GHz}$ is shaded in gray.

Figure 5

(Color online) Absorption spectra recorded at nearly the same frequencies in ${\text{Gd}}_2{\text{Sn}}_2{\text{O}}_7$ powder sample (squares) and in ${\text{Gd}}_2{\text{Ti}}_2{\text{O}}_7$ single crystal at $H\parallel \left[111\right]$ (circles); the arrow marks the transition in ${\text{Gd}}_2{\text{Ti}}_2{\text{O}}_7$ at $H=H_{c1}\simeq 30\text{kOe}$.