Evidence for Gapped Spin-Wave Excitations in the Frustrated ${\mathrm{Gd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ Pyrochlore Antiferromagnet from Low-Temperature Specific Heat Measurements

We have measured the low-temperature specific heat of the geometrically frustrated pyrochlore Heisenberg antiferromagnet ${\mathrm{Gd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ in zero magnetic field. The specific heat is found to drop exponentially below approximately 350 mK. This provides evidence for a gapped spin-wave spectrum due to an anisotropy resulting from single-ion effects and long-range dipolar interactions. The data are well fitted by linear spin-wave theory, ruling out unconventional low-energy magnetic excitations in this system, and allowing a determination of the pertinent exchange interactions in this material.

Figure 1

Specific heat of ${\mathrm{Gd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ as a function of temperature from this work (blue circles) between 115 and 800 mK. Previously measured data at higher temperatures (green diamonds) [5], the $T^2$ power law previously proposed (dotted red line) and a $T^3$ power law (dashed blue line) are also plotted. The upturn seen below 150 mK results from the nuclear electric quadrupole interaction (solid line).

Figure 2

$\log (C{T}^2)$ plotted versus $1/T$. The low-temperature limit of the magnetic specific heat is parametrized by a phenomenological form $C_m\propto (1/T^2)e^{-\Delta /T}$, which appears as a straight line. The specific heat is plotted before (squares) and after (circles) subtraction of a nuclear contribution. The linear fit is performed between the lowest temperature measured and 250 mK and gives $\Delta =1.40\pm 0.01\mathrm{K}$.

Figure 3

Fit predicted by linear spin-wave theory to $C_m(T)$ with resulting values of the exchange interactions. The best fit gives $J_2/|J_1|=0.01$ and $J_{31}/|J_1|=-0.01$. Deviation from theory occurs close to the transition, $T_c\simeq 1.0\mathrm{K}$, where magnon-magnon interactions become important.