Calculation of the Expected Zero Field Muon Relaxation Rate in the Geometrically Frustrated Rare Earth Pyrochlore Gd2Sn2O7 Antiferromagnet

TL;DR

This paper calculates the muon relaxation rate in Gd2Sn2O7, a geometrically frustrated antiferromagnet, revealing a discrepancy between theoretical predictions based on spin waves and experimental observations of persistent spin dynamics.

Contribution

It provides a quantitative calculation of muon relaxation from spin waves in Gd2Sn2O7, highlighting the paradox of persistent spin dynamics despite conventional gapped magnon behavior.

Findings

Calculated relaxation rate differs from experimental data at low temperatures.

Theoretical model predicts exponential decay of relaxation rate below 0.7K.

Persistent spin dynamics remain unexplained by conventional magnon theory.

Abstract

The magnetic insulator Gd2Sn2O7 is one of many geometrically frustrated magnetic materials known to exhibit a nonzero muon spin polarization relaxation rate, $\lambda(T)$, down to the lowest temperature (T) studied. Such behaviour is typically interpreted as a significant level of persisting spin dynamics (PSD) of the host material. In the case of Gd2Sn2O7, such PSD comes as a surprise since magnetic specific heat measurements suggest conventional gapped magnons, which would naively lead to an exponentially vanishing $\lambda(T)$ as $T \rightarrow 0$. In contrast to most materials that display PSD, the ordered phase of Gd2Sn2O7 is well characterized and both the nature and the magnitude of the interactions have been inferred from the magnetic structure and the temperature dependence of the magnetic specific heat. Based on this understanding, the temperature dependence of the muon spin polarization relaxation through the scattering of spin waves (magnons) is calculated. The result explicitly shows that, despite the unusual extensive number of weakly dispersive (gapped)excitations characterizing Gd2Sn2O7, a remnant of the zero modes of the parent frustrated pyrochlore Heisenberg antiferromagnet, the temperature dependence of the calculated $\lambda(T)$ differs dramatically from the experimental one. Indeed, the calculation conforms to the naive expectation of an exponential collapse of $\lambda(T)$ at temperatures below ~ 0.7K. This result, for the first time, illustrates crisply and quantitatively the paradox that presents itself with the pervasive occurrence of PSD in highly frustrated magnetic systems as evinced by muon spin relaxation measurements.