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

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 $T\to 0$. 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.

11 pages, 2 figures

References in corpus (8)

• Magnetic ordering in Gd2Sn2O7: the archetypal Heisenberg pyrochlore antiferromagnet
• Spin dynamics and magnetic order in magnetically frustrated Tb2Sn2O7
• Magnetic density of states at low energy in geometrically frustrated systems
• Direct evidence for a dynamical ground state in the highly frustrated Tb${}_2$Sn${}_2$O${}_7$ pyrochlore
• Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7 pyrochlore antiferromagnet from low-temperature specific heat measurements
• Easy-Axis Kagomé Antiferromagnet: Local-Probe Study of Nd${}_3$Ga${}_5$SiO${}_{14}$
• Low temperature specific heat and possible gap to magnetic excitations in the Heisenberg pyrochlore antiferromagnet Gd2Sn207
• Investigation of the magnetic fluctuations in Tb${}_2$Sn${}_2$O${}_7$ ordered spin ice by high resolution energy-resolved neutron scattering

Cited by in corpus (3)

• Magnetic Order in the Pyrochlore Iridates A2Ir2O7 (A = Y, Yb)
• Persistent spin dynamics intrinsic to amplitude-modulated long-range magnetic order
• Relief of Frustration in the Heisenberg Pyrochlore Antiferromagnet Gd${}_2$Pt${}_2$O${}_7$