Slow spin tunneling in the paramagnetic phase of the pyrochlore ${\mathrm{Nd}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$

Slow spin tunneling in the paramagnetic phase of the pyrochlore ${Nd}_{2} {Sn}_{2} O_{7}$

P. Dalmas de Réotier, A. Yaouanc, A. Maisuradze, A. Bertin, P. J. Baker, A. D. Hillier, and A. Forget

Phys. Rev. B 95, 134420 – Published 13 April 2017

Abstract

The insulating pyrochlore compound ${Nd}_{2} {Sn}_{2} O_{7}$ has been shown to undergo a second order magnetic phase transition at $T_{c} \approx 0.91$ K to a noncoplanar all-in–all-out magnetic structure of the ${Nd}^{3 +}$ magnetic moments. An anomalously slow paramagnetic spin dynamics has been evidenced from neutron backscattering and muon spin relaxation $(μ SR)$ . In the case of $μ SR$ this has been revealed through the strong effect of a 50 mT longitudinal field on the spin-lattice relaxation rate. Here, motivated by a recent successful work performed for ${Yb}_{2} {Ti}_{2} O_{7}$ and ${Yb}_{2} {Sn}_{2} O_{7}$ , analyzing the shape of the $μ SR$ longitudinal polarization function, we substantiate the existence of extremely slow paramagnetic spin dynamics in the microsecond time range for ${Nd}_{2} {Sn}_{2} O_{7}$ . Between 1.7 and 7 K, this time scale is temperature independent. This suggests a double spin-flip tunneling relaxation mechanism to be at play, probably involving spin substructures such as tetrahedra. Unexpectedly, the standard deviation of the field distribution at the muon site increases as the system is cooled. This exotic spin dynamics is in sharp contrast with the dynamics above 100 K which is driven by the Orbach relaxation mechanism involving single ${Nd}^{3 +}$ magnetic moments.

Received 22 December 2016
Revised 10 March 2017

DOI:https://doi.org/10.1103/PhysRevB.95.134420

Physics Subject Headings (PhySH)

Frustrated magnetism

Pyrochlores

Muon spin relaxation & rotation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. Dalmas de Réotier^1,2, A. Yaouanc^1,2, A. Maisuradze³, A. Bertin^1,2, P. J. Baker⁴, A. D. Hillier⁴, and A. Forget⁵

¹Université Grenoble Alpes, INAC-PHELIQS, F-38000 Grenoble, France
²CEA, INAC-PHELIQS, F-38000 Grenoble, France
³Department of Physics, Tbilisi State University, Chavchavadze 3, GE-0128 Tbilisi, Georgia
⁴ISIS Facility, STFC Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, United Kingdom
⁵SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France

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Vol. 95, Iss. 13 — 1 April 2017

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Figure 1
Asymmetry spectra recorded in the paramagnetic phase of a ${Nd}_{2} {Sn}_{2} O_{7}$ powder sample at four temperatures in various longitudinal fields. The spectra were recorded at MuSR. The experimental points are represented by black circles. The solid lines result from fits with the conventional dynamical KT model as explained in the main text. The spectra for consecutive external field values (indicated next to each spectrum) are vertically shifted by 0.03 unit for better visualization. The statistical uncertainties are indicated by vertical bars, the size of which is much less than the symbol size except near $10 μ s$ . Note that the spectra are displayed with a logarithmic time scale.
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Figure 2
Short-range correlations or two muon sites at low temperature in the paramagnetic phase of a ${Nd}_{2} {Sn}_{2} O_{7}$ powder sample. We display a ZF asymmetry spectrum recorded at 1.0 K with the MuSR spectrometer. The experimental points are represented by black circles and the corresponding fitting curve with short-range correlations taken into account and two muon sites as a red solid line. The blue dashed line results from the best fit with a single dynamical KT function [Eq. (1)].
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Figure 3
ZF asymmetry spectra recorded at low temperature with the EMU spectrometer. The experimental points are represented by black circles. The solid lines result from fits explained in the main text. The spectra for consecutive temperature values (indicated next to each spectrum) are vertically shifted by 0.03 unit for better visualization.
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Figure 4
Thermal dependence of $ν_{c}, Δ_{1}$ , and $A_{0}^{LF}$ extracted from the analysis of ZF spectra recorded at the EMU spectrometer.
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Figure 5
Field dependence of $Δ_{1}$ obtained from the two dynamical KT function model applied to the data shown in Fig. 1. When the spectral shape is too close to an exponential, the fits do not allow for an accurate determination of the parameters, which are therefore not displayed.
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Figure 6
Thermal dependence of the $μ SR$ relaxation rate $λ_{Z}$ measured in 0 or 50 mT longitudinal field in ${Nd}_{2} {Sn}_{2} O_{7}$ for temperatures larger than 10 K. The data are taken from Ref. [24]. The full line displays $λ_{Z} (T)$ for an Orbach relaxation mechanism: $λ_{Z}^{- 1} (T) = A_{O} + B_{O} exp (- Δ_{CEF} / k_{B} T)$ [39]. The fit to the data gives $A_{O}^{- 1} = 0.28 (1) μ s^{- 1}$ and $B_{O} = 118 (6) μ s$ , with $Δ_{CEF} = 39.8$ meV. The difference below $\approx 30$ K between the data recorded in 0 and 50 mT field has been discussed in Ref. [24].
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Physical Review B

covering condensed matter and materials physics

Slow spin tunneling in the paramagnetic phase of the pyrochlore ${Nd}_{2} {Sn}_{2} O_{7}$

P. Dalmas de Réotier, A. Yaouanc, A. Maisuradze, A. Bertin, P. J. Baker, A. D. Hillier, and A. Forget

Phys. Rev. B 95, 134420 – Published 13 April 2017

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Physical Review B

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Slow spin tunneling in the paramagnetic phase of the pyrochlore Nd2Sn2O7

P. Dalmas de Réotier, A. Yaouanc, A. Maisuradze, A. Bertin, P. J. Baker, A. D. Hillier, and A. Forget

Phys. Rev. B 95, 134420 – Published 13 April 2017

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Slow spin tunneling in the paramagnetic phase of the pyrochlore ${Nd}_{2} {Sn}_{2} O_{7}$