Influence of short-range spin correlations on the $\ensuremath{\mu}$SR polarization functions in the slow dynamic limit: Application to the quantum spin-liquid system Yb${}_{2}$Ti${}_{2}$O${}_{7}$

Influence of short-range spin correlations on the $μ$ SR polarization functions in the slow dynamic limit: Application to the quantum spin-liquid system Yb $_{2}$ Ti $_{2}$ O $_{7}$

A. Yaouanc, A. Maisuradze, and P. Dalmas de Réotier

Phys. Rev. B 87, 134405 – Published 5 April 2013

Abstract

Here we discuss how to account for short-range spin correlations on the measured muon spin relaxation spectra. The shape of the zero-field relaxation function is found to be highly sensitive to short-range spin correlations, as clearly inferred from the analysis of the published longitudinal relaxation function for the pyrochlore quantum spin-liquid system Yb $_{2}$ Ti $_{2}$ O $_{7}$ at low temperature. The field distribution at the muon site in this compound is found to be strongly asymmetric, i.e., to deviate substantially from the usually expected Gaussian function. This is a clear signature of short-range correlations of the spins. Our analysis yields the characteristic function of the component field distribution at the muon site of Yb $_{2}$ Ti $_{2}$ O $_{7}$ , a well-defined statistical physics quantity accessible to theory once an interaction Hamiltonian is available and the muon site is determined. As a by-product of our study, we have found that the validity of the so-called golden formula due to Kubo is limited.

Received 25 January 2013

DOI:https://doi.org/10.1103/PhysRevB.87.134405

Authors & Affiliations

A. Yaouanc

Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland and Institut Nanosciences et Cryogénie, SPSMS, CEA and Université Joseph Fourier, F-38054 Grenoble, France

A. Maisuradze

Physik-Institut der Universität Zürich, Winterthuerstrasse 190, CH-8057 Zürich, Switzerland and Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland

P. Dalmas de Réotier

Institut Nanosciences et Cryogénie, SPSMS, CEA and Université Joseph Fourier, F-38054 Grenoble, France

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Vol. 87, Iss. 13 — 1 April 2013

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Figure 1
(a) The normalized component field distributions $Δ \times D_{c} (B_{loc}^{α})$ of the low-temperature phase of the two-dimensional $XY$ model computed using Eqs. (17) and (18) for $〈 B_{loc}^{α} 〉 = - Δ$ , $- 0.5 Δ$ , 0, $0.5 Δ$ , and $Δ$ (from left to right). Note that the field is given in units of $Δ$ . For this model the skewness and excess kurtosis are equal to $- 0.8907$ and $4.415$ , respectively. The corresponding real and imaginary parts of $G (t)$ , solid and dotted lines, respectively, are presented in panel (b), and $P_{Z}^{stat} (t)$ in panel (c). For better visualization each plot of the $G (t)$ and $P_{Z}^{stat} (t)$ functions is shifted by 0.3 units. The time $t$ is in units of $1 / (γ_{μ} Δ)$ . The dashed lines refer to functions when the correlations are neglected; e.g., we plot the Kubo-Toyabe function in panel (c).Reuse & Permissions
Figure 2
Dependence of the normalized component field distribution $δ \times D_{c} (B_{loc}^{α})$ given by Eq. (19) (a), the related characteristic function $G (t)$ which is real (b), and zero-field polarization function $P_{Z}^{stat} (t)$ (c) on $η_{4}$ with $η_{3}$ set to zero. The curves are for $η_{4}$ $=$ 0, 0.4, 0.8, 1.2, 1.6, and 2.0. The field is in units of $δ$ and the time in $1 / (γ_{μ} δ)$ . The dotted line in panel (c) shows the $P_{Z}^{stat} (t)$ function calculated with Eq. (5) for $η_{3} = 0$ and $η_{4} = 2.0$ . The strong deviation from the corresponding result obtained with Eq. (3) is obvious.Reuse & Permissions
Figure 3
Dependence of the component field distribution $δ \times D_{c} (B_{loc}^{α})$ [panels (a), (d), (g), and (j)], the real and imaginary parts of the characteristic function $G (t)$ , solid and dotted lines, respectively [panels (b), (e), (h), and (k)], and the related zero-field polarization function $P_{Z}^{stat} (t)$ [panels (c), (f), (i), and (l)] on $η_{4}$ and $η_{3}$ . The drawings in the upper two panels are for $η_{4} = 0.50$ with $η_{3} = 0, 0.50, 0.65, 0.70, 0.74$ , and $0.76$ . In the lower two panels we present data for $η_{4} = 1.0$ with $η_{3} = 0, 1.00, 1.04, 1.10, 1.16$ , and $1.22$ . For each ${η_{3}, η_{4}}$ pair, the mean field $〈 B_{loc}^{α} 〉$ is set to zero in the lower panels. The units are as in Fig. 2.Reuse & Permissions
Figure 4
Same caption as in Fig. 3, but for $η_{4} = 1.50$ with $η_{3} = 0, 1.30, 1.45, 1.53, 1.60$ , and $1.65$ .Reuse & Permissions
Figure 5
Analysis of the $μ$ SR time spectrum measured at 0.200 K and in a 2 mT longitudinal field for a powder sample of Yb $_{2}$ Ti $_{2}$ O $_{7}$ (Ref. 3) $a_{0} P_{Z}^{\exp} (t)$ is shown in panel (c) (circles). The solid line is the best fit of the data using Eqs. (19), (25), (3), and (26) (see main text). The real (solid line) and imaginary (dotted line) parts of $G (t)$ are shown in panel (b). Corresponding $D_{c} (B_{loc}^{α})$ function is depicted in panel (a).Reuse & Permissions

Physical Review B

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Influence of short-range spin correlations on the $μ$ SR polarization functions in the slow dynamic limit: Application to the quantum spin-liquid system Yb $_{2}$ Ti $_{2}$ O $_{7}$

A. Yaouanc, A. Maisuradze, and P. Dalmas de Réotier

Phys. Rev. B 87, 134405 – Published 5 April 2013

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Influence of short-range spin correlations on the μSR polarization functions in the slow dynamic limit: Application to the quantum spin-liquid system Yb2Ti2O7

A. Yaouanc, A. Maisuradze, and P. Dalmas de Réotier

Phys. Rev. B 87, 134405 – Published 5 April 2013

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Influence of short-range spin correlations on the $μ$ SR polarization functions in the slow dynamic limit: Application to the quantum spin-liquid system Yb $_{2}$ Ti $_{2}$ O $_{7}$