Low-frequency spin dynamics in the $\mathrm{XY}$ quantum spin ice ${\mathrm{Yb}}_{2}{\mathrm{Pt}}_{2}{\mathrm{O}}_{7}$

Low-frequency spin dynamics in the $XY$ quantum spin ice ${Yb}_{2} {Pt}_{2} O_{7}$

S. K. Takahashi, A. Arsenault, C. Mauws, A. M. Hallas, C. Sarkis, K. A. Ross, C. R. Wiebe, M. Tachibana, G. M. Luke, and T. Imai

Phys. Rev. B 98, 104425 – Published 24 September 2018

Abstract

The XY pyrochlore ${Yb}_{2} {Ti}_{2} O_{7}$ , with pseudospin-1/2 at the ${Yb}^{3 +}$ site, has been celebrated as a potential host for the quantum spin ice state. The substitution of nonmagnetic Ti with Pt gives ${Yb}_{2} {Pt}_{2} O_{7}$ , a system with remarkably similar magnetic properties. The large nuclear gyromagnetic ratio ( $γ_{n} / 2 π = 9.15$ MHz/T) of ${}^{195}{Pt}$ makes ${Yb}_{2} {Pt}_{2} O_{7}$ an ideal material for NMR investigation of its unconventional magnetic properties. Based on the ${}^{195}{Pt}$ nuclear spin-lattice relaxation rate $1 / T_{1}$ and the magnetic specific heat $C_{p}$ measured in a broad range of magnetic field $B_{ext}$ , we demonstrate that the field-induced magnon gap linearly decreases with $B_{ext}$ but an additional low-energy mode of spin excitations emerges below $\sim 0.5$ T.

Received 27 December 2017

DOI:https://doi.org/10.1103/PhysRevB.98.104425

Physics Subject Headings (PhySH)

Frustrated magnetism Spin ice

Pyrochlores Quantum spin models

Nuclear magnetic resonance Specific heat measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. K. Takahashi¹, A. Arsenault¹, C. Mauws^2,3, A. M. Hallas^1,4, C. Sarkis⁵, K. A. Ross^5,6, C. R. Wiebe^1,2,3,6, M. Tachibana⁷, G. M. Luke^1,6, and T. Imai^1,6,*

¹Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1 Canada
²Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba, R3B 2E9 Canada
³Department of Chemistry, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 Canada
⁴Department of Physics and Astronomy, Rice University, 6100 Main MS-61 Houston, Texas 77005-1827, USA
⁵Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
⁶Canadian Institute for Advanced Research, 661 University Avenue, Toronto, Ontario, M5G 1M1 Canada
⁷National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

^*imai@mcmaster.ca

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Vol. 98, Iss. 10 — 1 September 2018

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Figure 1
Representative ${}^{195}{Pt}$ NMR line shapes measured at 2 T for various temperatures. Downward arrows mark the main peak for the field orientation of $⊥$ , whereas shoulders that move to lower frequencies at lower temperature arise from the $∥$ orientation. Dashed line represents the unshifted frequency. Inset: (a) The crystal structure of ${Yb}_{2} {Pt}_{2} O_{7}$ consisting of two networks of interwoven corner-sharing ${Yb}^{3 +}$ (blue) and ${Pt}^{4 +}$ (red) tetrahedra. Oxygens are not shown, for simplicity. (b) The local environment of the platinum sites where the oxygen is in green. When $B_{ext}$ is in plane with the hexagon of ${Yb}^{3 +}$ , we define it as perpendicular ( $⊥$ ). When $B_{ext}$ is out of plane, it is defined as parallel ( $| |$ ).
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Figure 2
NMR frequency shift at the main peak, ${}^{195}K_{⊥}$ (filled symbols), and at the shoulder, ${}^{195}K_{∥}$ (open symbols), as a function of temperature for various fields. Inset shows ${}^{195}K_{⊥}$ for temperatures below 20 K. The dashed line shows the constant offset due to ${}^{195}K_{chem} \sim 0.34 %$ .
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Figure 3
$1 / T_{1}$ as a function of $T$ measured at the main peak. Inset shows the magnetic-field dependence of $1 / T_{1}$ observed at 1.7 K. Solid line shows $1 / T_{1} \sim exp (Δ_{T_{1}} / k_{B} T)$ , where we extrapolated the observed field dependence of $Δ_{T_{1}}$ in the high-field regime linearly to below 1 T using the fit in Fig. 4.
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Figure 4
The magnetic-field dependence of the gap $Δ_{T_{1}}$ extracted from the exponential fit of $1 / T_{1}$ as shown in the inset. Also shown are $T^{*}$ , as defined in the inset of Fig. 5, and the specific-heat energy scale $ε_{C_{p}}$ . Solid line is a linear fit of $Δ_{T_{1}}$ above 1 T, which overestimates the data at 0.5 T and below.
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Figure 5
$1 / T_{1} T$ as a function of $T$ . Notice that the downturn due to the field-induced magnon gap at low temperatures is absent below 0.5 T. We overlay the results of superconducting quantum interference device (SQUID) measurements of the ${Yb}^{3 +}$ moment at 0.5 T using a dashed line. Inset: $1 / T_{1} T$ plotted as a function of ${}^{195}K_{_{⊥}}$ choosing temperature as the implicit parameter. Solid line represents the best linear fit to 0.5 T data. For fields of 1 T and higher, linearity breaks down with decreasing temperature due to opening of a gap. Downward arrows define $T$ *, where $1 / T_{1} T$ deviates 10% from the highest data point of linearity. The dashed arrow represents $T$ * for 0.5 T, which may be absent.
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Figure 6
Specific heat $C_{p}$ shown for select magnetic fields. Solid lines show the two-state system fits used to extract gap energies and entropies. Notice that the maximum temperature of $C_{p}$ increases from 0.5 to 0 T. Inset: Field dependence of the magnetic entropy release $Δ S$ associated with the high-temperature heat capacity anomaly.
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Physical Review B

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Low-frequency spin dynamics in the $XY$ quantum spin ice ${Yb}_{2} {Pt}_{2} O_{7}$

S. K. Takahashi, A. Arsenault, C. Mauws, A. M. Hallas, C. Sarkis, K. A. Ross, C. R. Wiebe, M. Tachibana, G. M. Luke, and T. Imai

Phys. Rev. B 98, 104425 – Published 24 September 2018

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Physical Review B

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Low-frequency spin dynamics in the XY quantum spin ice Yb2Pt2O7

S. K. Takahashi, A. Arsenault, C. Mauws, A. M. Hallas, C. Sarkis, K. A. Ross, C. R. Wiebe, M. Tachibana, G. M. Luke, and T. Imai

Phys. Rev. B 98, 104425 – Published 24 September 2018

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Low-frequency spin dynamics in the $XY$ quantum spin ice ${Yb}_{2} {Pt}_{2} O_{7}$