Antiferromagnetic spin ice correlations at ($\frac{1}{2}$,$\frac{1}{2}$,$\frac{1}{2}$) in the ground state of the pyrochlore magnet Tb${}_{2}$Ti${}_{2}$O${}_{7}$

Antiferromagnetic spin ice correlations at ( $\frac{1}{2}$ , $\frac{1}{2}$ , $\frac{1}{2}$ ) in the ground state of the pyrochlore magnet Tb $_{2}$ Ti $_{2}$ O $_{7}$

K. Fritsch, K. A. Ross, Y. Qiu, J. R. D. Copley, T. Guidi, R. I. Bewley, H. A. Dabkowska, and B. D. Gaulin

Phys. Rev. B 87, 094410 – Published 11 March 2013; Erratum Phys. Rev. B 87, 139903 (2013)

Abstract

We present high-resolution single-crystal time-of-flight neutron scattering measurements on the candidate quantum spin liquid pyrochlore Tb $_{2}$ Ti $_{2}$ O $_{7}$ at low temperature and in a magnetic field. At $\sim 70$ mK and in zero field, Tb $_{2}$ Ti $_{2}$ O $_{7}$ reveals diffuse magnetic elastic scattering at ( $\frac{1}{2}$ , $\frac{1}{2}$ , $\frac{1}{2}$ ) positions in reciprocal space, consistent with short-range correlated regions based on a two-in, two-out spin ice configuration on a doubled conventional unit cell. This elastic scattering is separated from very low-energy magnetic inelastic scattering by an energy gap of $\sim$ 0.06–0.08 meV. The elastic signal disappears under the application of small magnetic fields and upon elevating temperature. Pinch-point–like elastic diffuse scattering is observed near (1,1,1) and (0,0,2) in zero field at $\sim 70$ mK, in agreement with Fennell et al. [Phys. Rev. Lett. 109, 017201 (2012)], supporting the quantum spin ice interpretation of Tb $_{2}$ Ti $_{2}$ O $_{7}$ .

Received 27 September 2012

DOI:https://doi.org/10.1103/PhysRevB.87.094410

Erratum

Erratum: Antiferromagnetic spin ice correlations at $(\frac{1}{2}, \frac{1}{2}, \frac{1}{2})$ in the ground state of the pyrochlore magnet ${Tb}_{2} {Ti}_{2} O_{7}$ [Phys. Rev. B 87, 094410 (2013)]

K. Fritsch, K. A. Ross, Y. Qiu, J. R. D. Copley, T. Guidi, R. I. Bewley, H. A. Dabkowska, and B. D. Gaulin

Phys. Rev. B 87, 139903 (2013)

Authors & Affiliations

K. Fritsch¹, K. A. Ross^1,2,3, Y. Qiu^3,4, J. R. D. Copley³, T. Guidi⁵, R. I. Bewley⁵, H. A. Dabkowska⁶, and B. D. Gaulin^1,6,7

¹Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada
²Institute for Quantum Matter and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
³NIST Center for Neutron Research, NIST, Gaithersburg, Maryland 20899-8102, USA
⁴Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA
⁵ISIS Pulsed Neutron and Muon Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK
⁶Brockhouse Institute for Materials Research, Hamilton, Ontario, L8S 4M1, Canada
⁷Canadian Institute for Advanced Research, 180 Dundas St. W., Toronto, Ontario, M5G 1Z8, Canada

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Vol. 87, Iss. 9 — 1 March 2013

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Images

Figure 1
Neutron scattering data within the (H,H,L) plane of Tb $_{2}$ Ti $_{2}$ O $_{7}$ at $T$ $=$ 70 mK are shown for (a) $-$ 0.1 meV $<$ $E$ $<$ 0.1 meV, (b) 0.1 meV $<$ $E$ $<$ 0.6 meV, and (c) 1.0 $<$ $E$ $<$ 1.8 meV. Panel (d) shows a plot of intensity vs energy transfer at the ( $\frac{1}{2}$ , $\frac{1}{2}$ , $\frac{3}{2}$ ) position for fields $μ_{0} H = 0, 2, 3$ , and 4 T. The integration range is $H = [0.2, 0.8]$ r.l.u., $L = [1.2, 1.8]$ r.l.u.. The inset expands the intensity scale. All data shown were corrected for detector efficiency, and an empty can background was subtracted. The error bars are $\pm$ 1 $σ$ .Reuse & Permissions
Figure 2
Cuts of the elastic scattering data in Fig. 1a through the ( $\frac{3}{2}$ , $\frac{3}{2}$ , $\frac{3}{2}$ ) position along each of the [H,H,0], [H,H,H], and [0,0,L] directions are shown, along with fits to an Ornstein-Zernike form for the diffuse line shape. These data and associated fits show the short-range ordered, elastic antiferromagnetic Bragg features to be isotropic in Q, and characterized by a correlation length of $\sim 8$ Å.Reuse & Permissions
Figure 3
Comparison of the measured elastic diffuse scattering in the (H,H,L) plane of Tb $_{2}$ Ti $_{2}$ O $_{7}$ at 70 mK and $μ_{0}$ H $=$ 0 [panel (a)] to the calculated S(Q) discussed in the text [panel (b)]. The intensity scale in the calculation is normalized to the largest intensity at ( $\frac{1}{2}$ , $\frac{1}{2}$ , $\frac{3}{2}$ ). The spin arrangement between neighboring conventional unit cells is shown as a projection onto the $x y$ plane in panel (c). The ordered two-in, two-out spin configuration in a single unit cell is shown in panel (d), and this pattern is reversed in the neighboring cells [black vs grey arrows in panel (c)] to form “ $〈 \frac{1}{2}, \frac{1}{2}, \frac{1}{2} 〉$ ordered spin ice.” The spins are tilted from their local $〈$ 111 $〉$ axes by $\sim 12$ $^{\circ}$ .Reuse & Permissions
Figure 4
Elastic scattering data from LET, with the $T = 66$ mK, $μ_{0} H = 7$ T data set used as a background, shown in the [K,K,−K] vs [ $\frac{1}{2}$ H, $\frac{1}{2}$ H,H] plane at $μ_{0} H = 0$ , integrated from $E = [- 0.02, 0.02]$ meV, and [H,−H,0] $=$ $[- 0.6, - 0.4]$ r.l.u.. In the scattering geometry used in the LET experiment, the [K,K, $-$ K] direction is parallel to the vertical (field) direction. (a) The diffuse scattering at 66 mK, 0 T shown here corresponds to ( $-$ $\frac{1}{2}$ , $\frac{1}{2}$ , $-$ $\frac{1}{2}$ ), which arises at [ $\frac{1}{2}$ H, $\frac{1}{2}$ H,H] $=$ $-$ 0.33 r.l.u., [H, $-$ H,0] $=$ $- 0.5$ r.l.u., and [K,K,−K] $=$ 0.166 r.l.u.. This diffuse elastic scattering disappears upon either application of a $μ_{0} H = 0.25$ T field at $T = 66$ mK (b), or warming to 1.5 K (below $Θ_{CW}$ ) (c), or 60 K (above $Θ_{CW}$ ) (d). Panel (e) shows the field and temperature dependence of the diffuse elastic scattering at ( $-$ $\frac{1}{2}$ , $\frac{1}{2}$ , $-$ $\frac{1}{2}$ ) as shown in panel (a), integrating over [ $\frac{1}{2}$ H, $\frac{1}{2}$ H,H] $=$ [0,0.3] r.l.u..Reuse & Permissions
Figure 5
High-energy resolution data from LET, with the 66 mK, 7 T data set used as a background. Inelastic scattering integrated over [ $\frac{1}{2}$ H, $\frac{1}{2}$ H,H] $=$ [ $-$ 1.5,1.0] r.l.u. and [K,K, $-$ K] $=$ [ $-$ 0.5, 0.5] r.l.u. is shown for (a) $T = 66$ mK and $μ_{0} H = 0$ , (b) $T = 66$ mK and $μ_{0} H = 0.25$ T, (c) $T = 1.5$ K and $μ_{0} H = 0$ , and (d) $T = 60$ K and $μ_{0} H = 0$ . A spin gap of $\sim 0.06 - 0.08$ meV opens up below 1.5 K, which was not resolved previously. The spin gap correlates strongly with the appearance of the ( $\frac{1}{2}$ , $\frac{1}{2}$ , $\frac{1}{2}$ ) elastic magnetic peaks shown in Figs. 1, 2, 3, 4. (e) Field and temperature dependence of the low-energy inelastic scattering as shown in panels (a)–(c), integrated over the full [H, $-$ H,0] range. The inset to Fig. 5e shows the same data corrected for the Bose factor, that is, $χ^{''}$ (Q, E) [see Eq. (1)].Reuse & Permissions
Figure 6
Pinch-point like scattering in the ground state of Tb $_{2}$ Ti $_{2}$ O $_{7}$ observed on DCS at $\sim$ 70 mK for $μ_{0}$ $H$ $=$ 0 T in panel (a). Panel (b) shows diffuse scattering along the $〈$ 0,0,L $〉$ direction under application of a $μ_{0}$ $H$ $=$ 2T field, which might originate from anisotropic exchange. Both data sets show elastic scattering for $-$ 0.1 meV $<$ $E$ $<$ 0.1 meV and are displayed on a logarithmic intensity scale (compared to a linear scale in Fig. 1).Reuse & Permissions

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