Low-temperature heat transport in the geometrically frustrated antiferromagnets ${R}_{2}$Ti${}_{2}$O${}_{7}$ ($R$ = Gd and Er)

Low-temperature heat transport in the geometrically frustrated antiferromagnets $R_{2}$ Ti $_{2}$ O $_{7}$ ( $R$ = Gd and Er)

F. B. Zhang, Q. J. Li, Z. Y. Zhao, C. Fan, S. J. Li, X. G. Liu, X. Zhao, and X. F. Sun

Phys. Rev. B 89, 094403 – Published 4 March 2014

Abstract

We report a systematic study on the low-temperature thermal conductivity ( $κ$ ) of $R_{2}$ Ti $_{2}$ O $_{7}$ ( $R$ = Gd and Er) single crystals with different directions of magnetic field and heat current. It is found that the magnetic excitations mainly act as phonon scatterers rather than heat carriers, although these two materials have long-range magnetic orders at low temperatures. The low- $T$ $κ (H)$ isotherms of both compounds show rather complicated behaviors and have good correspondences with the magnetic transitions, where the $κ (H)$ curves show drastic dip- or steplike changes. In comparison, the field dependencies of $κ$ are more complicated in Gd $_{2}$ Ti $_{2}$ O $_{7}$ , due to the complexity of its low- $T$ phase diagram and field-induced magnetic transitions. These results demonstrate the significant coupling between spins and phonons in these materials and the ability of heat-transport properties probing the magnetic transitions.

Received 24 June 2013
Revised 14 February 2014

DOI:https://doi.org/10.1103/PhysRevB.89.094403

Authors & Affiliations

F. B. Zhang¹, Q. J. Li^1,2, Z. Y. Zhao¹, C. Fan¹, S. J. Li¹, X. G. Liu¹, X. Zhao^3,*, and X. F. Sun^1,†

¹Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
²School of Physics and Material Sciences, Anhui University, Hefei, Anhui 230601, People's Republic of China
³School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China

^*xiazhao@ustc.edu.cn
^†xfsun@ustc.edu.cn

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Vol. 89, Iss. 9 — 1 March 2014

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Figure 1
(a), (c) Temperature dependencies of the specific heat of Gd $_{2}$ Ti $_{2}$ O $_{7}$ single crystals for $H ∥$ [110] and $H ∥$ [111]. (b), (d) Zoom-in of the low-temperature plots. The sample sizes are $0.29 \times 0.32 \times 0.17$ mm $^{3}$ for $H ∥$ [110] and $0.53 \times 0.53 \times 0.09$ mm $^{3}$ for $H ∥$ [111], respectively. The magnetic fields were applied along the shortest dimensions of the samples.
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Figure 2
(a)–(c) Temperature dependencies of thermal conductivities of Gd $_{2}$ Ti $_{2}$ O $_{7}$ single crystals at zero and 14 T. The directions of heat current ( $J_{H}$ ) and magnetic field are along either the [111] or the [110] directions. Note that in panel (b), the magnetic fields along the [1 $\bar{1}$ 0] direction (equivalent to the [110]) are actually perpendicular to the [111] direction. The dashed lines indicate a $T^{3}$ temperature dependence. (d)–(f) The corresponding magnetic-field dependencies of thermal conductivities at low temperatures for the three different configurations. Two sets of data for $J_{H} ∥$ [111] were taken on a sample having a size of $3.9 \times 0.63 \times 0.17$ mm $^{3}$ . Another sample for $J_{H} ∥$ [110] has a size of $2.4 \times 0.65 \times 0.16$ mm $^{3}$ . The heat currents were flowing along the longest dimensions of these samples.
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Figure 3
Temperature-field phase diagrams of Gd $_{2}$ Ti $_{2}$ O $_{7}$ single crystals obtained from the specific-heat data for $H ∥$ [110] and $H ∥$ [111]. The characteristic fields of the $κ (H)$ curves are also plotted for comparison. PM is the high-temperature paramagnetic state. The P, F, and collinear states are three different phases mentioned in the main text.
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Figure 4
(a) Temperature dependencies of the specific heat of Er $_{2}$ Ti $_{2}$ O $_{7}$ single crystal for magnetic field along the [111] axis. Inset: Zoom-in of the low-temperature plot. The sample size is $0.46 \times 0.67 \times 0.08$ mm $^{3}$ , with the field direction along the shortest dimension. (b) The fits of the high-field data ( $H \geq$ 2 T) to Eq. (1) as described in the main text. The solid lines represent the fitting results and the dashed line shows the phonon contribution. Inset displays the fitting parameter $Δ$ .
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Figure 5
(a)–(c) Temperature dependencies of thermal conductivities of Er $_{2}$ Ti $_{2}$ O $_{7}$ single crystals for different directions of heat current ( $J_{H}$ ) and magnetic field. In panel (b), the magnetic fields along the [1 $\bar{1}$ 0] (equivalent to the [110]) are actually perpendicular to the [111] direction. In panel (c), both the heat current and the magnetic fields are along the [11 $\bar{2}$ ] direction, which is actually perpendicular to the [111] axis. The inset to panel (c) shows the zoom-in of the zero-field $κ (T)$ curves in temperature regime of 0.3–3 K, and the arrow indicates a weak change in slopes of these data. (d)–(f) The corresponding magnetic-field dependencies of thermal conductivities at low temperatures for the three different configurations. The sample sizes are $3.4 \times 0.65 \times 0.17$ mm $^{3}$ for $J_{H} ∥$ [111] and $4.0 \times 0.65 \times 0.18$ mm $^{3}$ for $J_{H} ⊥$ [111], respectively. The heat currents were flowing along the longest dimensions of them.
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Figure 6
Temperature-field phase diagram of Er $_{2}$ Ti $_{2}$ O $_{7}$ single crystal for $H ∥$ [111] from the specific-heat data. The low- $T$ $λ$ peak gives the antiferromagnetic transition temperature $T_{N}$ . The field dependence of $T_{N}$ displays the phase boundary of the long-range ordered (LRO) ground state, as shown by the dashed line. The higher field Schottky-like peaks may separate the “high- $T$ , low-field” thermally paramagnetic state and the “high-field, low- $T$ ” quantum paramagnetic state, as suggested by Ref. [30]. The characteristic dip fields of the $κ (H)$ isotherms are also shown for three configurations of the heat current ( $J_{H}$ ) and magnetic field.
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