by Max Hirschberger, Jason W. Krizan, R. J. Cava, and N. P. Ong Large thermal Hall conductivity of neutral spin excitations in a frustrated quantum magnet by Max Hirschberger, Jason W. Krizan, R. J. Cava, and N. P. Ong Science Volume 348(6230):106-109 April 3, 2015 Published by AAAS

Fig. 1 The thermal Hall effect in the pyrochlore Tb2Ti2O7. The thermal Hall effect in the pyrochlore Tb2Ti2O7. (A) Hall angle ratio −∂yT/|∂xT| measured at 15 K with thermal current density Jq flowing to the right (green circles). (Inset) Current was applied to heater H1, and the right edge was grounded to the bath. When Jq points to the left, the Hall angle ratio is inverted in sign (solid triangles) but unchanged in magnitude (to 2%). When the power is increased threefold (90 → 270 μW), −∂yT/|∂xT| is nearly unchanged, confirming linear response (open symbols). (B) Comparison between the thermal Hall signal in sample 1 (solid circles, with applied heater power 26 μW at 15 K) with the null signal in the nonmagnetic analog Y2Ti2O7, with heater power 38× larger (1 mW at 15 K) (open triangles). (Inset) Wave-packet model proposed in (3) for κxy in a ferromagnetic insulator. (C) T dependence of κ/T (≡ κxx/T at H = 0) for samples 1 and 2 (solid symbols). In sample 2, κxx/T at H = 8 T is also plotted as open circles. (D) The low-T behavior of κ/T. In sample 2, κ/T becomes T- independent below 1 K, which is similar to the case of a dirty metal. Max Hirschberger et al. Science 2015;348:106-109 Published by AAAS

Fig. 2 κxx/T vs. H in Tb2Ti2O7 at various temperatures. κxx/T vs. H in Tb2Ti2O7 at various temperatures. (A) For sample 1, in the interval 5 to 21 K, the thermal conductivity initially decreases as H increases but then goes through a broad minimum, before increasing steeply at larger H. (B) For sample 2, a new feature becomes apparent in low H and below 5K: At the step-field Hs ; 2 T (red arrow), κxx undergoes a step increase (by a factor of 4.5 at 0.84 K). Max Hirschberger et al. Science 2015;348:106-109 Published by AAAS

Fig. 3 Thermal Hall conductivity κxy/T versus H in Tb2Ti2O7 for sample 2. Thermal Hall conductivity κxy/T versus H in Tb2Ti2O7 for sample 2. (A) From 140 to 50 K, κxy/T is H-linear. Below 45 K, it develops pronounced curvature at large H, reaching its largest value near 12 K. The sign is always holelike. (B) Below 15 K, the weak-field slope [κxy/TB]0 is nearly T-independent. Below 3 K, the field profile shows additional features that become prominent as T → 0—namely, the sharp peak near 1 T and the broad maximum at 6 T. Max Hirschberger et al. Science 2015;348:106-109 Published by AAAS

Fig. 4 The Hall angle and its temperature dependence. The Hall angle and its temperature dependence. (A) Hall angle θH in weak H and low T (sample 2). Below 3 K, tanθH shows a prominent peak at the peak field Hp(T) (arrow). The Hall response is strongly suppressed when H > Hp (most evident at 0.84 K). (B) T-dependence of Hp [from (A), solid circles] and Hp′ [from (D), open circles] in sample 2 [H || (111)]. The dashed curve is H1 from (22). The thick solid curve is Hs. The region in which the Hall-angle slope tanθH/B is large is shown shaded (darkest hue represents largest tanθH). (C) Initial slope [κxy/TB]0 is nearly T-independent below 15 K in samples 1 and 2. (D) tanθH/B versus T in fixed H. At low T, θH/B reaches 9 × 10−3 rad/T. The positions of the broad maxima in tanθH/B define Hp′ (T) [open circles in (B)]. Max Hirschberger et al. Science 2015;348:106-109 Published by AAAS