Intrinsic Anomalous Nernst Effect Amplified by Disorder in a Half-Metallic Semimetal Linchao Ding, Jahyun Koo, Liangcai Xu, Xiaokang Li, Xiufang Lu, Lingxiao Zhao, Qi Wang, Qiangwei Yin, Hechang Lei, Binghai Yan, et al. To cite this version: Linchao Ding, Jahyun Koo, Liangcai Xu, Xiaokang Li, Xiufang Lu, et al.. Intrinsic Anomalous Nernst Effect Amplified by Disorder in a Half-Metallic Semimetal. Physical Review X, American Physical Society, 2019, 9 (4), pp.041061. 10.1103/PhysRevX.9.041061. hal-02434941 HAL Id: hal-02434941 https://hal.sorbonne-universite.fr/hal-02434941 Submitted on 10 Jan 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. 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PHYSICAL REVIEW X 9, 041061 (2019) Intrinsic Anomalous Nernst Effect Amplified by Disorder in a Half-Metallic Semimetal Linchao Ding ,1 Jahyun Koo,2 Liangcai Xu,1 Xiaokang Li ,1 Xiufang Lu,1 Lingxiao Zhao,1 Qi Wang,3 † ‡ Qiangwei Yin,3 Hechang Lei,3 Binghai Yan ,2,* Zengwei Zhu ,1, andKamranBehnia 4,5, 1Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China 2Department of Condensed Matter Physics, Weizmann Institute of Science, 7610001 Rehovot, Israel 3Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, China 4Laboratoire de Physique et Etude des Mat´eriaux (CNRS/Sorbonne Universit´e), Ecole Sup´erieure de Physique et de Chimie Industrielles, 10 Rue Vauquelin, 75005 Paris, France 5II. Physikalisches Institut, Universität zu Köln, 50937 Köln, Germany (Received 11 July 2019; revised manuscript received 22 October 2019; published 24 December 2019) Intrinsic anomalous Nernst effect, like its Hall counterpart, is generated by Berry curvature of electrons in solids. Little is known about its response to disorder. In contrast, the link between the amplitude of the ordinary Nernst coefficient and the mean-free path is extensively documented. Here, by studying Co3Sn2S2, a topological half-metallic semimetal hosting sizable and recognizable ordinary and anomalous Nernst responses, we demonstrate an anticorrelation between the amplitudes of carrier mobility and the A anomalous Sxy (the ratio of transverse electric field to the longitudinal temperature gradient in the absence of magnetic field). We argue that the observation, paradoxically, establishes the intrinsic origin of the anomalous Nernst effect in this system. We conclude that various intrinsic off-diagonal coefficients are set by the way the Berry curvature is averaged on a grid involving the mean-free path, the Fermi wavelength, and the de Broglie thermal length. DOI: 10.1103/PhysRevX.9.041061 Subject Areas: Condensed Matter Physics, Magnetism, Topological Insulators I. INTRODUCTION to be distinguished from the off-diagonal component of the thermoelectric tensor (αxy). The latter is the transverse Electrons in some solids do not flow along the applied temperature gradient generated by a longitudinal charge electric field or thermal gradient, even in zero magnetic flow (in the absence of electric field), which is often the field. The phenomena, known as the anomalous Hall effect immediate result of theoretical calculations. The two (AHE), the anomalous Nernst effect (ANE), and the coefficients are intimately connected to each other [3]. anomalous thermal Hall effect, may be caused either by A pioneer theoretical study of the intrinsic anomalous the geometric (Berry) curvature of Bloch functions or by Nernst effect [4] argued that it depends on the magnitude of the skew scattering of electrons off magnetic impurities. the magnetization in the host solid. The expected correla- Distinguishing between these intrinsic and extrinsic origins tion between the two properties became the mantra of many (see Refs. [1,2] for reviews) has motivated numerous of the numerous experimental studies of the ANE [5–16] in investigations during the past two decades. topological solids (for a review of such systems, see Here we focus on the anomalous Nernst effect. The S Refs. [17,18]). A prominent question, yet to be addressed, Nernst effect xy is a transverse electric field generated by a is the role of disorder in setting the amplitude of the ANE. longitudinal temperature gradient (in the absence of charge Does this transport property depend on the mean-free path? flow). It is directly accessible to the experimentalist and has If yes, since magnetization is a thermodynamic property, why? The ordinary Nernst effect (ONE) is expected to scale *[email protected] with mobility [3,19]. Experimental studies have not only † [email protected] confirmed this scaling across different systems, but also ‡ [email protected] found that the magnitude of the ONE in a given solid increases as it becomes cleaner (bismuth and URu2Si2 are Published by the American Physical Society under the terms of two prominent case studies) [3]. To the best of our the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to knowledge, this has not been the case of the ANE. the author(s) and the published article’s title, journal citation, In this paper, we show that this opportunity is offered for and DOI. the first time by the newly discovered magnetic Weyl 2160-3308=19=9(4)=041061(9) 041061-1 Published by the American Physical Society LINCHAO DING et al. PHYS. REV. X 9, 041061 (2019) (a) Co (b) 400 B5 semimetal Co3Sn2S2. This is a solid with a shandite Sn no. 12 S structure, which becomes a ferromagnet below 180 K 300 no. 30 a [20–22]. Theoretical calculations suggest that this semi- cm) no. 29 b 200 no. 31 μΩ metallic half-metal [23] with negative flatband magnetism ( y ρ [24] hosts Weyl nodes 60 meV off the Fermi level [25]. 100 c z x Previous experiments have found a large AHE [25,26],a a 0 large ANE [12,14], and surface-termination-dependent b 0 100 200 300 T (K) Fermi arcs [27]. (c) 1 (d) We report first on a significant improvement in the 80 B5 B5 quality of Co3Sn2S2 single crystals obtained by the no. 12 no. 30 60 cm) no. 12 chemical vapor transport (CVT) method. The improved 300K no. 29 ρ / no. 30 no. 31 μΩ ρ ( 40 quality shows itself in higher mobility compared to what 0.1 Liu et al.[23] was reported in previous studies [12,14,22,25,26]. This Wang et al. [24] ρ no. 29 Yang et al. [12] 20 Schnelle et al. [20] no. 31 allowed us to perform a systematic study of five different 0.03 0 100 200 300 0 200 400 600 800 1000 crystals with different impurity concentrations. We find T (K) T 2 (K2) that, as expected [3,19], the amplitude of the ordinary O Nernst response Sxy is proportional to mobility μ; On the FIG. 1. Crystal structure, resistivity, and sample-dependent other hand, the amplitude of the anomalous Nernst effect disorder. (a) Crystal structure of Co3Sn2S2. (b) Temperature A dependence of resistivity at zero field in five samples. The Sxy is proportional to the inverse of μ. We argue then that A residual resistivity ratio (RRR) ranges from 4 to 21. The inset the amplification of Sxy by disorder reflects the fact that the A shows an as-grown hexagonal-shape sample with a typical anomalous transverse thermoelectricity αxy depends on the dimension of 1.3 × 1 × 0.02 mm3. The orientations of x, y, Berry curvature (averaged over a reciprocal distance set by and z are defined as ½21¯ 10¯ , ½0110¯ , and [0001], respectively. the thermal de Broglie wavelength), but not on the mean- (c) Comparison of resistivity, normalized to its room-temperature free path. This is to be contrasted with the semiclassical αxy, value between the samples used in this study and four previous which scales with the square of the mean-free path [3].We reports. The previous RRR is comparable with the two dirtiest ρ T2 show that according to both theory and experiment, the samples in this study. (d) as the function in our samples. The prefactor of T-square resistivity is similar in all four samples Fermi surface of Co3Sn2S2 is complex. Finally, we deter- grown from chemical vapor transport method, but the difference mine the magnitude of the anomalous transverse thermo- A is residual resistivity leads to an upward shift. electric conductivity αxy in all five samples and find a qualitative agreement between theory and experiment with no need for invoking uncontrolled and unidentified extrin- fivefold change in residual resistivity barely affects inelas- sic dopants invoked previously [14]. It is remarkable that tic scattering. Indeed, the prefactor of the T-square resis- −2 the scaling between average mobility and the anomalous tivity [29] is the same (4.5 nΩ cm K ) (see Supplemental Nernst coefficient remains valid in spite of the multiplicity Material [28] for details). of Fermi surface pockets. Carrier mobility in each sample can be quantified using three distinct experimental inputs: (i) the amplitude of II. SAMPLES WITH DIFFERENT MOBILITIES magnetoresistance [Fig. 2(a)], (ii) the magnitude of the ordinary Hall conductivity and its field dependence, Co3Sn2S2 crystallizes in the shandite structure, which fitted to a two-band model [Fig. 2(b)] and yielding consists of ABC stacking of kagome sheets [see Fig. 1(a)]. mobility and concentration of electrons and holes (see A picture of a hexagonal sample with typical dimension of Ref.