Nernst Effect of High-Mobility Weyl Electrons in NdAlSi Enhanced by a Fermi Surface Nesting Instability

Open Access

Nernst Effect of High-Mobility Weyl Electrons in NdAlSi Enhanced by a Fermi Surface Nesting Instability

Rinsuke Yamada, Takuya Nomoto, Atsushi Miyake, Toshihiro Terakawa, Akiko Kikkawa, Ryotaro Arita, Masashi Tokunaga, Yasujiro Taguchi, Yoshinori Tokura, and Max Hirschberger

Phys. Rev. X 14, 021012 – Published 16 April 2024

Abstract

The thermoelectric Nernst effect of solids converts heat flow to beneficial electronic voltages. Here, using a correlated topological semimetal with high carrier mobility $μ$ in the presence of magnetic fluctuations, we demonstrate an enhancement of the Nernst effect close to a magnetic phase transition. A magnetic instability in NdAlSi modifies the carrier relaxation time on “hot spots” in momentum space, causing a strong band filling dependence of $μ$ . We quantitatively derive electronic band parameters from a novel two-band analysis of the Nernst effect $S_{x y}$ , in good agreement with quantum oscillation measurements and band calculations. While the Nernst response of NdAlSi behaves much like conventional semimetals at high temperatures, an additional contribution $Δ S_{xy}$ from electronic correlations appears just above the magnetic transition. Our work demonstrates the engineering of the relaxation time, or the momentum-dependent self-energy, to generate a large Nernst response independent of a material’s carrier density, i.e., for metals, semimetals, and semiconductors with large $μ$ .

Received 23 July 2023
Revised 31 January 2024
Accepted 5 March 2024

DOI:https://doi.org/10.1103/PhysRevX.14.021012

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Magnetic order Thermomagnetic effects Transport phenomena

Weyl semimetal

Quantum oscillation techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rinsuke Yamada ^1,*, Takuya Nomoto ², Atsushi Miyake³, Toshihiro Terakawa¹, Akiko Kikkawa⁴, Ryotaro Arita ^2,4, Masashi Tokunaga ³, Yasujiro Taguchi⁴, Yoshinori Tokura^1,4,5, and Max Hirschberger^1,4,†

¹Department of Applied Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
²Research Center for Advanced Science and Technology, The University of Tokyo, Komaba, Tokyo 153-8904, Japan
³The Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
⁴RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
⁵Tokyo College, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan

^*To whom correspondence should be addressed: ryamada@ap.t.u-tokyo.ac.jp
^†To whom correspondence should be addressed: hirschberger@ap.t.u-tokyo.ac.jp

Popular Summary

The thermoelectric Nernst effect in solids converts heat flow to electronic voltages, which promises to be a boon for energy-saving technologies. The two best-known contributions to this response are the normal Nernst effect, caused by the orbital motion of electrons, and the anomalous Nernst effect, which appears in the ground state of magnetic materials. Here, we reveal a new mechanism to enhance the Nernst effect via magnetic fluctuations, or spin dynamics.

For our analysis, we focus on the polar topological semimetal NdAlSi, which realizes both electronic correlations and magnetic order in a clean setting: At elevated temperatures, spin fluctuations cause enhanced scattering of Weyl electrons—massless, near-relativistic charge carriers—modifying their self-energy, or relaxation time, at certain “hot spots” in momentum space. Using a newly developed multiband analysis based on semiclassical transport theory, we quantitatively characterize the electronic structure via the thermoelectric effects, which we find to be in good agreement with band theory. The analysis reveals an additional Nernst signal, driven by the momentum- and energy-dependent relaxation time from magnetic fluctuations.

Enhanced thermoelectric Nernst responses can thus be anticipated in a plethora of correlated materials ranging from charge- and spin-density wave materials to the strongly correlated copper oxide superconductors.

Key Image

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 14, Iss. 2 — April - June 2024

Subject Areas

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Fermi surface nesting of Weyl points in NdAlSi. (a) Crystal structure of NdAlSi, with polar $c$ axis. (b) Spin texture in the $a b$ plane (plane I) with the magnetic ordering vector $Q \approx (2 / 3, 2 / 3, 0)$ along the [110] direction, as revealed in Ref. [22]. (c) Electronic structure in NdAlSi; one octant of the Brillouin zone is shown. There are four types of Fermi surfaces: a high-mobility Weyl $β$ pocket (brown), a Weyl $Σ$ pocket subject to Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions (red), a hole $γ$ pocket with quadratic electronic band dispersion (pink), and an electron $δ$ pocket with heavy electron mass (blue). In the Hall and Nernst effects, only the former three contribute dominantly (below). White solid lines indicate the extremal cross sections of electron orbits observed experimentally when a magnetic field is applied along the $a$ axis. (d) Two-dimensional cuts of Fermi surfaces at $k_{z} = 0$ , where traces corresponding to $E_{F} = - 4$ , $- 3$ , and 0 meV are shown. Yellow lines and a shaded region indicate the nesting plane with ordering vector $Q$ . Illustration: Weyl cones in the electronic band structure of $Σ$ .
Reuse & Permissions
Figure 2
High-mobility electrons from Weyl and trivial Fermi surface pockets in NdAlSi, detected by electrical transport. (a) Hall conductivity $σ_{x y}$ at various temperatures. The black dashed lines indicate fitting to a two-carrier model. Inset (top left): sample geometry, where magnetic field $B$ and electric current $J$ are applied along the $c$ axis and $a$ axis, respectively. Inset (bottom): two components of the fit, shown individually. (b) Carrier density of two Fermi surface sheets, estimated by two-carrier fitting (left axis). The parameters $μ_{1}$ , $n_{1}$ are assigned to a trivial ( $γ$ ) and $μ_{2}$ , $n_{2}$ to a Weyl-type ( $β$ ) Fermi surface sheet, respectively. Right axis: temperature dependence of the Seebeck effect divided by temperature, with enhancement above $T_{N}$ likely due to electron correlations on $Σ$ . (c) Carrier mobility of the trivial $γ$ and Weyl $β$ bands as a function of temperature.
Reuse & Permissions
Figure 3
Two-carrier analysis of the thermoelectric Nernst effect in NdAlSi. (a)–(h) Magnetic field dependence of Nernst effect $S_{x y}$ normalized by resistivity and temperature. Two-carrier decomposition of the Nernst effect is shown by black dotted lines; this represents a fit to Eq. (1) at $T \geq 35 K$ and a calculated curve according to Eq. (1), with extrapolated model parameters, at lower temperatures. An excess Nernst signal $Δ S_{xy}$ , beyond Eq. (1), appears at intermediate temperatures $T = 10 - 30 K$ , marked by pale red shading between the data and the semiclassical calculation. Inset: sample geometry for thermoelectric measurements, where the magnetic field and temperature gradient are applied along the crystallographic $c$ and $a$ axes, respectively. (i),(j) Temperature dependence of effective mass and Fermi velocity for $γ$ and $β$ pockets with quadratic and linear band dispersions, respectively. Corresponding electronic structure parameters estimated from quantum oscillation experiments are also shown as green dotted lines in panels (i) and (j).
Reuse & Permissions
Figure 4
Enhancement of thermoelectric Nernst effect due to electron correlations from a magnetic Fermi surface instability. (a)–(c) Magnetic field dependence of excess Nernst signal $Δ S_{xy}$ , normalized by temperature and longitudinal resistivity $ρ_{xx}$ , at 30 K, 12 K, and 2 K. A fit to Eq. (2) is indicated by the black line. (d) Illustration: contour lines of relaxation time $τ (k)$ in momentum space with a hot spot of $τ (k)$ , such as can be driven by magnetic ordering with the propagation vector $Q \approx (2 / 3, 2 / 3, 0)$ in NdAlSi, cf. Fig. 1. The arrows indicate a $k$ -space gradient of the relaxation time. For a given electron or hole on the Fermi surface, the effective energy dependence of $τ$ is a product of this gradient and the inverse Fermi velocity, $d τ / d E = d τ / d k \cdot d k / d E$ . (e) Energy derivative of carrier relaxation time $d τ / d E$ , derived from $Δ S_{xy}$ and attributed to correlations on the $Σ$ pocket. Yellow shading and a vertical dashed line mark the regime of strong fluctuations and the transition to long-range magnetic order at $T_{N} = 7.4 K$ , respectively.
Reuse & Permissions

Physical Review X