Fig. 1  The upper panel shows the set-up of the NMR experiment under uniaxial stress. The bottom panel shows the Fermi surface of Sr₂RuO₄. When approaching a van-Hove singularity, the density of state sharply increases.

Fig. 2  ¹⁷O NMR spectra under strain, for ¹⁷O -1/2↔1/2 transition. The left panel is for B//b, and the right panel is for B//c.

(Phys. Rev. X 9, 021044, DOI:https://doi.org/10.1103/PhysRevX.9.021044)

Background

Sr₂RuO₄ is one of the most fascinating unconventional superconductors. Although it shares the same crystalline structure with single-layer high-T_c cuprates, its T_c value is much lower than that of the high-T_c. At the early stage of its discovery, theorists predicted ap-wave pairing state in Sr₂RuO₄. The experimental evidence forp-wave pairing came primarily from NMR Knight shift, the phase-sensitive, and later, cantilever magnetometry measurements. However, controversies on its precise pairing symmetry have persisted. For example, the absence of T_c vs. strain cusp near zero strain in the uniaxial strain measurements on Sr₂RuO₄ appears to suggest that a simplep-wave on a single-band is not likely to explain the experimental data assuming that no complications from the nonuniformity of the strains exist. Bulk and local experimental probes are needed to elucidate this critical issue.

What we discover?

The effects of uniaxial compressive stress on the normal state ¹⁷O nuclear-magnetic-resonance properties of the unconventional superconductor Sr₂RuO₄ are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominala-axis strain ε_aa≡ε_v that maximizes the superconducting transition temperatureT_c. The spin susceptibility weakly increases on lowering the temperature below T≃10 K, consistent with an enhanced density of states associated with passing the Fermi energy through a van Hove singularity. Although such a Lifshitz transition occurs in theγband formed by the Ru d_xy states hybridized with in-plane O p_π orbitals, the large Hund’s coupling renormalizes the uniform spin susceptibility, which, in turn, affects the hyperfine fields of all nuclei. We estimate this “Stoner” renormalizationSby combining the data with first-principles calculations and conclude that this is an important part of the strain effect, with implications for superconductivity.

Why is this important?

This work is important for two reasons. First, because NMR measurements are both bulk and local, we thus provide solid evidence for a strain-induced van Hove singularity. Second, the normal state investigation has two ramifications: In the first approximation, this effect strongly favors some singlet pairings, such as extendeds,d_zx±id_yz, or d_x2−y2 mildly favors the d_xy pairing and less so any triplet pairing. However, this enhancement of the DOS through the Stoner factor boosts ferromagnetic spin fluctuations, which favors triplet states and seems to disfavor singlet pairing. This presumably would boost up new theoretical and experimental researches in the coming future.

Who did the research?

Yongkang Luo^1,2*,A. Pustogow¹, P. Guzman¹, A. P. Dioguardi³, S. M. Thomas³, F. Ronning³,

N. Kikugawa⁴, D. A. Sokolov⁵, F. Jerzembeck⁵, A. P. Mackenzie^5,6, C.W. Hicks⁵,

E. D. Bauer³, I. I. Mazin⁷, and S. E. Brown^1†

¹Department of Physics & Astronomy, University of California, Los Angeles, Los Angeles, California 90095, USA

²Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

³Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

⁴National Institute for Materials Science, Tsukuba 305-0003, Japan

⁵Max Planck Institute for Chemical Physics of Solids, Dresden 01187, Germany

⁶Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, United Kingdom

⁷Code 6393, Naval Research Laboratory, Washington, D.C. 20375, USA

Acknowledgements

This work was supported in part by the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory under Project No. 20170204ER. Y. L. acknowledges partial support through the LDRD and 1000 Youth Talents Plan of China. N. K. acknowledges the support from JSPS KAKNHI (Grant No. 18K04715). I. I.M. is supported by ONR through the NRL basic research program. This work is supported in part by the National Science Foundation.

(Grants No. DMR-1410343 and No. DMR-1709304).