Resolving the nature of magnetic field-induced quantum critical point and the origin of the novel electronic-nematic transition in CeRhIn5

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\Large{\textbf{{Resolving the nature of magnetic field-induced quantum critical point and the origin of the novel electronic-nematic transition in CeRhIn$_{5}$}}}
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\underline{Sanu MISHRA$^1$}, Jacob HORNUNG$^{2,3}$, Denis GORBUNOV$^2$, Daniel J. CAMPBELL$^1$, Matthias RABA$^1$, Johannes KLOTZ$^2$, Tobias FÖRSTER$^2$, Albin DEMUER$^1$, David LEBOEUF$^1$, Sergei ZHERLITSYN$^2$, Hisatomo HARIMA$^4$, Joachim WOSNITZA$^{2,3}$, Dai AOKI$^5$, Alix MCCOLLAM$^6$ and Ilya SHEIKIN$^1$
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\textit{$^1$Laboratoire National des Champs Magn\'{e}tiques Intenses (LNCMI-EMFL), CNRS, UGA, 38042, Grenoble, France}

\textit{$^2$Hochfeld-Magnetlabor Dresden (HLD-EMFL) and W\"{u}rzburg-Dresden Cluster of Excellence ct.qmat, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany}

\textit{$^3$Institut f\"ur Festk\"orper- und Materialphysik, TU Dresden, 01062 Dresden, Germany}

\textit{$^4$Graduate School of Science, Kobe University, Kobe 657-8501, Japan}

\textit{$^5$Institute for Materials Research, Tohoku University, Oarai, Ibaraki, 311-1313, Japan}

\textit{$^6$High Field Magnet Laboratory (HFML-EMFL), Radboud University, 6525 ED Nijmegen, The Netherlands}
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The heavy fermion compound CeRhIn$_{5}$ offers an ideal playground to investigate the rich physics of strongly correlated electron systems. It can be readily tuned to a quantum critical point (QCP) by hydrostatic pressure, chemical doping, and magnetic fields. While the pressure-induced quantum critical point is long accepted to be of the Kondo-breakdown type, the one induced by the magnetic field at $B_{c} \approx$ 50 T was suggested to be of the spin-density-wave type. This assumption is based on the observation of additional de Haas-van Alphen frequencies deep inside the antiferromagnetic state [1], above $B^{*}=$ 30 T, where a novel phase of enhanced in-plane electronic anisotropy emerges [2]. These additional frequencies were interpreted as a signature of an abrupt Fermi-surface reconstruction due to the field-induced itineracy of the $f$ electrons at $B^{*}$.

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\caption{CeRhIn$_{5}$ in high magnetic fields. (a) Evolution of the dHvA frequencies with magnetic fields, obtained in static fields upto 36 T in a dilution fridge and in pulsed fields upto 70 T in a $^3$He cryostat. (b) Magnetic field-temperature ($B-T$) phase diagram based on specific heat and ultrasound velocity measurements.}\label{fig:SCES2021}
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Our comprehensive angular-dependent de Haas-van Alphen study of CeRhIn$_{5}$ and its non-$f$ reference compound LaRhIn$_{5}$ establishes the localized character of the $f$ electrons inside and outside of the antiferromagnetic phase [3]. This rules out any significant field-induced Fermi-surface reconstruction, particularly across $B^{*}$ [see Fig. \ref{fig:SCES2021}(a)]. We suggest the field-induced quantum criticality in CeRhIn$_{5}$ does not conform with the established theoretical models. The persistent localization of the $f$ electrons in CeRhIn$_{5}$ across $B^{*}$ and $B_{c}$ excludes the previously suggested field-enhanced $c-f$ hybridization above $B^{*}$ as the origin of the electronic-nematic state, rendering its true origin elusive. Our observation of a distinct specific-heat anomaly at $B^{*}$ suggests it to be a real phase transition, probably weakly first-order [4]. Further, our ultrasound study for a field applied at 2$^\circ$ from the $c$ axis revealed anomalies at $B^{*}$ in all the symmetry-breaking ultrasonic modes. Similar anomalies of the opposite sign were observed at the well-established metamagnetic transition (AFM1 to AFM3) at $B_{m} \approx$ 20 T. In conjunction with the observation of both anomalies strictly within the antiferromagnetic state, this suggests that the transition at $B^{*}$ corresponds to a field-induced change of the magnetic structure from commensurate (AFM3) to incommensurate (AFM4) [see Fig. \ref{fig:SCES2021}(b)][5]. The magnetic origin of the $B^{*}$ transition is also confirmed by the observation of a distinct anomaly in magnetic torque at 30 T.

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[1] L. Jiao et al., Proc. Natl. Acad. Sci. U.S.A., \textbf{112}, 673 (2015).

[2] F. Ronning et al., Nature,
\textbf{548}, 313, 034714 (2017).

[3] S. Mishra et. al., Phys. Rev. Lett.,
\textbf{126}, 016403 (2021).

[4] S. Mishra et. al., Phys Rev. B,
\textbf{103}, 045110 (2021).

[5] S. Mishra et. al., Phys Rev. B,
\textbf{103}, 165124 (2021).

E-mail for corresponding author: sanumishra3$@$gmail.com
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