arXiv subjects

Christoph Geibel

Publications and source records attributed to Christoph Geibel.

At least 19 recordsLinked to original sources

arXiv2026

Evolution of electron spin resonance through a metallic quantum critical phase diagram

In the heavy-fermion metal YbRh2Si2, quantum criticality at a suppressed antiferromagnetic order is governed by the interplay of local magnetic moments and itinerant conduction electrons. We demonstrate how this can be investigated by a new experimental approach that enables the observation of electron spin resonance (ESR) across a broad range of frequencies and fields at very low temperatures. This allowed us to cover a large part of the phase diagram from the paramagnetic Fermi-liquid phase to the phase with antiferromagnetic order and including the quantum-critical regime. Both the ESR g-factor and the linewidth present distinct behaviors in these three regimes, providing further insight into the physics across a quantum critical point. Notably, when cooling down at a field directly towards the quantum critical point, both g-factor and linewidth continuously decrease. Furthermore, we observe a very good matching of the g-factor behavior upon field-tuning and temperature-tuning towards the quantum-critical point. We analyze and discuss the results in the context of present theories on ESR in strongly correlated electron systems.

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arXiv2026

Incommensurate modulation with $Q=0$ A-type Antiferromagnetic Order in CeRh$_2$As$_2$ revealed by NQR studies

We performed $^{75}$As nuclear quadrupole resonance (NQR) and nuclear magnetic resonance (NMR) measurements on a higher-quality single-crystalline CeRh$_2$As$_2$, a heavy-fermion superconductor exhibiting multiple superconducting (SC) phases under magnetic fields along the $c$ axis. This SC multiphase is believed to originate from staggered Rashba spin-orbit coupling associated with locally broken inversion symmetry. In addition to superconductivity, CeRh$_2$As$_2$ exhibits phase I below $T_0\sim0.5$ K and an antiferromagnetic (AFM) state below $T_{N}\sim 0.25$ K in the early-stage samples. In the higher-quality sample, the AFM transition becomes more pronounced, and $T_{N}$ increases to nearly coincide with $T_{SC}$. The NQR spectra at the As(1) site imply an internal field with an incommensurate distribution, indicating a two-dimensional incommensurate modulation of the magnetic structure superimposed on a $Q=0$ A-type AFM component. Moreover, a pronounced decrease in the NQR intensity at $T_0$ well-above $T_{N}$ and an abrupt increase in the internal field at $T_{N}$ suggest the emergence of a slowly fluctuating AFM order at $T_0$ which becomes static at $T_{N}$.

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arXiv2025

Conventional $s$-wave Superconductivity in LaRh$_2$As$_2$; the Analog without the 4$f$ Electrons of CeRh$_2$As$_2$

Superconductor LaRh$_2$As$_2$ has the same crystal structures as CeRh$_2$As$_2$, which exhibits superconducting (SC) multiphase in the $c$-axis magnetic field. Although the SC transition temperatures $T_c$ are similar, around 0.3 K, LaRh$_2$As$_2$ shows conventional type-II superconductivity with a small upper critical field $H_{c2}\sim$ 10 mT. At present, the SC properties of LaRh$_2$As$_2$ have not been clarified yet. We performed $^{75}$As-nuclear quadrupole resonance (NQR) measurements on LaRh$_2$As$_2$ to investigate the SC properties and gap structure. $1/T_1$ shows a clear coherence peak just below $T_c$ and an exponential decrease at lower temperatures, suggesting full-gap $s$-wave superconductivity. The numerical calculations based on an $s$-wave SC model reveal an SC gap size of $\Delta(0)/k_{B}T_{c} \sim 1.48$, consistent with the weak-coupling $s$-wave superconductivity. These results suggest that the 4$f$ electrons in CeRh$_2$As$_2$ not only enhance the orbital limiting field but also contribute to the formation of unconventional superconductivity with SC multiphase.

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arXiv2025

Multilayer Crystal Field states from locally broken centrosymmetry

Local charge, spin, or orbital degrees of freedom with intersite interactions are oftentimes sufficient to construct most quantum orders. This is conventionally true for f-electron systems, where the extent of the f-electrons and their associated crystal-electric-field (CEF) states are strongly localized. Here, polarized Raman spectroscopy measurements of a locally non-centrosymmetric compound, CeCoSi, unveil more CEF excitations than expected in the local model. We interpret this as experimental evidence for the entanglement of CEF states between cerium layers. This composite sublattice, spin, and orbital degree of freedom provides an unconsidered means to form novel orders, not only in this system, but in any system exhibiting globally preserved yet locally broken centrosymmetry.

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arXiv2025

Odd-parity superconductivity underpinned by antiferromagnetism in heavy fermion metal YbRh$_2$Si$_2$

Topological superconductors are essential elements of the periodic table of topological quantum matter. However, the relevant odd-parity spin-triplet superconductors are rare. We report high-resolution measurements of the complex electrical impedance of YbRh$_2$Si$_2$ down to 0.4 mK, that reveal the presence of several superconducting states, suppressed differently by magnetic field, both Pauli-limited and beyond the Pauli limit. Superconductivity is abruptly switched off at the critical field of the primary antiferromagnetic order. The onset of electro-nuclear spin density wave order enhances the superconductivity, which we account for by the simultaneous formation of a spin-triplet pair density wave. Together these observations provide compelling evidence for odd-parity superconductivity, and its underpinning by antiferromagnetism, and allow us to identify the topological helical state.

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arXiv2025

Magnetic Phase Diagram of YbRh\textsubscript{2}Si\textsubscript{2}: the Influence of Hyperfine Interactions

We report the determination of the magnetic phase diagram of the heavy fermion metal YbRh\textsubscript{2}Si\textsubscript{2} in magnetic fields up to 70\,mT applied perpendicular to the crystallographic c-axis. By a combination of heat capacity, magneto-caloric, and magneto-resistance measurements we map two antiferromagnetic phases: the electronic AFM1 below 70\,mK and electro-nuclear AFM2 below 1.5\,mK. The measurements extend into the microkelvin regime to explore the quantum phase transitions in this system. We demonstrate how the hyperfine interaction significantly modifies the phase diagram and the putative field-tuned quantum critical point. The determination of the rich magnetic properties of YbRh\textsubscript{2}Si\textsubscript{2} is essential to understanding the interplay of the two magnetic orders and superconductivity in this compound.

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arXiv2024

Appearance of $c$-axis magnetic moment in odd-parity antiferromagnetic state in CeRh$_2$As$_2$ revealed by $^{75}$As-NMR

CeRh$_2$As$_2$ shows the superconducting (SC) multiphase under the $c$-axis magnetic field, which is considered to originate from local inversion symmetry breaking at the Ce site. We reported that the antiferromagnetic (AFM) order is inside the SC phase and that the AFM state disappears at the transition field to the high-field SC phase. However, the magnetic structure in the AFM state has not been clarified yet. In this study, we performed $^{75}$As-NMR measurements in the SC phase in $H\parallel [110]$ to identify the magnetic structure. Comparing the NMR linewidth with $H \parallel c$, we found that the internal magnetic field is oriented to the $c$ axis. This suggests a $q = 0$ $A$-type AFM with the moments parallel to the $c$ axis. We also observed the reduction of the spin susceptibility, which indicates spin-singlet superconductivity in the low-field SC phase. This study provides an important clue to clarify the correlation between the SC multiphase, magnetism, and local inversion symmetry breaking.

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arXiv2024

Coexistence of local magnetism and superconductivity in the heavy-fermion CeRh$_2$As$_2$ revealed by $\mu$SR studies

The superconducting (SC) state ($T_\mathrm{c}$ = 0.3 K) of the heavy-fermion compound CeRh$_2$As$_2$, which undergoes an unusual field-induced transition to another high-field SC state, emerges from an unknown ordered state below $T_\mathrm{o}$ = 0.55 K. While an electronic multipolar order of itinerant Ce-4$f$ states was proposed to account for the $T_\mathrm{o}$ phase, the exact order parameter has not been known to date. Here, we report on muon spin relaxation ($\mu$SR) studies of the magnetic and SC properties in CeRh$_2$As$_2$ single crystals at low temperatures. We reveal a magnetic origin of the $T_\mathrm{o}$ order by identifying a spontaneous internal field below $T_\mathrm{o}$ = 0.55 K. Furthermore, we find evidence of a microscopic coexistence of local magnetism with bulk superconductivity. Our findings open the possibility that the $T_\mathrm{o}$ phase involves both dipole and higher order Ce-4$f$ moment degrees of freedom and accounts for the unusual non-Fermi liquid behavior.

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arXiv2024

Metallic local-moment magnetocalorics as a route to cryogenic refrigeration

Commercial adiabatic demagnetisation refrigerators still employ the same hydrated salts that were first introduced over 85 years ago. The inherent limitations of these insulating magnetocalorics - poor thermal conductivity at sub-Kelvin temperatures, low entropy density, corrosiveness - can be overcome by a new generation of rare-earth based metallic magnetocalorics. Here, we present the metallic magnetocaloric YbNi1.6 Sn as an attractive alternative to conventional refrigerants. YbNi1.6Sn retains high entropy into the 100 mK regime and avoids the noble metal constituents of alternative refrigerants. Demagnetisation tests demonstrate that YbNi1.6Sn enables economical and durable alternatives to traditional cooling devices for temperatures reaching below 120 mK. We find that the magnetocaloric properties of this material are facilitated by unusually small Kondo and RKKY interactions, which position YbNi1.6Sn in the extreme local moment limit on the generalised Kondo lattice phase diagram.

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arXiv2024

Investigation of the hyperfine coupling constant of locally noncentrosymmetric heavy-fermion superconductor CeRh$_{2}$As$_{2}$

We performed $^{75}$As-NMR measurements in $H\parallel ab$ to investigate the normal-state magnetic properties of CeRh$_2$As$_2$, a recently-discovered heavy-fermion superconductor. We compared the NMR Knight shift $K$ with the magnetic susceptibility $χ_{ab}$, and estimated the hyperfine coupling constant $A_{\mathrm{hf}}$ from the slope of the $K-χ$ plot. We observed that the magnitude of $A_{\mathrm{hf},ab}$ at the As(1) site changes at around 20 K owing to emerging the heavy-fermion state, which was also observed in $A_{\mathrm{hf}}$ at the As(2) site and in $H\parallel c$. The sign of $A_{\mathrm{hf},ab}$ at the As(1) site is negative in low temperature. These are important for the analysis of the NMR results of CeRh$_2$As$_2$ in the superconducting state.

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arXiv2024

Decoupling multi-phase superconductivity from normal state ordering in CeRh$_2$As$_2$

CeRh$_2$As$_2$ is a multi-phase superconductor with $T_{\textrm{c}}=0.26\,\textrm{K}$. The two superconducting (SC) phases, SC1 and SC2, observed for a magnetic field $H$ parallel to the $c$ axis of the tetragonal unit cell, have been interpreted as even- and odd-parity SC states, separated by a phase boundary at $μ_{\textrm{0}}H^{*}=4\,\textrm{T}$. Such parity switching is possible due to a strong Rashba spin-orbit coupling at the Ce sites located in locally non-centrosymmetric environments of the globally centrosymmetric lattice. Existence of another ordered state (Phase I) below a temperature $T_{\textrm{0}}\approx0.4\,\textrm{K}$ suggests an alternative interpretation of the $H^{*}$ transition: It separates a mixed SC+I (SC1) and a pure SC (SC2) state. Here, we present a detailed study of higher quality single crystals of CeRh$_2$As$_2$, showing much sharper signatures at $T_{\textrm{c}}=0.31\,\textrm{K}$ and $T_{\textrm{0}}=0.48\,\textrm{K}$. We refine the $T$-$H$ phase diagram of CeRh$_2$As$_2$ and demonstrate that $T_{0}(H)$ and $T_{\textrm{c}}(H)$ lines meet at $μ_{\textrm{0}}H\approx6\,\textrm{T}$, well above $H^{*}$, implying no influence of Phase I on the SC phase switching. A basic analysis with the Ginzburg-Landau theory indicates a weak competition between the two orders.

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arXiv2023

Exposing the odd-parity superconductivity in CeRh$_2$As$_2$ with hydrostatic pressure

Odd-parity superconductivity is a fundamentally interesting but rare state of matter with a potential for applications in topological quantum computing. Crystals with staggered locally noncentrosymmetric structures have been proposed as platforms where a magnetic field can induce a transition between even- and odd-parity superconducting (SC) states. The strongly correlated superconductor CeRh$_2$As$_2$ with the critical temperature $T_{\mathrm{c}}\approx0.4\,\mathrm{K}$ is likely the first example material showing such a phase transition, which occurs at the magnetic field $\mu_{0}H^{*}=4\,\mathrm{T}$ applied along the crystallographic $c$ axis. CeRh$_2$As$_2$ also undergoes a phase transition of an unknown origin at $T_{0}=0.5\,\mathrm{K}$. By subjecting CeRh$_2$As$_2$ to hydrostatic pressure and mapping the resultant changes to the SC phase diagrams we investigated how the lattice compression and changes to the electronic correlations affect the stability and relative balance of the two SC states. The abnormally high in-plane upper critical field becomes even higher close to a quantum critical point of the $T_{0}$ order. Remarkably, the SC phase-switching field $H^{*}$ is drastically reduced under pressure, dropping to $0.3\,\mathrm{T}$ at $2.7\,\mathrm{GPa}$. This result signals an apparent strengthening of the local noncentrosymmetricity and forecasts a possible stabilization of the putative odd-parity state down to zero field, hitherto not considered by theoretical models.

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arXiv2023

Pressure-tuned quantum criticality in the locally non-centrosymmetric superconductor CeRh$_2$As$_2$

The unconventional superconductor CeRh$_2$As$_2$ (critical temperature $T_{\mathrm{c}}\approx0.4\,\mathrm{K}$) displays an exceptionally rare magnetic-field-induced transition between two distinct superconducting (SC) phases, proposed to be states of even and odd parity of the SC order parameter, which are enabled by a locally noncentrosymmetric structure. The superconductivity is preceded by a phase transition of unknown origin at $T_{0}\approx0.5\,\mathrm{K}$. Electronic low-temperature properties of CeRh$_2$As$_2$ show pronounced non-Fermi-liquid behavior, indicative of a proximity to a quantum critical point (QCP). The role of quantum fluctuations and normal state orders for the superconductivity in a system with staggered Rashba interaction is currently an open question, pertinent to explaining the occurrence of two-phase superconductivity. In this work, using measurements of resistivity and specific heat under hydrostatic pressure, we show that the $T_{0}$ order vanishes completely at a modest pressure of $P_{0}=0.5\,\mathrm{GPa}$, revealing a QCP. In line with the quantum criticality picture, the linear temperature dependence of the resistivity at $P_{0}$ evolves into a Fermi-liquid quadratic dependence as quantum critical fluctuations are suppressed by increasing pressure. Furthermore, the domelike behavior of $T_{\mathrm{c}}$ around $P_{0}$ implies that the fluctuations of the $T_{0}$ order are involved in the SC pairing mechanism.

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arXiv2023

Ce$_{2}$Ir$_{3}$Ga$_{5}$ : a new locally non-centrosymmetric heavy fermion system

Recently, a new type of unconventional superconductivity with a field-induced transition between two different superconducting (SC) states was discovered in the heavy fermion system CeRh$_{2}$As$_{2}$. This unusual SC state was proposed to be based on specific symmetries of the underlying structure, i.e., a globally centrosymmetric layered structure, but where the Ce-layers themselves lack inversion symmetry. This new type of SC state has attracted strong interest, prompting the search for further heavy fermion systems crystallizing in structures with appropriate symmetries. We report the discovery and the study of a new Ce-based heavy fermion system with a globally centrosymmetric structure but without inversion symmetry on the Ce-site, Ce$_{2}$Ir$_{3}$Ga$_{5}$. A single crystal X-ray diffraction study revealed an orthorhombic U$_{2}$Co$_{3}$Si$_{5}$ type structure. Resistivity, specific heat, and magnetization measurements indicate a moderate-heavy fermion behavior with a Kondo energy scale of the order of 40 K. Most experimental results suggest the absence of magnetic order, but a tiny anomaly in the specific heat opens the possibility for a very weak, itinerant type of ordering.

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arXiv2023

Parity transition of spin-singlet superconductivity using sub-lattice degrees of freedom

Recently, a superconducting (SC) transition from low-field (LF) to high-field (HF) SC states was reported in CeRh$_2$As$_2$, indicating the existence of multiple SC states. It has been theoretically noted that the existence of two Ce sites in the unit cell, the so-called sub-lattice degrees of freedom owing to the local inversion symmetry breaking at the Ce sites, can lead to the appearance of multiple SC phases even under an interaction inducing spin-singlet superconductivity. CeRh$_2$As$_2$ is considered as the first example of multiple SC phases owing to this sub-lattice degree of freedom. However, microscopic information about the SC states has not yet been reported. In this study, we measured the SC spin susceptibility at two crystallographically inequivalent As sites using nuclear magnetic resonance for various magnetic fields. Our experimental results strongly indicate a spin-singlet state in both SC phases. In addition, the antiferromagnetic phase, which appears within the SC phase, only coexists with the LF SC phase; there is no sign of magnetic ordering in the HF SC phase. The present work reveals unique SC properties originating from the locally noncentrosymmetric characteristics.

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arXiv2022

Two-dimensional XY-type Magnetic Properties of Locally Noncentrosymmetric Superconductor CeRh$_2$As$_2$

We performed $^{75}$As-NMR measurements to investigate the normal-state magnetic properties of CeRh$_2$As$_2$, a recently-discovered heavy-fermion superconductor. The magnitude and temperature dependence of the Knight shift at the As(2) site indicate easy-plane-type magnetic anisotropy in CeRh$_2$As$_2$. With regard to spin fluctuations, the temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ arising from the 4$f$ electrons decreases from high-temperature constant behavior on cooling at $\sim$ 40~K, which is typical behavior of heavy-fermion systems. In addition, $1/T_1$ becomes constant at low temperatures, suggesting spatially two-dimensional antiferromagnetic fluctuations. Two-dimensional magnetic correlations in the real space are quite rare among heavy-fermion superconductors, and they may be a key factor in the unique superconducting multi-phase in CeRh$_2$As$_2$.

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arXiv2021

Observation of antiferromagnetic order as odd-parity multipoles inside the superconducting phase in CeRh$_{2}$As$_{2}$

Spatial inversion symmetry in crystal structures is closely related to the superconducting (SC) and magnetic properties of materials. Recently, several theoretical proposals that predict various interesting phenomena caused by the breaking of the local inversion symmetry have been presented. However, experimental validation has not yet progressed owing to the lack of model materials. Here we present evidence for antiferromagnetic (AFM) order in CeRh$_{2}$As$_{2}$ (SC transition temperature $T_{\rm SC} \sim 0.37$~K), wherein the Ce site breaks the local inversion symmetry. The evidence is based on the observation of different extents of broadening of the nuclear quadrupole resonance spectrum at two crystallographically inequivalent As sites. This AFM ordering breaks the inversion symmetry of this system, resulting in the activation of an odd-parity magnetic multipole. Moreover, the onset of antiferromagnetism $T_{\rm N}$ within an SC phase, with $T_{\rm N} < T_{\rm SC}$, is quite unusual in systems wherein superconductivity coexists or competes with magnetism. Our observations show that CeRh$_{2}$As$_{2}$ is a promising system to study how the absence of local inversion symmetry induces or influences unconventional magnetic and SC states, as well as their interaction.

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arXiv2021

Possible Pressure-Induced Charge-Density Wave Quantum Critical Point in LuPd2In

We investigated the effect of application of hydrostatic pressure on the charge-density wave (CDW) state in Lu(Pt$_{1-x}$Pd$_x$)$_2$In by electrical-resistivity measurements. In Lu(Pt$_{0.7}$Pd$_{0.3}$)$_{2}$In we find an increase of the CDW transition temperature upon application of pressure, which is not expected based on simple volume arguments, but in line with results of a theoretical work by Kim et al. [Phys. Rev. Lett. 125, 157001 (2020).]. Combining experimental and theoretical results suggests the existence of a CDW quantum critical point in stoichiometric LuPd$_2$In around $p\approx20$ GPa.

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