Magnetic Quantum Critical Point Research Articles

Ferromagnetic quantum critical point protected by nonsymmorphic symmetry in a Kondo metal

Quantum critical points (QCPs), zero-temperature phase transitions, are windows to fundamental quantum-mechanical phenomena associated with universal behaviour. Magnetic QCPs have been extensively investigated in the vicinity of antiferromagnetic order. However, QCPs are rare in metallic ferromagnets due to the coupling of the order parameter to electronic soft modes. Recently, antisymmetric spin-orbit coupling in noncentrosymmetric systems was suggested to protect ferromagnetic QCPs. Nonetheless, multiple centrosymmetric materials host FM QCPs, suggesting a more general mechanism behind their protection. In this context, CeSi2-δ, a dense Kondo lattice crystallising in a centrosymmetric structure, exhibits ferromagnetic order when Si is replaced with Ag. We report that the Ag-substitution to CeSi1.97 linearly suppresses the ferromagnetic order towards a QCP, accompanied by concurrent strange-metal behaviour. Herein, we suggest that, despite the centrosymmetric structure, spin-orbit coupling arising from the local noncentrosymmetric structure, in combination with nonsymmorphic symmetry, can protect ferromagnetic QCPs. Our findings offer a general guideline for discovering new ferromagnetic QCPs and highlight one new family of materials within which the interplay of topology and quantum phase transitions can be investigated in the context of strongly correlated systems.

Magnon interactions in a moderately correlated Mott insulator

Quantum fluctuations in low-dimensional systems and near quantum phase transitions have significant influences on material properties. Yet, it is difficult to experimentally gauge the strength and importance of quantum fluctuations. Here we provide a resonant inelastic x-ray scattering study of magnon excitations in Mott insulating cuprates. From the thin film of SrCuO2, single- and bi-magnon dispersions are derived. Using an effective Heisenberg Hamiltonian generated from the Hubbard model, we show that the single-magnon dispersion is only described satisfactorily when including significant quantum corrections stemming from magnon-magnon interactions. Comparative results on La2CuO4 indicate that quantum fluctuations are much stronger in SrCuO2 suggesting closer proximity to a magnetic quantum critical point. Monte Carlo calculations reveal that other magnetic orders may compete with the antiferromagnetic Néel order as the ground state. Our results indicate that SrCuO2—due to strong quantum fluctuations—is a unique starting point for the exploration of novel magnetic ground states.

Pressure-induced magnetic phase and structural transition in SmSb2

Abstract Motivated by the recent discovery of unconventional superconductivity around a magnetic quantum critical point in pressurized CeSb2, here we present a high-pressure study of an isostructural antiferromagnetic (AFM) SmSb2 through electrical transport and synchrotron x-ray diffraction measurements. At P C ~2.5 GPa, we found a pressure-induced magnetic phase transition accompanied by a Cmca→P4/nmm structural phase transition. In the pristine AFM phase below P C, the AFM transition temperature of SmSb2 is insensitive to pressure; in the emergent magnetic phase above P C, however, the magnetic critical temperature increases rapidly with increasing pressure. In addition, at ambient pressure, the magnetoresistivity (MR) of SmSb2 increases suddenly upon cooling below the AFM transition temperature and presents linear nonsaturating behavior under high field at 2 K. With increasing pressure above P C, the MR behavior remains similar to that observed at ambient pressure, both in terms of temperature- and field-dependent MR. This leads us to argue an AFM-like state for SmSb2 above P C. Within the investigated pressure of up to 45.3 GPa and the temperature of down to1.8 K, we found no signature of superconductivity in SmSb2.

Evidence for charge delocalization crossover in the quantum critical superconductor CeRhIn5.

The nature of charge degrees-of-freedom distinguishes scenarios for interpreting the character of a second order magnetic transition at zero temperature, that is, a magnetic quantum critical point (QCP). Heavy-fermion systems are prototypes of this paradigm, and in those, the relevant question is where, relative to a magnetic QCP, does the Kondo effect delocalize their f-electron degrees-of-freedom. Herein, we use pressure-dependent Hall measurements to identify a finite-temperature scale Eloc that signals a crossover from f-localized to f-delocalized character. As a function of pressure, Eloc(P) extrapolates smoothly to zero temperature at the antiferromagnetic QCP of CeRhIn5 where its Fermi surface reconstructs, hallmarks of Kondo-breakdown criticality that generates critical magnetic and charge fluctuations. In 4.4% Sn-doped CeRhIn5, however, Eloc(P) extrapolates into its magnetically ordered phase and is decoupled from the pressure-induced magnetic QCP, which implies a spin-density-wave (SDW) type of criticality that produces only critical fluctuations of the SDW order parameter. Our results demonstrate the importance of experimentally determining Eloc to characterize quantum criticality and the associated consequences for understanding the pairing mechanism of superconductivity that reaches a maximum Tc in both materials at their respective magnetic QCP.

Dielectric Relaxation by Quantum Critical Magnons.

We report the experimental observation of dielectric relaxation by quantum critical magnons. Complex capacitance measurements reveal a dissipative feature with a temperature-dependent amplitude due to low-energy lattice excitations and an activation behavior of the relaxation time. The activation energy softens close to a field-tuned magnetic quantum critical point at H=H_{c} and follows single-magnon energy for H>H_{c}, showing its magnetic origin. Our study demonstrates the electrical activity of coupled low-energy spin and lattice excitations, an example of quantum multiferroic behavior.

Enhanced Superconducting Pairing Strength near a Pure Nematic Quantum Critical Point

The quest for high-temperature superconductivity at ambient pressure is a central issue in physics. In this regard, the relationship between unconventional superconductivity and the quantum critical point (QCP) associated with the suppression of some form of symmetry-breaking order to zero temperature has received particular attention. The key question is how the strength of the electron pairs changes near the QCP, and this can be verified by high-field experiments. However, such studies are limited mainly to superconductors with magnetic QCPs, and the possibility of unconventional mechanisms by which nonmagnetic QCP promotes strong pairing remains a nontrivial issue. Here, we report systematic measurements of the upper critical field $H_{{\rm c2}}$ in nonmagnetic FeSe$_{1-x}$Te$_{x}$ superconductors, which exhibit a QCP of electronic nematicity characterized by spontaneous rotational-symmetry breaking. As the magnetic field increases, the superconducting phase of FeSe$_{1-x}$Te$_{x}$ shrinks to a narrower dome surrounding the nematic QCP. The analysis of $H_{{\rm c2}}$ reveals that the Pauli-limiting field is enhanced toward the QCP, implying that the pairing interaction is significantly strengthened via nematic fluctuations emanated from the QCP. Remarkably, this nonmagnetic nematic QCP is not accompanied by a divergent effective mass, distinct from the magnetically mediated pairing. Our observation opens up a nonmagnetic route to high-temperature superconductivity.

Pure nematic quantum critical point accompanied by a superconducting dome

SignificanceThe notion of the quantum critical point (QCP) is at the core of modern condensed matter physics. Near a QCP of the symmetry-breaking order, associated quantum-mechanical fluctuations are intensified, which can lead to unconventional superconductivity. Indeed, dome-shaped superconducting phases are often observed near the magnetic QCPs, which supports the spin fluctuation-driven superconductivity. However, the fundamental question remains as to whether a nonmagnetic QCP of electronic nematic order characterized by spontaneous rotational symmetry breaking can promote superconductivity in real materials. Here, we provide an experimental demonstration that a pure nematic QCP exists near the center of a superconducting dome in nonmagnetic FeSe[Formula: see text] Tex. This result evidences that nematic fluctuations enhanced around the nematic QCP can boost superconductivity.

Thermodynamic properties of nodal superconductors close to a magnetic quantum critical point

In this work we study thermodynamic manifestations of the quantum criticality in multiband unconventional superconductors. As a guiding example we consider the scenario of magnetic quantum critical point in the model that captures superconductivity coexistence with the spin-density wave. We show that in situations when the superconducting order parameter has incidental nodes at isolated points, quantum magnetic fluctuations lead to the renormalization of the relative $T$-linear slope of the London penetration depth. This leads to the nonmonotonic dependence of the penetration depth as a function of doping and the concomitant peak structure across the quantum critical point. In addition, we determine contribution of magnetic fluctuations to the specific heat at the onset of the coexistence phase. Our theoretical analysis is corroborated by making a comparison of our results with the recent experimental data from the low-temperature thermodynamic measurements at optimal composition in BaFe$_2$(As$_{1-x}$P$_x$)$_2$.

Magnetic ground state of the one-dimensional ferromagnetic chain compoundsM(NCS)2(thiourea)2(M=Ni,Co)

The magnetic properties of the two isostructural molecule-based magnets, Ni(NCS)$_{2}$(thiourea)$_{2}$, $S$ = 1, [thiourea = SC(NH$_2$)$_2$] and Co(NCS)$_{2}$(thiourea)$_{2}$, $S$ = 3/2, are characterised using several techniques in order to rationalise their relationship with structural parameters and ascertain magnetic changes caused by substitution of the spin. Zero-field heat capacity and muon-spin relaxation measurements reveal low-temperature long-range ordering in both compounds, in addition to Ising-like ($D < 0$) single-ion anisotropy ($D_{\rm{Co}} \sim$ -100 K, $D_{\rm{Ni}} \sim$ -10 K). Crystal and electronic structure, combined with DC-field magnetometry, affirm highly quasi-one-dimensional behaviour, with ferromagnetic intrachain exchange interactions $J_{\rm{Co}}\approx+4$ K and $J_{\rm{Ni}}\sim+100$ K and weak antiferromagnetic interchain exchange, on the order of $J'$ $\sim-0.1$ K. Electron charge and spin-density mapping reveals through-space exchange as a mechanism to explain the large discrepancy in $J$-values despite, from a structural perspective, the highly similar exchange pathways in both materials. Both species can be compared to the similar compounds $M$Cl$_2$(thiourea)$_4$, $M$ = Ni(II) (DTN) and Co(II) (DTC), where DTN is know to harbour two magnetic field-induced quantum critical points. Direct comparison of DTN and DTC with the compounds studied here shows that substituting the halide Cl$^-$ ion, for the NCS$^-$ ion, results in a dramatic change in both the structural and magnetic properties.

Spin dynamics in NaFeAs and NaFe0.53Cu0.47As probed by resonant inelastic x-ray scattering

The parent compounds of iron-based superconductors are magnetically-ordered bad metals, with superconductivity appearing near a putative magnetic quantum critical point. The presence of both Hubbard repulsion and Hund's coupling leads to rich physics in these multiorbital systems, and motivated descriptions of magnetism in terms of itinerant electrons or localized spins. The NaFe$_{1-x}$Cu$_x$As series consists of magnetically-ordered bad metal ($x=0$), superconducting ($x\approx0.02$) and magnetically-ordered semiconducing/insulating ($x\approx0.5$) phases, providing a platform to investigate the connection between superconductivity, magnetism and electronic correlations. Here we use X-ray absorption spectroscopy and resonant inelastic X-ray scattering to study the valence state of Fe and spin dynamics in two NaFe$_{1-x}$Cu$_x$As compounds ($x=0$ and 0.47). We find that magnetism in both compounds arises from Fe$^{2+}$ atoms, and exhibits underdamped dispersive spin waves in their respective ordered states. The dispersion of spin excitations in NaFe$_{0.53}$Cu$_{0.47}$As is consistent with being quasi-one-dimensional. Compared to NaFeAs, the band top of spin waves in NaFe$_{0.53}$Cu$_{0.47}$As is slightly softened with significantly more spectral weight of the spin excitations. Our results indicate the spin dynamics in NaFe$_{0.53}$Cu$_{0.47}$As arise from localized magnetic moments and suggest the iron-based superconductors are proximate to a correlated insulating state with localized iron moments.

Theory of strain-induced magnetic order and splitting of Tc and TTRSB in Sr2RuO4

The internal structure of the superconducting state in Sr$_2$RuO$_4$ remains elusive at present, and exhibits evidence for time-reversal symmetry breaking. Recent muon spin relaxation measurements under uniaxial strain have revealed an increasing splitting between the superconducting critical temperature $T_c$ and the onset of time-reversal symmetry breaking $T_{\rm TRSB}$ with applied strain [Grinenko et al., arXiv:2001.08152]. In addition, static magnetic order is induced by the uniaxial strain beyond $\sim$1 GPa, indicating that unstrained Sr$_2$RuO$_4$ is close to a magnetic quantum critical point. Here, we perform a theoretical study of the magnetic susceptibility and the associated pairing structure as a function of uniaxial strain. It is found that the recent muon relaxation data can be qualitatively explained from the perspective of spin-fluctuation mediated pairing and the associated strain-dependence of accidentally degenerate pair states in unstrained Sr$_2$RuO$_4$. In addition, while unstrained Sr$_2$RuO$_4$ features mainly $(2\pi/3,2\pi/3)$ magnetic fluctuations, uniaxial strain promotes $(\pi,\pm\pi/2)$ magnetism.

Impact of isoelectronic substitution and hydrostatic pressure on the quantum critical properties of CeRhSi3

There is an ongoing dispute in the community about the absence of a magnetic quantum critical point (QCP) in the noncentrosymmetric heavy fermion compound CeRhSi3. In order to explore this question we prepared single crystals of CeRh(Si1−xGex)3 with x = 0.05 and 0.15 and determined the temperature–pressure (T–p) phase diagram by means of measurements of the electrical resistivity. The substitution of isoelectronic but large Ge enforces a lattice volume increase resulting in a weakening of the Kondo interaction. As a result, the x = 0.05 and x = 0.15 compound exhibit a transition into the antiferromagnetic (AFM) at higher temperatures being TN = 4.7 K and TN1 = 19.7 K, respectively. Application of pressure suppresses TN (TN1) monotonically and pressure induced superconductivity is observed in both Ge-substituted compounds above p ⩾ 2.16 GPa (x = 0.05) and p ⩾ 2.93 GPa (x = 0.15). Extrapolation of TN(p) → 0 of CeRh(Si0.95Ge0.05)3 yields a critical pressure of pc ≈ 3.4 GPa (in CeRh(Si0.85Ge0.15)3 pc ≈ 3.5 GPa) pointing to the presence of an AFM QCP located deep inside the superconducting state.

Divergent Nematic Susceptibility near the Pseudogap Critical Point in a Cuprate Superconductor

Superconductivity is a quantum phenomenon caused by bound pairs of electrons. In diverse families of strongly correlated electron systems, the electron pairs are not bound together by phonon exchange but instead by some other kind of bosonic fluctuations. In these systems, superconductivity is often found near a magnetic quantum critical point (QCP) where a magnetic phase vanishes in the zero-temperature limit. Moreover, the maximum of superconducting transition temperature Tc frequently locates near the magnetic QCP, suggesting that the proliferation of critical spin fluctuations emanating from the QCP plays an important role in Cooper pairing. In cuprate superconductors, however, the superconducting dome is usually separated from the antiferromagnetic phase and Tc attains its maximum value near the verge of enigmatic pseudogap state that appears below doping-dependent temperature T*. Thus a clue to the pairing mechanism resides in the pseudogap and associated anomalous transport properties. Recent experiments suggested a phase transition at T*, yet, most importantly, relevant fluctuations associated with the pseudogap have not been identified. Here we report on direct observations of enhanced nematic fluctuations in (Bi,Pb)2Sr2CaCu2O8+d by elastoresistance measurements, which couple to twofold in-plane electronic anisotropy, i.e. electronic nematicity. The nematic susceptibility shows Curie-Weiss-like temperature dependence above T*, and an anomaly at T* evidences a second-order transition with broken rotational symmetry. Near the pseudogap end point, where Tc is not far from its peak in the superconducting dome, nematic susceptibility becomes singular and divergent, indicating the presence of a nematic QCP. This signifies quantum critical fluctuations of a nematic order, which has emerging links to the high-Tc superconductivity and strange metallic behaviours in cuprates.

Magnetism trends in doped Ce-Cu intermetallics in the vicinity of quantum criticality: Realistic Kondo lattice models based on dynamical mean-field theory

The quantum critical point (QCP) in the archetypical heavy-fermion compound ${\mathrm{CeCu}}_{6}$ doped by Au is described, accounting for the localized $4f$ electron of Ce, using realistic electronic structure calculations combined with dynamical mean-field theory. Magnetism trends in $\mathrm{Ce}{({\mathrm{Cu}}_{1\ensuremath{-}\ensuremath{\epsilon}}{\mathrm{Au}}_{\ensuremath{\epsilon}})}_{6}$ ($0&lt;\ensuremath{\epsilon}\ensuremath{\ll}1$) are compared with those in Co-doped ${\mathrm{CeCu}}_{5}$, which resides on the nonferromagnetic side of the composition space of one of the earliest rare-earth permanent magnet compounds, $\mathrm{Ce}{(\mathrm{Co},\mathrm{Cu})}_{5}$. The construction of a realistic Doniach phase diagram shows that the system crosses over a magnetic quantum critical point in the Kondo lattice in $0.2&lt;x&lt;0.4$ of $\mathrm{Ce}{({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{5}$. Comparison between Au-doped ${\mathrm{CeCu}}_{6}$ and Co-doped ${\mathrm{CeCu}}_{5}$ reveals that the swept region in the vicinity of QCP for the latter thoroughly covers that of the former. The implications of these trends on the coercivity of the bulk rare-earth permanent magnets are discussed.

Visualization of Local Magnetic Moments Emerging from Impurities in Hund's Metal States of FeSe.

Understanding the origin of the magnetism of high temperature superconductors is crucial for establishing their unconventional pairing mechanism. Recently, theory predicts that FeSe is close to a magnetic quantum critical point, and thus weak perturbations such as impurities could induce local magnetic moments. To elucidate such quantum instability, we have employed scanning tunneling microscopy and spectroscopy. In particular, we have grown FeSe film on superconducting Pb(111) using molecular beam epitaxy and investigated magnetic excitation caused by impurities in the proximity-induced superconducting gap of FeSe. Our study provides deep insight into the origin of the magnetic ordering of FeSe by showing the way local magnetic moments develop in response to impurities near the magnetic quantum critical point.

Approaching itinerant magnetic quantum criticality through a Hund's coupling induced electronic crossover in the YFe2Ge2 superconductor

Here, by conducting a systematic $^{89}$Y NMR study, we explore the nature of the magnetic ground state in a newly discovered iron-based superconductor YFe$_2$Ge$_2$. An incoherent-to-coherent crossover due to the Hund's coupling induced electronic correlation is revealed below the crossover temperature $T^*\sim 75\pm15\,\mathrm{K}$. During the electronic crossover, both the Knight shift ($K$) and the bulk magnetic susceptibility ($\chi$) exhibit a similar nonmonotonic temperature dependence, and a so-called Knight shift anomaly is also revealed by a careful $K$-$\chi$ analysis. Such an electronic crossover has been also observed in heavily hole-doped pnictide superconductors \emph{A}Fe$_2$As$_2$ (\emph{A} = K, Rb, and Cs), which is ascribed to the Hund's coupling induced electronic correlation. Below $T^*$, the spin-lattice relaxation rate divided by temperature $(1/T_1T)$ shows a similar suppression as the Knight shift, suggesting the absence of critical spin fluctuations. This seems to be in conflict with a predicted magnetic quantum critical point (QCP) near this system. However, considering a $\mathbf{q}$-dependent "filter" effect on the transferred hyperfine field, a predominant spin fluctuation with A-type correlation would be perfectly filtered out at $^{89}$Y sites, which is consistent with the recent inelastic neutron scattering results. Therefore, our results confirm that, through a Hund's coupling induced electronic crossover, the magnetic ground state of YFe$_2$Ge$_2$ becomes close to an itinerant magnetic QCP with A-type spin fluctuations. In addition, the possible superconducting pairing due to spin fluctuations is also discussed.

In115 NQR study with evidence for two magnetic quantum critical points in dual Ce site superconductor Ce3PtIn11

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Singular charge fluctuations at a magnetic quantum critical point.

Strange metal behavior is ubiquitous in correlated materials, ranging from cuprate superconductors to bilayer graphene, and may arise from physics beyond the quantum fluctuations of a Landau order parameter. In quantum-critical heavy-fermion antiferromagnets, such physics may be realized as critical Kondo entanglement of spin and charge and probed with optical conductivity. We present terahertz time-domain transmission spectroscopy on molecular beam epitaxy-grown thin films of YbRh2Si2, a model strange-metal compound. We observed frequency over temperature scaling of the optical conductivity as a hallmark of beyond-Landau quantum criticality. Our discovery suggests that critical charge fluctuations play a central role in the strange metal behavior, elucidating one of the long-standing mysteries of correlated quantum matter.

Navigating the Trends in the Proximity to Magnetic Quantum Critical Point and Superconductivity for Ce-Based Heavy-Fermion Compounds

Pressure-induced magnetic quantum phase transition of CeRhIn$_5$ is described from first principles based on a realistic Kondo lattice model. Simulations of CeRhIn$_5$ above ambient pressure up to P=5 [GPa] show that it is driven from an antiferromagnetic phase into the paramagnetic phase crossing the possible QCP around P=2 [GPa], being consistent with the experimental trends. Our calculations suggest a possibility for a coexistence phase around $P\stackrel{<}{\sim} 3$ [GPa]. On the basis of the data from our realistic simulations, a comprehensive materials navigator is compiled including pressure dependent CeRhIn5 to possibly provide a guideline for further discovery of Ce-based heavy fermion superconductors.

One-loop effective potential for two-dimensional competing scalar order parameters

Using the method of the effective potential of quantum field theory, we compute the quantum corrections to the phase diagram of systems with competing order parameters. This is specially useful to study metallic systems with competing antiferromagnetic and superconducting ground states. We focus on the two-dimensional case that is relevant for high Tc superconductors and heavy fermion systems. We consider two different types of couplings between the order parameters and obtain the modifications in the phase diagrams due to critical quantum fluctuations in these systems with conflicting orders. We consider z=1, as well as a dissipative z=2 dynamics, typical of antiferromagnetic metals close to the magnetic quantum critical point. Our results show that these depend strongly on both dimensionality and dynamics of the propagators describing the excitations of the possible ordered states. We find stable unconventional coexisting phases, as well as the enhancement of the region of coexistence by fluctuations.