Magnetic and Electronic Quantum Criticality in YbRh2Si2

Friedemann, Sven; Westerkamp, T.; Brando, M.; Oeschler, N.; Gegenwart, P.; Krellner, C.; Geibel, C.; MaQuilon, S.; Fisk, Z.; Steglich, F.; Wirth, S.

doi:10.1007/s10909-010-0201-8

Cited by 11 publications

(14 citation statements)

References 37 publications

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“…As may be seen in Fig. 4(a), our model, with T * =50 K, H QC =0.055 T, η H = 0.07 T -1 and α=0.8, yields good agreement with experiments for the field-dependent Néel temperature (10), the delocalization line (15,(24)(25)(26)(27)(28), and the quantum critical line (26). The corresponding field dependence of f 0 (H) is plotted in Fig.…”

Section: Ybrh 2 Sisupporting

confidence: 72%

“…4, that candidate quantum critical point changes with pressure and magnetic field (26), and so represents a target of opportunity for the primarily collective framework developed in this paper. On the other hand, there are signatures of quantum critical behavior that appears to be of purely local origin, such as a line of quantum critical points that change with magnetic field, but are almost unchanged by pressure (26)(27)(28), that may be ascribed to changes induced by single-ion Kondo physics, that the phenomenological model developed here for combined collective and local hybridization cannot presently address.…”

Section: Ybrh 2 Simentioning

confidence: 92%

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Quantum critical behavior in heavy electron materials

Yang

Pines

2014

Proc. Natl. Acad. Sci. U.S.A.

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Quantum critical behavior in heavy electron materials is typically brought about by changes in pressure or magnetic field. In this paper, we develop a simple unified model for the combined influence of pressure and magnetic field on the effectiveness of the hybridization that plays a central role in the two-fluid description of heavy electron emergence. We show that it leads to quantum critical and delocalization lines that accord well with those measured for CeCoIn 5 , yields a quantitative explanation of the field and pressure-induced changes in antiferromagnetic ordering and quantum critical behavior measured for YbRh 2 Si 2 , and provides a valuable framework for describing the role of magnetic fields in bringing about quantum critical behavior in other heavy electron materials.heavy fermion | quantum criticality | two-fluid model O ne of the most striking examples of emergent behavior in quantum matter is the emergence of the itinerant heavy electron liquid in materials that contain a Kondo lattice of localized f electrons coupled to background conduction electrons. Although we do not yet have a microscopic picture of heavy electron emergence and subsequent behavior, a phenomenological two-fluid model has been shown to provide a quantitative description of the way in which the collective hybridization of the localized f electron spin liquid (SL) with the background conduction electrons in a Kondo lattice gives rise to a new state of matter, the Kondo liquid (KL) heavy electron state, that coexists with a SL of partially hybridized local moments over much of the phase diagram (1-7). One can, for example, decompose the static spin susceptibility or spin-lattice relaxation rate into KL and hybridized SL components, e.g., χðT; pÞ = f ðT; pÞχ KL ðT; pÞ + ½1 − f ðT; pÞ χ SL ðT; pÞ;[1]where the strength of the KL component is measured by (1) f ðT; pÞ = minT p , the coherence temperature at which the KL emerges (2), sets the energy scale for its subsequent universal behavior (3-5), brought about by the collective hybridization, and f 0 (p) measures its effectiveness (1).The two-fluid model enables one to follow in detail the emergent behavior of both the KL and the residual hybridized local moments. The point at which f(T,p) = 1 is special, as it marks a delocalization phase transition from partially localized to fully itinerant heavy electron behavior. When the hybridization effectiveness parameter f 0 = 1, that phase transition occurs at absolute zero temperature, and represents a quantum critical point (QCP) that gives rise to unusual quantum critical behavior in the itinerant heavy electrons that is sometimes observed up to comparatively high temperatures (8, 9). Quite generally, if f 0 < 1, the hybridized SL becomes antiferromagnetically ordered, whereas the coexisting KL may become superconducting. On the other hand, if f 0 > 1, the delocalization phase transition will occur along a line of quantum criticality that is determined by T p and the strength of the hybridization effectiveness, and, in the two-fluid...

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Section: Ybrh 2 Sisupporting

confidence: 72%

Section: Ybrh 2 Simentioning

confidence: 92%

Quantum critical behavior in heavy electron materials

Yang

Pines

2014

Proc. Natl. Acad. Sci. U.S.A.

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“…4(b). 43) For Yb(Rh 0.975 Ir 0.025 ) 2 Si 2 the critical field of the Néel phase is slightly reduced compared to pure YbRh 2 Si 2 . Apparently, the critical field of the T (B)-line seems to be reduced by almost the same amount.…”

Section: )mentioning

confidence: 96%

Break Up of Heavy Fermions at an Antiferromagnetic Instability

et al. 2011

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We present results of high-resolution, low-temperature measurements of the Hall coefficient, thermopower, and specific heat on stoichiometric YbRh 2 Si 2 . They support earlier conclusions of an electronic (Kondo-breakdown) quantum critical point concurring with a field induced antiferromagnetic one. We also discuss the detachment of the two instabilities under chemical pressure. Volume compression/expansion (via substituting Rh by Co/Ir) results in a stabilization/weakening of magnetic order. Moderate Ir substitution leads to a non-Fermi-liquid phase, in which the magnetic moments are neither ordered nor screened by the Kondo effect. The so-derived zero-temperature global phase diagram promises future studies to explore the nature of the Kondo breakdown quantum critical point without any interfering magnetism.KEYWORDS: quantum criticality, heavy fermion, YbRh 2 Si 2 , Kondo breakdown Different types of quantum critical pointsQuantum phase transitions in matter arise due to competing interactions, which result in competing ground-state properties. When a quantum phase transition is continuous it marks a quantum critical point (QCP). In the last decade, antiferromagnetic (AF) heavy-fermion metals turned out to be model systems to study quantum criticality. In these systems, QCPs are caused by the competition between the local Kondo and the non-local Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction. Studies on the interplay between these two phenomena have revealed different types of QCPs.1) In the itinerant, spin-density-wave (SDW) scenario the heavy fermions keep their integrity at the QCP. In such a case the QCP can be treated as a continuous classical phase transition in an effective dimension d + z, where d is the spatial dimensionality and z, the dynamic exponent defined via ξ t ∼ ξ z r , describes the number of additional spatial dimensions that the time dimension corresponds to. ξ r and ξ t denote the correlation length and correlation time which both diverge at a QCP.2-4) Several heavy-fermion compounds, e. g., CeCu 2 Si 2 , 5) CeNi 2 Ge 2 6) and Ce 1−x La x Ru 2 Si 2 7) were found to exhibit this type of itinerant AF QCP.However, in a few heavy-fermion metals the AF instability appears to be accompanied by a breakdown of the Kondo effect, [8][9][10] 15)The two FL phases adjacent to the QCP appear to posses different Fermi surfaces as inferred from a variety of electronic transport measurements closely related to the Fermi surface properties. Most important evidence stems from Hall effect measurements in the so called crossed-field geometry. Here, two perpendicular magnets are used to disentangle the two tasks of the magnetic field: One field, B 1 , generates the Hall response, and a second field, B 2 , tunes the ground state of the sample. The power of the crossed-field setup lies in the ability to extract the initial-slope Hall coefficient as a linear response to B 1 despite measuring at a finite tuning field B 2 .Isotherms of the field dependent Hall coefficient R H (B 2 ) depicted in Fig. 1(a) show...

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“…It still has to be tested whether the scaling behavior of the Hall crossover persists under lattice changes which might help to understand the nature of the emergent non-Fermi-liquid phase. While the existing experiments have indicated a finite range of chemical pressure in which the two concur [206], this issue deserves further investigation, especially under external pressure. It is also important to examine how this relates to the unconventional critical scaling seen in both the specific heat and Hall effect [207].…”

Section: Hall Effect and Scaling Behaviormentioning

confidence: 91%

Hall effect in heavy fermion metals

Nair

Wirth

Friedemann

et al. 2012

Advances in Physics

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The heavy fermion systems present a unique platform in which strong electronic correlations give rise to a host of novel, and often competing, electronic and magnetic ground states. Amongst a number of potential experimental tools at our disposal, measurements of the Hall effect have emerged as a particularly important one in discerning the nature and evolution of the Fermi surfaces of these enigmatic metals. In this article, we present a comprehensive review of Hall effect measurements in the heavy-fermion materials, and examine the success it has had in contributing to our current understanding of strongly correlated matter. Particular emphasis is placed on its utility in the investigation of quantum critical phenomena which are thought to drive many of the exotic electronic ground states in these systems. This is achieved by the description of measurements of the Hall effect across the putative zero-temperature instability in the archetypal heavy-fermion metal YbRh 2 Si 2 . Using the CeM In 5 (with M = Co, Ir) family of systems as a paradigm, the influence of (antiferro-)magnetic fluctuations on the Hall effect is also illustrated. This is compared to prior Hall effect measurements in the cuprates and other strongly correlated systems to emphasize on the generality of the unusual magnetotransport in materials with non-Fermi liquid behavior. Advances in Physics Hallreview7x 7. Comparison to Hall effect of other correlated materials 62 7.1. Copper oxide superconductors and related systems 62 7.1.1. Cuprates 62 7.1.2. Comparison of cuprates and heavy-fermion systems 67 7.1.3. Hall effect in oxy-pnictides and related systems 69 7.2. Other systems of related interest 70 7.3. Colossal magnetoresistive manganites 70 8. Summary 73 9. AppendixAdvances in Physics Hallreview7x 6 a) b) T N SDW non-FL LFL δ T c δ T 0 T T N antiferromagnetic order * LFL T non-FL LFL δ T c δ T 0 Figure 1. Comparison of quantum criticality in a) the spin-density wave (SDW) and b) the locally critical scenario.δ refers to an external control parameter for tuning the material to its QCP at δc. The hatched areas indicate phase space regions within which the heavy quasi-particles are formed, whereas the arrows illustrate the existence of local magnetic moments. In the local scenario (b) the quasi-particles themselves break apart at δc. At finite temperatures the quasiparticles disintegrate within a crossover range indicated by the T * line. T LFL marks the temperature below which LFL behavior is found, whereas T 0 denotes the onset temperature for initial Kondo screening.

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Magnetic and Electronic Quantum Criticality in YbRh2Si2

Cited by 11 publications

References 37 publications

Quantum critical behavior in heavy electron materials

Quantum critical behavior in heavy electron materials

Break Up of Heavy Fermions at an Antiferromagnetic Instability

Hall effect in heavy fermion metals

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