Low temperature electron spin resonance of the Kondo ion in a heavy fermion metal: YbRh2Si2

On the Ytterbium Valence and the Physical Properties in Selected Intermetallic Phases

The present review summarizes important aspects of the crystal chemistry of ytterbium-based intermetallic compounds along with a selection of their outstanding physical properties. These originate in many cases from the ytterbium valence. Different valence states are possible here, divalent (4f14), intermediate-valent, or trivalent (4f13) ytterbium, resulting in simple diamagnetic, Pauli or Curie-Weiss paramagnetic, or valence fluctuating behavior. Especially, some of the Yb3+ intermetallics have gained deep interest due to their Kondo or heavy Fermion ground states. We have summarized their property investigations using magnetic and transport measurements, specific heat data, NMR, ESR, and Mössbauer spectroscopy, elastic and inelastic neutron scattering, and XAS data as well as detailed thermoelectric measurements.

Electronuclear Transition into a Spatially Modulated Magnetic State in YbRh_{2}Si_{2}

The nature of the antiferromagnetic order in the heavy fermion metal YbRh_{2}Si_{2}, its quantum criticality, and superconductivity, which appears at low mK temperatures, remain open questions. We report measurements of the heat capacity over the wide temperature range 180  μK-80  mK, using current sensing noise thermometry. In zero magnetic field we observe a remarkably sharp heat capacity anomaly at 1.5 mK, which we identify as an electronuclear transition into a state with spatially modulated electronic magnetic order of maximum amplitude 0.1  μ_{B}. We also report results of measurements in magnetic fields in the range 0 to 70 mT, applied perpendicular to the c axis, which show eventual suppression of this order. These results demonstrate a coexistence of a large moment antiferromagnet with putative superconductivity.

Electron spin resonance of the itinerant ferromagnets LaCrGe3, CeCrGe3and PrCrGe3

We report electron spin resonance of the itinerant ferromagnets LaCrGe₃, CeCrGe₃, and PrCrGe₃. These compounds show well defined and very similar spectra of itinerant Cr 3dspins in the paramagnetic temperature region. Upon cooling and crossing the Cr-ferromagnetic ordering (below around 90 K) strong spectral structures start to dominate the resonance spectra in a quite different manner in the three compounds. In the Ce- and Pr-compounds the resonance is only visible in the paramagnetic region whereas in the La-compound the resonance can be followed far below the ferromagnetic ordering temperature. This behavior will be discussed in terms of the specific interplay between the 4fand 3dmagnetism which appears quite remarkable since CeCrGe₃displays heavy fermion behavior even in the magnetically ordered state.

Uniaxial and fourfold basal anisotropy in GdRh2Si2

The magnetocrystalline anisotropy of GdRh₂Si₂ is examined in detail via the electron spin resonance (ESR) of its well-localised Gd³⁺ moments. Below T _N = 107 K, long range magnetic order sets in with ferromagnetic layers in the (aa)-plane stacked antiferromagnetically along the c-axis of the tetragonal structure. Interestingly, the easy-plane anisotropy allows for the observation of antiferromagnetic resonance at X- and Q-band microwave frequencies. In addition to the easy-plane anisotropy we have also quantified the weaker fourfold anisotropy within the easy plane. The obtained resonance fields are modelled in terms of eigenoscillations of the two antiferromagnetically coupled sublattices. Conversely, this model provides plots of the eigenfrequencies as a function of field and the specific anisotropy constants. Such calculations have rarely been done. Therefore our analysis is prototypical for other systems with fourfold in-plane anisotropy. It is demonstrated that the experimental in-plane ESR data may be crucial for a precise knowledge of the out-of-plane anisotropy.

Detection of Two Phenomena Opposite to the Expected Ones

Both phenomena mentioned in the title were revealed by the electron paramagnetic resonance (EPR) method. The first phenomenon was found in superconducting La metal with Er impurities—the spin relaxation rate of the erbium impurities was sharply decreasing after transition into the superconducting state instead of the expected, i.e., the well-known Hebel–Slichter peak. The second unexpected phenomenon was discovered in the YbRh2Si2 compound—an excellent EPR signal from the Yb ions was observed at temperatures below the Kondo temperature determined thermodynamically, while according to the existing belief the EPR signal should not be observed at these temperatures due to the Kondo effect. In this tribute to K. Alex Müller, I describe the nature of the detected phenomena.

A novel method of ESR oscillating magnetization value determination in strongly correlated metals

We propose a powerful method of direct measurement of oscillating magnetization by the electron spin resonance, based on dependence of resonant conditions on geometry of the experiment. Theoretical consideration of the matter leads to a simple expression for oscillating magnetization. Approbation of this method is implemented by means of cavity ESR spectrometer (60 GHz) on two diverse metallic systems, where static magnetization at the resonance field varies by an order of magnitude. Quantitative values of oscillating magnetization (905 G for EuB6 at T = 4.2 K and 94 G for CeB6 at T = 1.8 K) are in appropriate agreement with the one obtained by the other methods.

Strong Coupling of Microwave Photons to Antiferromagnetic Fluctuations in an Organic Magnet

Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (circuit QED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temperature, and we demonstrate strong coupling at base temperature. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multispin modes in organic crystals are suitable for circuit QED, offering a platform for their coherent manipulation. They also utilize the circuit QED architecture as a way to probe spin correlations at low temperature.

Fe(III)-based metal-organic framework-derived core-shell nanostructure: Sensitive electrochemical platform for high trace determination of heavy metal ions

A new core-shell nanostructured composite composed of Fe(III)-based metal-organic framework (Fe-MOF) and mesoporous Fe₃O₄@C nanocapsules (denoted as Fe-MOF@mFe₃O₄@mC) was synthesized and developed as a platform for determining trace heavy metal ions in aqueous solution. Herein, the mFe₃O₄@mC nanocapsules were prepared by calcining the hollow Fe₃O₄@C that was obtained using the SiO₂ nanoparticles as the template, followed by composing the Fe-MOF. The Fe-MOF@mFe₃O₄@mC nanocomposite demonstrated excellent electrochemical activity, water stability and high specific surface area, consequently resulting in the strong biobinding with heavy-metal-ion-targeted aptamer strands. Furthermore, by combining the conformational transition interaction, which is caused by the formation of the G-quadruplex between a single-stranded aptamer and high adsorbed amounts of heavy metal ions, the developed aptasensor exhibited a good linear relationship with the logarithm of heavy metal ion (Pb²⁺ and As³⁺) concentration over the broad range from 0.01 to 10.0nM. The detection limits were estimated to be 2.27 and 6.73 pM toward detecting Pb²⁺ and As³⁺, respectively. The proposed aptasensor showed good regenerability, excellent selectivity, and acceptable reproducibility, suggesting promising applications in environment monitoring and biomedical fields.

Magnetic resonance anisotropy in CeB6: an entangled state of the art

Electron spin resonance (ESR) in strongly correlated metals is an exciting phenomenon, as strong spin fluctuations in this class of materials broaden extremely the absorption line below the detection limit. In this respect, ESR observation in CeB₆ provides a unique chance to inspect Ce³⁺ magnetic state in the antiferroquadrupole (AFQ) phase. We apply the original high frequency (60 GHz) experimental technique to extract the temperature and angular dependences of g-factor, line width and oscillating magnetization. Experimental data show unambiguously that the modern ESR theory in the AFQ phase considering the Γ₈ ground state of Ce³⁺ ion completely fails to predict both the g-factor magnitude and its angular dependence. Alignment of the external magnetic field along [100] axis induces a strong (more than twofold) broadening of ESR line width with respect to the other crystallographic directions and results also in the anomalous temperature dependences of the g-factor and oscillating magnetization. In this experimental geometry the latter parameter surprisingly exceeds total static magnetization by 20% at T* ~ 2.5 K. We argue that the unusual physical picture of ESR in CeB₆ may be strongly affected by spin fluctuations and dynamic collective effects predominantly pronounced in [100] direction.

Emergence of superconductivity in the canonical heavy-electron metal YbRh₂Si₂

The smooth disappearance of antiferromagnetic order in strongly correlated metals commonly furnishes the development of unconventional superconductivity. The canonical heavy-electron compound YbRh2Si2 seems to represent an apparent exception from this quantum critical paradigm in that it is not a superconductor at temperature T ≥ 10 millikelvin (mK). Here we report magnetic and calorimetric measurements on YbRh2Si2, down to temperatures as low as T ≈ 1 mK. The data reveal the development of nuclear antiferromagnetic order slightly above 2 mK and of heavy-electron superconductivity almost concomitantly with this order. Our results demonstrate that superconductivity in the vicinity of quantum criticality is a general phenomenon.

Thermal Conductivity through the Quantum Critical Point in YbRh_{2}Si_{2} at Very Low Temperature

The thermal conductivity of YbRh_{2}Si_{2} has been measured down to very low temperatures under field in the basal plane. An additional channel for heat transport appears below 30 mK, both in the antiferromagnetic and paramagnetic states, respectively, below and above the critical field suppressing the magnetic order. This excludes antiferromagnetic magnons as the origin of this additional contribution to thermal conductivity. Moreover, this low temperature contribution prevails a definite conclusion on the validity or violation of the Wiedemann-Franz law at the field-induced quantum critical point.

Intense low-energy ferromagnetic fluctuations in the antiferromagnetic heavy-fermion metal CeB6

Heavy-fermion metals exhibit a plethora of low-temperature ordering phenomena . Among these are the so-called hidden-order phases that, in contrast to conventional magnetic order, are invisible to standard neutron diffraction experiments. One of the structurally most simple hidden-order compounds, CeB6, has been intensively studied for an elusive phase that was attributed to the antiferroquadrupolar ordering of cerium-4f moments . As the ground state of CeB6 is characterized by a more conventional antiferromagnetic (AFM) order , the low-temperature physics of this system has generally been assumed to be governed solely by AFM interactions between the dipolar and multipolar Ce moments . Here we overturn this established picture by observing an intense ferromagnetic (FM) low-energy collective mode that dominates the magnetic excitation spectrum of CeB6. Inelastic neutron-scattering data reveal that the intensity of this FM excitation significantly exceeds that of conventional spin-wave magnons emanating from the AFM wavevectors, thus placing CeB6 much closer to a FM instability than previously anticipated. This propensity for ferromagnetism may account for much of the unexplained behaviour of CeB6, and should lead to a re-examination of existing theories that have so far largely neglected the role of FM interactions.

Theory of the electron spin resonance in the heavy fermion metal β-YbAlB4

The heavy fermion metal β-YbAlB4 exhibits a bulk room temperature conduction electron spin resonance (ESR) signal which evolves into an Ising-anisotropic f-electron signal exhibiting hyperfine features at low temperatures. We develop a theory for this phenomenon based on the development of resonant scattering off a periodic array of Kondo centers. We show that the hyperfine structure arises from the scattering off the Yb atoms with nonzero nuclear spin, while the constancy of the ESR intensity is a consequence of the presence of crystal electric field excitations of the order of the hybridization strength.

From incommensurate correlations to mesoscopic spin resonance in YbRh2Si2

Spin fluctuations are reported near the magnetic field-driven quantum critical point in YbRh(2)Si(2). On cooling, ferromagnetic fluctuations evolve into incommensurate correlations located at q(0) = ±(δ,δ), with δ = 0.14 ± 0.04 r.l.u. At low temperatures, an in-plane magnetic field induces a sharp intradoublet resonant excitation at an energy E(0) = gμ(B)μ(0)H with g = 3.8 ± 0.2. The intensity is localized at the zone center, indicating precession of spin density extending ξ = 6 ± 2 Å beyond the 4f site.

Kondo lattice with heavy fermions: peculiarities of spin kinetics

A model of spin relaxation of Kondo lattices is proposed to explain the angular dependence of the electron spin resonance (ESR) parameters in the heavy fermion compounds Y bIr(2)Si(2) and Y bRh(2)Si(2). A perturbational scaling approach reveals a collective spin motion of Yb ions with conduction electrons in the bottleneck regime. A common energy scale due to the Kondo effect regulates the temperature dependence of different kinetic coefficients to result in a mutual cancelation of all divergent parts in a collective spin mode. The angular dependence of the ESR intensity, linewidth and resonant frequency is shown to be in good agreement with experimental data on Y bIr(2)Si(2) and Y bRh(2)Si(2). In particular, the unexpectedly weak dependence of the ESR intensity on the orientation of the microwave magnetic field agrees with the properties of the discussed model.

Electron spin resonance in YbRh2Si2: local-moment, unlike-spin and quasiparticle descriptions

Electron spin resonance (ESR) in the Kondo lattice compound YbRh(2)Si(2) has stimulated discussion as to whether the low-field resonance outside the Fermi liquid regime in this material is more appropriately characterized as a local-moment phenomenon or one that requires a Landau quasiparticle interpretation. In earlier work, we outlined a collective mode approach to the ESR that involves only the local 4f moments. In this paper, we extend the collective mode approach to a situation where there are two subsystems of unlike spins: the pseudospins of the ground multiplet of the Yb ions and the spins of the itinerant conduction electrons. We assume a weakly anisotropic exchange interaction between the two subsystems. With suitable approximations our expression for the g-factor also reproduces that found in recent unlike-spin quasiparticle calculations. It is pointed out that the success of the local-moment approach in describing the resonance is due to the fact that the susceptibility of the Yb subsystem dominates that of the conduction electrons with the consequence that the relative shift in the resonance frequency predicted by the unlike-spin models (and absent in the local-moment models) is ≪ 1. The connection with theoretical studies of a two-component model with like spins is also discussed.

Quantum critical Kondo quasiparticles probed by ESR in β-YbAlB₄

Electron spin resonance (ESR) can probe conduction electrons (CE) and local moment (LM) spin systems in different materials. A CE spin resonance (CESR) is observed in metallic systems based on light elements or with enhanced Pauli susceptibility. LM ESR can be seen in compounds with paramagnetic ions and localized d or f electrons. Here we report a remarkable and unprecedented ESR signal in the heavy-fermion superconductor β-YbAlB₄ [S. Nakatsuji et al., Nature Phys. 4, 603 (2008)] which behaves as a CESR at high temperatures and acquires characteristics of the Yb³⁺ LM ESR at low temperature. This dual behavior strikes as an in situ unique observation of the Kondo quasiparticles in a quantum critical regime. The proximity to a quantum critical point may favor the appearance of this dual character of the ESR signal in β-YbAlB₄.

Electron spin resonance of the ferromagnetic Kondo lattice CeRuPO

The spin dynamics of the ferromagnetic Kondo lattice CeRuPO is investigated by electron spin resonance (ESR) at microwave frequencies of 1, 9.4 and 34 GHz. The measured resonance can be ascribed to a rarely observed bulk Ce(3 + ) resonance in a metallic Ce compound and can be followed below the ferromagnetic transition temperature T(C) = 14 K. At T > T(C) the interplay between the RKKY exchange interaction and the crystal electric field anisotropy determines the ESR parameters. Near T(C) the spin-relaxation rate is influenced by the critical fluctuations of the order parameter.

Anisotropic electron spin resonance of Y bIr₂Si₂

A series of electron spin resonance (ESR) experiments were performed on a single crystal of the heavy fermion metal Y bIr₂Si₂ to map out the anisotropy of the ESR-intensity I(ESR) which is governed by the microwave field component of the g-factor. The temperature dependencies of I(ESR)(T) and g(T) were measured for different orientations and compared within the range 2.6 K ≤ T ≤ 16 K. The analysis of the intensity dependence on the crystal orientation with respect to both the direction of the microwave field and the static magnetic field revealed remarkable features: the intensity variation with respect to the direction of the microwave field was found to be one order of magnitude smaller than expected from the g-factor anisotropy. Furthermore, we observed a weak basal plane anisotropy of the ESR parameters which we interpret to be an intrinsic sample property.

Kondo resonance narrowing in d- and f-electron systems

We develop a simple scaling theory for the effect of Hund's interactions on the Kondo effect, showing how an exponential narrowing of the Kondo resonance develops in magnetic ions with large Hund's interaction. Our theory accounts for the exponential reduction of the Kondo temperature with spin S of the Hund's coupled moment, first observed in d-electron alloys in the 1960s, and more recently encountered in numerical calculations on multiband Hubbard models. We discuss the consequences of Kondo resonance narrowing for the Mott transition in d-band materials, particularly iron pnictides, and the narrow ESR linewidth recently observed in ferromagnetically correlated f-electron materials.

Tuning the hybridization at the surface of a heavy-fermion system

Electron-hybridization phenomena in YbRh_{2}Si_{2} were probed by angle-resolved photoemission. It was shown that the Yb 4f-Rh 4d hybridization strength in the surface region of this heavy-fermion material can be varied by deposition of Ag. Site-specific charge transfer from adatoms leads to change of the energy overlap of the interacting states close to the Fermi energy. Our study demonstrates a new way to tune the hybridization between 4f and valence electrons as well as the induced strong correlation effects at the surface of heavy-fermion systems.

The effects of anisotropy and Yb-Yb interactions on the low-field electron spin resonance in Yb(2)Rh(2)Si(2) and YbIr(2)Si(2)

The effect of anisotropy on the low-field electron spin resonance in the Kondo lattice compounds YbRh(2)Si(2) and YbIr(2)Si(2) is assessed. It is shown that the g-shift in YbRh(2)Si(2) is a consequence of the anisotropy in the Yb-Yb interactions as mirrored in the molecular field parameters characterizing the resonant susceptibility. It is also pointed out that the large residual linewidth for YbIr(2)Si(2) results from the modification of the Korringa contribution that occurs when the Curie susceptibility of the isolated ion is replaced by the resonant susceptibility with an experimentally determined molecular field parameter.

Evolution of the Kondo state of YbRh2Si2 probed by high-field ESR

An electron spin resonance (ESR) study of the heavy fermion compound YbRh2Si2 for fields up to approximately 8 T reveals a strongly anisotropic signal in the Kondo state below approximately 25 K. A similarity between the T dependence of the ESR parameters and that of the specific heat and the 29Si nuclear magnetic resonance data gives evidence that the ESR response is given by heavy fermions. Tuning the Kondo effect on the 4f states with magnetic fields approximately 2-8 T and temperature 2-25 K yields a gradual change of the ESR g factor and linewidth which reflects the evolution of the Kondo state in this Kondo lattice system.

Relevance of ferromagnetic correlations for the electron spin resonance in Kondo lattice systems

Electron spin resonance (ESR) measurements of the ferromagnetic (FM) Kondo lattice system CeRuPO show a well defined ESR signal which is related to the Ce3+ magnetism. In contrast, no ESR could be observed in the antiferromagnetic (AFM) homologue CeOsPO. Additionally, we detect an ESR signal in ferromagnetic YbRh while it was absent in a number of Ce or Yb intermetallic compounds with dominant AFM exchange. Thus, the observation of an ESR signal in a Kondo lattice is neither specific to Yb nor to the proximity to a quantum critical point, but seems to be connected to the presence of FM fluctuations. These conclusions not only provide a basic concept to understand the ESR in Kondo lattice systems even well below the Kondo temperature (as observed in YbRh2Si2) but point out ESR as a prime method to investigate directly the spin dynamics of the Kondo ion.

Photoemission insight into heavy-fermion behavior in YbRh2Si2

As shown by angle-resolved photoemission (PE), hybridization of bulk Yb 4f(2+) states with a shallow-lying valence band of the same symmetry leads in YbRh2Si2 to dispersion of a 4f PE signal in the region of the Kondo resonance with a Fermi-energy crossing close to Gamma[over ]. Additionally, renormalization of the valence state results in the formation of a heavy band that disperses parallel to the 4f originating signal. The symmetry and character of the states are probed by circular dichroism and the photon-energy dependence of the PE cross sections.

Energy dispersion of 4f-derived emissions in photoelectron spectra of the heavy-fermion compound YbIr2Si2

Angle-resolved photoemission spectra of the heavy-fermion system YbIr(2)Si(2) are reported that reveal strong momentum (k) dependent splittings of the 4f(13) bulk and surface emissions around the expected intersection points of the 4f final states with valence bands in the Brillouin zone. The obtained dispersion is explained in terms of a simplified periodic Anderson model by a k dependence of the electron hopping matrix element disregarding clearly interpretation in terms of a single-impurity model.

Valence and magnetic ordering in intermediate valence compounds: TmSe versus SmB(6)

The intermediate valence systems TmSe and SmB(6) have been investigated up to 16 and 18 GPa by ac microcalorimetry with a pressure (p) tuning realized in situ at low temperature. For TmSe, the transition from an antiferromagnetic insulator for p<3 GPa to an antiferromagnetic metal at higher pressure has been confirmed. A drastic change in the p variation of the Néel temperature (T(N)) is observed at 3 GPa. In the metallic phase (p>3 GPa), T(N) is found to increase linearly with p. A similar linear p increase of T(N) is observed for the quasitrivalent compound TmS, which is at ambient pressure equivalent to TmSe at p∼7 GPa. In the case of SmB(6) long range magnetism has been detected above p∼8 GPa, i.e. at a pressure slightly higher than the pressure of the insulator to metal transition. However a homogeneous magnetic phase occurs only above 10 GPa. The magnetic and electronic properties are related to the renormalization of the 4f wavefunction either to the divalent or the trivalent configurations. As observed in SmS, long range magnetism in SmB(6) occurs already far below the pressure where a trivalent Sm(3+) state will be reached. It seems possible to describe roughly the physical properties of the intermediate valence equilibrium by assuming formulae for the Kondo lattice temperature depending on the valence configuration. Comparison is also made with the appearance of long range magnetism in cerium and ytterbium heavy fermion compounds.

Ferromagnetic quantum critical fluctuations in YbRh2(Si0.95Ge0.05)2

The bulk magnetic susceptibility chi(T,B) of YbRh(2)(Si(0.95)Ge(0.05))(2) has been investigated close to the field-induced quantum critical point at B(c) = 0.027 T. For B < or= 0.05 T a Curie-Weiss law with a negative Weiss temperature is observed at temperatures below 0.3 K. Outside this region, the susceptibility indicates ferromagnetic quantum critical fluctuations, chi(T) proportional, variantT-0.6 above 0.3 K. At low temperatures the Pauli susceptibility follows chi(0) proportional, variant(B-B(c))(-0.6) and scales with the coefficient of the T(2) term in the electrical resistivity. The Sommerfeld-Wilson ratio is highly enhanced and increases up to 30 close to the critical field.

Grüneisen ratio divergence at the quantum critical point in CeCu(6-x)Agx

The heavy-fermion system CeCu6-xAgx is studied at its antiferromagnetic quantum critical point, xc=0.2, by low-temperature (T> or =50 mK) specific heat, C(T), and volume thermal expansion, beta(T), measurements. Whereas C/T proportional to log((T0/T) would be compatible with the predictions of the itinerant spin-density-wave (SDW) theory for two-dimensional critical spin fluctuations, beta(T)/T and the Grüneisen ratio, Gamma(T) proportional to beta/C, diverge much weaker than expected, in strong contrast to this model. Both C and beta, plotted as a function of the reduced temperature t=T/T0 with T0=4.6 K, are similar to what was observed for YbRh2(Si(0.95)Ge(0.05))2 (T0=23.3 K), indicating a striking discrepancy to the SDW prediction in both systems.