Crystal field of Yb<Superscript>3+</Superscript> tetragonal centers in the YbRh<Subscript>2</Subscript>Si<Subscript>2</Subscript> intermetallic compound

The spectra of electron paramagnetic resonance and inelastic neutron scattering in crystals of the heavy-fermion intermetallic compound YbRh₂Si₂ are interpreted. The phenomenological potentials of the crystal electric field of Yb³⁺ tetragonal centers and the parameter of the Hamiltonian for the spin-orbit interaction of electrons are determined from the experimental energy level schemes. A comparison of the results obtained from experimental data on electron paramagnetic resonance, inelastic neutron scattering, and Mössbauer spectroscopy shows that the most probable ground state of Yb³⁺ ions in the YbRh₂Si₂ crystal is the Kramers doublet Γ _t6 ^? .     

Field-dependent collective ESR mode in YbRh2Si2

Electron spin resonance (ESR) experiments in YbRh₂Si₂ Kondo lattice at different field/frequencies and H_⊥c revealed: (i) a strong field dependent Yb³⁺ spin-lattice relaxation, (ii) a weak field and T-dependent effectiveg-value, (iii) a suppression of the ESR intensity beyond 15% of Lu-doping, and (iv) a strong sample and Lu-doping (≤15%) dependence of the ESR data. These results suggest that the ESR signal in YbRh₂Si₂ may be due to a coupled Yb³⁺-conduction electron resonant collective mode with a subtle field-dependent spins dynamic.     

Electron spin resonance investigation of the Heavy-Fermion compound CeCu2(Si1−x Ge x )2

The Kondo-lattice system CeCu₂(Si_1?x Ge _x )₂ exhibits an alloying induced transition from a coherent Fermi-liquid (x=0) with strongly enhanced effective masses to an antiferromagnetically ordered heavy-fermion system (x=1). This transition is studied by Gd³⁺ ESR in oriented powder samples. The temperature dependence of the ESR line width follows a characteristic pattern which allows one to distinguish between the different ground states. The results obtained in polycrystalline CeCu₂Si₂ are in good agreement with the measurements performed in single crystals. Finally we compare our results with⁶³Cu-NMR data obtained from CeCu₂Si₂ and CeCu₂Ge₂.     

Electron spin resonance in the Heusler alloy YbRh2Pb

An electron spin resonance (ESR) signal was observed in a concentrated Kondo lattice, Heusler alloy YbRh₂Pb. It is attributed to the combined effect of the 4f local magnetic moments of Yb³⁺ and conduction electrons. It is shown that the significant broadening and disappearance of the ESR line at temperatures above 20 K is caused by the processes of the spin-lattice relaxation of the Yb³⁺ ions through the first excited Stark doublet with an activation energy Δ ≈ 73.5 K. A comparison of the ESR data for YbRh₂Pb and some other undoped intermetallic compounds based on ytterbium, cerium, and europium indicates that hybridized electronic states occurring as the result of hybridization between the localized 4f electrons and the collectivized conduction electrons constitute a fundamentally new source of ESR.     

Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu2Si2 versus YbRh2Si2

In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu₂Si₂, fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu₂Si₂. In YbRh₂Si₂, superconductivity appears to be suppressed at T???10?mK by AF order (T_N?=?70?mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at T_A slightly above 2?mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at T_c?=?2?mK. Like the pressure – induced QCP in CeRhIn₅, the magnetic field – induced one in YbRh₂Si₂ is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavy – fermion superconductors and other families of unconventional superconductors with higher T_cs, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.     

Tuning the dispersion of 4f bands in the heavy-fermion material YbRh2Si2

Localized Yb 4f and itinerant Rh 4d states are subject to substantial hybridization effects in the heavy-fermion material YbRh₂Si₂. The proximity to the Fermi level and the high anisotropy in k space naturally raise questions regarding the role of these hybridization effects for the observed, unusual physical properties. Using angle-resolved photoemission spectroscopy (ARPES) we found that the non-dispersive behavior of the localized Yb f states is broken around the Γ point due to interaction with approaching Rh 4d bands. The intriguing point here is that the hybridization strength turns out to be systematically tunable by electron doping of the material. Gradual deposition of silver atoms onto the atomically clean, silicon terminated surface of YbRh₂Si₂ leads to transfer of Ag 5s charge into the Rh 4d bands. This substantially changes the energy overlap, and thus the hybridization strength, between the interacting Yb 4f and Rh 4d bands in the surface and subsurface region. The shown possibility to control the variation of the f-d hybridization at the surface of heavy-fermion materials may also be helpful for other ARPES studies on the diverse phenomena in electron-correlated materials.     

Electron paramagnetic resonance of Yb<Superscript>3+</Superscript> ions in a concentrated YbRh<Subscript>2</Subscript>Si<Subscript>2</Subscript> compound with heavy fermions

The EPR signal from localized ytterbium ions was observed in an undoped YbRh₂Si₂ compound with heavy fermions in the temperature range from 1.5 to 25 K. The exponential contribution dominating the temperature dependence of EPR line width at temperatures above 15 K was shown to be caused by the random transitions from the ground to the first excited Stark sublevel of the Yb³⁺(4f¹³) ion with the activation energy Δ=115 K.     

Nature of the quantum critical point as disclosed by extraordinary behavior of magnetotransport and the lorentz number in the heavy-fermion metal YbRh2Si2

Physicists are engaged in vigorous debate on the nature of the quantum critical points (QCP) governing the low-temperature properties of heavy-fermion metals. Recent experimental observations of the much-studied compound YbRh₂Si₂ in the regime of vanishing temperature incisively probe the nature of its magnetic-field-tuned QCP. The jumps revealed both in the residual resistivity ??₀ and the Hall resistivity R _H, along with violation of the Wiedemann-Franz law, provide vital clues to the origin of such non-Fermi-liquid behavior. The empirical facts point unambiguously to association of the observed QCP with a fermion-condensation phase transition. Based on this insight, the resistivities ??₀ and R _H are predicted to show jumps at the crossing of the QCP produced by application of a magnetic field, with attendant violation of the Wiedemann-Franz law. It is further demonstrated that experimentally identifiable multiple energy scales are related to the scaling behavior of the effective mass of the quasiparticles responsible for the low-temperature properties of such heavy-fermion metals.     

Magnetostriction of monocrystalline URu2Si2

We report magnetostriction measurements on a monocrystalline sample of the heavy-fermion compound URu₂Si₂, below (at 4.2 K) and above (at 20 K) the Néel temperature. For a field direction along the tetragonal axis the magnetostriction is strongly anisotropic; the volume effect amounts to 1.4 × 10^-6T^-1 at 8 T and 4.2 K. For a field direction in the tetragonal plane the magnetostriction is nearly two orders of magnitude smaller, and less anisotropic.     

Strongly correlated Fermi-systems: Non-Fermi liquid behavior, quasiparticle effective mass and their interplay

Basing on the density functional theory of fermion condensation, we analyze the non-Fermi liquid behavior of strongly correlated Fermi-systems such as heavy-fermion metals. When deriving equations for the effective mass of quasiparticles, we consider solids with a lattice and homogeneous systems. We show that the low-temperature thermodynamic and transport properties are formed by quasiparticles, while the dependence of the effective mass on temperature, number density, magnetic fields, etc., gives rise to the non-Fermi liquid behavior. Our theoretical study of the heat capacity, magnetization, energy scales, the longitudinal magnetoresistance and magnetic entropy are in good agreement with the remarkable recent facts collected on the heavy-fermion metal YbRh₂Si₂.     

Evolution of the 4f electron localization from YbRh2Si2 to YbRh2Pb studied by electron spin resonance

We report on electron spin resonance (ESR) experiments on the Heusler alloy YbRh₂Pb and compare its spin dynamics with that of several other Yb-based intermetallics. A detailed analysis of the derived ESR parameters indicates the extremely weak hybridization, more localized distribution of the 4f states, and a smaller RKKY interaction in YbRh₂Pb. These findings reveal the important interplay between hybridization effects, chemical substitution, and crystalline electric field interactions that determines the ground state properties of strongly correlated electron systems.     

Muon spin relaxation in CeCu2Si2 and muon knight shift in various heavy-fermion systems

Positive muon spin precession has been observed in various heavy-fermion systems in the transverse external magnetic field. In the superconductor CeCu_2.1Si₂, the relaxation rate of muon spins increases rapidly with decreasing temperature below T_C. This is interpreted as the results of the inhomogeneous fields due to the imperfect penetration of the external field into the type-II superconducting state. The magnetic-field penetration depth λ is derived from the observed muon spin relaxation rate. λ is about 1200 ∢ at T∼0.5T_C, and the temperature dependence of λ is consistent with the relation expected for a BCS superconductor. We have also measured the muon Knight shift K_μ in the normal (or paramagnetic) state of various heavy-fermion systems. K_μ is large and negative (about −1000∼−3000 ppm at T=10 K) for CeCu₂Si₂, UPt₃ and CeAl₃, while more complicated signals are measured in CePb₃ and CeB₆. The negative muon Knight shift in the non-magnetic heavy-fermion systems is discussed in terms of the Kondo-coupling between the conduction- and f-electrons.     

Europium valencies in substituted EuCu2Si2 systems

Mössbauer studies of¹⁵¹Eu in EuCu_2?x Pt _x Si₂, EuCu₂Si_2?x Ge _x and Eu _x Gd_1?x Mn₂Si₂ (x≤0.25) at temperatures between 90 K and 425 K have been performed. All spectra are composed of at least two subspectra, corresponding to stable Eu²⁺ and intermediate valent Eu. The isomer shift of the stable divalent Eu (ordered magnetically up to 400 K in Eu_0.25Gd_0.75Mn₂Si₂) isS ₂=?7.5 mm/sec in comparison toS ₂=?10.5 mm/s for stable Eu²⁺ in EuMn₂Ge₂. This shows that the Eu²⁺ is under heavy internal pressure in these systems. From the temperature dependence of the hyperfine interaction parameters and line intensities conclusions are derived concerning interconfigurational excitation energies, their inhomogeneous width and recoil free fraction behaviour.     

Magnetic properties and structural chemistry of ternary silicides (RE,Th, U)Ru2Si2 (RE = RARE EARTH)

Ternary silicides (RE, Th, U)Ru₂Si₂ have been synthesized from the elements. All the compounds (RE = Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) were found to be isotypic and to crystallize with the structure type of ThCr₂Si₂ (ordered derivative of the BaAl₄-type). The magnetic behavior of these alloys was studied in the temperature range 1.5 K < T < 1100 K. Magnetic susceptibilities at temperatures T > 300 K closely follow a typical Van Vleck paramagnetism of free RE³⁺-ions. In the case of CeRu₂Si₂ susceptibilities are well described for 20 K < T < 1100 K by a Van Vleck paramagnetism of widely spaced multiplets; the observed effective paramagnetic moment μ_eff = 2.12 BM indicates a high percentage (85%) of Ce³⁺. SmRu₂Si₂ yields an effective moment μ_eff = 0.54 BM, which compares reasonably well with the Hund's rule J = 5/2 ground level for free Sm⁺ and a low-lying excited level with J = 7/2. For temperatures T > 15 K the magnetic susceptibility as a function of temperature follows the “Van Vleck behavior” for free Sm³⁺. At low temperatures ferromagnetic ordering was encountered for (Pr, Nd, Ho, Er, Tm)Ru₂Si₂, whereas antiferromagnetic ordering was observed for (Sm, Gd, Tb, Dy)Ru₂Si₂. The ordering temperatures are generally below 55 K. No superconductivity was found for temperatures as low as 1.8 K.     

Study of hyperfine interactions in the intermetallic compound CePd2Si2 using PAC technique with 111Cd as probe nuclei

Perturbed γ???γ angular correlation spectroscopy (PAC) has been used to investigate the hyperfine interactions in the intermetallic compound CePd₂Si₂ using ¹¹¹In→¹¹¹Cd probe nuclei. Samples of CePd₂Si₂ were prepared by melting constituent elements in an arc furnace under pure argon atmosphere. Carrier-free ¹¹¹In nuclei were introduced into the samples by thermal diffusion at 800°C in vacuum during 12 h. The measurements were performed in the temperature range of 4.2–300 K. Above the magnetic transition temperature (T _N ?=?10 K), the results show two distinct and well defined quadrupole interactions that were assigned to probe nuclei occupying Ce and Si sites in the compound. The quadrupole frequencies were found to decrease linearly with increasing temperature. The PAC spectra taken below 10 K were analyzed with a model including combined electric quadrupole plus magnetic dipole interactions, from which the hyperfine magnetic field was determined.     

Exotic superconducting state embedded in the hidden order state of URu2Si2

The heavy-fermion compound URu₂Si₂ has mystified researchers since the superconducting state (T_c = 1.45 K) is embedded within the enigmatic ‘‘hidden order” phase (T_h = 17.5 K). Here, we report charge and thermal transport measurements on ultraclean single crystals of URu₂Si₂ with very large residual-resistivity-ratio down to 30 m K (∼T_c/50), which reveal a number of unprecedented superconducting properties. The results provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology. We propose a gap function with chiral d-wave form Δ(k) = Δ₀k_z(k_x + ik_y). We also demonstrate that a distinct flux line lattice melting transition with outstanding characters occurs well below the upper critical fields even at sub-Kelvin temperature. The intriguing superconducting state of URu₂Si₂ adds a unique and exciting example to the list of unconventional superconductors.     

Why could electron spin resonance be observed in a heavy fermion Kondo lattice?

We develop a theoretical basis for understanding the spin relaxation processes in Kondo lattice systems with heavy fermions as experimentally observed by electron spin resonance (ESR). The Kondo effect leads to a common energy scale that regulates a logarithmic divergence of different spin kinetic coefficients and supports a collective spin motion of the Kondo ions with conduction electrons. We find that the relaxation rate of a collective spin mode is greatly reduced due to a mutual cancellation of all the divergent contributions even in the case of the strongly anisotropic Kondo interaction. The contribution to the ESR linewidth caused by the local magnetic field distribution is subject to motional narrowing supported by ferromagnetic correlations. The developed theoretical model successfully explains the ESR data of YbRh₂Si₂ in terms of their dependence on temperature and magnetic field.     

Europium valency in EuCu2−x Fe x Si2, EuCu2Si2−x Ge x,EuCu2−x Si2+x and EuNi2−x Si2+x

Mössbauer spectroscopy, X-ray photoemission spectroscopy and magnetization studies of EuCu_2?x Fe _x Si₂, EuCu₂Si_2?x Ge _x , EuCu_2?x Si_2+x , and EuNi_2?x Si_2+x have been performed. In EuFe₂Si₂ and EuNi₂Si₂ the Eu ion is trivalent, in EuCu₂Si₂ it is of intermediate valency. In all systems withx=0, many inequivalent Eu sites of intermediate valency are formed. In EuCu_2?x Fe _x Si₂, the average valency of Eu moves nonmonotonically toward Eu³⁺. In EuCu₂Si_2?x Ge _x , EuCu_2?x Si_2+x and EuNi_2?x Si_2+x , the Eu average valency moves quickly towards Eu²⁺. In all three systems, whenx=1, all Eu ions are already stable divalent. The systems EuCuSi₃ and EuNiSi₃ order magnetically at 40 K and 34 K, and exhibit hyperfine fields of 323 kOe and 458 kOe, respectively. XPS and Mössbauer isomer shift determinations of the average Eu valence as a function of temperature in EuCu_1.5Fe_0.5Si₂ are in good agreement. The experimental observations concerning the Eu valencies can not be explained solely in terms of the local volume available to the Eu ion; the nature of chemical environment plays a dominant role.     

Nuclear magnetic resonance study of the heavy-fermion system URu2Si2

Nuclear magnetic resonance (NMR) and relaxation studies on ²⁹Si have been carried out on the heavy Fermion system URu₂Si₂. Above the Kondo temperature of about 60 K, the nuclear relaxation time T₁ is nearly temperature independent, which is consistent with the occurrence of fluctuations of localized U moments. Below about 60 K T₁ is inversely proportional to temperature suggesting that the system behaves like a Fermi liquid. A sharp increase in T₁ occurs below 17 K which is probably associated with the opening of an energy gap at the Fermi surface due to the formation of a spin density wave state. Below about 10 K, T₁ reacquires the inverse temperature dependence observed in the 17 K ∼ 60 K temperature range.     

Magnetic ordering in HoRu2Si2, HoRh2Si2, TbRh2Si2 and TbIr2Si2 by neutron diffraction

Neutron diffraction study of polycrystalline HoRu₂Si₂, HoRh₂Si₂, TbRh₂Si₂, and TbIr₂Si₂ was performed in the temperature range between 4.2 and 300 K. For HoRu₂Si₂ the magnetic spin alignment of a linear transverse wave mode below the Néel temperature 19 K is observed. This static moment wave is propagating along the b-axis with k=(0, 0.2, 0) and is polarized in the c-axis. The root-mean-square and maximum saturation moments per Ho atom are 9.26 and 13.09μ_B, respectively. HoRh₂Si₂, TbRh₂Si₂ an TbIr₂Si₂ are simple collinear antiferromagnets of +-+- type with Néel temperatures of (27±1), (98±2) and (72±3) K, respectively. For TbRh₂Si₂ and TbIr₂Si₂ magnetic moments are localized on RE ions only and are aligned along the tetragonal axis, while for HoRh₂Si₂ they form an angle ø = (28±3)°.