Tailoring of magnetism & electron transport of manganate thin films by controlling the Mn-O-Mn bond angles via strain engineering

Strain engineering beyond substrate limitation of colossal magnetoresistant thin (La0.6Pr0.4)0.7Ca0.3MnO3 (LPCMO) films on LaAlO3-buffered SrTiO3 (LAO/STO) substrates has been demonstrated using metalorganic aerosol deposition technique. By growing partially relaxed 7-27 nm thick heteroepitaxial LAO buffer layers on STO a perfect lattice matching to the LPCMO has been achieved. As a result, strain-free heteroepitaxial 10-20 nm thick LPCMO/LAO/STO films with bulk-like ferromagnetic metallic ground state were obtained. Without buffer the coherently strained thin LPCMO/STO and LPCMO/LAO films were insulating and weakly magnetic. The reason for the optimized magnetotransport in strain-free LPCMO films was found to be a large octahedral Mn-O-Mn bond angle φOOR ~ 166-168° as compared to the significantly smaller one of φOOR ~ 152-156° determined for the tensile (LPCMO/STO) and compressively (LPCMO/LAO) strained films.

Antiferromagnetic Correlations in Strongly Valence Fluctuating CeIrSn

CeIrSn with a quasikagome Ce lattice in the hexagonal basal plane is a strongly valence fluctuating compound, as we confirm by hard x-ray photoelectron spectroscopy and inelastic neutron scattering, with a high Kondo temperature of T_{K}∼480  K. We report a negative in-plane thermal expansion α/T below 2 K, which passes through a broad minimum near 0.75 K. Volume and a-axis magnetostriction for B∥a are markedly negative at low fields and change sign before a sharp metamagnetic anomaly at 6 T. These behaviors are unexpected for Ce-based intermediate valence systems, which should feature positive expansivity. Rather they point towards antiferromagnetic correlations at very low temperatures. This is supported by muon spin relaxation measurements down to 0.1 K, which provide microscopic evidence for a broad distribution of internal magnetic fields. Comparison with isostructural CeRhSn suggests that these antiferromagnetic correlations emerging at T≪T_{K} result from geometrical frustration.

Thermodynamic Perspective on Field-Induced Behavior of α-RuCl_{3}

Measurements of the magnetic Grüneisen parameter (Γ_{B}) and specific heat on the Kitaev material candidate α-RuCl_{3} are used to access in-plane field and temperature dependence of the entropy up to 12 T and down to 1 K. No signatures corresponding to phase transitions are detected beyond the boundary of the magnetically ordered region, but only a shoulderlike anomaly in Γ_{B}, involving an entropy increment as small as 10^{-5}Rlog2. These observations put into question the presence of a phase transition between the purported quantum spin liquid and the field-polarized state of α-RuCl_{3}. We show theoretically that at low temperatures Γ_{B} is sensitive to crossings in the lowest excitations within gapped phases, and identify the measured shoulderlike anomaly as being of such origin. Exact diagonalization calculations demonstrate that the shoulderlike anomaly can be reproduced in extended Kitaev models that gain proximity to an additional phase at finite field without entering it. We discuss manifestations of this proximity in other measurements.

Spin liquids in geometrically perfect triangular antiferromagnets

The cradle of quantum spin liquids, triangular antiferromagnets show strong proclivity to magnetic order and require deliberate tuning to stabilize a spin-liquid state. In this brief review, we juxtapose recent theoretical developments that trace the parameter regime of the spin-liquid phase, with experimental results for Co-based and Yb-based triangular antiferromagnets. Unconventional spin dynamics arising from both ordered and disordered ground states are discussed, and the notion of a geometrically perfect triangular system is scrutinized to demonstrate non-trivial imperfections that may assist magnetic frustration in stabilizing dynamic spin states with peculiar excitations.

Realization of the kagome spin ice state in a frustrated intermetallic compound

Spin ices are exotic phases of matter characterized by frustrated spins obeying local "ice rules," in analogy with the electric dipoles in water ice. In two dimensions, one can similarly define ice rules for in-plane Ising-like spins arranged on a kagome lattice. These ice rules require each triangle plaquette to have a single monopole and can lead to different types of orders and excitations. Using experimental and theoretical approaches including magnetometry, thermodynamic measurements, neutron scattering, and Monte Carlo simulations, we establish HoAgGe as a crystalline (i.e., nonartificial) system that realizes the kagome spin ice state. The system features a variety of partially and fully ordered states and a sequence of field-induced phases at low temperatures, all consistent with the kagome ice rule.

Rearrangement of Uncorrelated Valence Bonds Evidenced by Low-Energy Spin Excitations in YbMgGaO_{4}

dc-magnetization data measured down to 40 mK speak against conventional freezing and reinstate YbMgGaO_{4} as a triangular spin-liquid candidate. Magnetic susceptibility measured parallel and perpendicular to the c axis reaches constant values below 0.1 and 0.2 K, respectively, thus indicating the presence of gapless low-energy spin excitations. We elucidate their nature in the triple-axis inelastic neutron scattering experiment that pinpoints the low-energy (E≤J_{0}∼0.2  meV) part of the excitation continuum present at low temperatures (T<J_{0}/k_{B}), but completely disappearing upon warming the system above T≫J_{0}/k_{B}. In contrast to the high-energy part at E>J_{0} that is rooted in the breaking of nearest-neighbor valence bonds and persists to temperatures well above J_{0}/k_{B}, the low-energy one originates from the rearrangement of the valence bonds and thus from the propagation of unpaired spins. We further extend this picture to herbertsmithite, the spin-liquid candidate on the kagome lattice, and argue that such a hierarchy of magnetic excitations may be a universal feature of quantum spin liquids.

Pressure dependence of spin canting in ammonium metal formate antiferromagnets

High-pressure single-crystal X-ray diffraction at ambient temperature and high-pressure SQUID measurements down to 2 K were performed up to ∼2.5 GPa on ammonium metal formates, [NH₄][M(HCOO)₃] where M = Mn²⁺, Fe²⁺, and Ni²⁺, in order to correlate structural variations to magnetic behaviour. Similar structural distortions and phase transitions were observed for all compounds, although the transition pressures varied with the size of the metal cation. The antiferromagnetic ordering in [NH₄][M(HCOO)₃] compounds was maintained as a function of pressure, and the magnetic ordering transition temperature changed within a few kelvins depending on the structural distortion and the metal cation involved. These compounds, in particular [NH₄][Fe(HCOO)₃], showed greatest sensitivity to the degree of spin canting upon compression, clearly visible from the twenty-fold increase in the low-temperature magnetisation for [NH₄][Fe(HCOO)₃] at 1.4 GPa, and the change from purely antiferromagnetic to weakly ferromagnetic ordering in [NH₄][Mn(HCOO)₃] at 1 GPa. The variation in the exchange couplings and spin canting was checked with density-functional calculations that reproduce well the increase in canted moment within [NH₄][Fe(HCOO)₃] upon compression, and suggest that the Dzyaloshinskii-Moriya (DM) interaction is evolving as a function of pressure. The pressure dependence of spin canting is found to be highly dependent on the metal cation, as magnetisation magnitudes did not change significantly for when M = Ni²⁺ or Mn²⁺. These results demonstrate that the overall magnetic behaviour of each phase upon compression was not only dependent on the structural distortions but also on the electronic configuration of the metal cation.

Breakdown of Magnetic Order in the Pressurized Kitaev Iridate β-Li_{2}IrO_{3}

Temperature-pressure phase diagram of the Kitaev hyperhoneycomb iridate β-Li_{2}IrO_{3} is explored using magnetization, thermal expansion, magnetostriction, and muon spin rotation measurements, as well as single-crystal x-ray diffraction under pressure and ab initio calculations. The Néel temperature of β-Li_{2}IrO_{3} increases with the slope of 0.9  K/GPa upon initial compression, but the reduction in the polarization field H_{c} reflects a growing instability of the incommensurate order. At 1.4 GPa, the ordered state breaks down upon a first-order transition, giving way to a new ground state marked by the coexistence of dynamically correlated and frozen spins. This partial freezing in the absence of any conspicuous structural defects may indicate the classical nature of the resulting pressure-induced spin liquid, an observation paralleled to the increase in the nearest-neighbor off-diagonal exchange Γ under pressure.

Models and materials for generalized Kitaev magnetism

The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev materials based on spin-orbital dependent bond interactions and provide a comprehensive overview of its implications in real materials. We set the focus on experimental results and current theoretical understanding of planar honeycomb systems (Na₂IrO₃, α-Li₂IrO₃, and α-RuCl₃), three-dimensional Kitaev materials (β- and γ-Li₂IrO₃), and other potential candidates, completing the review with the list of open questions awaiting new insights.

The world's smallest capacitive dilatometer, for high-resolution thermal expansion and magnetostriction in high magnetic fields

For the characterization of novel quantum phases of matter, it is often required to study materials under multi-extreme conditions, in particular down to very low temperatures and in very high magnetic fields. We developed the world's smallest high-resolution capacitive dilatometer suitable for temperatures down to 10 mK and usage in high magnetic fields up to 37.5 T. Despite the extreme miniaturization, the capacitive dilatometer can resolve length changes down to 0.01 Å. This is an unprecedented resolution in a capacitive dilatometer of this compact size. Many cryogenic devices have limited space. Due to the extremely reduced cell size (3 cm³, 12 g), implementation or new applications in many of these sample space lacking devices are now possible. As an important example, the minute device can now be rotated in any standard cryostat, including dilution refrigerators or the commercial physical property measurement system. The present super compact design provides also for high resolution thermal expansion and magnetostriction measurements in a 15.2 mm diameter tube, enabling its use in the 32 mm bore, 37.5 T Bitter magnet at the High Field Magnet Laboratory in Nijmegen down to a temperature of 300 mK.

Nearest-neighbour resonating valence bonds in YbMgGaO4

Since its proposal by Anderson, resonating valence bonds (RVB) formed by a superposition of fluctuating singlet pairs have been a paradigmatic concept in understanding quantum spin liquids. Here, we show that excitations related to singlet breaking on nearest-neighbour bonds describe the high-energy part of the excitation spectrum in YbMgGaO₄, the effective spin-1/2 frustrated antiferromagnet on the triangular lattice, as originally considered by Anderson. By a thorough single-crystal inelastic neutron scattering study, we demonstrate that nearest-neighbour RVB excitations account for the bulk of the spectral weight above 0.5 meV. This renders YbMgGaO₄ the first experimental system where putative RVB correlations restricted to nearest neighbours are observed, and poses a fundamental question of how complex interactions on the triangular lattice conspire to form this unique many-body state.

The signature of short range resonating valence bonds (RVB) to understand quantum spin liquids is yet to be explored. Here, Li et al. observe the putative RVB correlations restricted to nearest neighbours in YbMgGaO₄, responsible for the high-energy spin excitations.

Entropy Evolution in the Magnetic Phases of Partially Frustrated CePdAl

In the heavy-fermion metal CePdAl, long-range antiferromagnetic order coexists with geometric frustration of one-third of the Ce moments. At low temperatures, the Kondo effect tends to screen the frustrated moments. We use magnetic fields B to suppress the Kondo screening and study the magnetic phase diagram and the evolution of the entropy with B employing thermodynamic probes. We estimate the frustration by introducing a definition of the frustration parameter based on the enhanced entropy, a fundamental feature of frustrated systems. In the field range where the Kondo screening is suppressed, the liberated moments tend to maximize the magnetic entropy and strongly enhance the frustration. Based on our experiments, this field range may be a promising candidate to search for a quantum spin liquid.

Crystalline Electric-Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO_{4}

We apply moderate-high-energy inelastic neutron scattering (INS) measurements to investigate Yb^{3+} crystalline electric field (CEF) levels in the triangular spin-liquid candidate YbMgGaO_{4}. Three CEF excitations from the ground-state Kramers doublet are centered at the energies ℏω=39, 61, and 97 meV in agreement with the effective spin-1/2 g factors and experimental heat capacity, but reveal sizable broadening. We argue that this broadening originates from the site mixing between Mg^{2+} and Ga^{3+} giving rise to a distribution of Yb-O distances and orientations and, thus, of CEF parameters that account for the peculiar energy profile of the CEF excitations. The CEF randomness gives rise to a distribution of the effective spin-1/2 g factors and explains the unprecedented broadening of low-energy magnetic excitations in the fully polarized ferromagnetic phase of YbMgGaO_{4}, although a distribution of magnetic couplings due to the Mg/Ga disorder may be important as well.

Grüneisen parameter studies on heavy fermion quantum criticality

The Grüneisen parameter, experimentally determined from the ratio of thermal expansion to specific heat, quantifies the pressure dependence of characteristic energy scales of matter. It is highly enhanced for Kondo lattice systems, whose properties are strongly dependent on the pressure sensitive antiferromagnetic exchange interaction between f- and conduction electrons. In this review, we focus on the divergence of the Grüneisen parameter and its magnetic analogue, the adiabatic magnetocaloric effect, for heavy-fermion metals near quantum critical points. We compare experimental results with current theoretical models, including the effect of strong geometrical frustration. We also discuss the possibility of using materials with the divergent magnetic Grüneisen parameter for adiabatic demagnetization cooling to very low temperatures.

Single crystal growth from separated educts and its application to lithium transition-metal oxides

Thorough mixing of the starting materials is the first step of a crystal growth procedure. This holds true for almost any standard technique, whereas the intentional separation of educts is considered to be restricted to a very limited number of cases. Here we show that single crystals of α-Li₂IrO₃ can be grown from separated educts in an open crucible in air. Elemental lithium and iridium are oxidized and transported over a distance of typically one centimeter. In contrast to classical vapor transport, the process is essentially isothermal and a temperature gradient of minor importance. Single crystals grow from an exposed condensation point placed in between the educts. The method has also been applied to the growth of Li₂RuO₃, Li₂PtO₃ and β-Li₂IrO₃. A successful use of this simple and low cost technique for various other materials is anticipated.

Super-heavy electron material as metallic refrigerant for adiabatic demagnetization cooling

Low-temperature refrigeration is of crucial importance in fundamental research of condensed matter physics, because the investigations of fascinating quantum phenomena, such as superconductivity, superfluidity, and quantum criticality, often require refrigeration down to very low temperatures. Currently, cryogenic refrigerators with (3)He gas are widely used for cooling below 1 K. However, usage of the gas has been increasingly difficult because of the current worldwide shortage. Therefore, it is important to consider alternative methods of refrigeration. We show that a new type of refrigerant, the super-heavy electron metal YbCo2Zn20, can be used for adiabatic demagnetization refrigeration, which does not require (3)He gas. This method has a number of advantages, including much better metallic thermal conductivity compared to the conventional insulating refrigerants. We also demonstrate that the cooling performance is optimized in Yb1-x Sc x Co2Zn20 by partial Sc substitution, with x ~ 0.19. The substitution induces chemical pressure that drives the materials to a zero-field quantum critical point. This leads to an additional enhancement of the magnetocaloric effect in low fields and low temperatures, enabling final temperatures well below 100 mK. This performance has, up to now, been restricted to insulators. For nearly a century, the same principle of using local magnetic moments has been applied for adiabatic demagnetization cooling. This study opens new possibilities of using itinerant magnetic moments for cryogen-free refrigeration.

Muon Spin Relaxation Evidence for the U(1) Quantum Spin-Liquid Ground State in the Triangular Antiferromagnet YbMgGaO_{4}

Muon spin relaxation (μSR) experiments on single crystals of the structurally perfect triangular antiferromagnet YbMgGaO_{4} indicate the absence of both static long-range magnetic order and spin freezing down to 0.048 K in a zero field. Below 0.4 K, the μ^{+} spin relaxation rates, which are proportional to the dynamic correlation function of the Yb^{3+} spins, exhibit temperature-independent plateaus. All these μSR results unequivocally support the formation of a gapless U(1) quantum spin liquid ground state in the triangular antiferromagnet YbMgGaO_{4}.

A uniaxial stress capacitive dilatometer for high-resolution thermal expansion and magnetostriction under multiextreme conditions

Thermal expansion and magnetostriction are directional dependent thermodynamic quantities. For the characterization of novel quantum phases of matter, it is required to study materials under multi-extreme conditions, in particular, down to very low temperatures, in very high magnetic fields or under high pressure. We developed a miniaturized capacitive dilatometer suitable for temperatures down to 20 mK and usage in high magnetic fields, which exerts a large spring force between 40 to 75 N on the sample. This corresponds to a uniaxial stress up to 3 kbar for a sample with cross section of (0.5 mm)(2). We describe design and performance test of the dilatometer which resolves length changes with high resolution of 0.02 Å at low temperatures. The miniaturized device can be utilized in any standard cryostat, including dilution refrigerators or the commercial physical property measurement system.

Multiple Metamagnetic Quantum Criticality in Sr_{3}Ru_{2}O_{7}

Bilayer strontium ruthenate Sr_{3}Ru_{2}O_{7} displays pronounced non-Fermi liquid behavior at magnetic fields around 8 T, applied perpendicular to the ruthenate planes, which previously has been associated with an itinerant metamagnetic quantum critical end point (QCEP). We focus on the magnetic Grüneisen parameter Γ_{H}, which is the most direct probe to characterize field-induced quantum criticality. We confirm quantum critical scaling due to a putative two-dimensional QCEP near 7.845(5) T, which is masked by two ordered phases A and B, identified previously by neutron scattering. In addition, we find evidence for a QCEP at 7.53(2) T and determine the quantum critical regimes of both instabilities and the effect of their superposition.

Characteristic signatures of quantum criticality driven by geometrical frustration

Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn, where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion, and magnetic Grüneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven be geometrical frustration. We also discovered a spin flop-type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin liquid-like state.

Persistent Detwinning of Iron-Pnictide EuFe_{2}As_{2} Crystals by Small External Magnetic Fields

Our comprehensive study on EuFe_{2}As_{2} reveals a dramatic reduction of magnetic detwinning fields compared to other AFe_{2}As_{2} (A=Ba, Sr, Ca) iron pnictides by indirect magnetoelastic coupling of the Eu^{2+} ions. We find that only ∼0.1  T are sufficient for persistent detwinning below the local Eu^{2+} ordering; above T_{Eu}=19  K, higher fields are necessary. Even after the field is switched off, a significant imbalance of twin domains remains constant up to the structural and electronic phase transition (190 K). This persistent detwinning provides the unique possibility to study the low temperature electronic in-plane anisotropy of iron pnictides without applying any symmetry-breaking external force.

Quantum criticality in a metallic spin liquid

When magnetic order is suppressed by frustrated interactions, spins form a highly correlated fluctuating 'spin liquid' state down to low temperatures. The magnetic order of local moments can also be suppressed when they are fully screened by conduction electrons through the Kondo effect. Thus, the combination of strong geometrical frustration and Kondo screening may lead to novel types of quantum phase transition. We report low-temperature thermodynamic measurements on the frustrated Kondo lattice Pr₂Ir₂O₇, which exhibits a chiral spin liquid state below 1.5 K as a result of the frustrated interaction between Ising 4f local moments and their interplay with Ir conduction electrons. Our results provide a first clear example of zero-field quantum critical scaling that emerges in a spin liquid state of a highly frustrated metal.

Quantum bicriticality in the heavy-fermion metamagnet YbAgGe

Bicritical points, at which two distinct symmetry-broken phases become simultaneously unstable, are typical for spin-flop metamagnetism. Interestingly, the heavy-fermion compound YbAgGe also possesses such a bicritical point (BCP) with a low temperature T(BCP)≈0.3  K at a magnetic field of μH(BCP)≈4.5  T. In its vicinity, YbAgGe exhibits anomalous behavior that we attribute to the influence of a quantum bicritical point that is close in parameter space yet can be reached by tuning T(BCP) further to zero. Using high-resolution measurements of the magnetocaloric effect, we demonstrate that the magnetic Grüneisen parameter ΓH indeed both changes sign and diverges as required for quantum criticality. Moreover, ΓH displays a characteristic scaling behavior but only on the low-field side H≲H(BCP), indicating a pronounced asymmetry with respect to the critical field. We speculate that the small value of T(BCP) is related to the geometric frustration of the Kondo lattice of YbAgGe.

Zero-field quantum critical point in CeCoIn5

Quantum criticality in the normal and superconducting states of the heavy-fermion metal CeCoIn5 is studied by measurements of the magnetic Grüneisen ratio ΓH and specific heat in different field orientations and temperatures down to 50 mK. A universal temperature over magnetic field scaling of ΓH in the normal state indicates a hidden quantum critical point at zero field. Within the superconducting state, the quasiparticle entropy at constant temperature increases upon reducing the field towards zero, providing additional evidence for zero-field quantum criticality.

Interplay between Kondo suppression and Lifshitz transitions in YbRh2Si2 at high magnetic fields

We investigate the magnetic field dependent thermopower, thermal conductivity, resistivity, and Hall effect in the heavy fermion metal YbRh2Si2. In contrast to reports on thermodynamic measurements, we find in total three transitions at high fields, rather than a single one at 10 T. Using the Mott formula together with renormalized band calculations, we identify Lifshitz transitions as their origin. The predictions of the calculations show that all experimental results rely on an interplay of a smooth suppression of the Kondo effect and the spin splitting of the flat hybridized bands.

EuFe2(As(1-x)P(x))2: reentrant spin glass and superconductivity

By systematic investigations of the magnetic, transport, and thermodynamic properties of single crystals of EuFe(2)(As(1-x)P(x))(2) (0≤x≤1), we explore the complex interplay of superconductivity and Eu(2+) magnetism. Below 30 K, two magnetic transitions are observed for all P substituted crystals, suggesting a revision of the phase diagram. In addition to the canted A-type antiferromagnetic order of Eu(2+) at ∼20  K, a spin glass transition is discovered at lower temperatures. Most remarkably, the reentrant spin glass state of EuFe(2)(As(1-x)P(x))(2) coexists with superconductivity around x≈0.2.

Anomalous reduction of the Lorenz ratio at the quantum critical point in YbAgGe

We report measurements of the electrical and thermal transport on the hexagonal heavy-fermion metal YbAgGe for temperatures T ≥ 40  mK and in magnetic fields H∥ab up to 14 T. This distorted kagome-lattice system displays a series of magnetic states and a quantum critical point at H(c) = 4.5  T. The Lorenz ratio L(T)/L0 displays a marked reduction only close to H(c). A T-linear contribution below 120 mK, present at all different fields, allows us to extrapolate the Lorenz ratio towards T = 0. At the critical field this yields L/L0 = 0.92±0.03, suggesting a violation of the Wiedemann-Franz law due to strong inelastic scattering.

Coherent excitations and electron-phonon coupling in Ba/EuFe2As2 compounds investigated by femtosecond time- and angle-resolved photoemission spectroscopy

We employed femtosecond time- and angle-resolved photoelectron spectroscopy to analyze the response of the electronic structure of the 122 Fe-pnictide parent compounds Ba/EuFe(2)As(2) and optimally doped BaFe(1.85)Co(0.15)As(2) near the Γ point to optical excitation by an infrared femtosecond laser pulse. We identify pronounced changes of the electron population within several 100 meV above and below the Fermi level, which we explain as a combination of (i) coherent lattice vibrations, (ii) a hot electron and hole distribution, and (iii) transient modifications of the chemical potential. The responses of the three different materials are very similar. In the coherent response we identify three modes at 5.6, 3.3, and 2.6 THz. While the highest frequency mode is safely assigned to the A(1g) mode, the other two modes require a discussion in comparison to the literature. Employing a transient three temperature model we deduce from the transient evolution of the electron distribution a rather weak, momentum-averaged electron-phonon coupling quantified by values for λ<ω(2)> between 30 and 70 meV(2). The chemical potential is found to present pronounced transient changes reaching a maximum of 15 meV about 0.6 ps after optical excitation and is modulated by the coherent phonons. This change in the chemical potential is particularly strong in a multiband system like the 122 Fe-pnictide compounds investigated here due to the pronounced variation of the electron density of states close to the equilibrium chemical potential.

Crystal-field splitting and correlation effect on the electronic structure of A2IrO3

The electronic structure of the honeycomb lattice iridates Na(2)IrO(3) and Li(2)IrO(3) has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split d-d excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of j(eff)=3/2 states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of j(eff) physics in A(2)IrO(3). We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both Na(2)IrO(3) and Li(2)IrO(3) can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr(2)IrO(4).

Thermopower as a sensitive probe of electronic nematicity in iron pnictides

We study the in-plane anisotropy of the thermoelectric power and electrical resistivity on detwinned single crystals of isovalent substituted EuFe(2)(As(1-x)P(x))(2). Compared to the resistivity anisotropy, the thermopower anisotropy is more pronounced and clearly visible already at temperatures much above the structural and magnetic phase transitions. Most remarkably, the thermopower anisotropy changes sign below the structural transition. This is associated with the interplay of two contributions due to anisotropic scattering and orbital polarization, which dominate at high and low temperatures, respectively.

Na2IrO3 as a novel relativistic Mott insulator with a 340-meV gap

We study Na2IrO3 by angle-resolved photoemission spectroscopy, optics, and band structure calculations in the local-density approximation (LDA). The weak dispersion of the Ir 5d-t(2g) manifold highlights the importance of structural distortions and spin-orbit (SO) coupling in driving the system closer to a Mott transition. We detect an insulating gap Δ(gap)≃340  meV which, at variance with a Slater-type description, is already open at 300 K and does not show significant temperature dependence even across T(N)≃15  K. An LDA analysis with the inclusion of SO and Coulomb repulsion U reveals that, while the prodromes of an underlying insulating state are already found in LDA+SO, the correct gap magnitude can only be reproduced by LDA+SO+U, with U=3  eV. This establishes Na2IrO3 as a novel type of Mott-like correlated insulator in which Coulomb and relativistic effects have to be treated on an equal footing.

Quasiparticle entropy in the high-field superconducting phase of CeCoIn(5)

The heavy-fermion superconductor CeCoIn(5) displays an additional transition within its superconducting (SC) state, whose nature is characterized by high-precision studies of the isothermal field dependence of the entropy, derived from combined specific heat and magnetocaloric effect measurements at temperatures T≥100  mK and fields H≤12  T aligned along different directions. For any of these conditions, we do not observe an additional entropy contribution upon tuning at constant temperature by magnetic field from the homogeneous SC into the presumed Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) SC state. By contrast, for H∥[100] a reduction of entropy was found that quantitatively agrees with the expectation for spin-density-wave order without FFLO superconductivity. Our data exclude the formation of a FFLO state in CeCoIn(5) for out-of-plane field directions, where no spin-density-wave order exists.

Spin waves and revised crystal structure of honeycomb iridate Na2IrO3

We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order below T(N)=15.3  K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90° Ir-O-Ir bonds required for dominant Kitaev exchange.

Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A2IrO3

Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2IrO3 (A=Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from θ≈-125  K for Na2IrO3 to θ≈-33  K for Li2IrO3, while the ordering temperature remains roughly the same T(N)≈15  K. Using functional renormalization group calculations we show that this evolution of θ and T(N) as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2IrO3 is deep in a magnetically ordered regime, while Li2IrO3 appears to be close to a spin-liquid regime.

Ultrafast momentum-dependent response of electrons in antiferromagnetic EuFe2As2 driven by optical excitation

Employing the momentum sensitivity of time- and angle-resolved photoemission spectroscopy we demonstrate the analysis of ultrafast single- and many-particle dynamics in antiferromagnetic EuFe(2)As(2). Their separation is based on a temperature-dependent difference of photoexcited hole and electron relaxation times probing the single-particle band and the spin density wave gap, respectively. Reformation of the magnetic order occurs at 800 fs, which is 4 times slower compared to electron-phonon equilibration due to a smaller spin-dependent relaxation phase space.

Magnetism and superconductivity in Eu0.2Sr0.8(Fe0.86Co0.14)2As2 probed by 75As NMR

We report bulk superconductivity (SC) in Eu(0.2)Sr(0.8)(Fe(0.86)Co(0.14))(2)As(2) single crystals by means of electrical resistivity, magnetic susceptibility and specific heat measurements with T(c) is approximately equal to 20 K and an antiferromagnetic (AFM) ordering of Eu(2+) moments at T(N) is approximately equal to 2.0 K in zero field. (75)As NMR experiments have been performed in the two external field directions (H is parallel to ab) and (H is parallel to c). (75)As-NMR spectra are analysed in terms of first-order quadrupolar interaction. Spin-lattice relaxation rates (1/T(1)) follow a T(3) law in the temperature range 4.2-15 K. There is no signature of a Hebel-Slichter coherence peak just below the SC transition, indicating a non-s-wave or s(±) type of superconductivity. In the temperature range 160-18 K 1/T(1)T follows the C/(T+θ) law reflecting 2D AFM spin fluctuations.

Symmetry-breaking lattice distortion in Sr₃Ru₂O₇

The electronic nematic phase of Sr₃Ru₂O₇ is investigated by high-resolution in-plane thermal expansion measurements in magnetic fields close to 8 T applied at various angles Θ off the c axis. At Θ < 10° we observe a very small (10⁻⁷) lattice distortion which breaks the fourfold in-plane symmetry, resulting in nematic domains with interchanged a and b axis. At Θ ≳ 10° the domains are almost fully aligned and thermal expansion indicates an area-preserving lattice distortion of order 2 × 10⁻⁶ which is likely related to orbital ordering. Since the system is located in the immediate vicinity of a metamagnetic quantum critical end point, the results represent the first observation of a structural relaxation driven by quantum criticality.

High-resolution alternating-field technique to determine the magnetocaloric effect of metals down to very low temperatures

The magnetocaloric effect or "magnetic Grüneisen ratio" Γ(H)=T(-1)(dT/dH)(S) quantifies the cooling or heating of a material when an applied magnetic field is changed under adiabatic conditions. Recently, this property has attracted considerable interest in the field of quantum criticality. Here, we report the development of a low-frequency alternating-field technique for measurements of the magnetocaloric effect down to very low temperatures, which is an important property for the study of quantum critical points. We focus, in particular, on highly conducting metallic samples and discuss the influence of eddy current heating. By comparison with magnetization and specific heat measurements, we demonstrate that our fast and accurate technique gives quantitatively correct values for the magnetocaloric effect under truly adiabatic conditions.

Evidence for a non-Fermi-liquid phase in Ge-substituted YbRh2Si2

The canonical view of heavy fermion quantum criticality assumes a single quantum critical point separating the paramagnet from the antiferromagnet. However, recent experiments on Yb-based heavy fermion compounds suggest the presence of non-Fermi liquid behavior over a finite zero-temperature region. Using detailed susceptibility and transport measurements we show that the classic quantum critical system, Ge-substituted YbRh(2)Si(2), also displays such behavior. We advance arguments that this is not due to a disorder-smeared quantum critical point, but represents a new class of metallic phase.

Superconductivity versus quantum criticality: what can we learn from heavy fermions?

Two quantum critical point (QCP) scenarios are being discussed for different classes of antiferromagnetic (AF) heavy-fermion (HF) systems. In the itinerant one, where AF order is of the spin-density wave (SDW) type, the heavy 'composite' charge carriers keep their integrity at the QCP. The second one implies a breakdown of the Kondo effect and a disintegration of the composite fermions at the AF QCP. We discuss two isostructural compounds as exemplary materials for these two different scenarios: CeCu(2)Si(2) exhibits a three-dimensional (3D) SDW QCP and superconductivity, presumably mediated by SDW fluctuations, as strongly suggested by recent inelastic neutron scattering experiments. In Y bRh(2)Si(2), the AF QCP is found to coincide with a Kondo-destroying one. However, in the latter compound these two QCPs can be detached by varying the average unit-cell volume, e.g. through the application of chemical pressure, as realized by partial substitution of either Ir or Co for Rh. A comparison of CeCu(2)Si(2) and Y bRh(2)Si(2) indicates that the apparent differences in quantum critical behaviour go along with disparate behaviour concerning the (non-) existence of superconductivity (SC). No sign of SC could be detected in Y bRh(2)Si(2) down to mK temperatures. A potential correlation between the specific nature of the QCP and the occurrence of SC, however, requires detailed studies on further quantum critical HF superconductors, e.g. on β-Y bAlB(4), UBe(13), CeCoIn(5) and CeRhIn(5).

Quantum oscillations in the anomalous phase in Sr3Ru2O7

We report measurements of quantum oscillations detected in the putative nematic phase of Sr3Ru2O7. Improvements in sample purity enabled the resolution of small amplitude de Haas-van Alphen (dHvA) oscillations between two first order metamagnetic transitions delimiting the phase. Two distinct frequencies were observed, whose amplitudes follow the normal Lifshitz-Kosevich profile. Variations of the dHvA frequencies are explained in terms of a chemical potential shift produced by reaching a peak in the density of states, and an anomalous field dependence of the oscillatory amplitude provides information on domains.

Evolution of quantum criticality in CeNi(9-x)Cu(x)Ge(4)

Crystal structure, specific heat, thermal expansion, magnetic susceptibility and electrical resistivity studies of the heavy fermion system CeNi(9-x)Cu(x)Ge(4) (0≤x≤1) reveal a continuous tuning of the ground state by Ni/Cu substitution from an effectively fourfold-degenerate non-magnetic Kondo ground state of CeNi(9)Ge(4) (with pronounced non-Fermi-liquid features) towards a magnetically ordered, effectively twofold-degenerate ground state in CeNi(8)CuGe(4) with T(N) = 175 ± 5 mK. Quantum critical behavior, [Formula: see text], is observed for [Formula: see text]. Hitherto, CeNi(9-x)Cu(x)Ge(4) represents the first system where a substitution-driven quantum phase transition is connected not only with changes of the relative strength of the Kondo effect and RKKY interaction, but also with a reduction of the effective crystal field ground state degeneracy.

Kondo-cluster-glass state near a ferromagnetic quantum phase transition

We report on a comprehensive study of CePd(1-x)Rh(x) (0.6 <or= x <or= 0.95) poly- and single crystals close to the ferromagnetic instability by means of low-temperature ac susceptibility, magnetization, and volume thermal expansion. The signature of ferromagnetism in this heavy-fermion system can be traced from 6.6 K in CePd down to 25 mK for x = 0.87. Despite pronounced non-Fermi-liquid effects in both specific heat and thermal expansion, the Grüneisen ratio does not diverge as T --> 0, providing evidence for the absence of a quantum critical point. Instead, a peculiar "Kondo-cluster-glass" state is found for x >or= 0.65, and the non-Fermi-liquid effects in the specific heat, ac susceptibility, and magnetization are compatible with the quantum Griffiths phase scenario.

Divergence of the magnetic Grüneisen ratio at the field-induced quantum critical point in YbRh2Si2

The heavy-fermion metal YbRh2Si2 is studied by low-temperature magnetization M(T) and specific-heat C(T) measurements at magnetic fields close to the quantum critical point (H_{c}=0.06 T, H perpendicularc). Upon approaching the instability, dM/dT is more singular than C(T), leading to a divergence of the magnetic Grüneisen ratio Gamma_{mag}=-(dM/dT)/C. Within the Fermi-liquid regime, Gamma_{mag}=-G_{r}(H-H_{c};{fit}) with G_{r}=-0.30+/-0.01 and H_{c};{fit}=(0.065+/-0.005) T which is consistent with scaling behavior of the specific-heat coefficient in YbRh2(Si0.95Ge0.05)_{2}. The field dependence of dM/dT indicates an inflection point of the entropy as a function of magnetic field upon passing the line T;{ small star, filled}(H) previously observed in Hall and thermodynamic measurements.

Dimensional crossover of quantum critical behavior in CeCoIn5

The nature of quantum criticality in CeCoIn5 is studied by low-temperature thermal expansion alpha(T). At the field-induced quantum critical point at H = 5 T a crossover scale T* approximately 0.3 K is observed, separating alpha(T)/T proportional, variant T(-1) from a weaker T(-1/2) divergence. We ascribe this change to a crossover in the dimensionality of the critical fluctuations which may be coupled to a change from unconventional to conventional quantum criticality. Disorder, whose effect on quantum criticality is studied in CeCoIn(5-x)Sn(x) (0 < or = x < or = 0.18), shifts T* towards higher temperatures.

Multiple Energy Scales at a Quantum Critical Point

We report thermodynamic measurements in a magnetic-field-driven quantum critical point of a heavy fermion metal, YbRh2Si2. The data provide evidence for an energy scale in the equilibrium excitation spectrum that is in addition to the one expected from the slow fluctuations of the order parameter. Both energy scales approach zero as the quantum critical point is reached, thereby providing evidence for a new class of quantum criticality.

Quantum criticality in the cubic heavy-fermion system CeIn3-xSnx

We report a comprehensive study of CeIn3-xSnx (0.55<or=x< or=0.8) single crystals close to the antiferromagnetic quantum-critical point (QCP) at xc approximately 0.37 by means of the low-temperature thermal expansion and Grüneisen parameter. This system represents the first example for a cubic heavy fermion in which TN can be suppressed continuously down to T=0. A characteristic sign change of the Grüneisen parameter between the antiferromagnetic and paramagnetic states indicates the accumulation of entropy close to the QCP. The observed quantum-critical behavior is compatible with the predictions of the itinerant theory for three-dimensional critical spin fluctuations. This has important implications for the role of the dimensionality in heavy-fermion QCPs.