Field-tunable spin-density-wave phases in Sr3Ru2O7.

The conduction electrons in a metal experience competing interactions with each other and the atomic nuclei. This competition can lead to many types of magnetic order in metals. For example, in chromium the electrons order to form a spin-density-wave (SDW) antiferromagnetic state. A magnetic field may be used to perturb or tune materials with delicately balanced electronic interactions. Here, we show that the application of a magnetic field can induce SDW magnetic order in a quasi-2D metamagnetic metal, where none exists in the absence of the field. We use magnetic neutron scattering to show that the application of a large (B ≈ 8 T) magnetic field to the perovskite metal Sr3Ru2O7 (refs 3-7) can be used to tune the material through two magnetically ordered SDW states. The ordered states exist over relatively small ranges in field (≲0.4 T), suggesting that their origin is due to a new mechanism related to the electronic fine structure near the Fermi energy, possibly combined with the stabilizing effect of magnetic fluctuations. The magnetic field direction is shown to control the SDW domain populations, which naturally explains the strong resistivity anisotropy or 'electronic nematic' behaviour observed in this material.

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.

Collapse of the Mott Gap and Emergence of a Nodal Liquid in Lightly Doped Sr(2)IrO(4).

We report angle resolved photoemission experiments on the electron doped Heisenberg antiferromagnet (Sr(1-x)La(x))(2)IrO(4). For a doping level of x=0.05, we find an unusual metallic state with coherent nodal excitations and an antinodal pseudogap bearing strong similarities with underdoped cuprates. This state emerges from a rapid collapse of the Mott gap with doping resulting in a large underlying Fermi surface that is backfolded by a (π,π) reciprocal lattice vector which we attribute to the intrinsic structural distortion of Sr(2)IrO(4).

Spin-wave spectrum of the quantum ferromagnet on the pyrochlore lattice Lu2V2O7.

Neutron inelastic scattering has been used to probe the spin dynamics of the quantum (S=1/2) ferromagnet on the pyrochlore lattice Lu(2)V(2)O(7). Well-defined spin waves are observed at all energies and wave vectors, allowing us to determine the parameters of the Hamiltonian of the system. The data are found to be in excellent overall agreement with a minimal model that includes a nearest-neighbor Heisenberg exchange J = 8.22(2) meV and a Dzyaloshinskii-Moriya interaction (DMI) D = 1.5(1) meV. The large DMI term revealed by our study is broadly consistent with the model originally used to explain the magnon Hall effect in this compound [Onose et al., Science 329, 297 (2010) and Ideue et al., Phys. Rev. B 85, 134411 (2012)]. However, our ratio of D/J = 0.18(1) is roughly half of their value, and is much larger than those found in other theoretical studies [Xiang et al., Phys. Rev. B 83, 174402 (2011) and Mook et al., Phys. Rev. B 89,134409 (2014)].

Coherent quasiparticles with a small fermi surface in lightly doped Sr(3)Ir(2)O(7).

We characterize the electron doping evolution of (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7} by means of angle-resolved photoemission. Concomitant with the metal insulator transition around x≈0.05 we find the emergence of coherent quasiparticle states forming a closed small Fermi surface of volume 3x/2, where x is the independently measured La concentration. The quasiparticle weight Z remains large along the entire Fermi surface, consistent with the moderate renormalization of the low-energy dispersion, and no pseudogap is observed. This indicates a conventional, weakly correlated Fermi liquid state with a momentum independent residue Z≈0.5 in lightly doped Sr_{3}Ir_{2}O_{7}.

Thermodynamics of phase formation in the quantum critical metal Sr3Ru2O7.

The behavior of matter near zero temperature continuous phase transitions, or "quantum critical points" is a central topic of study in condensed matter physics. In fermionic systems, fundamental questions remain unanswered: the nature of the quantum critical regime is unclear because of the apparent breakdown of the concept of the quasiparticle, a cornerstone of existing theories of strongly interacting metals. Even less is known experimentally about the formation of ordered phases from such a quantum critical "soup." Here, we report a study of the specific heat across the phase diagram of the model system Sr(3)Ru(2)O(7), which features an anomalous phase whose transport properties are consistent with those of an electronic nematic. We show that this phase, which exists at low temperatures in a narrow range of magnetic fields, forms directly from a quantum critical state, and contains more entropy than mean-field calculations predict. Our results suggest that this extra entropy is due to remnant degrees of freedom from the highly entropic state above T(c). The associated quantum critical point, which is "concealed" by the nematic phase, separates two Fermi liquids, neither of which has an identifiable spontaneously broken symmetry, but which likely differ in the topology of their Fermi surfaces.

Robustness of basal-plane antiferromagnetic order and the J(eff)=1/2 state in single-layer iridate spin-orbit Mott insulators.

The magnetic structure and electronic ground state of the layered perovskite Ba(2)IrO(4) have been investigated using x-ray resonant magnetic scattering. Our results are compared with those for Sr(2)IrO(4), for which we provide supplementary data on its magnetic structure. We find that the dominant, long-range antiferromagnetic order is remarkably similar in the two compounds and that the electronic ground state in Ba(2)IrO(4), deduced from an investigation of the x-ray resonant magnetic scattering L(3)/L(2) intensity ratio, is consistent with a J(eff)=1/2 description. The robustness of these two key electronic properties to the considerable structural differences between the Ba and Sr analogues is discussed in terms of the enhanced role of the spin-orbit interaction in 5d transition metal oxides.

Strain control of a bandwidth-driven spin reorientation in Ca3Ru2O7.

The layered-ruthenate family of materials possess an intricate interplay of structural, electronic and magnetic degrees of freedom that yields a plethora of delicately balanced ground states. This is exemplified by Ca3Ru2O7, which hosts a coupled transition in which the lattice parameters jump, the Fermi surface partially gaps and the spins undergo a 90∘ in-plane reorientation. Here, we show how the transition is driven by a lattice strain that tunes the electronic bandwidth. We apply uniaxial stress to single crystals of Ca3Ru2O7, using neutron and resonant x-ray scattering to simultaneously probe the structural and magnetic responses. These measurements demonstrate that the transition can be driven by externally induced strain, stimulating the development of a theoretical model in which an internal strain is generated self-consistently to lower the electronic energy. We understand the strain to act by modifying tilts and rotations of the RuO6 octahedra, which directly influences the nearest-neighbour hopping. Our results offer a blueprint for uncovering the driving force behind coupled phase transitions, as well as a route to controlling them.

z+: Neutron cross section separation from wide-angle uniaxial polarization analysis.

We introduce a simple method to extract the nuclear coherent and isotope incoherent, spin incoherent, and magnetic neutron scattering cross section components from powder scattering data measured using a single neutron beam polarization direction and a position-sensitive detector with large out-of-plane coverage. The method draws inspiration from polarized small-angle neutron scattering and contrasts with conventional so-called "xyz" polarization analysis on wide-angle instruments, which requires measurements with three orthogonal polarization directions. The viability of the method is demonstrated on both simulated and experimental data for the classical "spin ice" system Ho2Ti2O7, the latter from the LET direct geometry spectrometer at the ISIS facility. The cross section components can be reproduced with good fidelity by either fitting the out-of-plane angle dependence around a Debye-Scherrer cone or grouping the data by angle and performing a matrix inversion. The limitations of the method and its practical uses are discussed.

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 â‰³ 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.

Magnetic-field-controlled spin fluctuations and quantum critically in Sr3Ru2O7.

When the transition temperature of a continuous phase transition is tuned to absolute zero, new ordered phases and physical behaviour emerge in the vicinity of the resulting quantum critical point. Sr3Ru2O7 can be tuned through quantum criticality with magnetic field at low temperature. Near its critical field Bc it displays the hallmark T-linear resistivity and a [Formula: see text] electronic heat capacity behaviour of strange metals. However, these behaviours have not been related to any critical fluctuations. Here we use inelastic neutron scattering to reveal the presence of collective spin fluctuations whose relaxation time and strength show a nearly singular variation with magnetic field as Bc is approached. The large increase in the electronic heat capacity and entropy near Bc can be understood quantitatively in terms of the scattering of conduction electrons by these spin-fluctuations. On entering the spin-density-wave ordered phase present near Bc, the fluctuations become stronger suggesting that the order is stabilised through an "order-by-disorder" mechanism.

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.

Magnetic field-tuned quantum criticality in the metallic ruthenate Sr3Ru2O7.

The concept of quantum criticality is proving to be central to attempts to understand the physics of strongly correlated electrons. Here, we argue that observations on the itinerant metamagnet Sr3Ru2O7 represent good evidence for a new class of quantum critical point, arising when the critical end point terminating a line of first-order transitions is depressed toward zero temperature. This is of interest both in its own right and because of the convenience of having a quantum critical point for which the tuning parameter is the magnetic field. The relationship between the resultant critical fluctuations and novel behavior very near the critical field is discussed.

Selective probing of magnetic order on Tb and Ir sites in stuffed Tb2Ir2O7  using resonant x-ray scattering.

We study the magnetic structure of the 'stuffed' (Tb-rich) pyrochlore iridate Tb2+x Ir2-x O7-y  (x ∼ 0.18), using resonant elastic x-ray scattering (REXS). In order to disentangle contributions from Tb and Ir magnetic sublattices, experiments were performed at the Ir L 3 and Tb M 5 edges, which provide selective sensitivity to Ir 5d and Tb 4f  magnetic moments, respectively. At the Ir L 3 edge, we found the onset of long-range [Formula: see text] magnetic order below [Formula: see text] K, consistent with the expected signal of all-in all-out (AIAO) magnetic order. Using a single-ion model to calculate REXS cross-sections, we estimate an ordered magnetic moment of [Formula: see text] at 5 K. At the Tb M 5 edge, long-range [Formula: see text] magnetic order appeared below ∼[Formula: see text] K, also consistent with an AIAO magnetic structure on the Tb site. Additional insight into the magnetism of the Tb sublattice is gleaned from measurements at the M 5 edge in applied magnetic fields up to 6 T, which is found to completely suppress the Tb AIAO magnetic order. In zero applied field, the observed gradual onset of the Tb sublattice magnetisation with temperature suggests that it is induced by the magnetic order on the Ir site. The persistence of AIAO magnetic order, despite the greatly reduced ordering temperature and moment size compared to stoichiometric Tb2Ir2O7, for which [Formula: see text] K and [Formula: see text], indicates that stuffing could be a viable means of tuning the strength of electronic correlations, thereby potentially offering a new strategy to achieve topologically non-trivial band crossings in pyrochlore iridates.

Critical fluctuations in the spin-orbit Mott insulator Sr3Ir2O7.

X-ray magnetic critical scattering measurements and specific heat measurements were performed on the perovskite iridate [Formula: see text]. We find that the magnetic interactions close to the Néel temperature [Formula: see text] are three-dimensional. This contrasts with previous studies which suggest two-dimensional behaviour like Sr2IrO4. Violation of the Harris criterion ([Formula: see text]) means that weak disorder becomes relevant. This leads a rounding of the antiferromagnetic phase transition at [Formula: see text], and modifies the critical exponents relative to the clean system. Specifically, we determine that the critical behaviour of [Formula: see text] is representative of the diluted 3D Ising universality class.

In situ strain tuning of the metal-insulator-transition of Ca2RuO4 in angle-resolved photoemission experiments.

Pressure plays a key role in the study of quantum materials. Its application in angle resolved photoemission (ARPES) studies, however, has so far been limited. Here, we report the evolution of the k-space electronic structure of bulk Ca2RuO4, lightly doped with Pr, under uniaxial strain. Using ultrathin plate-like crystals, we achieve uniaxial strain levels up to -4.1%, sufficient to suppress the insulating Mott phase and access the previously unexplored electronic structure of the metallic state at low temperature. ARPES experiments performed while tuning the uniaxial strain reveal that metallicity emerges from a marked redistribution of charge within the Ru t2g shell, accompanied by a sudden collapse of the spectral weight in the lower Hubbard band and the emergence of a well-defined Fermi surface which is devoid of pseudogaps. Our results highlight the profound roles of lattice energetics and of the multiorbital nature of Ca2RuO4 in this archetypal Mott transition and open new perspectives for spectroscopic measurements.

Similarity of scattering rates in metals showing T-linear resistivity.

Many exotic compounds, such as cuprate superconductors and heavy fermion materials, exhibit a linear in temperature (T) resistivity, the origin of which is not well understood. We found that the resistivity of the quantum critical metal Sr(3)Ru(2)O(7) is also T-linear at the critical magnetic field of 7.9 T. Using the precise existing data for the Fermi surface topography and quasiparticle velocities of Sr(3)Ru(2)O(7), we show that in the region of the T-linear resistivity, the scattering rate per kelvin is well approximated by the ratio of the Boltzmann constant to the Planck constant divided by 2π. Extending the analysis to a number of other materials reveals similar results in the T-linear region, in spite of large differences in the microscopic origins of the scattering.

Locking of iridium magnetic moments to the correlated rotation of oxygen octahedra in Sr2IrO4 revealed by x-ray resonant scattering.

Sr2IrO4 is a prototype of the class of Mott insulators in the strong spin-orbit interaction (SOI) limit described by a Jeff = 1/2 ground state. In Sr2IrO4, the strong SOI is predicted to manifest itself in the locking of the canting of the magnetic moments to the correlated rotation by 11.8(1)° of the oxygen octahedra that characterizes its distorted layered perovskite structure. Using x-ray resonant scattering at the Ir L3 edge we have measured accurately the intensities of Bragg peaks arising from different components of the magnetic structure. From a careful comparison of integrated intensities of peaks due to basal-plane antiferromagnetism, with those due to b-axis ferromagnetism, we deduce a canting of the magnetic moments of 12.2(8)°. We thus confirm that in Sr2IrO4 the magnetic moments rigidly follow the rotation of the oxygen octahedra, indicating that, even in the presence of significant non-cubic structural distortions, it is a close realization of the Jeff = 1/2 state.

Entropy landscape of phase formation associated with quantum criticality in Sr3Ru2O7.

Low-temperature phase transitions and the associated quantum critical points are a major field of research, but one in which experimental information about thermodynamics is sparse. Thermodynamic information is vital for the understanding of quantum many-body problems. We show that combining measurements of the magnetocaloric effect and specific heat allows a comprehensive study of the entropy of a system. We present a quantitative measurement of the entropic landscape of Sr3Ru2O7, a quantum critical system in which magnetic field is used as a tuning parameter. This allows us to track the development of the entropy as the quantum critical point is approached and to study the thermodynamic consequences of the formation of a novel electronic liquid crystalline phase in its vicinity.