A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2.

Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo2(AsO4)2, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo2(AsO4)2 is a promising QSL candidate.

High-precision measurements of terahertz polarization states with a fiber coupled time-domain THz spectrometer.

We present a new method for high precision measurements of polarization rotation in the frequency range from 0.2 to 2.2 THz using a fiber coupled time-domain THz spectrometer. A free standing wire-grid polarizer splits THz light into orthogonal components that are then measured by two separate detectors simultaneously. We theoretically model the uncertainties introduced by optical component non-idealities and predict that we may expect to achieve accuracies of 0.8% when anti-symmetrizing the response with respect to an applied field. Anti-symmetrization improves accuracy by more than four orders of magnitude. We demonstrate this method on a 2D electron gas in magnetic field and show that we achieve a precision of 20 µrad (1.1 mdeg) for small polarization rotation angles. A detailed description of the technique and data analysis procedure is provided, demonstrating its capability to precisely measure polarization states in the 0.2 to 2.2 THz range.

Bonding and Suppression of a Magnetic Phase Transition in EuMn2P2.

Electrons in solids often adopt complex patterns of chemical bonding driven by the competition between energy gains from covalency and delocalization, and energy costs of double occupation to satisfy Pauli exclusion, with multiple intermediate states in the transition between highly localized, and magnetic, and delocalized, and nonmagnetic limits. Herein, we report a chemical pressure-driven transition from a proper Mn magnetic ordering phase transition to a Mn magnetic phase crossover in EuMn2P2 the limiting end member of the EuMn2X2 (X = Sb, As, P) family of layered materials. This loss of a magnetic ordering occurs despite EuMn2P2 remaining an insulator at all temperatures, and with a phase transition to long-range Eu antiferromagnetic order at TN ≈ 17 K. The absence of a Mn magnetic phase transition contrasts with the formation of long-range Mn order at T ≈ 130 K in isoelectronic EuMn2Sb2 and EuMn2As2. Temperature-dependent specific heat and 31P NMR measurements provide evidence for the development of short-range Mn magnetic correlations from T ≈ 250-100 K, interpreted as a precursor to covalent bond formation. Density functional theory calculations demonstrate an unusual sensitivity of the band structure to the details of the imposed Mn and Eu magnetic order, with an antiferromagnetic Mn arrangement required to recapitulate an insulating state. Our results imply a picture in which long-range Mn magnetic order is suppressed by chemical pressure, but that antiferromagnetic correlations persist, narrowing bands and producing an insulating state.

Observation of 4- and 6-Magnon Bound States in the Spin-Anisotropic Frustrated Antiferromagnet FeI_{2}.

We observe a wealth of multimagnon bound states in the strongly anisotropic spin-1 triangular antiferromagnet FeI_{2} using time-domain terahertz spectroscopy. These unconventional excitations can arise in ordered magnets due to attractive magnon-magnon interactions and alter their properties. We analyze the energy-magnetic field spectrum via an exact diagonalization method for a dilute gas of interacting magnons and detect up to 4- and 6-magnon bound states, hybridized with single magnons. This zoo of tunable interacting quasiparticles provides a unique platform to study decay and renormalization, reminiscent of the few-body problems found in cold-atom, nuclear, and particle physics.

A Large Effective Phonon Magnetic Moment in a Dirac Semimetal.

We investigated the magnetoterahertz response of the Dirac semimetal Cd3As2 and observed a particularly low frequency optical phonon as well as a very prominent and field-sensitive cyclotron resonance. As the cyclotron frequency is tuned with the field to pass through the phonon, the phonon becomes circularly polarized, as shown by a notable splitting in its response to right- and left-hand polarized light. This splitting can be expressed as an effective phonon magnetic moment that is approximately 2.7 times the Bohr magneton, which is almost 4 orders of magnitude larger than ab initio calculations predict for phonon magnetic moments in nonmagnetic insulators. This exceedingly large value is due to the coupling of the phonons to the cyclotron motion and is controlled directly by the electron-phonon coupling constant. This field-tunable circular-polarization-selective coupling provides new functionality for nonlinear optics to create light-induced topological phases in Dirac semimetals.

Tunable Magnon Interactions in a Ferromagnetic Spin-1 Chain.

NiNb_{2}O_{6} is an almost ideal realization of a 1D spin-1 ferromagnetic Heisenberg chain compound with weak unidirectional anisotropy. Using time-domain THz spectroscopy, we measure the low-energy electrodynamic response of NiNb_{2}O_{6} as a function of temperature and external magnetic field. At low temperatures, we find a magnonlike spin excitation, which corresponds to the lowest energy excitation at q∼0. At higher temperatures, we unexpectedly observe a temperature-dependent renormalization of the spin-excitation energy, which has a strong dependence on field direction. Using theoretical arguments, exact diagonalizations, and finite temperature dynamical Lanczos calculations, we construct a picture of magnon-magnon interactions that naturally explains the observed renormalization. We show how magnetic field strength and direction may be used to directly tune the sign of the magnon-magnon interaction. This unique scenario is a consequence of the spin-1 nature and has no analog in the more widely studied spin-1/2 systems.

Efficient Terahertz Harmonic Generation with Coherent Acceleration of Electrons in the Dirac Semimetal Cd_{3}As_{2}.

We report strong terahertz (∼10^{12} Hz) high harmonic generation at room temperature in thin films of Cd_{3}As_{2}, a three-dimensional Dirac semimetal. Third harmonics are detectable with a tabletop light source and can be as strong as 100 V/cm by applying a fundamental field of 6.5 kV/cm inside the film, demonstrating an unprecedented efficiency for terahertz frequency conversion. Our time-resolved terahertz spectroscopy and calculations also clarify the microscopic mechanism of the nonlinearity originating in the coherent acceleration of Dirac electrons in momentum space. Our results provide clear insights for nonlinear currents of Dirac electrons driven by the terahertz field under the influence of scattering, paving the way toward novel devices for high-speed electronics and photonics based on topological semimetals.

Subterahertz Momentum Drag and Violation of Matthiessen's Rule in an Ultraclean Ferromagnetic SrRuO_{3} Metallic Thin Film.

SrRuO_{3}, a ferromagnet with an approximately 160 K Curie temperature, exhibits a T^{2}-dependent dc resistivity below ≈30 K. Nevertheless, previous optical studies in the infrared and terahertz range show non-Drude dynamics at low temperatures, which seem to contradict Fermi-liquid predictions. In this work, we measure the low-frequency THz range response of thin films with residual resistivity ratios, ρ_{300K}/ρ_{4K}≈74. At temperatures below 30 K, we find both a sharp zero frequency mode which has a width narrower than k_{B}T/ℏ as well as a broader zero frequency Lorentzian that has at least an order of magnitude larger scattering. Both features have temperature dependences consistent with a Fermi liquid with the wider feature explicitly showing a T^{2} scaling. Above 30 K, there is a crossover to a regime described by a single Drude peak that we believe arises from strong interband electron-electron scattering. Such two channel Drude transport sheds light on reports of the violation of Matthiessen's rule and extreme sensitivity to disorder in metallic ruthenates.

Resolving Continua of Fractional Excitations by Spinon Echo in THz 2D Coherent Spectroscopy.

We show that the new technique of terahertz 2D coherent spectroscopy is capable of giving qualitatively new information about fractionalized spin systems. For the prototypical example of the transverse field Ising chain, we demonstrate theoretically that, despite the broad continuum of excitations in linear response, the 2D spectrum contains sharp features that are a coherent signature of a "spinon echo," which gives previously inaccessible information such as the lifetime of the two-spinon excited state. The effects of disorder and finite lifetime, which are practically indistinguishable in the linear optical or neutron response, manifest in dramatically different fashion in the 2D spectra. Our results may be directly applicable to model quasi-1D transverse field Ising chain systems such as CoNb_{2}O_{6}, but the concept can be applied to fractionalized spin systems in general.

Magnetoterahertz Response and Faraday Rotation from Massive Dirac Fermions in the Topological Crystalline Insulator Pb_{0.5}Sn_{0.5}Te.

Pb_{1-x}Sn_{x}Te has been shown to be an interesting tunable topological crystalline insulator system. We present a magnetoterahertz spectroscopic study of thin films of Pb_{0.5}Sn_{0.5}Te. The complex Faraday rotation angle and optical conductivity in the circular basis are extracted without any additional assumptions. Our quantitative measures of the THz response allow us to show that the sample studied contains two types of bulk carriers. One is p type and originates in 3D Dirac bands. The other is n type and appears to be from more conventional 3D bands. These two types of carriers display different cyclotron resonance dispersions. Through simulating the cyclotron resonance of hole carriers, we can determine the Fermi energy and Fermi velocity. Furthermore, the scattering rates of p-type and n-type carriers were found to show opposite field dependences, which can be attributed to their different Landau level broadening behaviors under magnetic field. Our work provides a new way to isolate real topological signatures of bulk states in Dirac and Weyl semimetals.

Locating the Missing Superconducting Electrons in the Overdoped Cuprates La_{2-x}Sr_{x}CuO_{4}.

Overdoped high-temperature cuprate superconductors have often been understood within the standard BCS framework of superconductivity. However, measurements in a variety of overdoped cuprates indicate that the superfluid density is much smaller than expected from BCS theory and decreases smoothly to zero as the doping is increased. Here, we combine time-domain THz spectroscopy with kHz range mutual inductance measurements on the same overdoped La_{2-x}Sr_{x}CuO_{4} films to determine the total, superfluid, and uncondensed spectral weight as a function of doping. A significant fraction of the carriers remains uncondensed in a wide Drude-like peak as T→0, while the superfluid density remains linear in temperature. These observations are seemingly inconsistent with existing, realistic theories of impurity scattering suppressing the superfluid density in a BCS-like d-wave superconductor. Our large measurement frequency range gives us a unique look at the low frequency spectral weight distribution, which may suggest the presence of quantum phase fluctuations as the critical doping is approached.

Nodeless Bulk Superconductivity in the Time-Reversal Symmetry Breaking Bi/Ni Bilayer System.

Epitaxial bilayer films of Bi(110) and Ni host a time-reversal symmetry breaking superconducting order with an unexpectedly high transition temperature T_{c}=4.1 K. Using time-domain THz spectroscopy, we measure the low energy electrodynamic response of a Bi/Ni bilayer thin film from 0.2 to 2 THz as a function of temperature and magnetic field. We analyze the data in the context of a Bardeen-Cooper-Schrieffer-like superconductor with a finite normal-state scattering rate. In a zero magnetic field, all states in the film become fully gapped, providing important constraints into possible pairing symmetries. Our data appear to rule out the odd-frequency pairing that is natural for many ferromagnetic-superconductor interfaces. By analyzing the magnetic field-dependent response in terms of a pair-breaking parameter, we determine that superconductivity develops over the entire bilayer sample which may point to the p-wave like nature of unconventional superconductivity.

Absence of Cyclotron Resonance in the Anomalous Metallic Phase in InO_{x}.

It is observed that many thin superconducting films with not too high disorder level (generally R_{N}/□<2000 Ω) placed in magnetic field show an anomalous metallic phase where the resistance is low but still finite as temperature goes to zero. Here we report in weakly disordered amorphous InO_{x} thin films that this anomalous metal phase possesses no cyclotron resonance and hence non-Drude electrodynamics. The absence of a finite frequency resonant mode can be associated with a vanishing downstream component of the vortex current parallel to the supercurrent and an emergent particle-hole symmetry of this metal, which establishes its non-Fermi-liquid character.

Asymmetric Splitting of an Antiferromagnetic Resonance via Quartic Exchange Interactions in Multiferroic Hexagonal HoMnO_{3}.

The symmetric splitting of two spin-wave branches in an antiferromagnetic resonance (AFR) experiment has been an essential measurement of antiferromagnets for over half a century. In this work, circularly polarized time-domain THz spectroscopy experiments performed on the low symmetry multiferroic hexagonal HoMnO_{3} reveal an AFR of the Mn sublattice to split asymmetrically in an applied magnetic field, with an ≈50% difference in g factors between the high and low energy branches of this excitation. The temperature dependence of the g factors, including a drastic renormalization at the Ho spin ordering temperature, reveals this asymmetry to unambiguously stem from Ho-Mn interactions. Theoretical calculations demonstrate that the AFR asymmetry is not explained by conventional Ho-Mn exchange mechanisms alone and is only reproduced if quartic spin interactions are also included in the spin Hamiltonian. Our results provide a paradigm for the optical study of such novel interactions in hexagonal manganites and low symmetry antiferromagnets in general.

Magneto-Optical Signature of Massless Kane Electrons in Cd_{3}As_{2}.

We report on optical reflectivity experiments performed on Cd_{3}As_{2} over a broad range of photon energies and magnetic fields. The observed response clearly indicates the presence of 3D massless charge carriers. The specific cyclotron resonance absorption in the quantum limit implies that we are probing massless Kane electrons rather than symmetry-protected 3D Dirac particles. The latter may appear at a smaller energy scale and are not directly observed in our infrared experiments.

High-Resolution Faraday Rotation and Electron-Phonon Coupling in Surface States of the Bulk-Insulating Topological Insulator Cu_{0.02}Bi_{2}Se_{3}.

We have utilized time-domain magnetoterahertz spectroscopy to investigate the low-frequency optical response of the topological insulator Cu_{0.02}Bi_{2}Se_{3} and Bi_{2}Se_{3} films. With both field and frequency dependence, such experiments give sufficient information to measure the mobility and carrier density of multiple conduction channels simultaneously. We observe sharp cyclotron resonances (CRs) in both materials. The small amount of Cu incorporated into the Cu_{0.02}Bi_{2}Se_{3} induces a true bulk insulator with only a single type of conduction with a total sheet carrier density of ~4.9×10^{12}/cm^{2} and mobility as high as 4000 cm^{2}/V·s. This is consistent with conduction from two virtually identical topological surface states (TSSs) on the top and bottom of the film with a chemical potential ~145 meV above the Dirac point and in the bulk gap. The CR broadens at high fields, an effect that we attribute to an electron-phonon interaction. This assignment is supported by an extended Drude model analysis of the zero-field Drude conductance. In contrast, in normal Bi_{2}Se_{3} films, two conduction channels were observed, and we developed a self-consistent analysis method to distinguish the dominant TSSs and coexisting trivial bulk or two-dimensional electron gas states. Our high-resolution Faraday rotation spectroscopy on Cu_{0.02}Bi_{2}Se_{3} paves the way for the observation of quantized Faraday rotation under experimentally achievable conditions to push the chemical potential in the lowest Landau level.

Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid Candidate FeSc2S4.

Theoretical models of the spin-orbital liquid (SOL) FeSc2S4 have predicted it to be in close proximity to a quantum critical point separating a spin-orbital liquid phase from a long-range ordered magnetic phase. Here, we examine the magnetic excitations of FeSc2S4 through time-domain terahertz spectroscopy under an applied magnetic field. At low temperatures an excitation emerges that we attribute to a singlet-triplet excitation from the SOL ground state. A threefold splitting of this excitation is observed as a function of applied magnetic field. As singlet-triplet excitations are typically not allowed in pure spin systems, our results demonstrate the entangled spin and orbital character of singlet ground and triplet excited states. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc2S4's proximity to the quantum critical point. In the context of these models, we estimate the characteristic length of the singlet correlations to be ξ/(a/2)≈8.2 (where a/2 is the nearest neighbor lattice constant), which establishes FeSc2S4 as a SOL with long-range entanglement.

Optical birefringence and dichroism of cuprate superconductors in the THz regime.

The presence of optical polarization anisotropies, such as Faraday or Kerr effects, linear birefringence, and magnetoelectric birefringence are evidence for broken symmetry states of matter. The recent discovery of a Kerr effect using near-IR light in the pseudogap phase of the cuprates can be regarded as a strong evidence for a spontaneous symmetry breaking and the existence of an anomalous long-range ordered state. In this work we present a high precision study of the polarimetry properties of the cuprates in the THz regime. While no Faraday effect was found in this frequency range to the limits of our experimental uncertainty (1.3 milli-radian or 0.07°), a small but significant polarization rotation was detected that derives from an anomalous linear dichroism. In YBa2Cu3Oy the effect has a temperature onset that mirrors the pseudogap temperature T* and is enhanced in magnitude in underdoped samples. In x=1/8 La2-xBaxCuO4, the effect onsets above room temperature, but shows a dramatic enhancement near a temperature scale known to be associated with spin- and charge-ordered states. These features are consistent with a loss of both C4 rotation and mirror symmetry in the electronic structure of the CuO2 planes in the pseudogap state.

Hierarchy of bound states in the one-dimensional ferromagnetic Ising chain CoNb2O6 investigated by high-resolution time-domain terahertz spectroscopy.

Kink bound states in the one-dimensional ferromagnetic Ising chain compound CoNb2O6 have been studied using high-resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schrödinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near 2 times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states--two pairs of kinks on neighboring chains.

Microwave spectroscopy evidence of superconducting pairing in the magnetic-field-induced metallic state of InO(x) films at zero temperature.

We investigate the field-tuned quantum phase transition in a 2D low-disorder amorphous InO(x) film in the frequency range of 0.05 to 16 GHz employing microwave spectroscopy. In the zero-temperature limit, the ac data are consistent with a scenario where this transition is from a superconductor to a metal instead of a direct transition to an insulator. The intervening metallic phase is unusual with a small but finite resistance that is much smaller than the normal state sheet resistance at the lowest measured temperatures. Moreover, it exhibits a superconducting response on short length and time scales while global superconductivity is destroyed. We present evidence that the true quantum critical point of this 2D superconductor metal transition is located at a field B(sm) far below the conventionally defined critical field B(cross) where different isotherms of magnetoresistance cross each other. The superfluid stiffness in the low-frequency limit and the superconducting fluctuation frequency from opposite sides of the transition both vanish at B≈B(sm). The lack of evidence for finite-frequency superfluid stiffness surviving B(cross) signifies that B(cross) is a crossover above which superconducting fluctuations make a vanishing contribution to dc and ac measurements.