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An ongoing limitation of terahertz spectroscopy is that the technique is generally limited to the study of relatively large samples of order 4 mm across due to the generally large size of the focal beam spot. We present a nested concentric parabolic reflector design which can reduce the terahertz focal spot size. This parabolic reflector design takes advantage of the feature that reflected rays experience a relative time delay which is the same for all paths. The increase in effective optical path for reflected light is equivalent to the aperture diameter itself. We have shown that the light throughput of an aperture of 2 mm can be increased by a factor 15 as compared to a regular aperture of the same size at low frequencies. This technique can potentially be used to reduce the focal spot size in terahertz spectroscopy and enable the study of smaller samples.

An important and continuing theme of modern solid state physics is the realization of exotic excitations in materials (e.g. quasiparticles) that have no analogy (or have not yet been observed) in the actual physical vacuum of free space. Although they are not fundamental particles, such quasiparticles do constitute the most basic description of the excited states of the "vacuum" in which they reside. In this regard the magnetic textures of the excited states of spin ices, magnetic pyrochlore oxides with dominant Ising interactions, are proposed to be modeled as effective magnetic charge monopoles. Recent inelastic neutron scattering experiments have established the pyrochlore material Yb$_2$Ti$_2$O$_7$ (YbTO) as a quantum spin ice, where in addition to the Ising interactions there are substantial transverse terms that may induce quantum dynamics and - in principle - coherent monopole motion. Here we report a combined time domain terahertz spectroscopy (TDTS) and microwave cavity study of YbTO to probe its complex dynamic magnetic susceptibility. We find that the form of the susceptibility is consistent with monopole motion and a magnetic monopole conductivity can be defined and measured. Using the unique phase sensitive capabilities of these techniques, we observe a sign change in the reactive part of the magnetic response. In generic models of monopole motion this is only possible through introducing inertial effects, e.g. a mass dependent term, to the equations of motion. Analogous to conventional electric charge systems, measurement of the conductivity's spectral weight allows us to derive a value for the magnetic monopole mass, which we find to be approximately 1800 electron masses. Our results establish the magnetic monopoles of quantum spin ice as true coherently propagating quasiparticles of this system.

Theoretical models of the spin-orbital liquid (SOL) FeSc$_2$S$_4$ 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 FeSc$_2$S$_4$ 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 three-fold splitting of this excitation is observed as a function of applied magnetic field. As singlet-triplet excitations are forbidden in inversion symmetric pure spin systems, our results demonstrate the non-trivial character of the entangled spin-orbital singlet ground state. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc$_2$S$_4$'s proximity to the quantum critical point. In the context of these models, we estimate that the characteristic length of the singlet correlations to be $\xi/ (\textbf{a}/2) \approx 8.2$ (where $\textbf{a}/2$ is the nearest neighbor lattice constant) which establishes FeSc$_2$S$_4$ as a SOL with long-range entanglement., Comment: 5 Pages, 4 Figures

In condensed matter systems, the formation of long range order (LRO) with broken symmetry is often accompanied by new types of excitations. However, in many magnetic pyrochlore oxides, geometrical frustration suppresses conventional LRO while at the same time non-trivial spin correlations are observed. For such materials, a natural question to ask then is what is the nature of the excitations in this highly correlated state without broken symmetry? Frequently the application of a symmetry breaking field can stabilize excitations whose properties still reflect certain aspects of the anomalous state without long-range order. Here we report evidence of novel magnetic excitations in the quantum spin ice material Yb$_2$Ti$_2$O$_7$, obtained from time-domain terahertz spectroscopy (TDTS). At large fields, both magnon and two-magnon-like excitations are observed in a $<$001$>$ directed magnetic field illustrating the stabilization of a field induced LRO state. The unique ability of TDTS to measure complex response functions allows a direct study of magnetic responses in different polarization channels, revealing the existence of an unusual left-hand polarized magnon. The g-factors of these excitations are dramatically enhanced in the low-field limit, showing a cross-over of these one- and two-magnon states into features consistent with quantum string-like excitations proposed to exist in quantum spin ice in a small $<$001$>$ applied field., Comment: 15 pages

We present THz range optical conductivity data of a thin film of the near quantum critical heavy fermion compound CeFe$_2$Ge$_2$. Our complex conductivity measurements find a deviation from conventional Drude-like transport in a temperature range previously reported to exhibit unconventional behavior. We calculate the frequency dependent effective mass and scattering rate using an extended Drude model analysis. We find the inelastic scattering rate can be described by a temperature dependent power-law $\omega^{n(T)}$ where $n(T)$ approaches $\sim1.0 \pm 0.2$ at 1.5 K. This is compared to the $\rho \sim T^{1.5}$ behavior claimed in dc resistivity data and the $\rho \sim T^{2}$ expected from Fermi-liquid theory. In addition to a low temperature mass renormalization, we find an anomalous mass renormalization that persists to high temperature. We attribute this to a Hund's coupling in the Fe states in a manner similar to that recently proposed in the ferro-pnictides. CeFe$_2$Ge$_2$ appears to be a very interesting system where one may study the interplay between the usual $4f$ lattice Kondo effect and this Hund's enhanced Kondo effect in the $3d$ states., Comment: 6 pages, 4 figures, Supplemental Material

We present the technical details of a broadband microwave spectrometer for measuring the complex conductance of thin films covering the range from 50 MHz up to 16 GHz in the temperature range 300 mK to 6 K and at applied magnetic fields up to 8 Tesla. We measure the complex reflection from a sample terminating a coaxial transmission line and calibrate the signals with three standards with known reflection coefficients. Thermal isolation of the heat load from the inner conductor is accomplished by including a section of NbTi superconducting cable (transition temperature around 8 $-$ 9 K) and hermetic seal glass bead adapters. This enables us to stabilize the base temperature of the sample stage at 300 mK. However, the inclusion of this superconducting cable complicates the calibration procedure. We document the effects of the superconducting cable on our calibration procedure and the effects of applied magnetic fields and how we control the temperature with great repeatability for each measurement. We have successfully extracted reliable data in this frequency, temperature and field range for thin superconducting films and highly resistive graphene samples.

LiZn$_2$Mo$_3$O$_8$ has been proposed to contain $S~=~1/2$ Mo$_3$O$_{13}$ magnetic clusters arranged on a triangular lattice with antiferromagnetic nearest-neighbor interactions. Here, microwave and terahertz electron spin resonance (ESR), $^7$Li nuclear magnetic resonance (NMR), and muon spin rotation ($\mu \textrm{SR}$) spectroscopies are used to characterize the local magnetic properties of LiZn$_2$Mo$_3$O$_8$. These results show the magnetism in LiZn$_2$Mo$_3$O$_8$ arises from a single isotropic $S~=~1/2$ electron per cluster and that there is no static long-range magnetic ordering down to $T~=~0.07\,\textrm{K}$. Further, there is evidence of gapless spin excitations with spin fluctuations slowing down as the temperature is lowered. These data indicate strong spin correlations which, together with previous data, suggest a low-temperature resonating valence-bond state in LiZn$_2$Mo$_3$O$_8$., Comment: 18 pages, 5 figures

The presence of optical polarization anisotropies, such as Faraday/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$^\circ$), a small but significant polarization rotation was detected that derives from an anomalous linear dichroism. In YBa$_2$Cu$_3$O$_y$ the effect has a temperature onset that mirrors the pseudogap temperature T$^*$ and is enhanced in magnitude in underdoped samples. In $x=1/8$ La$_{2-x}$Ba$_{x}$CuO$_4$, 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 C$_4$ rotation and mirror symmetry in the electronic structure of the CuO$_2$ planes in the pseudogap state., Comment: 5 pages, 4 figures

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 $\approx B_{sm}$. 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., Comment: 10 pages, 10 figures

We present time-domain THz spectroscopy data of a thin film of the Kondo-lattice antiferromagnet CeCu$_2$Ge$_2$. The low frequency complex conductivity has been obtained down to temperatures below the onset of magnetic order. At low temperatures a narrow Drude-like peak forms, which is similar to ones found in other heavy fermion compounds that do not exhibit magnetic order. Using this data in conjunction with DC resistivity measurements, we obtain the frequency dependence of the scattering rate and effective mass through an extended Drude model analysis. The zero frequency limit of this analysis yields evidence for large mass renormalization even in the magnetic state, the scale of which agrees closely with that obtained from thermodynamic measurements., Comment: 4 pages, 3 figures