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We present magneto-optical Kerr effect (MOKE) spectrometer based on a modified Martin-Puplett interferometer, utilizing continuous wave sub-THz low-power radiation in broad frequency range. This spectrometer is capable of measuring the frequency dependence of the MOKE response function, both the Kerr rotation and ellipticity, simultaneously with sub-milliradian accuracy without the need for reference measurement. The instrument's versatility allow it to be coupled to a cryostat with optical windows enabling studies of a variety of quantum materials such as unconventional superconductors, two-dimensional electron gas systems, quantum magnets, and other system showing optical Hall response, at sub-Kelvin temperatures and in high magnetic fields. We demonstrate the functionality of the MOKE spectrometer using an undoped InSb wafer as a test sample.

Although BiFeO$_3$ is one of the most studied multiferroic materials, recent magnetization and neutron scattering studies have revealed a new magnetic phase in this compound - the transverse conical phase. To study the collective spin excitations of this phase, we performed THz spectroscopy in magnetic fields up to 17 T at and above room temperature. We observed five spin-wave branches in the magnetic phase with long wavelength conical modulation. Using a numerical spin dynamics model we found two kinds of excitations with magnetic moments oscillating either along or perpendicular to the static fields. Remarkably, we detected strong directional dichroism, an optical manifestation of the magnetoelectric effect, for two spin-wave modes of the conical phase. According to our experiments, the stability of the conical state is sensitive to the magnetic field history and it can become (meta)stable at or close to zero magnetic field, which may allow exploiting its magnetoelectric properties at room temperature.

Magnetic structures and spin excitations are studied across the phase diagram of the geometrically frustrated S = 3/2 quantum antiferromagnet Cs2CoBr4 in magnetic fields applied along the magnetic easy axis, using neutron diffraction, inelastic neutron scattering and THz absorption spectroscopy. The data are analyzed, where appropriate, using extended SU (4) linear spin wave theory. A minimal magnetic Hamiltonian is proposed based on measurements in the high field polarized state. It deviates considerably from the previously considered models. Additional dilatometry experiments highlight the importance of magnetoelastic coupling in this system., Comment: 14 pages, 10 figures, Accepted to Phys. Rev. B

High-resolution neutron and THz spectroscopies are used to study the magnetic excitation spectrum of Cs$_2$CoBr$_4$, a distorted-triangular-lattice antiferromagnet with nearly XY-type anisotropy. What was previously thought of as a broad excitation continuum [Phys. Rev. Lett. 129, 087201 (2022)] is shown to be a series of dispersive bound states reminiscent of "Zeeman ladders" in quasi-one-dimensional Ising systems. At wave vectors where inter-chain interactions cancel at the Mean Field level, they can indeed be interpreted as bound finite-width kinks in individual chains. Elsewhere in the Brillouin zone their true two-dimensional structure and propagation are revealed., Comment: 11 pages, 8 figures

Recent neutron scattering experiments suggested that frustrated magnetic interactions give rise to antiferromagnetic spiral and fractional skyrmion lattice phases in MnSc$_2$S$_4$. Here, to trace the signatures of these modulated phases, we studied the spin excitations of MnSc$_2$S$_4$ by THz spectroscopy at 300 mK up to 12 T. We found a single magnetic resonance with linearly increasing frequency in field. The corresponding $g$-factor of Mn$^{2+}$ ions $g$ = 1.96, and the absence of other resonances imply very weak anisotropies and negligible contribution of higher harmonics to the spiral state. The significant difference between the dc magnetic susceptibility and the lowest-frequency ac susceptibility in our experiment implies the existence of mode(s) below 100 GHz.

We investigated the spin excitations of magnetoelectric $\text{LiFePO}_4$ by THz absorption spectroscopy in magnetic fields up to 33$\,$T. By studying their selection rules, we found not only magnetic-dipole, but also electric-dipole active (electromagnons) and magnetoelectric resonances. The magnetic field dependence of four strong low-energy modes is reproduced well by our four-sublattice spin model for fields applied along the three orthorhombic axes. From the fit, we refined the exchange couplings, single-ion anisotropies, and the Dzyaloshinskii-Moriya interaction parameters. Additional spin excitations not described by the mean-field model are observed at higher frequencies. Some of them shows a strong shift with magnetic field, up to 4$\,\text{cm}^{-1}/\text{T}$, when the field is applied along the easy axis. Based on this field dependence, we attribute these high frequency resonances to excitation of higher spin multipoles and of two magnons, which become THz-active due to the low symmetry of the magnetically ordered state.

We report the magnetic field dependence of the THz absorption and non-reciprocal directional dichroism spectra of BiFeO$_3$ measured on the three principal crystal cuts for fields applied along the three principal directions of each cut. From the systematic study of the light polarization dependence we deduced the optical selection rules of the spin-wave excitations. Our THz data, combined with small-angle neutron scattering results showed that i) an in-plane magnetic field rotates the $\mathbf{q}$ vectors of the cycloids perpendicular to the magnetic field, and ii) the selection rules are mostly determined by the orientation of the $\mathbf{q}$ vector with respect to the electromagnetic fields. We observed a magnetic field history dependent change in the strength and the frequency of the spin-wave modes, which we attributed to the change of the orientation and the length of the cycloidal $\mathbf{q}$ vector, respectively. Finally, we compared our experimental data with the results of linear spin-wave theory that reproduces the magnetic field dependence of the spin-wave frequencies and most of the selection rules, from which we identified the spin-polarization coupling terms relevant for the optical magnetoelectric effect.

Infrared absorption spectroscopy study of endohedral water molecule in a solid mixture of H$_2$O@C$_{60}$ and C$_{60}$ was carried out at liquid helium temperature. From the evolution of the spectra during the ortho-para conversion process, the spectral lines were identified as para- and ortho-water transitions. Eight vibrational transitions with rotational side peaks were observed in the mid-infrared: $\omega_1$, $\omega_2$, $\omega_3$, $2\omega_1$, $2\omega_2$, $\omega_1 +\omega_3$, $\omega_2 +\omega_3$, and $2\omega_2+\omega_3$. The vibrational frequencies $\omega_2$ and 2$\omega_2$ are lower by 1.6\% and the rest by 2.4\%, as compared to free \water/. A model consisting of a rovibrational Hamiltonian with the dipole and quadrupole moments of water interacting with the crystal field was used to fit the infrared absorption spectra. The electric quadrupole interaction with the crystal field lifts the degeneracy of the rotational levels. The finite amplitudes of the pure $v_1$ and $v_2$ vibrational transitions are consistent with the interaction of the water molecule dipole moment with a lattice-induced electric field. The permanent dipole moment of encapsulated \water/ is found to be $0.5\pm 0.1$ D as determined from the far-infrared rotational line intensities. The translational mode of the quantized center of mass motion of \water/ in the molecular cage of C$_{60}$ was observed at 110cm$^{-1}$ (13.6meV).

Non-reciprocal directional dichroism, also called the optical-diode effect, is an appealing functional property inherent to the large class of non-centrosymmetric magnets. However, the in-situ electric control of this phenomenon is challenging as it requires a set of conditions to be fulfilled: Special symmetries of the magnetic ground state, spin-excitations with comparable magnetic- and electric-dipole activity and switchable electric polarization. We demonstrate the isothermal electric switch between domains of Ba$_2$CoGe$_2$O$_7$ possessing opposite magnetoelectric susceptibilities. Combining THz spectroscopy and multiboson spin-wave analysis, we show that unbalancing the population of antiferromagnetic domains generates the non-reciprocal light absorption of spin excitations., Comment: version accepted

The Ising chain in transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, topological defects, quantum criticality, and duality. Although the quasi-1D ferromagnet CoNb$_2$O$_6$ has been put forward as the best material example of the transverse field Ising model, it exhibits significant deviations from ideality. Through a combination of THz spectroscopy and theory, we show that CoNb$_2$O$_6$ in fact is well described by a different model with strong bond dependent interactions, which we dub the {\it twisted Kitaev chain}, as these interactions share a close resemblance to a one-dimensional version of the intensely studied honeycomb Kitaev model. In this model the ferromagnetic ground state of CoNb$_2$O$_6$ arises from the compromise between two distinct alternating axes rather than a single easy axis. Due to this frustration, even at zero applied field domain-wall excitations have quantum motion that is described by the celebrated Su-Schriefer-Heeger model of polyacetylene. This leads to rich behavior as a function of field. Despite the anomalous domain wall dynamics, close to a critical transverse field the twisted Kitaev chain enters a universal regime in the Ising universality class. This is reflected by the observation that the excitation gap in CoNb$_2$O$_6$ in the ferromagnetic regime closes at a rate precisely twice that of the paramagnet. This originates in the duality between domain walls and spin-flips and the topological conservation of domain wall parity. We measure this universal ratio `2' to high accuracy -- the first direct evidence for the Kramers-Wannier duality in nature., Comment: 6 pages, 3 figures; 5 pages, 7 figures (Supplemental)

We investigated the static and dynamic magnetic properties of the polar ferrimagnet Mn$_2$Mo$_3$O$_8$ in three magnetically ordered phases via magnetization, magnetic torque, and THz absorption spectroscopy measurements. The observed magnetic field dependence of the spin-wave resonances, including Brillouin zone-center and zone-boundary excitations, magnetization, and torque, are well described by an extended two-sublattice antiferromagnetic classical mean-field model. In this orbitally quenched system, the competing weak easy-plane and easy-axis single-ion anisotropies of the two crystallographic sites are determined from the model and assigned to the tetra- and octahedral sites, respectively, by ab initio calculations.

The significance of spin-lattice coupling in the phase diagram of the quantum spin-icepyrochlore Tb2Ti2O7 has been a topic of debate for some time. Here, we focus on the aspect of vibronic coupling, which occurs between the Tb3+ electronic levels and transverse acoustic phonons, by studying their dependence on a magnetic field applied along the cubic h111i direction. Our experimental THz spectroscopy measurements, combined with quantitative theoretical quantum calculations, show that indeed vibronic effects are observed at 3 K. An analysis incorporating quadrupolar spin-lattice effects in the Hamiltonian is therefore relevant in this compound, which is no longer optically isotropic but magnetically birefringent.

The coexisting magnetic and ferroelectric orders in multiferroic materials give rise to a handful of novel magnetoelectric phenomena, such as the absorption difference for the opposite propagation directions of light called the non-reciprocal directional dichroism (NDD). Usually these effects are restricted to low temperature, where the multiferroic phase develops. In this paper we report the observation of NDD in the paramagnetic phase of Sr2CoSi2O7 up to temperatures more than ten times higher than its N\'eel temperature (7 K) and in fields up to 30 T. The magnetically induced polarization and NDD in the disordered paramagnetic phase is readily explained by the single-ion spin-dependent hybridization mechanism, which does not necessitate correlation effects between magnetic ions. The Sr2CoSi2O7 provides an ideal system for a theoretical case study, demonstrating the concept of magnetoelectric spin excitations in a paramagnet via analytical as well as numerical approaches. We applied exact diagonalization of a spin cluster to map out the temperature and field dependence of the spin excitations, as well as symmetry arguments of the single ion and lattice problem to get the spectrum and selection rules., Comment: 15 pages, 7 figures

We report on terahertz spectroscopy of quantum spin dynamics in $\alpha$-RuCl$_3$, a system proximate to the Kitaev honeycomb model, as a function of temperature and magnetic field. An extended magnetic continuum develops below the structural phase transition at $T_{s2}=62$K. With the onset of a long-range magnetic order at $T_N=6.5$K, spectral weight is transferred to a well-defined magnetic excitation at $\hbar \omega_1 = 2.48$meV, which is accompanied by a higher-energy band at $\hbar \omega_2 = 6.48$meV. Both excitations soften in magnetic field, signaling a quantum phase transition at $B_c=7$T where we find a broad continuum dominating the dynamical response. Above $B_c$, the long-range order is suppressed, and on top of the continuum, various emergent magnetic excitations evolve. These excitations follow clear selection rules and exhibit distinct field dependencies, characterizing the dynamical properties of the field-induced quantum spin liquid.

Competing exchange interactions can produce complex magnetic states together with spin-induced electric polarizations. With competing interactions on alternating triangular and kagome layers, the swedenborgite CBO may have one of the largest measured spin-induced polarizations of about 1700 nC/cm$^2$ below its ferrimagnetic transition temperature at 70 K. Powder neutron-diffraction data, magnetization measurements, and spin-wave resonance frequencies in the THz range reveal that the complex spin order of multiferroic CBO can be described as a triangular array of c-axis chains ferrimagnetically coupled to each other in the ab plane. Magnetostriction on bonds that couple those chains produces the large spin-induced polarization of CBO., Comment: 3 figures

Spin excitations were studied by absorption spectroscopy in CaBaCo4O7 which is a type-I multiferroic compound with the largest magnetic-order induced ferroelectric polarization ({\Delta}P=17mC/m2) reported, so far. We observed two optical magnon branches: a solely electric dipole allowed one and a mixed magnetoelectric resonance. The entangled magnetization and polarization dynamics of the magnetoelectric resonance gives rise to unidirectional light absorption, i.e. that magnon mode absorbs the electromagnetic radiation for one propagation direction but not for the opposite direction. Our systematic study of the magnetic field and temperature dependence of magnon modes provides information about the energies and symmetries of spin excitations, which is required to develop a microscopic spin model of CaBaCo4O7., Comment: 5 pages, 4 figures

Multiferroics permit the magnetic control of the electric polarization and electric control of the magnetization. These static magnetoelectric (ME) effects are of enormous interest: The ability to read and write a magnetic state current-free by an electric voltage would provide a huge technological advantage. Dynamic or optical ME effects are equally interesting because they give rise to unidirectional light propagation as recently observed in low-temperature multiferroics. This phenomenon, if realized at room temperature, would allow the development of optical diodes which transmit unpolarized light in one, but not in the opposite direction. Here, we report strong unidirectional transmission in the room-temperature multiferroic BiFeO$_3$ over the gigahertz--terahertz frequency range. Supporting theory attributes the observed unidirectional transmission to the spin-current driven dynamic ME effect. These findings are an important step toward the realization of optical diodes, supplemented by the ability to switch the transmission direction with a magnetic or electric field.

We derive a sum rule to demonstrate that the static magnetoelectric (ME) effect is governed by optical transitions that are simultaneously excited via the electric and magnetic components of light. By a systematic analysis of magnetic point groups, we show that the ME sum rule is applicable to a broad variety of non-centrosymmetric magnets including ME multiferroic compounds. Due to the dynamical ME effect, the optical excitations in these materials can exhibit directional dichroism, i.e. the absorption coefficient can be different for counter-propagating light beams. According to the ME sum rule, the magnitude of the linear ME effect of a material is mainly determined by the directional dichroism of its low-energy optical excitations. Application of the sum rule to the multiferroic Ba$_2$CoGe$_2$O$_7$, Sr$_2$CoSi$_2$O$_7$ and Ca$_2$CoSi$_2$O$_7$ shows that in these compounds the static ME effect is mostly governed by the directional dichroism of the spin-wave excitations in the GHz-THz spectral range. On this basis, we argue that the studies of directional dichroism and the application of ME sum rule can promote the synthesis of new materials with large static ME effect.

Hydrogen is one of the few molecules which has been incarcerated in the molecular cage of C$_{60}$ and forms endohedral supramolecular complex H$_2$@C$_{60}$. In this confinement hydrogen acquires new properties. Its translational motion becomes quantized and is correlated with its rotations. We applied infrared spectroscopy to study the dynamics of hydrogen isotopologs H$_2$, D$_2$ and HD incarcerated in C$_{60}$. The translational and rotational modes appear as side bands to the hydrogen vibrational mode in the mid infrared part of the absorption spectrum. Because of the large mass difference of hydrogen and C$_{60}$ and the high symmetry of C$_{60}$ the problem is identical to a problem of a vibrating rotor moving in a three-dimensional spherical potential. The translational motion within the C$_{60}$ cavity breaks the inversion symmetry and induces optical activity of H$_2$. We derive potential, rotational, vibrational and dipole moment parameters from the analysis of the infrared absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H$_2$@C$_{60}$. The same parameters were used to predict H$_2$ energies inside C$_{70}$[Xu et al., J. Chem. Phys., {\bf 130}, 224306 (2009)]. We compare the predicted energies and the low temperature infrared absorption spectra of H$_2$@C$_{70}$., Comment: Updated author list

We have studied the magnetic field dependence of far-infrared active magnetic modes in a single ferroelectric domain \BFO/ crystal at low temperature. The modes soften close to the critical field of 18.8\,T along the [001] (pseudocubic) axis, where the cycloidal structure changes to the homogeneous canted antiferromagnetic state and a new strong mode with linear field dependence appears that persists at least up to 31\,T. A microscopic model that includes two \DM/ interactions and easy-axis anisotropy describes closely both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field. The good agreement of theory with experiment suggests that the proposed model provides the foundation for future technological applications of this multiferroic material., Comment: Added Randy S. Fishman to the author list, he contributed the theory

We studied spin excitations of the multiferroic Ba2CoGe2O7 in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. We show that a multi-boson spin-wave theory can capture these unconventional modes, that include spin-stretching modes associated with an oscillating magnetic dipole (or only quadrupole) moment. The lack of the inversion symmetry allows these modes to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S > 1/2 spin systems with strong single-ion anisotropy and/or non-centrosymmetric lattice structure., Comment: 5+4 pages, 3 figures, supplement added, manuscript revised

Fermi showed that electrons, as a result of their quantum nature, form a gas of particles where the temperature and density follow the so called Fermi distribution. In a metal, as shown by Landau, that despite their strong Coulomb interaction with each other and the positive background ions, the electrons continue to act like free quantum mechanical particles but with enhanced masses. This state of matter, the Landau-Fermi liquid, is recognized experimentally by an electrical resistivity that is proportional to the square of the absolute temperature plus a term proportional to the square of the frequency of the applied field. Calculations show that, if electron-electron scattering dominates the resistivity in a Landau Fermi liquid, the ratio of the two terms, $b$ has the universal value of {\em b} = 4. We find that in the normal state of the heavy Fermion metal URu$_2$Si$_2$, instead of the Fermi liquid value of 4 the coefficient $b$ =1 $\pm$ 0.1. This unexpected result implies that the electrons in this material are experiencing a unique scattering process. This scattering is intrinsic and we suggest that, the uranium $f$ electrons do not hybridize to form a coherent Fermi liquid but instead act like a dense array of elastic impurities, interacting incoherently with the charge carriers. This behavior is not restricted to URu$_2$Si$_2$. Fermi liquid like states with $b \neq$ 4 have been observed in a number of disparate systems but the significance of this result has not been recognized., Comment: 5 pages, 6 figures

The optical conductivity of Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ shows a clear signature of the superconducting gap, but a simple $s$-wave description fails in accounting for the low frequency response. This task is achieved by introducing an extra Drude peak in the superconducting state representing sub-gap absorption, other than thermally broken pairs. This extra peak and the coexisting $s$-wave response respect the total sum rule indicating a common origin for the carriers. We discuss the possible origins for this absorption as (i) quasiparticles due to pair-breaking from interband impurity scattering in a two band $s_{\pm}$ gap symmetry model, which includes (ii) the possible existence of impurity levels within an isotropic gap model; or (iii) an indication that one of the bands is highly anisotropic., Comment: 5 pages, 4 figures

Magnetic excitations in cycloidal magnet LiCu$_2$O$_2$ are explored using THz absorption spectroscopy in magnetic fields up to 12 T. Below the spin ordering temperature we observe eight optically active transitions in the spin system of LiCu$_2$O$_2$ in the energy range from 4 to 30 cm$^{-1}$. In magnetic field the number of modes increases and the electric polarization flop is seen as a change in magnetic field dependence of mode energies. The polarization dependence of two of the modes in zero magnetic field fits the selection rules for the cycloid tilted by $\theta=41\pm1^{\circ}$ from the bc plane. For the remaining six modes electric and magnetic dipole approximations cannot explain the observed polarization dependence. We do not see the electromagnon in the explored energy range although there is evidence that it could exist below 4 cm$^{-1}$., Comment: 4 pages, 4 figures, submitted to PRB for publication as Rapid Communication

We report the observation of quantized translational and rotational motion of molecular hydrogen inside the cages of C60. Narrow infrared absorption lines at the temperature of 6K correspond to vibrational excitations in combination with translational and rotational excitations and show well resolved splittings due to the coupling between translational and rotational modes of the endohedral H2 molecule. A theoretical model shows that H2 inside C60 is a three-dimensional quantum rotor moving in a nearly spherical potential. The theory provides both the frequencies and the intensities of the observed infrared transitions. Good agreement with the experimental results is obtained by fitting a small number of empirical parameters to describe the confining potential, as well as the ortho to para ratio., Comment: Submitted to The Journal of Chemical Physics, 4 pages, 2 eps figures

Optical spectroscopy on single crystals of the new iron arsenide superconductor Ba{0.55}K{0.45}Fe2As2 shows that the infrared spectrum consists of two major components: a strong metallic Drude band and a well separated mid infrared absorption centered at 0.7 eV. It is difficult to separate the two components unambiguously but several fits of Lorentzian peaks suggest a model with a Drude peak having a plasma frequency of 1.8 to 2.1 eV and a midinfrared peak with a plasma frequency of 2.5 eV. In contrast to the cuprate superconductors the scattering rate obtained from the extended Drude model saturates at 150 meV as compared to 500 meV for a typical cuprate. Detailed analysis of the frequency dependent scattering rate shows that the charge carriers interact with broad bosonic spectrum with a peak at 25 meV and a coupling constant lambda =approx 2 at low temperature. As the temperature increases this coupling weakens to lambda=0.6 at ambient temperature. This suggests a bosonic spectrum that is similar to what is seen in the lower Tc cuprates., Comment: 4 pages, 4 figures

Terahertz reflectance spectra of the Ca-intercalated graphite CaC6 reveal a superconducting gap below 11K. The gap signature lacks a sharp onset to full reflectivity at 2Delta, but rather shows a distribution of gap values consistent with an anisotropic gap. The experimental data were successfully fitted to the gap distribution obtained from density functional calculations by Sanna et al. (Phys.Rev. B75, 020511, 2007). The temperature dependence of the superconducting gap is characteristic for a BCS type superconductor.

Using far-infrared spectroscopy we have studied the magnetic field and temperature dependence of the spin gap modes in the chains of Sr$_{14}$Cu$_{24}$O$_{41}$. Two triplet modes T$_1$ and T$_2$ were found in the center of the Brillouin zone at $\Delta_1=9.65$ meV and $\Delta_2=10.86$ meV in zero magnetic field. The T$_1$ mode was excited when the electric field vector ${\bf E}$ of the light was polarized along the b axis (perpendicular to the planes of chains and ladders) and T$_2$ was excited for ${\bf E}\parallel {\bf a}$ (perpendicular to the chains and along the rungs). Up to the maximum magnetic field of 18 T, applied along the chains, the electron $g$ factors of these two modes were similar, $g_{1c}=2.049$ and $g_{2c}=2.044$. Full linewidth at half maximum for both modes was 1 cm$^{-1}$ (0.12 meV) at 4K and increased with $T$. The temperature dependence of mode energies and line intensities was in agreement with the inelastic neutron scattering results from two groups [Matsuda {\it et al.}, Phys. Rev. B {\bf 59}, 1060 (1999) and Regnault {\it et al.}, Phys. Rev. B {\bf 59}, 1055 (1999)]. The T$_1$ mode has not been observed by inelastic neutron scattering in the points of the $k$-space equivalent to the center of the Brillouin zone. Our study indicates that the zone structure model of magnetic excitations of Sr$_{14}$Cu$_{24}$O$_{41}$ must be modified to include a triplet mode at 9.65 meV in the center of the magnetic Brillouin zone.

We have studied spin excitation spectra in the Shastry-Sutherland model compound SrCu$_2$(BO$_3$)$_2$ in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at 24 cm$^{-1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in SrCu$_2$(BO$_3$)$_2$. One is $a$-polarized and creates an intra-dimer dynamic DM along the c axis. The other is $c$-polarized and creates an intra-dimer dynamic DM interaction, it is in the $(ab)$ plane and perpendicular to the dimer axis. Singlet levels at 21.5 and 28.6 cm$^{-1}$ anti-cross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and inter-dimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static inter-dimer DM in the c-direction $d_1=0.7$ cm$^{-1}$ splits the triplet state sub-levels in zero field [C\'{e}pas et al., Phys. Rev. Lett. \textbf{87}, 167205 (2001)]. The static intra-dimer DM in the $(ab)$ plane (perpendicular to the dimer axis) $d_2=1.8$ cm$^{-1}$, allowed by the buckling of CuBO$_3$ planes, couples the triplet state to the 28.6 cm$^{-1}$ singlet as is seen from the avoided crossing., Comment: 12 pages with 7 figures, some references corrected

We have studied far infrared transmission spectra of alpha'-NaV2O5 between 3 and 200cm-1 in polarizations of incident light parallel to a, b, and c crystallographic axes in magnetic fields up to 33T. The triplet origin of an excitation at 65.4cm-1 is revealed by splitting in the magnetic field. The magnitude of the spin gap at low temperatures is found to be magnetic field independent at least up to 33T. All other infrared-active transitions appearing below Tc are ascribed to zone-folded phonons. Two different dynamic Dzyaloshinskii-Moriya (DM) mechanisms have been discovered that contribute to the oscillator strength of the otherwise forbidden singlet to triplet transition. 1. The strongest singlet to triplet transition is an electric dipole transition where the polarization of the incident light's electric field is parallel to the ladder rungs, and is allowed by the dynamic DM interaction created by a high frequency optical a-axis phonon. 2. In the incident light polarization perpendicular to the ladder planes an enhancement of the singlet to triplet transition is observed when the applied magnetic field shifts the singlet to triplet resonance frequency to match the 68cm-1 c-axis phonon energy. The origin of this mechanism is the dynamic DM interaction created by the 68cm-1 c-axis optical phonon. The strength of the dynamic DM is calculated for both mechanisms using the presented theory., Comment: 21 pages, 22 figures. Version 2 with replaced fig. 18 were labels had been lost

The charge response in the spin chain/ladder compound Sr_14-xCa_xCu_24O_41 is characterized by DC resistivity, low-frequency dielectric spectroscopy and optical spectroscopy. We identify a phase transition below which a charge-density wave (CDW) develops in the ladder arrays. Calcium doping suppresses this phase with the transition temperature decreasing from 210 K for x=0 to 10 K for x=9, and the CDW gap from 130 meV down to 3 meV, respectively. This suppression is due to the worsened nesting originating from the increase of the inter-ladder tight-binding hopping integrals, as well as from disorder introduced at the Sr sites. These results altogether speak in favor of two-dimensional superconductivity under pressure., Comment: 4 pages, 4 figures, accepted for publication in PRL

The electrodynamic response of the spin-ladder compound Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ ($x=0, 3, 9$) has been studied from radiofrequencies up to the infrared. At temperatures below 250 K a pronounced absorption peak appears around 12 cm$^{-1}$ in Sr$_{14}$Cu$_{24}$O$_{41}$ for the radiation polarized along the chains/ladders (${\bf E}\parallel {\bf c}$). In addition a strongly temperature dependent dielectric relaxation is observed in the kHz - MHz range. We explain this behavior by a charge density wave which develops in the ladders sub-system and produces a mode pinned at 12 cm$^{-1}$. With increasing Ca doping the mode shifts up in frequency and eventually disappears for $x=9$ because the dimensionality of the system crosses over from one to two dimensions, giving way to the superconducting ground state under pressure., Comment: One name added to author list 4 pages, 2 figures, email: gorshunov@pi1.physik.uni-stuttgart.de

We present optical conductivity data for Lu(Ni$_{1-x}$Co$_x$)$_2$B$_2$C over a wide range of frequencies and temperatures for x=0 and x=0.09. Both materials show evidence of being good Drude metals with the infrared data in reasonable agreement with dc resistivity measurements at low frequencies. An absorption threshold is seen at approximately 700 cm-1. In the cobalt-doped material we see a superconducting gap in the conductivity spectrum with an absorption onset at 24 +/- 2 cm-1 = 3.9$ +/- 0.4 k_BT_c suggestive of weak to moderately strong coupling. The pure material is in the clean limit and no gap can be seen. We discuss the data in terms of the electron-phonon interaction and find that it can be fit below 600 cm-1 with a plasma frequency of 3.3 eV and an electron-phonon coupling constant lambda_{tr}=0.33 using an alpha^{2}F(omega) spectrum fit to the resistivity., Comment: 10 pages with 10 embedded figures, submitted to PRB

The interplane optical spectrum of the organic superconductor kappa-(BEDT-TTF)2Cu[N(CN)2]Br was investigated in the frequency range from 40 to 40,000 cm-1. The optical conductivity was obtained by Kramers-Kronig analysis of the reflectance. The absence of a Drude peak at low frequency is consistent with incoherent conductivity but in apparent contradiction to the metallic temperature dependence of the DC resistivity. We set an upper limit to the interplane transfer integral of tb = 0.1 meV. A model of defect-assisted interplane transport can account for this discrepancy. We also assign the phonon lines in the conductivity to the asymmetric modes of the ET molecule., Comment: 7 pages with embedded figures, submitted to PRB

Using far-infrared spectroscopy in magnetic fields up to 12T we have studied a two-dimensional dimer spin gap system SrCu_2(BO_3)_2. We found several infrared active modes in the dimerized state (below 10K) in the frequency range from 3 to 100cm^-1. The measured splitting from the ground state to the excited triplet M_S=0 sublevel is Delta_1=24.2cm^-1 and the other two triplet state sublevels in zero magnetic field are 1.4cm^-1 below and above the M_S=0 sublevel. Another multiplet is at Delta_2=37.6cm^-1 from the ground state. A strong electric dipole active transition polarized in the (ab)-plane is activated in the dimer spin system below 15K at 52cm^-1., Comment: 4 pages including 5 figures, submitted to PRB, instrumental arte facts removed

We report on far infrared measurements on Zn and Si doped crystals of the spin-Peierls compound CuGeO3. Zn doping has the effect of introducing several new absorption lines, polarized in the ab-plane, between 5 and 55 cm-1. The intensity of the absorption grows with Zn concentration but saturates above 2% Zn. One line at 10 cm-1 loses intensity above 4K, and a second line at 20 cm-1 is absent at low temperatures but grows to peak at about 40K in agreement with a three level model with two excited states 10 and 30 cm-1 above the ground state. As the doping is increased these lines broaden, and a temperature independent absorption developes over the entire range from 5 to 55 cm-1. These features are magnetic field independent up to 16T and are absent in Si doped samples. We suggest the new absorption is due to localized lattice modes of the zinc ion and the surrounding GeO4 tetrahedra., Comment: 4 pages, Revtex, 4 postscript figures. Submitted to Phys. Rev. Lett