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The entanglement of electronic spin and orbital degrees of freedom is often the precursor to emergent behaviors in condensed matter systems. With considerable spin-orbit coupling strength, the cobalt atom on a honeycomb lattice offers a platform that can make accessible the study of novel magnetic ground states. Using temperature-dependent Raman spectroscopy and high-magnetic field Raman and infrared (IR) spectroscopy, we studied the lattice and spin-orbital excitations in CoTiO$_3$, an antiferromagnetic material that exhibits topologically protected magnon Dirac crossings in the Brillouin zone. Under the application of an external magnetic field up to 22 T along the crystal's $c$-axis, we observed the splitting of both the spin-orbital excitations and a phonon nearby in energy. Using density functional theory (DFT), we identify a number of new modes that below the antiferromagnetic (AFM) transition become Raman-active due to the zone-folding of the Brillouin zone caused by the doubling of the magnetic unit cell. We use a model that includes both the spin and orbital degrees of freedom of the Co$^{2+}$ ions to explain the spin-orbital excitation energies and their behavior in an applied field. Our experimental observations along with several deviations from the model behavior point to significant coupling between the spin-orbital and the lattice excitations.

The magnetic interactions that determine magnetic order and magnon energies typically involve only two spins. While rare, multi-spin interactions can also appear in quantum magnets and be the driving force in the ground state selection and in the nature of its excitations. By performing time-domain terahertz and magneto-Raman spectroscopy measurements combined with theoretical modeling, we determine the origin of the magnon excitation gap in Dirac antiferromagnet CoTiO$_3$. By adding a ring-exchange interaction in a hexagonal plaquette of the honeycomb lattice to both an XXZ spin model and to a low energy spin-orbital flavor wave model, a gap is generated in the magnon spectrum at the Brillouin zone center. With this addition, the flavor wave model reproduces a large swath of experimental results including terahertz, Raman, inelastic neutron scattering, and magnetization experiments., Comment: 8 pages, 4 figures in main text, 27 pages and 11 figures in supplement. Published May 21st, 2024 in PRB

We report on the results of simulations of the terahertz response of a split ring resonator (SRR) metamaterial coupled to a hypothetical antiferromagnetic material characterized by a magnon resonance. The simulations were done using finite difference time domain (FDTD) techniques. By adjusting the magnon frequency we find a hybridization of the resonant normal modes of the SRR and the magnon manifested as an avoided crossing. By varying the physical separation between the metamaterial and the antiferromagnet with a dielectric spacer, we evaluated the coupling strength between the two., Comment: 13 pages, 7 firgures

Magnetic excitations in van der Waals (vdW) materials, especially in the two-dimensional (2D) limit, are an exciting research topic from both the fundamental and applied perspectives. Using temperature-dependent, magneto-Raman spectroscopy, we identify the hybridization of two-magnon excitations with two separate E$_\mathrm{g}$ phonons in MnPSe$_3$, a magnetic vdW material that could potentially host 2D antiferromagnetism. Results from first principles calculations of the phonon and magnon spectra further support our identification. The Raman spectra's rich temperature dependence through the magnetic transition displays an avoided-crossing behavior in the phonons' frequency and a concurrent decrease in their lifetimes. We construct a model based on the interaction between a discrete level and a continuum that reproduces these observations. The strong magnon-phonon hybridization reported here highlights the need to understand its effects on spin transport experiments in magnetic vdW materials.

Polarization-resolved Raman spectroscopy was performed and analyzed from large, high quality, mono-domain single crystal of {\alpha}-RuCl3, a proximate Kitaev quantum spin liquid. Spectra were collected with laser polarizations parallel and perpendicular to the honeycomb plane. Pairs of nearly degenerate phonons were discovered and show either a 4-fold or 2-fold polarization angle dependence in their Raman intensity, thereby providing evidence to definitively assign the bulk crystal point group as C2h. The low frequency continuum that is often attributed to scattering from pairs of Majorana fermions was also examined and found to disappear when the laser excitation and scattered photon polarizations were perpendicular to the honeycomb plane. This disappearance, along with the behavior of the phonon spectrum in the same polarization configuration, strongly suggests that the scattering continuum is 2-dimensional. We argue that this scattering continuum originates from the Kitaev magnetic interactions that survives up to room temperature, a scale larger than the bare Kitaev exchange energy of approximately 50 K., Comment: 8 pages, 5 figures

We studied the effects on the terahertz transmission of gammadion metamatials by adjusting the size and periodicity of the metamaterial, while keeping the periodicity and size fixed, respectively. The terahertz transmission responses of these metamaterials were analyzed using terahertz time domain spectroscopy as well as finite difference time domain electromagnetic simulations. We have found that increasing size or periodicity results in a red shift of the resonant frequency, and that increasing size or decreasing periodicity results in the formation of a second resonant frequency. We associate these effects with the changing lengths of the microstrip lines that make up the metamaterial, as well as the changing strength of nearest-neighbor coupling between gammadions., Comment: 4 pages, 3 figures

Light-matter interactions are key in providing fundamental information about materials. Even in the linear-response regime, the spectroscopic response of a material encodes in it many properties of the ground state as well as of its excitations. This knowledge has been critical in our understanding of novel quantum materials, and the further improvement and extensions of linear spectroscopy will continue to be key in the exploration of novel states of matter. We report the development of broadband circular polarization spectroscopy in the terahertz range of the electromagnetic spectrum. We take advantage of a recent design of a broadband quarter wave plate, based on the Fresnel rhomb concept, and use it in conjunction with a polarization modulation technique to provide direct information of the response of a material to circularly polarized THz radiation; a new capability shown here for the first time. As an example of this technique we study the cyclotron resonance of a 2D electron gas from a AlGaAs-GaAs quantum well. We demonstrate the unique advantages that this technique will bring in the study of novel quantum materials., Comment: 7 pages, 4 figures

Time domain terahertz spectroscopy typically uses mechanical delay stages that inherently suffer from non-uniform sampling positions. We review, simulate, and experimentally test the ability of corrective cubic spline and Shannon re-gridding algorithms to mitigate the inherent sampling position noise. We present simulations and experimental results that show re-gridding algorithms can increase the signal to noise ratio within the frequency range of 100 GHz to 2 THz. We also predict that re-gridding corrections will become increasingly important to both spectroscopy and imaging as THz technology continues to improve and higher frequencies become experimentally accessible., Comment: 10 pages, 3 figures

We present an investigation of the multiferroic lacunar spinel compound GeV$_4$S$_8$ using time-domain terahertz spectroscopy. We find three absorptions which either appear or shift at the antiferromagnetic transition temperature, T$_N = 17$ K, as S=1 magnetic moments develop on vanadium tetrahedra. Two of these absorptions are coupled to the magnetic state and one only appears below the N\'{e}el temperature, and is interpreted as a magnon. We also observe isosbestic points in the dielectric constant in both the temperature and frequency domains. Further, we perform analysis on the isosbestic features to reveal an interesting collapse into a single curve as a function of both frequency and temperature, behavior which exists throughout the phase transitions. This analysis suggests the importance of spectral changes in the terahertz range which are linear in frequency and temperature., Comment: 7 pages, 4 figures. V2 in response to referees

Intense, single-cycle terahertz (THz) pulses offer a promising approach for understanding and controlling the properties of a material on an ultrafast time scale. In particular, resonantly exciting phonons leads to a better understanding of how they couple to other degrees of freedom in the material (e.g., ferroelectricity, conductivity and magnetism) while enabling coherent control of lattice vibrations and the symmetry changes associated with them. However, an ultrafast method for observing the resulting structural changes at the atomic scale is essential for studying phonon dynamics. A simple approach for doing this is optical second harmonic generation (SHG), a technique with remarkable sensitivity to crystalline symmetry in the bulk of a material as well as at surfaces and interfaces. This makes SHG an ideal method for probing phonon dynamics in topological insulators (TI), materials with unique surface transport properties. Here, we resonantly excite a polar phonon mode in the canonical TI Bi$_2$Se$_3$ with intense THz pulses and probe the subsequent response with SHG. This enables us to separate the photoinduced lattice dynamics at the surface from transient inversion symmetry breaking in the bulk. Furthermore, we coherently control the phonon oscillations by varying the time delay between a pair of driving THz pulses. Our work thus demonstrates a versatile, table-top tool for probing and controlling ultrafast phonon dynamics in materials, particularly at surfaces and interfaces, such as that between a TI and a magnetic material, where exotic new states of matter are predicted to exist.

We studied the novel multiferroic material Sr$_2$FeSi$_2$O$_7$, and found 3 absorption modes above the magnetic ordering transition temperature using time-domain terahertz spectroscopy. These absorption modes can be explained as the optical transitions between the spin-orbit coupling and crystal field split 3d$^6$ Fe$^{2+}$ ground state term in this material. Consideration of the compressed tetrahedral environment of the Fe$^{2+}$ site is crucial to understand the excitations. We point out, however, discrepancies between the single-site atomic picture and the experimental results., Comment: 5 pages, 3 figures, 1 table. Submitted. Small correction to figure 3 and corresponding discussion