Gadolinium Spin Decoherence Mechanisms at High Magnetic Fields.

Favorable relaxation processes, high-field spectral properties, and biological compatibility have made spin-7/2 Gd3+-based spin labels an increasingly popular choice for protein structure studies using high-field electron paramagnetic resonance. However, high-field relaxation and decoherence in ensembles of half-integer high-spin systems, such as Gd3+, remain poorly understood. We report spin-lattice (T1) and phase memory (TM) relaxation times at 8.6 T (240 GHz), and we present the first comprehensive model of high-field, high-spin decoherence accounting for both the electron spin concentration and temperature. The model includes four principal mechanisms driving decoherence: energy-conserving electron spin flip-flops, direct "T1" spin-lattice relaxation-driven electron spin flip processes, indirect T1-driven flips of nearby electron spins, and nuclear spin flip-flops. Mechanistic insight into decoherence can inform the design of experiments making use of Gd3+ as spin probes or relaxivity agents and can be used to measure local average interspin distances as long as 17 nm.

Order-of-magnitude SNR improvement for high-field EPR spectrometers via 3D printed quasi-optical sample holders.

Here, we present a rapidly prototyped, cost-efficient, and 3D printed quasi-optical sample holder for improving the signal-to-noise ratio (SNR) in modern, resonator-free, and high-field electron paramagnetic resonance (HFEPR) spectrometers. Such spectrometers typically operate in induction mode: The detected EPR ("cross-polar") signal is polarized orthogonal to the incident ("co-polar") radiation. The sample holder makes use of an adjustable sample positioner that allows for optimizing the sample position to maximize the 240-gigahertz magnetic field B1 and a rooftop mirror that allows for small rotations of the microwave polarization to maximize the cross-polar signal and minimize the co-polar background. When optimally tuned, the sample holder was able to improve co-polar isolation by ≳20 decibels, which is proven beneficial for maximizing the SNR in rapid-scan, pulsed, and continuous-wave EPR experiments. In rapid-scan mode, the improved SNR enabled the recording of entire EPR spectra of a narrow-line radical in millisecond time scales, which, in turn, enabled real-time monitoring of a sample's evolving line shape.

Spectroscopically Orthogonal Spin Labels in Structural Biology at Physiological Temperatures.

Electron paramagnetic resonance spectroscopy (EPR) is mostly used in structural biology in conjunction with pulsed dipolar spectroscopy (PDS) methods to monitor interspin distances in biomacromolecules at cryogenic temperatures both in vitro and in cells. In this context, spectroscopically orthogonal spin labels were shown to increase the information content that can be gained per sample. Here, we exploit the characteristic properties of gadolinium and nitroxide spin labels at physiological temperatures to study side chain dynamics via continuous wave (cw) EPR at X band, surface water dynamics via Overhauser dynamic nuclear polarization at X band and short-range distances via cw EPR at high fields. The presented approaches further increase the accessible information content on biomolecules tagged with orthogonal labels providing insights into molecular interactions and dynamic equilibria that are only revealed under physiological conditions.

Terahertz EPR spectroscopy using a 36-tesla high-homogeneity series-connected hybrid magnet.

Electron Paramagnetic Resonance (EPR) is a powerful technique to study materials and biological samples on an atomic scale. High-field EPR in particular enables extracting very small g-anisotropies in organic radicals and half-filled 3d and 4f metal ions such as MnII (3d5) or GdIII (4f7), and resolving EPR signals from unpaired spins with very close g-values, both of which provide high-resolution details of the local atomic environment. Before the recent commissioning of the high-homogeneity Series Connected Hybrid magnet (SCH, superconducting + resistive) at the National High Magnetic Field Laboratory (NHMFL), the highest-field, high-resolution EPR spectrometer available was limited to 25 T using a purely resistive "Keck" magnet at the NHMFL. Herein, we report the first EPR experiments performed using the SCH magnet capable of reaching the field of 36 T, corresponding to an EPR frequency of 1 THz for g = 2. The magnet's intrinsic homogeneity (25 ppm, that is 0.9 mT at 36 T over 1 cm diameter, 1 cm length cylinder) was previously established by NMR. We characterized the magnet's temporal stability (5 ppm, which is 0.2 mT at 36 T over one-minute, the typical acquisition time) using 2,2-diphenyl-1-picrylhydrazyl (DPPH). This high resolution enables resolving the weak g-anisotropy of 1,3-bis(diphenylene)-2-phenylallyl (BDPA), Δg = 2.5 × 10-4 obtained from measurements at 932 GHz and 33 T. Subsequently, we recorded EPR spectra at multiple frequencies for two GdIII complexes with potential applications as spin labels. We demonstrated a significant reduction in line broadening in Gd[DTPA], attributed to second order zero field splitting, and a resolution enhancement of g-tensor anisotropy for Gd[sTPATCN]-SL.

Triggered Functional Dynamics of AsLOV2 by Time-Resolved Electron Paramagnetic Resonance at High Magnetic Fields.

We present time-resolved Gd-Gd electron paramagnetic resonance (TiGGER) at 240 GHz for tracking inter-residue distances during a protein's mechanical cycle in the solution state. TiGGER makes use of Gd-sTPATCN spin labels, whose favorable qualities include a spin-7/2 EPR-active center, short linker, narrow intrinsic linewidth, and virtually no anisotropy at high fields (8.6 T) when compared to nitroxide spin labels. Using TiGGER, we determined that upon light activation, the C-terminus and N-terminus of AsLOV2 separate in less than 1 s and relax back to equilibrium with a time constant of approximately 60 s. TiGGER revealed that the light-activated long-range mechanical motion is slowed in the Q513A variant of AsLOV2 and is correlated to the similarly slowed relaxation of the optically excited chromophore as described in recent literature. TiGGER has the potential to valuably complement existing methods for the study of triggered functional dynamics in proteins.

Trigonal Bipyramidal V3+ Complex as an Optically Addressable Molecular Qubit Candidate.

Synthetic chemistry enables a bottom-up approach to quantum information science, where atoms can be deterministically positioned in a quantum bit or qubit. Two key requirements to realize quantum technologies are qubit initialization and read-out. By imbuing molecular spins with optical initialization and readout mechanisms, analogous to solid-state defects, molecules could be integrated into existing quantum infrastructure. To mimic the electronic structure of optically addressable defect sites, we designed the spin-triplet, V3+ complex, (C6F5)3trenVCNtBu (1). We measured the static spin properties as well as the spin coherence time of 1 demonstrating coherent control of this spin qubit with a 240 GHz electron paramagnetic resonance spectrometer powered by a free electron laser. We found that 1 exhibited narrow, near-infrared photoluminescence (PL) from a spin-singlet excited state. Using variable magnetic field PL spectroscopy, we resolved emission into each of the ground-state spin sublevels, a crucial component for spin-selective optical initialization and readout. This work demonstrates that trigonally symmetric, heteroleptic V3+ complexes are candidates for optical spin addressability.

Dressed Rabi Oscillation in a Crystalline Organic Radical.

Free electron laser-powered pulsed electron paramagnetic resonance experiments performed at 240 GHz/8.56 T on the crystalline organic radical 1,3-bisdiphenylene-2-phenylallyl reveal a tip-angle dependent resonant frequency. Frequency shifts as large as 11 MHz (45 ppm) are observed during a single Rabi oscillation. We attribute the frequency shifts to a "dressing" of the nutation by spin-spin interactions. A nonlinear semiclassical model which includes a temperature- and sample-geometry-dependent demagnetizing field reproduces experimental results. Because experiments are performed without a cavity, radiation damping, the most common nonlinear interaction in magnetic resonance, is negligible in our experiments.

Spin current from sub-terahertz-generated antiferromagnetic magnons.

Spin dynamics in antiferromagnets has much shorter timescales than in ferromagnets, offering attractive properties for potential applications in ultrafast devices1-3. However, spin-current generation via antiferromagnetic resonance and simultaneous electrical detection by the inverse spin Hall effect in heavy metals have not yet been explicitly demonstrated4-6. Here we report sub-terahertz spin pumping in heterostructures of a uniaxial antiferromagnetic Cr2O3 crystal and a heavy metal (Pt or Ta in its ß phase). At 0.240 terahertz, the antiferromagnetic resonance in Cr2O3 occurs at about 2.7 tesla, which excites only right-handed magnons. In the spin-canting state, another resonance occurs at 10.5 tesla from the precession of induced magnetic moments. Both resonances generate pure spin currents in the heterostructures, which are detected by the heavy metal as peaks or dips in the open-circuit voltage. The pure-spin-current nature of the electrically detected signals is unambiguously confirmed by the reversal of the voltage polarity observed under two conditions: when switching the detector metal from Pt to Ta, reversing the sign of the spin Hall angle7-9, and when flipping the magnetic-field direction, reversing the magnon chirality4,5. The temperature dependence of the electrical signals at both resonances suggests that the spin current contains both coherent and incoherent magnon contributions, which is further confirmed by measurements of the spin Seebeck effect and is well described by a phenomenological theory. These findings reveal the unique characteristics of magnon excitations in antiferromagnets and their distinctive roles in spin-charge conversion in the high-frequency regime.

Optical frequency combs from high-order sideband generation.

We report on the generation of frequency combs from the recently-discovered phenomenon of high-order sideband generation (HSG). A near-band gap continuous-wave (cw) laser with frequency fNIR was transmitted through an epitaxial layer containing GaAs/AlGaAs quantum wells that were driven by quasi-cw in-plane electric fields FTHz between 4 and 50 kV/cm oscillating at frequencies fTHz between 240 and 640 GHz. Frequency combs with teeth at fsideband = fNIR + nfTHz (n even) were produced, with maximum reported n > 120, corresponding to a maximum comb span > 80 THz. Comb spectra with the identical product fTHz × FTHz were found to have similar spans and shapes in most cases, as expected from the picture of HSG as a scattering-limited electron-hole recollision phenomenon. The HSG combs were used to measure the frequency and linewidth of our THz source as a demonstration of potential applications.

Multi-step phase-cycling in a free-electron laser-powered pulsed electron paramagnetic resonance spectrometer.

Electron paramagnetic resonance (EPR) is a powerful tool for research in chemistry, biology, physics and materials science, which can benefit significantly from moving to frequencies above 100 GHz. In pulsed EPR spectrometers driven by powerful sub-THz oscillators, such as the free electron laser (FEL)-powered EPR spectrometer at UCSB, control of the duration, power and relative phases of the pulses in a sequence must be performed at the frequency and power level of the oscillator. Here we report on the implementation of an all-quasioptical four-step phase cycling procedure carried out directly at the kW power level of the 240 GHz pulses used in the FEL-powered EPR spectrometer. Phase shifts are introduced by modifying the optical path length of a 240 GHz pulse with precision-machined dielectric plates in a procedure we call phase cycling with optomechanical phase shifters (POPS), while numerical receiver phase cycling is implemented in post-processing. The POPS scheme was successfully used to reduce experimental dead times, enabling pulsed EPR of fast-relaxing spin systems such as gadolinium complexes at temperatures above 190 K. Coherence transfer pathway selection with POPS was used to perform spin echo relaxation experiments to measure the phase memory time of P1 centers in diamond in the presence of a strong unwanted FID signal in the background. The large excitation bandwidth of FEL-EPR, together with phase cycling, enabled the quantitative measurement of instantaneous electron spectral diffusion, from which the P1 center concentration was estimated to within 10%. Finally, phase cycling enabled saturation-recovery measurements of T1 in a trityl-water solution at room temperature - the first FEL-EPR measurement of electron T1.

Quantitative analysis of zero-field splitting parameter distributions in Gd(iii) complexes.

The magnetic properties of paramagnetic species with spin S > 1/2 are parameterized by the familiar g tensor as well as "zero-field splitting" (ZFS) terms that break the degeneracy between spin states even in the absence of a magnetic field. In this work, we determine the mean values and distributions of the ZFS parameters D and E for six Gd(iii) complexes (S = 7/2) and critically discuss the accuracy of such determination. EPR spectra of the Gd(iii) complexes were recorded in glassy frozen solutions at 10 K or below at Q-band (∼34 GHz), W-band (∼94 GHz) and G-band (240 GHz) frequencies, and simulated with two widely used models for the form of the distributions of the ZFS parameters D and E. We find that the form of the distribution of the ZFS parameter D is bimodal, consisting roughly of two Gaussians centered at D and -D with unequal amplitudes. The extracted values of D (σD) for the six complexes are, in MHz: Gd-NO3Pic, 485 ± 20 (155 ± 37); Gd-DOTA/Gd-maleimide-DOTA, -714 ± 43 (328 ± 99); iodo-(Gd-PyMTA)/MOMethynyl-(Gd-PyMTA), 1213 ± 60 (418 ± 141); Gd-TAHA, 1361 ± 69 (457 ± 178); iodo-Gd-PCTA-[12], 1861 ± 135 (467 ± 292); and Gd-PyDTTA, 1830 ± 105 (390 ± 242). The sign of D was adjusted based on the Gaussian component with larger amplitude. We relate the extracted P(D) distributions to the structure of the individual Gd(iii) complexes by fitting them to a model that superposes the contribution to the D tensor from each coordinating atom of the ligand. Using this model, we predict D, σD, and E values for several additional Gd(iii) complexes that were not measured in this work. The results of this paper may be useful as benchmarks for the verification of quantum chemical calculations of ZFS parameters, and point the way to designing Gd(iii) complexes for particular applications and estimating their magnetic properties a priori.

Gd3+-Gd3+ distances exceeding 3 nm determined by very high frequency continuous wave electron paramagnetic resonance.

Electron paramagnetic resonance spectroscopy in combination with site-directed spin labeling is a very powerful tool for elucidating the structure and organization of biomolecules. Gd3+ complexes have recently emerged as a new class of spin labels for distance determination by pulsed EPR spectroscopy at Q- and W-band. We present CW EPR measurements at 240 GHz (8.6 Tesla) on a series of Gd-rulers of the type Gd-PyMTA-spacer-Gd-PyMTA, with Gd-Gd distances ranging from 1.2 nm to 4.3 nm. CW EPR measurements of these Gd-rulers show that significant dipolar broadening of the central |-1/2〉 → |1/2〉 transition occurs at 30 K for Gd-Gd distances up to ∼3.4 nm with Gd-PyMTA as the spin label. This represents a significant extension for distances accessible by CW EPR, as nitroxide-based spin labels at X-band frequencies can typically only access distances up to ∼2 nm. We show that this broadening persists at biologically relevant temperatures above 200 K, and that this method is further extendable up to room temperature by immobilizing the sample in glassy trehalose. We show that the peak-to-peak broadening of the central transition follows the expected 1/r3 dependence for the electron-electron dipolar interaction, from cryogenic temperatures up to room temperature. A simple procedure for simulating the dependence of the lineshape on interspin distance is presented, in which the broadening of the central transition is modeled as an S = 1/2 spin whose CW EPR lineshape is broadened through electron-electron dipolar interactions with a neighboring S = 7/2 spin.

High-precision gigahertz-to-terahertz spectroscopy of aqueous salt solutions as a probe of the femtosecond-to-picosecond dynamics of liquid water.

Because it is sensitive to fluctuations occurring over femtoseconds to picoseconds, gigahertz-to-terahertz dielectric relaxation spectroscopy can provide a valuable window into water's most rapid intermolecular motions. In response, we have built a vector network analyzer dielectric spectrometer capable of measuring absorbance and index of refraction in this frequency regime with unprecedented precision. Using this to determine the complex dielectric response of water and aqueous salt solutions from 5.9 GHz to 1.12 THz (which we provide in the supplementary material), we have obtained strong new constraints on theories of water's collective dynamics. For example, while the salt-dependencies we observe for water's two slower relaxations (8 and 1 ps) are easily reconciled with suggestions that they arise due to rotations of fully and partially hydrogen bonded molecules, respectively, the salt-dependence of the fastest relaxation (180 fs) appears difficult to reconcile with its prior assignment to liberations of single hydrogen bonds.

Determining the oligomeric structure of proteorhodopsin by Gd3+ -based pulsed dipolar spectroscopy of multiple distances.

The structural organization of the functionally relevant, hexameric oligomer of green-absorbing proteorhodopsin (G-PR) was obtained from double electron-electron resonance (DEER) spectroscopy utilizing conventional nitroxide spin labels and recently developed Gd3+ -based spin labels. G-PR with nitroxide or Gd3+ labels was prepared using cysteine mutations at residues Trp58 and Thr177. By combining reliable measurements of multiple interprotein distances in the G-PR hexamer with computer modeling, we obtained a structural model that agrees with the recent crystal structure of the homologous blue-absorbing PR (B-PR) hexamer. These DEER results provide specific distance information in a membrane-mimetic environment and across loop regions that are unresolved in the crystal structure. In addition, the X-band DEER measurements using nitroxide spin labels suffered from multispin effects that, at times, compromised the detection of next-nearest neighbor distances. Performing measurements at high magnetic fields with Gd3+ spin labels increased the sensitivity considerably and alleviated the difficulties caused by multispin interactions.

Theory of low-power ultra-broadband terahertz sideband generation in bi-layer graphene.

In a semiconductor illuminated by a strong terahertz (THz) field, optically excited electron-hole pairs can recombine to emit light in a broad frequency comb evenly spaced by twice the THz frequency. Such high-order THz sideband generation is of interest both as an example of extreme nonlinear optics and also as a method for ultrafast electro-optical modulation. So far, this phenomenon has only been observed with large field strengths (~10 kV cm(-1)), an obstacle for technological applications. Here we predict that bi-layer graphene generates high-order sidebands at much weaker THz fields. We find that a THz field of strength 1 kV cm(-1) can produce a high-sideband spectrum of about 30 THz, 100 times broader than in GaAs. The sidebands are generated despite the absence of classical collisions, with the quantum coherence of the electron-hole pairs enabling recombination. These remarkable features lower the barrier to desktop electro-optical modulation at THz frequencies, facilitating ultrafast optical communications.

Self-assembled ErSb nanostructures with optical applications in infrared and terahertz.

Plasmonic effects have proven to be very efficient in coupling light to structures much smaller than its wavelength. Efficient coupling is particularly important for the infrared or terahertz (λ ∼ 0.3 mm) region where semiconductor structures and devices may be orders of magnitude smaller than the wavelength and this can be achieved through nanostructures that have a desired plasmonic response. We report and demonstrate a self-assembly method of embedding controllable semimetallic nanostructures in a semiconducting matrix in a ErSb/GaSb material system grown by molecular beam epitaxy. The plasmonic properties of the ErSb/GaSb are characterized and quantified by three polarization-resolved spectroscopy techniques, spanning more than 3 orders of magnitude in frequency from 100 GHz up to 300 THz. Surface plasmons cause the semimetallic nanostructures to resonate near 100 THz (3 µm wavelength), indicating the semimetal as a potential infrared plasmonic material. The highly conductive ErSb nanowires polarize electromagnetic radiation in a broad range from 0.2 up to ∼100 THz, providing a new platform for electromagnetics in the infrared and terahertz frequency ranges.

Extending the distance range accessed with continuous wave EPR with Gd3+ spin probes at high magnetic fields.

Interspin distances between 0.8 nm and 2.0 nm can be measured through the dipolar broadening of the continuous wave (cw) EPR spectrum of nitroxide spin labels at X-band (9.4 GHz, 0.35 T). We introduce Gd(3+) as a promising alternative spin label for distance measurements by cw EPR above 7 Tesla, where the |-1/2〉 to |1/2〉 transition narrows below 1 mT and becomes extremely sensitive to dipolar broadening. To estimate the distance limits of cw EPR with Gd(3+), we have measured spectra of frozen solutions of GdCl3 at 8.6 T (240 GHz) and 10 K at concentrations ranging from 50 mM to 0.1 mM, covering a range of average interspin distances. These experiments show substantial dipolar broadening at distances where line broadening cannot be observed with nitroxides at X-band. This data, and its agreement with calculated dipolar-broadened lineshapes, show Gd(3+) to be sensitive to distances as long as ∼3.8 nm. Further, the linewidth of a bis-Gd(3+) complex with a flexible ∼1.6 nm bridge is strongly broadened as compared to the mono-Gd(3+) complex, demonstrating the potential for application to pairwise distances. Gd-DOTA-based chelates that can be functionalized to protein surfaces display linewidths narrower than aqueous GdCl3, implying they should be even more sensitive to dipolar broadening. Therefore, we suggest that the combination of tailored Gd(3+) labels and high magnetic fields can extend the longest interspin distances measurable by cw EPR from 2.0 nm to 3.8 nm. cw EPR data at 260 K demonstrate that the line broadening remains clear out to similar average interspin distances, offering Gd(3+) probes as promising distance rulers at temperatures higher than possible with conventional pulsed EPR distance measurements.

Phase cycling with a 240 GHz, free electron laser-powered electron paramagnetic resonance spectrometer.

Electron paramagnetic resonance (EPR) powered by a free electron laser (FEL) has been shown to dramatically expand the capabilities of EPR at frequencies above ~100 GHz, where other high-power sources are unavailable. High-power pulses are necessary to achieve fast (<10 ns) spin rotations in order to alleviate the limited excitation bandwidth and time resolution that typically hamper pulsed EPR at these high frequencies. While at these frequencies, an FEL is the only source that provides ~1 kW of power and can be tuned continuously up to frequencies above 1 THz, it has only recently been implemented for one- and two-pulse EPR, and the capabilities of the FEL as an EPR source are still being expanded. This manuscript presents phase cycling of two pulses in an FEL-EPR spectrometer operating at 240 GHz. Given that the FEL, unlike amplifiers, cannot be easily phase-locked to a reference source, we instead apply retrospective data processing to measure the relative phase of each FEL pulse in order to correct the signal phase accordingly. This allows the measured signal to be averaged coherently, and the randomly changing phase of the FEL pulse results in a stochastic phase cycle, which, in the limit of many pulses, efficiently cancels artifacts and improves sensitivity. Further, the relative phase between the first and second pulse, which originates from the difference in path length traversed by each pulse, can be experimentally measured without phase-sensitive detection. We show that the relative phase of the two pulses can be precisely tuned, as well as distinctly switched by a fixed amount, with the insertion of a dielectric material into the quasi-optical path of one of the pulses. Taken together, these techniques offer many of the advantages of arbitrary phase control, and allow application of phase cycling to dramatically enhance signal quality in pulsed EPR experiments utilizing high-power sources that cannot be phase-locked.

Terahertz electron-hole recollisions in GaAs/AlGaAs quantum wells: robustness to scattering by optical phonons and thermal fluctuations.

Electron-hole recollisions are induced by resonantly injecting excitons with a near-IR laser at frequency fNIR into quantum wells driven by a 10 kV/cm field oscillating at fTHz=0.57 THz. At T=12 K, up to 18 sidebands are observed at frequencies fsideband=fNIR+2nfTHz, with -8≤2n≤28. Electrons and holes recollide with total kinetic energies up to 57 meV, well above the ELO=36 meV threshold for longitudinal optical (LO) phonon emission. Sidebands with order up to 2n=22 persist up to room temperature. A simple model shows that LO phonon scattering suppresses but does not eliminate sidebands associated with kinetic energies above ELO.

Distance measurements across randomly distributed nitroxide probes from the temperature dependence of the electron spin phase memory time at 240 GHz.

At 8.5 T, the polarization of an ensemble of electron spins is essentially 100% at 2 K, and decreases to 30% at 20 K. The strong temperature dependence of the electron spin polarization between 2 and 20 K leads to the phenomenon of spin bath quenching: temporal fluctuations of the dipolar magnetic fields associated with the energy-conserving spin "flip-flop" process are quenched as the temperature of the spin bath is lowered to the point of nearly complete spin polarization. This work uses pulsed electron paramagnetic resonance (EPR) at 240 GHz to investigate the effects of spin bath quenching on the phase memory times (T(M)) of randomly-distributed ensembles of nitroxide molecules below 20 K at 8.5 T. For a given electron spin concentration, a characteristic, dipolar flip-flop rate (W) is extracted by fitting the temperature dependence of T(M) to a simple model of decoherence driven by the spin flip-flop process. In frozen solutions of 4-Amino-TEMPO, a stable nitroxide radical in a deuterated water-glass, a calibration is used to quantify average spin-spin distances as large as r=6.6 nm from the dipolar flip-flop rate. For longer distances, nuclear spin fluctuations, which are not frozen out, begin to dominate over the electron spin flip-flop processes, placing an effective ceiling on this method for nitroxide molecules. For a bulk solution with a three-dimensional distribution of nitroxide molecules at concentration n, we find W∝n∝1/r(3), which is consistent with magnetic dipolar spin interactions. Alternatively, we observe W∝n(32) for nitroxides tethered to a quasi two-dimensional surface of large (Ø∼200 nm), unilamellar, lipid vesicles, demonstrating that the quantification of spin bath quenching can also be used to discern the geometry of molecular assembly or organization.