Spin Nutation Research Articles

Selective Transition Enhancement in a g-Engineered Diradical.

A diradical with engineered g-asymmetry was synthesized by grafting a nitroxide radical onto the [Y(Pc)2]⋅ radical platform. Various spectroscopic techniques and computational studies revealed that the electronic structures of the two spin systems remained minimally affected within the diradical system. Fluid-solution Electron Paramagnetic Resonance (EPR) experiments revealed a weak exchange coupling with |J| ~ 0.014 cm-1, subsequently rationalized by CAS-SCF calculations. Frozen solution continuous-wave (CW) EPR experiments showed a complicated and power-dependent spectrum that eluded analysis using the point-dipole model. Pulse EPR manipulations with varying microwave powers, or under varying magnetic fields, demonstrated that different resonances could be selectively enhanced or suppressed, based on their different tipping angles. In particular, Field-Swept Echo-Detected (FSED) spectra revealed absorptions of MW power-dependent intensities, while Field-Swept Spin Nutation (FSSN) experiments revealed two distinct Rabi frequencies. This study introduces a methodology to synthesize and characterize g-asymmetric two-spin systems, of interest in the implementation of spin-based CNOT gates.

All-Electrical Readout of Coherently Controlled Spins in Silicon Carbide.

Spin defects in silicon carbide are promising candidates for quantum sensing applications as they exhibit long coherence times even at room temperature. However, spin readout methods that rely on fluorescence detection can be challenging due to poor photon collection efficiency. Here, we demonstrate coherent spin control and all-electrical readout of a small ensemble of spins in a SiC junction diode using pulsed electrically detected magnetic resonance. A lock-in detection scheme based on a three stage modulation cycle is implemented, significantly enhancing the signal-to-noise ratio. This technique enabled observation of coherent spin dynamics, specifically Rabi spin nutation, spin dephasing, and spin decoherence. The use of these protocols for magnetometry applications is evaluated.

Erratum: Constraining black-hole binary spin precession and nutation with sequential prior conditioning [Phys. Rev. D 106 , 024019 (2022)

1 MoreReceived 5 April 2023DOI:https://doi.org/10.1103/PhysRevD.107.109901© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitationGravitational wave sourcesGravitational wavesPhysical SystemsAstronomical black holesTechniquesBayesian methodsGravitation, Cosmology & Astrophysics

Molecular-Engineered Biradicals Based on the YIII-Phthalocyanine Platform

A mixed-ligand phthalocyanine/porphyrin yttrium(III) radical double-decker complex (DD) was synthesized using the custom-made 5,10,15-tris(4-methoxyphenyl)-20-(4-((trimethylsilyl)ethynyl)phenyl)porphyrin. The trimethylsilyl functionality was then used to couple two such complexes into biradicals through rigid tethers. Glaser coupling was used to synthesize a short-tethered biradical (C1) and Sonogashira coupling to synthesize longer-tethered ones (C2 and C3). Field-swept echo-detected (FSED), saturation recovery, and spin nutation-pulsed electron paramagnetic resonance experiments revealed marked similarities of the magnetic properties of DD with those of the parent [Y(pc)2]• complex, both in the solid state and in CD2Cl2/CDCl3 4:1 frozen glasses. FSED experiments on the biradicals C2 and C3 revealed a spectral broadening with respect to the spectra of DD and [Y(pc)2]• assigned to the effect of dipolar interactions in solution. Apart from the main resonance, satellite features were also observed, which were simulated with dipole-dipole pairs of shortest distances, suggesting spin delocalization on the organic tether. FSED experiments on C1 yielded spectral line shapes that could not be simulated as the integration of the off-resonance echoes was complicated by field-dependent modulations. While, for all dimers, the on-resonance spin nutation experiments yielded Rabi oscillations of the same frequencies, off-resonance nutations on C1 yielded Rabi oscillations that could be assigned to a MS = -1 to MS = 0 transition within a S = 1 multiplet. The DFT calculations showed that the trans conformation of the complexes was significantly more stable than the cis one and that it induced a marked spin delocalization over the rigid organic tether. This "spin leakage" was most pronounced for the shortest biradical C1.

Signatures of spin precession and nutation in isolated black-hole binaries

The spin precession of binary black holes (BBHs) that originate from isolated high-mass binary stars is determined by the interplay of phenomena such as tides, winds, accretion, common-envelope evolution, natal kicks, and stellar core-envelope coupling. In previous work, we identified regions of the parameter space that may produce BBHs with large misalignments from natal kicks and high spin magnitudes from three mechanisms - tides, accretion, or inheritance via minimal core-envelope coupling. Here, we explore the spin precession of such BBHs using five parameters that describe the amplitude and frequency with which the orbital angular momentum precesses and nutates about the total angular momentum, modulating the gravitational-wave emission. Precession is generally possible for sufficiently strong natal kicks provided at least one of the black holes is spinning. Nutation is a consequence of spin-spin coupling and depends on the three spin-up mechanisms. Tidal synchronization can leave a distinct correlation between the aligned effective spin and the nutation frequency, but does not produce large nutations. When a black hole accretes $\gtrsim 20\%$ of its companion's envelope, the precession frequency and amplitude are large. A much smaller amount of accretion, e.g., $\approx 2\%$, is needed to provide a large precession frequency and amplitude when the accretor is a Wolf-Rayet (WR) star. The inheritance of high natal WR spins ($\gtrsim 5\%$ of their maximum breakup value) via minimal core-envelope coupling is the most promising mechanism for producing nutating BBHs, implying that a measurement of nutation from gravitational-wave observations may suggest isolated-binary origin with minimal core-envelope coupling.

Constraining black-hole binary spin precession and nutation with sequential prior conditioning

We investigate the detectability of subdominant spin effects in merging black-hole binaries using current gravitational-wave data. Using a phenomenological model that separates the spin dynamics into precession (azimuthal motion) and nutation (polar motion), we present constraints on the resulting amplitudes and frequencies. We also explore current constraints on the spin morphologies, indicating if binaries are trapped near spin-orbit resonances. We dissect such weak effects from the signals using a sequential prior conditioning approach, where parameters are progressively re-sampled from their posterior distribution. This allows us to investigate whether the data contain additional information beyond what is already provided by quantities that are better measured, namely the masses and the effective spin. For the current catalog of events, we find no significant measurements of weak spin effects such as nutation and spin-orbit locking. We synthesize a source with a high nutational amplitude and show that near-future detections will allow us to place powerful constraints, hinting that we may be at the cusp of detecting spin nutations in gravitational-wave data.

Nutation spin waves in ferromagnets

Magnetization dynamics and spin waves in ferromagnets are investigated using the inertial Landau-Lifshitz-Gilbert equation. Taking inertial magnetization dynamics into account, dispersion relations describing the propagation of nutation spin waves in an arbitrary direction relative to the applied magnetic field are derived via Maxwell's equations. It is found that the inertia of magnetization causes the hybridization of electromagnetic waves and nutation spin waves in ferromagnets, hybrid nutation spin waves emerge, and the redshift of frequencies of precession spin waves is initiated, which transforms to precession-nutation spin waves. These effects depend sharply on the direction of wave propagation relative to the applied magnetic field. Moreover, the waves propagating parallel to the applied field are circularly polarized, while the waves propagating perpendicular to that field are elliptically polarized. The characteristics of these spin nutation waves are also analyzed.

Magnetization switching in the inertial regime

We have numerically solved the Landau-Lifshitz-Gilbert (LLG) equation in its standard and inertial forms to study the magnetization switching dynamics in a $3d$ thin film ferromagnet. The dynamics is triggered by ultrashort magnetic field pulses of varying width and amplitude in the picosecond and Tesla range. We have compared the solutions of the two equations in terms of switching characteristic, speed and energy analysis. Both equations return qualitatively similar switching dynamics, characterized by regions of slower precessional behavior and faster ballistic motion. In case of inertial dynamics, ballistic switching is found in a 25 % wider region in the parameter space given by the magnetic field amplitude and width. The energy analysis of the dynamics is qualitatively different for the standard and inertial LLG equations. In the latter case, an extra energy channel, interpreted as the kinetic energy of the system, is available. Such extra channel is responsible for a resonant energy absorption at THz frequencies, consistent with the occurence of spin nutation.

Influence of intersublattice coupling on the terahertz nutation spin dynamics in antiferromagnets

Spin nutation resonance has been well-explored in one-sublattice ferromagnets. Here, we investigate the spin nutation in two-sublattice antiferromagnets as well as, for comparison, ferrimagnets with inter-and intra-sublattice nutation coupling. In particular, we derive the susceptibility of the two-sublattice magnetic system in response to an applied external magnetic field. To this end, the antiferromagnetic and ferrimagnetic (sub-THz) precession and THz nutation resonance frequencies are calculated. Our results show that the precession resonance frequencies and effective damping decrease with intra-sublattice nutation coupling, while they increase with inter -sublattice nutation in an antiferromagnet. However, we find that the THz nutation resonance frequencies decrease with both the intra-and inter-sublattice nutation couplings. For ferrimagnets, conversely, we calculate two nutation modes with distinct frequencies, unlike antiferromagnets. The exchange-like precession resonance frequency of ferrimagnets decreases with intra-sublattice nutation coupling and increases with inter-sublattice nutation coupling, like antiferromagnets, but the ferromagnetic-like precession frequency of ferrimagnets is practically invariant to the intra and inter-sublattice nutation couplings.

A taxonomy of black-hole binary spin precession and nutation

Binary black holes with misaligned spins will generically induce both precession and nutation of the orbital angular momentum $\bf{L}$ about the total angular momentum $\bf{J}$. These phenomena modulate the phase and amplitude of the gravitational waves emitted as the binary inspirals to merger. We introduce a "taxonomy" of binary black-hole spin precession that encompasses all the known phenomenology, then present five new phenomenological parameters that describe generic precession and constitute potential building blocks for future gravitational waveform models. These are the precession amplitude $\langle\theta_L\rangle$, the precession frequency $\langle \Omega_L\rangle$, the nutation amplitude $\Delta\theta_L$, the nutation frequency $\omega$, and the precession-frequency variation $\Delta\Omega_L$. We investigate the evolution of these five parameters during the inspiral and explore their statistical properties for sources with isotropic spins. In particular, we find that nutation of $\bf{L}$ is most prominent for binaries with high spins ($\chi \gtrsim 0.5$) and moderate mass ratios ($q \sim 0.6$).

Nutation dynamics and multifrequency resonance in a many-body seesaw

The multifrequency resonance has been widely explored in the context of single-particle models, of which the modulating Rabi model has been the most widely investigated. It has been found that with diagonal periodic modulation, steady dynamics can be realized in some well-defined discrete frequencies. These frequencies are independent of off-diagonal couplings. In this work, we generalize this physics to the many-body seesaw realized using the tilted Bose–Hubbard model. We find that the wave function will recover to its initial condition when the modulation frequency is commensurate with the initial energy level spacing between the ground and the first excited levels. The period is determined by the driving frequency and commensurate ratio. In this case, the wave function will be almost exclusively restricted to the lowest two instantaneous energy levels. By projecting the wave function to these two relevant states, the dynamics is exactly the same as that for the spin precession dynamics and nutation dynamics around an oscillating axis. We map out the corresponding phase diagram, and show that, in the low-frequency regime, the state is thermalized, and in the strong modulation limit, the dynamics is determined by the effective Floquet Hamiltonian. The measurement of these dynamics from the mean position and mean momentum in phase space are also discussed. Our results provide new insights into multifrequency resonance in the many-body system.

Room-temperature spin nutations in a magnetically condensed phase of [Y(pc)2]˙.

FID-detected nutations of the antiferromagnetic crystal form of [Y(pc)2]˙ demonstrated that its radical spin can be coherently driven in its magnetically condensed undeuterated phase and at room temperature. Liquid-helium nutations revealed additional Rabi oscillations assigned to transitions within higher-multiplicity states of finite-sized chain fragments.

Isotope Effect in the Magneto-Optoelectronic Response of Organic Light-Emitting Diodes Based on Donor-Acceptor Exciplexes.

The isotope effect is studied in the magneto-electroluminescence (MEL) and pulsed electrically detected magnetic resonance of organic light-emitting diodes based on thermally activated delayed fluorescence (TADF) from donor-acceptor exciplexes that are either protonated (H) or deuterated (D). It is found that at ambient temperature, the exchange of H to D has no effect on the spin-dependent current and MEL responses in the devices. However, at cryogenic temperatures, where the reverse intersystem crossing (RISC) from triplet to singlet exciplex diminishes, a pronounced isotope effect is observed. These results show that the RISC process is not governed by the hyperfine interaction as thought previously, but proceeds through spin-mixing in the triplet exciplex. The observations are corroborated by electrically detected transient spin nutation experiments that show relatively long dephasing time at ambient temperature, and interpreted in the context of a model that involves exchange and hyperfine interactions in the spin triplet exciplex. These findings deepen the understanding of the RISC process in TADF materials.

Wide nutation: binary black-hole spins repeatedly oscillating from full alignment to full anti-alignment

Within the framework of 2PN black-hole binary spin precession, we explore configurations where one of the two spins oscillates from being completely aligned with the orbital angular momentum to being completely anti-aligned with it during a single precession cycle. This wide nutation is the extreme limit of the generic phenomenon of spin nutation in black-hole binaries. Crucially, wide nutation happens on the short precession time scale and it is not a secular effect due to gravitational-wave radiation reaction. The spins of these binaries, therefore, flip repeatedly as one of these special configurations is entered. Binaries with total mass M, mass ratio q, and dimensionless spin () of the more (less) massive black hole are allowed to undergo wide nutation at binary separations . Sources that are more likely to nutate widely have similar masses and effective spins close to zero.

ELDOR-detected NMR: A general and robust method for electron-nuclear hyperfine spectroscopy?

ELDOR-detected NMR (EDNMR) performed at higher magnetic fields is becoming an increasingly popular alternative to conventional ENDOR for the characterization of electron-nuclear hyperfine interactions owing to its enhanced sensitivity. However there are two key problems that limit its widespread adoption, with factors controlling: (i) lineshape distortions and; (ii) overall spectral resolution, still largely understood only at a qualitative level. Indeed highly anisotropic (dipolar) coupled species are particularly problematic in the EDNMR experiment. Nor is it clear as to whether line intensities measured in EDNMR can provide quantitative information. Here we describe how all these problems can be overcome for a nitroxide radical as model system. We introduce a simulation procedure/protocol for the simulation of EDNMR line-shapes collected over a range of high turning angle (HTA) pulse lengths. It is shown that spectral line-shapes can be robustly reproduced and that the intensities of spectral lines and the spin nutation behavior can be quantitatively assessed. This broadens the scope of the EDNMR experiment as a generally applicable, quantitative double resonance method.

In vivo proton observed carbon edited (POCE) 13 C magnetic resonance spectroscopy of the rat brain using a volumetric transmitter and receive-only surface coil on the proton channel.

In vivo carbon-13 (13 C) MR spectroscopy (MRS) is capable of measuring energy metabolism and neuroenergetics, noninvasively in the brain. Indirect (1 H-[13 C]) MRS provides sensitivity benefits compared with direct 13 C methods, and normally includes a 1 H surface coil for both localization and signal reception. The aim was to develop a coil platform with homogenous B1+ and use short conventional pulses for short echo time proton observed carbon edited (POCE) MRS. A 1 H-[13 C] MRS coil platform was designed with a volumetric resonator for 1 H transmit, and surface coils for 1 H reception and 13 C transmission. The Rx-only 1 H surface coil nullifies the requirement for a T/R switch before the 1 H preamplifier; the highpass filter and preamplifier can be placed proximal to the coil, thus minimizing sensitivity losses inherent with POCE-MRS systems described in the literature. The coil platform was evaluated with a PRESS-POCE sequence (TE = 12.6 ms) on a rat model. The coil provided excellent localization, uniform spin nutation, and sensitivity. 13 C labeling of Glu-H4 and Glx-H3 peaks, and the Glx-H2 peaks were observed approximately 13 and 21 min following the infusion of 1-13 C glucose, respectively. A convenient and sensitive platform to study energy metabolism and neurotransmitter cycling is presented. Magn Reson Med 79:628-635, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Shapiro like steps reveals molecular nanomagnets’ spin dynamics

We present an accurate way to detect spin dynamics of a nutating molecular nanomagnet by inserting it in a tunnel Josephson junction and studying the current voltage (I-V) characteristic. The spin nutation of the molecular nanomagnet is generated by applying two circularly polarized magnetic fields. We demonstrate that modulation of the Josephson current by the nutation of the molecular nanomagnet’s spin appears as a stepwise structure like Shapiro steps in the I-V characteristic of the junction. Width and heights of these Shapiro-like steps are determined by two parameters of the spin nutation, frequency and amplitude of the nutation, which are simply tuned by the applied magnetic fields.

Proton decoupling and recoupling under double-nutation irradiation in solid-state NMR.

The effect of (1)H decoupling in magic-angle spinning solid-state NMR is studied under radiofrequency irradiation causing simultaneous nutations around a pair of orthogonal axes. Double-nutation with an arbitrary pair of nutation frequencies is implemented through modulation of the amplitude, phase, and frequency of the transmitting pulses. Similarity and difference of double-nutation decoupling and two-pulse phase-modulation decoupling schemes [A. E. Bennett, C. M. Rienstra, M. Auger, K. V. Lakshmi, and R. G. Griffin, J. Chem. Phys. 103, 6951-6958 (1995) and I. Scholz, P. Hodgkinson, B. H. Meier, and M. Ernst, J. Chem. Phys. 130, 114510 (2009)] are discussed. The structure of recoupling bands caused by interference of the (1)H spin nutation with sample spinning is studied by both experiments and numerical simulations.

The effective phase of soft RF pulses

ABSTRACTIn this article, the seemingly trivial relation between the spin nutation phase and the phase of radiofrequency (RF) pulses used in NMR is discussed, which in the case of soft (selective) pulses appears more subtle. Unlike hard pulses applied at a common carrier frequency, soft pulses usually have different frequency offsets in the same sequence and their nutation phase cannot be directly linked with the RF phase shift, as the phase shift has no absolute meaning for waves of different frequency. The problem is further complicated in MRI, where RF pulses are accompanied by a time‐dependent slice selection field gradient leading to surprising effects, for example, when two consecutive pulses of identical frequency and phase rotate the spins around different axes depending on slice position. A rule is described that lets the effective nutation phase be derived from the time course the RF phase. Ways to control this time course using various options of digital synthesis are presented. The discussion is illustrated by two popular MRI sequences—fast spin echo (RARE) and balanced steady‐state free precession (true FISP)—whose phase sensitivity easily leads to a pitfall when the frequency synthesis is not programmed with sufficient care. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 43A: 127–137, 2015.

Spin nutation effects in molecular nanomagnet–superconductor tunnel junctions

We study the spin nutation effects of a molecular nanomagnet on the Josephson current through a superconductor|molecular nanomagnet|superconductor tunnel junction. We explicitly demonstrate that, due to the spin nutation of the molecular nanomagnet, two oscillatory terms emerge in the ac Josephson current in addition to the conventional ac Josephson current. Some resonances occur in the junction due to the interactions of the transported quasiparticles with the bias voltage and molecular nanomagnet spin dynamics. Their appearance indicates that the energy exchanged during these interactions is in the range of the superconducting energy gap. We also show that the spin nutation is able to convert the ac Josephson current to a dc current, which is interesting for applications.