Figure 4 - uploaded by Sam Schott
Content may be subject to copyright.
Dependance of spin relaxation times on the effective SOC. (a) Spin lattice relaxation time vs ?g for all measured molecules. Error bars represent 95% confidence intervals. Dashed line shows the expected proportionality T 2 ? (?g) ?2 for relaxation via SOC fields. (b) Spin coherence time vs ?g for all measured molecules. Error bars show the 95% confidence intervals. (c) Dependence of T 1 and T 2 on the correlation time ? C of field fluctuations from the Redfield theory. Model values of ? L /2? = 9.4 GHz and B 2 x,y,z = 0.2 mT were used for the plot. (d) Correlation times ? C as estimated from the Redfield theory and plotted against rotational correlation times obtained from DOSY NMR diffusion constants (when available). Error bars from 95% confidence intervals of T 1 and T 2 and error propagation.
Source publication
The control of spins and spin to charge conversion in organics requires understanding the molecular spin-orbit coupling (SOC), and a means to tune its strength. However, quantifying SOC strengths indirectly through spin relaxation effects has proven diffi- cult due to competing relaxation mechanisms. Here we present a systematic study of the g-tens...
Contexts in source publication
Context 1
... the sample as shown in Fig. 3 and Supplementary Fig. 3. The resulting values for T 1 reveal a strong correlation between spin lattice relaxation times and g-shifts: we observe a change in T 1 over four orders of magnitude, from 212 µs for molecules with small g-shifts (e.g. C-C12-DTBTBT) down to 0.15 µs (BSBS, DNSS) for the largest g-shifts (Fig. 4a). This demonstrates the impact of tuning the g-factor beyond changing the coupling of a spin to the external magnetic field. By increasing the spin density at selenium or sulphur atoms, we increase the effective SOC for the spin and as result the transition rate between spin-up and spin-down levels increases as ...
Context 2
... can be written as F(t) = µ B ∆g(t) · B. This incorporates a time dependance from lattice vibrations or molecular tumbling. Assuming that the amplitude of the SOC fluctuations approximately scales with ∆g itself, one expects that the spectral densities follow the proportionality k q (ω) ∝ (∆g) 2 and the relaxation time to follow T 1 ∝ (∆g) −2 . Fig. 4a shows that T 1 indeed follows this proportionality with a remarkable accuracy. We conclude that spin lattice relaxation is therefore dominated by the effective SOC at magnetic fields of ∼ 350 ...
Context 3
... where τ C is the correlation time of field fluctuations and F 2 q is the mean square of the fluctuating field 22 . Fig. 4c shows the dependence of both relaxation times on τ C in this model and demonstrates that spin lattice relaxation becomes most effective when the frequency τ −1 C matches the energy difference between the Zeeman split ...
Context 4
... resulting values are on the order of τ −1 C = 2.5-50 GHz (Fig. 4c). For comparison, simulations of intramolecular vibrational modes of DNTT predict frequencies of 6-50 THz for stretching modes along the molecule's symmetry axes, distortions of the phenyl rings and vibrations of the C-H bonds, in ascending order 24 . They exceed the Zeeman splitting by orders of magnitude and are therefore less ...
Context 5
... we consider molecular SOC fields that are static in the molecule's rest frame but fluctuate relative to the external field (and thus the spin quantization axis) with the tumbling motion of molecules in a solution. From diffusion-ordered nuclear magnetic resonance spectroscopy (DOSY NMR) measurements at a concentration of 0.2 mg mL −1 , we can calculate the Stokes radius and resulting rotational correlation times for the molecules (Supplementary Note 4). The solubility of DNTT and DNSS in dichloromethane was too small to record DOSY NMR spectra but the rotational correlation times τ diff C for the remaining molecules are shown in Fig. 4c together with τ C values estimated from the spin lifetime ratios. ...
Context 6
... measurements at a concentration of 0.2 mg mL −1 , we can calculate the Stokes radius and resulting rotational correlation times for the molecules (Supplementary Note 4). The solubility of DNTT and DNSS in dichloromethane was too small to record DOSY NMR spectra but the rotational correlation times τ diff C for the remaining molecules are shown in Fig. 4c together with τ C values estimated from the spin lifetime ratios. Even though the values of τ C are only rough estimates, derived under the previously discussed assumptions, we observe an approximate agreement with τ diff C . It is therefore likely that the observed relaxation times are indeed a result of SOC fields which fluctuate due ...
Similar publications
We consider spin relaxation of finite-size spin chains exchanged coupled with a one-dimensional (1D) electron gas at the edge of a quantum spin Hall (QSH) insulator. Spin lifetimes can be enhanced due to two independent mechanisms. First, the suppression of spin-flip forward scattering inherent in the spin momentum locking of the QSH edges. Second,...
A quantum spin liquid is a state of matter where unpaired electrons’ spins, although entangled, do not show magnetic order even at the zero temperature. The realization of a quantum spin liquid is a long-sought goal in condensed-matter physics. Although neutron scattering experiments on the two-dimensional spin-1/2 kagome lattice ZnCu3(OD)6Cl2 and...
A charge excitation in a two-dimensional Mott insulator is strongly coupled with the surrounding spins, which is observed as magnetic-polaron formations of doped carriers and a magnon sideband in the Mott-gap transition spectrum. However, the dynamics related to the spin sector are difficult to measure. Here, we show that pump-probe reflection spec...
We develop a simple method for measuring the electron spin relaxation times \(T_1\), \(T_2\) and \(T_2^*\) in semiconductors and demonstrate its exemplary application to n-type GaAs. Using an abrupt variation of the magnetic field acting on electron spins, we detect the spin evolution by measuring the Faraday rotation of a short laser pulse. Depend...
Single‐crystal diamond substrates presenting a high concentration of negatively charged nitrogen‐vacancy centers (NV⁻) are on high demand for the development of optically pumped solid‐state sensors such as magnetometers, thermometers, or electrometers. While nitrogen impurities can be easily incorporated during crystal growth, the creation of vacan...
Citations
... Table I presents these prototypical proton and electron Cartesian coordinates, as well as additional parameters used to create the relevant spin Hamiltonian. Notice that no electron relaxation arising from inter-radical dipolar interactions are here considered; if present, these could be prevented by lowering the polarizing agent concentrations [11,56]. ...
... These effects will arise from the mixing between spin and orbital angular momenta, as driven by spin-orbit coupling (SOC). Although detrimental for MF-JDNP, these SOCs can be suppressed by eliminating the heavy atoms (heavier than 19 F) from the biradical structure, thereby restoring sufciently slow electron relaxation rates to support MF-JDNP [56,65]. Alternatives to bypass such electron relaxation mechanisms competing with Redeld relaxation are also important in spintronics, and therefore are actively being sought [56]. ...
... Although detrimental for MF-JDNP, these SOCs can be suppressed by eliminating the heavy atoms (heavier than 19 F) from the biradical structure, thereby restoring sufciently slow electron relaxation rates to support MF-JDNP [56,65]. Alternatives to bypass such electron relaxation mechanisms competing with Redeld relaxation are also important in spintronics, and therefore are actively being sought [56]. Additional electron relaxation mechanisms might arise due to vibrations and collisions with surrounding diamagnetic molecules [66]; however, these processes are not expected in biradicals that make weak intermolecular interactions with the solvent. ...
J-driven dynamic nuclear polarization (JDNP) was recently proposed for enhancing the sensitivity of solution-state nuclear magnetic resonance (NMR), while bypassing the limitations faced by conventional (Overhauser) DNP at magnetic fields of interest in analytical applications. Like Overhauser DNP, JDNP also requires saturating the electronic polarization using high-frequency microwaves known to have poor penetration and associated heating effects in most liquids. The present microwave-free JDNP (MF-JDNP) proposal seeks to enhance solution NMR's sensitivity by shuttling the sample between higher and lower magnetic fields, with one of these fields providing an electron Larmor frequency that matches the interelectron exchange coupling Jex. If spins cross this so-called JDNP condition sufficiently fast, we predict that a sizable nuclear polarization will be created without microwave irradiation. This MF-JDNP proposal requires radicals whose singlet–triplet self-relaxation rates are dominated by dipolar hyperfine relaxation, and shuttling times that can compete with these electron relaxation processes. This paper discusses the theory behind the MF-JDNP, as well as proposals for radicals and conditions that could enable this new approach to NMR sensitivity enhancement.
... Table I presents these prototypical proton and electron Cartesian coordinates, as well as additional parameters used to create the relevant spin Hamiltonian. Notice that no electron relaxation arising from inter-radical dipolar interactions are here considered; if present, these could be prevented by lowering the polarizing agent concentrations [11,56]. ...
... These effects will arise from the mixing between spin and orbital angular momenta, as driven by spin-orbit coupling (SOC). Although detrimental for MF-JDNP, these SOCs can be suppressed by eliminating the heavy atoms (heavier than 19 F) from the biradical structure, thereby restoring sufciently slow electron relaxation rates to support MF-JDNP [56,65]. Alternatives to bypass such electron relaxation mechanisms competing with Redeld relaxation are also important in spintronics, and therefore are actively being sought [56]. ...
... Although detrimental for MF-JDNP, these SOCs can be suppressed by eliminating the heavy atoms (heavier than 19 F) from the biradical structure, thereby restoring sufciently slow electron relaxation rates to support MF-JDNP [56,65]. Alternatives to bypass such electron relaxation mechanisms competing with Redeld relaxation are also important in spintronics, and therefore are actively being sought [56]. Additional electron relaxation mechanisms might arise due to vibrations and collisions with surrounding diamagnetic molecules [66]; however, these processes are not expected in biradicals that make weak intermolecular interactions with the solvent. ...
J-driven Dynamic Nuclear Polarization (JDNP) was recently proposed for enhancing the sensitivity of solution-state nuclear magnetic resonance (NMR), while bypassing the limitations faced by conventional (Overhauser) DNP at magnetic fields of interest in analytical applications. Like Overhauser DNP, JDNP also requires saturating the electronic polarization using high-frequency microwaves, known to have poor penetration and associated heating effects in most liquids. The present microwave-free JDNP (MF-JDNP) proposal seeks to enhance the sensitivity of the solution state NMR by shuttling the sample between higher and lower magnetic fields, with one of these fields providing an electron Larmor frequency that matches the inter-electron exchange coupling Jex. If spins cross this so-called JDNP condition sufficiently fast, we predict that a sizable nuclear polarization will be created without microwave irradiation. This MF-JDNP proposal requires radicals whose singlet/triplet self-relaxation rates are dominated by dipolar hyperfine relaxation, and shuttling times that can compete with these electron relaxation processes. This communication discusses the theory behind the MF-JDNP, as well as proposals for radicals and conditions that could enable this new approach to NMR sensitivity enhancement.
... [45][46][47] Tuning spin-orbit coupling in molecular systems and their subsequent trESR signatures, as demonstrated here, is not only of paramount importance to blue OLED development but may also find resonance more broadly in the development of organic materials for light-controlled quantum information and spintronics. [78][79][80][81][82] ...
Molecular organic fluorophores are currently used in organic light-emitting diodes, though non-emissive triplet excitons generated in devices incorporating conventional fluorophores limit the efficiency. This limit can be overcome in materials that have intramolecular CT excitonic states and associated small singlet-triplet energy; triplets can be converted to emissive singlet excitons resulting in efficient delayed fluorescence. However, the mechanistic details of the spin interconversion have not yet been fully resolved. We report transient ESR studies that allow direct probing of the spin conversion in a series of delayed fluorescence fluorophores with varying energy gaps between LE and CT triplets. The observation of distinct triplet signals, unusual in transient ESR, suggests that multiple triplets mediate the photophysics for efficient light emission in delayed fluorescence emitters. We reveal that as the energy separation between LE and CT triplets decreases, spin interconversion changes from a direct, singlet-triplet mechanism to an indirect mechanism involving intermediate states.
... Generally speaking, spin-orbital coupling (SOC) and hyperfine interaction (HFI) are two basic sources of spin relaxation in semiconducting organics [6]. Effective SOC strength is subject to thin film morphology, heavy-atom incorporation and molecular geometry [67,68]. These factors did not encounter obvious structure-to-structure variation among these four polymers due to proximate morphological behavior and backbone coplanarity as stated above. ...
During the past years, charge transport performance of solution-processed donor-acceptor (D-A) conjugated polymers has been explosively studied for successful instance of record-breaking carrier mobility. By contrast, corresponding spin dynamics was far-less probed except handful pioneering reports. Herein, we successfully observed room-temperature stable magnetoresistance (MR) response in organic spin valves using ambipolar naphthalenediimide-based D-A type conjugated polymers. Additionally, we found spin transport performance of these polymer-inserted junction was sensitive to chemical structures of polymer repeating units. Both alkyl-chain extension in the acceptor unit and cyano-group substitution in the donor unit can induce evident MR drop. Furthermore, we discovered spin dynamics inside these ambipolar materials exhibited disparate electrical dependence from classical unipolar small-molecule medium. Neither increased bias current size nor reversed polarity can downsize junction MR response in the spin valves based on these conjugated polymers hence verified underlying great potential of ambipoalr media in spintronics devices. We would like to emphasize that no spinterface effect happened even when these solution-processed polymers contacted directly with ferromagnetic electrodes according to comprehensive magnetization study. This spin-related exploration opened a new avenue to understand spintronics from material level, and also unveiled inspiring potential of solution-processed D-A type conjugated polymers on future spin-memory devices.
... This analysis, also reported in the work of Mirzoyan et al. [21], further supports the findings of Albino et al. [20] and provides a more quantitative ground for study of spin-phonon coupling in terms of experimental observables such as the static g-shifts or electronic optical excitations. Interestingly, the correlation between the static g-shift and spin relaxation time was empirically observed in the context of organic radicals [28]. ...
Molecular electronic spins represent one of the most promising building blocks for the design of quantum computing architectures. However, the advancement of this technology requires the increase of spin lifetime at ambient temperature. Spin-phonon coupling has been recognized as the key interaction dictating spin relaxation at high temperature in molecular crystals and the search for chemical-design principles to control such interaction are a fundamental challenge in the field. Here we present a multi-reference first-principles analysis of the g-tensor and the spin-phonon coupling in a series of four exa-coordinate Vanadium(IV) molecular complexes, where the catecholate ligand donor atom is progressively changed from Oxygen to Sulphur, Selenium and Tellurium. A ligand field interpretation of the multi-reference electronic structure theory results made it possible to rationalize the correlation between the molecular g-shifts and the average spin-phonon coupling coefficients, revealing the role of spin-orbit coupling, chemical bond covalency and energy splitting of d-like orbitals in spin relaxation. Our study reveals the simultaneous increase of metal-ligand covalency and electronic excited state energy separation as key elements of an optimal strategy towards long spin-lattice lifetimes in molecular qubits.
... Given the importance of spin, it may be surprising that the microscopic mechanisms for spin relaxation are not better understood in organic materials. The strengths of HFIs and spin-orbit coupling have recently been investigated at a molecular level, depending on the elemental composition and geometry of the conjugated systems [11][12][13][14] . However, the relationship between charge motion and spin dynamics has only been studied for a few model systems [15][16][17][18][19] and remains poorly understood, in particular for state-of-the-art conjugated polymers with high charge-carrier mobilities. ...
Polymeric semiconductors exhibit exceptionally long spin lifetimes, and recently observed micrometre spin diffusion lengths in conjugated polymers demonstrate the potential for organic spintronics devices. Weak spin–orbit and hyperfine interactions lie at the origin of their long spin lifetimes, but the coupling mechanism of a spin to its environment remains elusive. Here, we present a systematic study of polaron spin lifetimes in field-effect transistors with high-mobility conjugated polymers as an active layer. We demonstrate how spin relaxation is governed by the charges’ hopping motion at low temperatures, whereas an Elliott–Yafet-like relaxation due to a transient localization of the carrier wavefunctions is responsible for spin relaxation at high temperatures. In this regime, charge, spin and structural dynamics are intimately related and depend sensitively on the local conformation of polymer backbones and the crystalline packing of the polymer chains.
... Clear singlet-triplet crossings seen for T T a,b therefore indicate an additional mixing mech- anism. As with the high-field effect, this can be pro- vided by a ∆g Hamiltonian term which mixes singlet and triplets to first order ( Fig. 6B and Supplementary Information) with strength ∼ ∆g eff B ∼ 10 −3 B for an expected ∆g eff ∼ 10 −3 [31]. Additionally, this crossing can be mediated by hyperfine interactions, with typical strengths of ∼mT in organic semiconductors [32,33]. ...
Significance
Pairs of spins in molecular materials have attracted significant interest as intermediates in photovoltaic devices and light-emitting diodes. However, isolating the local spin and electronic environments of such intermediates has proved challenging due to the complex structures in which they reside. Here we show how exchange coupling can be used to select and characterize multiple coexisting pairs, enabling joint measurement of their exchange interactions and optical profiles. We apply this to spin-1 pairs formed by photon absorption whose coupling gives rise to total-spin S = 0,1 and 2-pair configurations with drastically different properties. This presents a way of identifying the molecular conformations involved in spin-pair processes and generating design rules for more effective use of interacting spins.
Molecular semiconductors (MSCs), characterized by a longer spin lifetime than most of other materials due to their weak spin relaxation mechanisms, especially at room temperature, together with their abundant chemical tailorability and flexibility, are regarded as promising candidates for spintronic applications. Molecular spintronics, as an emerging subject that utilizes the unique properties of MSCs to study spin-dependent phenomena and properties, has attracted wide attention. In molecular spintronic devices, MSCs play the role as medium for information transport, process, and storage, in which the efficient spin inject–transport process is the prerequisite. Herein, we focus mainly on summarizing and discussing the recent advances in theoretical principles towards spin transport of MSCs in terms of the injection of spin-polarized carriers through the ferromagnetic metal/MSC interface and the subsequent transport within the MSC layer. Based on the theoretical progress, we cautiously present targeted design strategies of MSCs that contribute to the optimization of spin-transport efficiency and give favorable approaches to exploring accessional possibilities of spintronic materials. Finally, challenges and prospects regarding current spin transport are also presented, aiming to promote the development and application of the rosy and energetic field of molecular spintronics.
