Field-dependent Relaxation Research Articles

Pulsed MPI Relaxometry of Brownian and Néel Field-Dependent Relaxation in Superparamagnetic Magnetite Nanoparticles Confirm Theory and Simulations.

Superparamagnetic iron oxide nanoparticles (SPIOs) are used as tracers in Magnetic Particle Imaging (MPI). It is crucial to understand the magnetic properties of SPIOs for optimizing MPI imaging contrast, resolution, and sensitivity. Brownian and Néel relaxation theory developed in the early 1950s posits that relaxation times can vary with particle size, shell thickness, medium viscosity, and the applied field strength. Magnetic relaxation can soon provide a unique imaging capability, the ability to distinguish bound from unbound MPI tracers in vivo. Yet experimental validation of these theories has not been completed. In this paper, a novel method of pulsed magnetic field relaxometry is used to directly probe the relaxation behavior of superparamagnetic magnetite nanoparticles over a spectrum of magnetic field amplitudes, providing the first experimental validation of theoretical relaxation models. It is also shown that closed-form approximations generated in the early 1970s accurately match both data and numerical Fokker Planck computational models, which are computationally burdensome. This means researchers can trust these approximations for future modeling. All the findings can be translated to sinusoidal excitations used in conventional MPI scanningtrajectories.

Structural dynamics of first-order phase transition in giant magnetocaloric La(Fe,Si)13: The free energy landscape

Maximizing the performance of magnetic refrigerators and thermomagnetic energy harvesters is imperative for their successful implementation and can be done by maximizing their operation frequency. One of the features delimiting the frequency and efficiency of such devices is the phase transition kinetics of their magnetocaloric/thermomagnetic active material. While previous studies have described the magnetic component governing the kinetics of the magnetovolume phase transition in La(Fe,Si)13 giant magnetocaloric materials, a comprehensive description of its structural component has yet to be explored. In this study, in situ synchrotron X-ray diffraction is employed to describe the structural changes upon magnetic field application/removal. Long magnetic field dependent relaxation times up to a few hundred seconds are observed after the driving field is paused. The phase transition is found to be highly asymmetric upon magnetic field cycling due to the different Gibbs energy landscapes and the absence of an energy barrier upon field removal. An exponential relationship is found between the energy barriers and the relaxation times, suggesting the process is governed by a non-thermal activation over an energy barrier process. Such fundamental knowledge on first-order phase transition kinetics suggests pathways for materials optimization and smarter design of magnetic field cycling in real-life devices.

Slow magnetic relaxation and strong magnetic coupling in the nitroxyl radical complexes of lanthanide(iii) with diamagnetic ground state (Ln = Lu, Eu).

Radical lanthanide complexes are appealing platforms to investigate the possibility to engineer relevant magnetic couplings between the two magnetic centers by exploiting the strongly donating magnetic orbitals of the radical. In this paper, we report a spectroscopic and magnetic study on [LnRad(NO3)3], where Ln = Eu3+ or Lu3+ and Rad is the tridentate tripodal nitroxyl radical 4,4-dimethyl-2,2-bis(pyridin-2-yl)-1,3-oxazolidine-3-oxyl. A thorough magnetic investigation by Electron Paramagnetic Resonance (EPR) spectroscopy and magnetometry, fully supported by ab initio calculations, allowed us to unravel an unprecedentedly large antiferromagnetic coupling between the Eu3+ and the radical (J 12 = +19.5 cm-1, +J 12 S 1 S 2 convention). Remarkably, both europium and lutetium complexes showed slow magnetization dynamics below 20 K. The field and temperature dependent relaxation dynamics, dominated by Raman and direct processes were modelled simultaneously, allowing us to assess that the Raman process is field dependent.

Exploring weak ligand-protein interactions by relaxometry of long-lived spin order.

Relaxation times of nuclear spins often serve as a valuable source of information on the dynamics of various biochemical processes. Measuring relaxation as a function of the external magnetic field turned out to be extremely useful for the studies of weak ligand-protein interactions. We demonstrate that observing the relaxation of the long-lived spin order instead of longitudinal magnetization extends the capability of this approach. We studied the field-dependent relaxation of the longitudinal magnetization and the singlet order (SO) of methylene protons in alanine-glycine dipeptide and citrate in the presence of human serum albumin (HSA). As a result, SO relaxation proved to be more sensitive to ligand-protein interaction, providing higher relaxation contrast for various HSA concentrations. To assess the parameters of the binding process in more details, we utilized a simple analytical relaxation model to fit the experimental field dependences for both SO and T1 relaxation. We also tested the validity of our approach in the experiments with trimethylsilylpropanoic acid (TSP) used as a competitor in ligand binding with HSA.

Field- and concentration-dependent relaxation of magnetic nanoparticles and optimality conditions for magnetic fluid hyperthermia

The field-dependent relaxation dynamics of suspended magnetic nanoparticles continues to present a fascinating topic of basic science that at the same time is highly relevant for several technological and biomedical applications. Renewed interest in the intriguing behavior of magnetic nanoparticles in response to external fields has at least in parts be driven by rapid advances in magnetic fluid hyperthermia research. Although a wealth of experimental, theoretical, and simulation studies have been performed in this field in recent years, several contradictory findings have so far prevented the emergence of a consistent picture. Here, we present a dynamic mean-field theory together with comprehensive computer simulations of a microscopic model system to systematically discuss the influence of several key parameters on the relaxation dynamics, such as steric and dipolar interactions, the external magnetic field strength and frequency, as well as the ratio of Brownian and Néel relaxation time. We also discuss the specific and intrinsic loss power as measures of the efficiency of magnetic fluid heating and discuss optimality conditions in terms of fluid and field parameters. Our results are helpful to reconcile contradictory findings in the literature and provide an important step towards a more consistent understanding. In addition, our findings also help to select experimental conditions that optimize magnetic fluid heating applications.

Microsecond Motion of the Bacterial Transporter EmrE in Lipid Bilayers.

The bacterial transporter EmrE is a homo-dimeric membrane protein that effluxes cationic polyaromatic substrates against the concentration gradient by coupling to proton transport. As the archetype of the small multidrug resistance family of transporters, EmrE structure and dynamics provide atomic insights into the mechanism of transport by this family of proteins. We recently determined high-resolution structures of EmrE in complex with a cationic substrate, tetra(4-fluorophenyl)phosphonium (F4-TPP+), using solid-state NMR spectroscopy and an S64V-EmrE mutant. The substrate-bound protein exhibits distinct structures at acidic and basic pH, reflecting changes upon binding or release of a proton from residue E14, respectively. To obtain insight into the protein dynamics that mediate substrate transport, here we measure 15N rotating-frame spin-lattice relaxation (R1ρ) rates of F4-TPP+-bound S64V-EmrE in lipid bilayers under magic-angle spinning (MAS). Using perdeuterated and back-exchanged protein and 1H-detected 15N spin-lock experiments under 55 kHz MAS, we measured 15N R1ρ rates site-specifically. Many residues show spin-lock field-dependent 15N R1ρ relaxation rates. This relaxation dispersion indicates the presence of backbone motions at a rate of about 6000 s-1 at 280 K for the protein at both acidic and basic pH. This motional rate is 3 orders of magnitude faster than the alternating access rate but is within the range estimated for substrate binding. We propose that these microsecond motions may allow EmrE to sample different conformations to facilitate substrate binding and release from the transport pore.

Magnetic-field-dependent electric-charge transport in hadronic medium at finite temperature

Electric charge transport of hadronic matter at finite temperature and magnetic field is studied within the linear sigma model. Anisotropic transport coefficients associated with the charge transport are estimated both in the weak and strong regimes of the magnetic field using the transport theory approach. In a weakly magnetized medium, the magnetic field effects are incorporated through the Lorentz force term in the Boltzmann equation. Strong magnetic field puts further constraints on the motion of charged particles through Landau quantization. Magnetic field-dependent thermal relaxation time is obtained from interaction rates of hadrons with the S-matrix approach by considering the Landau level kinematics of the charged hadrons. Mean-field effects are embedded in the analysis through the temperature-dependent hadron masses. Further, the hadronic medium response to a time-varying external electric field is studied in weak and strong magnetic field regimes. It is seen that electromagnetic responses of the hadronic matter have a strong dependence on the mean-field effects, sigma mass, the strength of the external fields, and its evolution in the medium.

Large Protein Assemblies for High-Relaxivity Contrast Agents: The Case of Gadolinium-Labeled Asparaginase.

Biologics are emerging as the most important class of drugs and are used to treat a large variety of pathologies. Most of biologics are proteins administered in large amounts, either by intramuscular injection or by intravenous infusion. Asparaginase is a large tetrameric protein assembly, currently used against acute lymphoblastic leukemia. Here, a gadolinium(III)-DOTA derivative has been conjugated to asparaginase, and its relaxation properties have been investigated to assess its efficiency as a possible theranostic agent. The field-dependent 1H longitudinal relaxation measurements of water solutions of gadolinium(III)-labeled asparaginase indicate a very large increase in the relaxivity of this paramagnetic protein complex with respect to small gadolinium chelates, opening up the possibility of its use as an MRI contrast agent.

Longest relaxation time versus maximum loss peak in the field-dependent longitudinal dynamics of suspended magnetic nanoparticles

Magnetic nanoparticles in suspensions provide fascinating model systems to study field-induced effects. Their response to external fields also opens up promising new applications, e.g., in hyperthermia. Despite significant research efforts, several basic questions regarding the influence of external fields on the magnetization dynamics are still open. Here we revisit the classical model of a suspended magnetic nanoparticle with combined internal and Brownian dynamics in the presence of an external field and discuss the field-dependent longitudinal relaxation. While internal and Brownian dynamics are independent in the field-free case, the coupling of both processes when an external field is present leads to richer and more complicated behavior. Using a highly efficient and accurate solver to the underlying Fokker-Planck equation allows us to study a broad parameter range. We identify different dynamical regimes and study their respective properties. In particular, we discuss corrections to the popular rigid-dipole approximation which are captured in terms of a simplified diffusion-jump model in the Brownian-dominated regime with rare N\'eel relaxation events. In addition, we discover a regime with surprising mode-coupling effects for magnetically soft nanoparticles. We explain our findings with the help of a perturbation theory, showing that in this regime the magnetization relaxation at late times is slaved by the slow Brownian motion of the nanoparticle. We discuss consequences of these findings such as the discrepancy of the longest relaxation time and the inverse frequency of the loss peak of the magnetic susceptibility.

Shear viscosity of hadronic matter at finite temperature and magnetic field

We calculate the transport coefficient of hadronic matter in the presence of temperature and magnetic field using the linear sigma model. In the relaxation time approximation, we estimate the shear viscosity over entropy density $\eta/s$. The point-like interaction rates of hadrons are evaluated through the $S$-matrix approach in the presence of a magnetic field to obtain the temperature and magnetic field-dependent relaxation time. We observe that the transport coefficients are anisotropic in the presence of the magnetic field. We calculate the temperature and magnetic field-dependent anisotropic shear viscosity coefficients by incorporating the estimated relaxation time. The value of viscosity over entropy density is lower in the presence of a magnetic field than the value of it in a thermal medium. The behavior of the perpendicular components of the shear-viscous coefficient is also discussed. We consider the temperature-dependent hadron masses from mean-field effects in this work.

Inversion of Hyperpolarized 13C NMR Signals through Cross-Correlated Cross-Relaxation in Dissolution DNP Experiments.

Dissolution dynamic nuclear polarization (DDNP) is a versatile tool to boost signal amplitudes in solution-state nuclear magnetic resonance (NMR) spectroscopy. For DDNP, nuclei are spin-hyperpolarized “ex situ” in a dedicated DNP device and then transferred to an NMR spectrometer for detection. Dramatic signal enhancements can be achieved, enabling shorter acquisition times, real-time monitoring of fast reactions, and reduced sample concentrations. Here, we show how the sample transfer in DDNP experiments can affect NMR spectra through cross-correlated cross-relaxation (CCR), especially in the case of low-field passages. Such processes can selectively invert signals of 13C spins in proton-carrying moieties. For their investigations, we use schemes for simultaneous or “parallel” detection of hyperpolarized 1H and 13C nuclei. We find that 1H → 13C CCR can invert signals of 13C spins if the proton polarization is close to 100%. We deduce that low-field passage in a DDNP experiment, a common occurrence due to the introduction of so-called “ultra-shielded” magnets, accelerates these effects due to field-dependent paramagnetic relaxation enhancements that can influence CCR. The reported effects are demonstrated for various molecules, laboratory layouts, and DDNP systems. As coupled 13C–1H spin systems are ubiquitous, we expect similar effects to be observed in various DDNP experiments. This might be exploited for selective spectroscopic labeling of hydrocarbons.

Evidence of fully gapped superconductivity in NbReSi: A combined μSR and NMR study

We report a comprehensive study of the noncentrosymmetric NbReSi superconductor by means of muon-spin rotation and relaxation ($\mu$SR) and nuclear magnetic resonance (NMR) techniques. NbReSi is a bulk superconductor with $T_c = 6.5$ K, characterized by a large upper critical field, which exceeds the Pauli limit. Both the superfluid density $\rho_\mathrm{sc}(T)$ (determined via transverse-field $\mu$SR) and the spin-lattice relaxation rate $T_1^{-1}(T)$ (determined via NMR) suggest a nodeless superconductivity (SC) in NbReSi. We also find signatures of multigap SC, here evidenced by the field-dependent muon-spin relaxation rate and the electronic specific-heat coefficient. The absence of spontaneous magnetic fields below $T_c$, as evinced from zero-field $\mu$SR measurements, indicates a preserved time-reversal symmetry in the superconducting state of NbReSi. Finally, we discuss possible reasons for the unusually large upper critical field of NbReSi, most likely arising from its anisotropic crystal structure.

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Temperature-dependent magnetodielectric, magnetoimpedance, and magnetic field controlled dielectric relaxation response in KBiFe2O5

In this work, polycrystalline KBiFe2O5 (KBFO), belonging to the brownmillerite class of monoclinic structure with space group P2/c, is synthesized using a solid-state reaction route. Magnetodielectric (MD) and magnetoimpedance (MI) characteristics of KBFO are studied over a wide temperature (10–300 K), magnetic field (0–1.3 T), and frequency (100 Hz to 1 MHz) range. Zero-field-cool (ZFC) and field-cool (FC) magnetization data show a bifurcation around 11 K, indicating blocking temperature (TB). At room temperature, MD and MI data as a function of the magnetic field shows maximum MD and MI coupling to be ∼−0.6% and ∼0.7%, respectively, at 50 kHz. With the decrease in temperature from 300 K to 50 K, magnetodielectric strength decreases (−0.6% to −0.06%), whereas magnetization increases from canted-antiferromagnetic (MS ≈ 0.16 emu g−1) to a weak ferromagnetic state (MS ≈ 0.44 emu g−1). It indicates the existence of Inverse Dzyaloshinskii-Moriya interaction causing MD coupling in KBFO. MD behavior is also reflected in magnetic field-dependent dielectric relaxation phenomena demonstrated through magnetic field-dependent activation energies. The difference in activation energies of magnetic field-dependent conduction mechanism (Eg ≈ 0.370 ± 0.018 eV) and MD loss relaxation (Eg ≈ 0.183 ± 0.006 eV) indicate both have a different origin. The presence of the capacitive MI effect demonstrates that the observed magnetodielectric coupling is intrinsic. The existence of both temperatures-dependent MD and MI coupling in KBFO makes it suitable for dynamic random access memory as well as novel magnetic sensors.

Multiscale Water Dynamics on Protein Surfaces: Protein-Specific Response to Surface Ions.

Proteins function in crowded aqueous environments, interacting with a diverse range of compounds, and among them, dissolved ions. These interactions are water-mediated. In the present study, we combine field-dependent NMR relaxation (NMRD) and theory to probe water dynamics on the surface of proteins in concentrated aqueous solutions of hen egg-white lysozyme (LZM) and bovine serum albumin (BSA). The experiments reveal that the presence of salts (NaCl or NaI) leads to an opposite ion-specific response for the two proteins: an addition of salt to LZM solutions increases water relaxation rates with respect to the salt-free case, while for BSA solutions, a decrease is observed. The magnitude of the change depends on the ion identity. The developed model accounts for the non-Lorentzian shape of the NMRD profiles and reproduces the experimental data over four decades in Larmor frequency (10 kHz to 110 MHz). It is applicable up to high protein concentrations. The model incorporates the observed ion-specific effects via changes in the protein surface roughness, represented by the surface fractal dimension, and the accompanying changes in the surface water residence times. The response is protein-specific, linked to geometrical aspects of the individual protein surfaces, and goes beyond protein-independent Hofmeister-style ordering of ions.

Shear viscosity and electrical conductivity of the relativistic fluid in the presence of a magnetic field: A massless case

We have explored the shear viscosity and electrical conductivity calculations for bosonic and fermionic media, without and with presence of an external magnetic field. For numerical visualisation, we have dealt with their simplified massless expressions. In the presence of a magnetic field, five independent velocity gradient tensors can be designed, and so their corresponding proportional coefficients, connected with the viscous stress tensor, provide us five components of the shear viscosity coefficient. In the existing literature, two sets of viscous stress tensors are available. Starting from them, the present work has obtained expressions for two sets of five shear viscosity coefficients, which can be ultimately classified into three basic components – parallel, perpendicular and Hall components as one get similar expression for the electrical conductivity at the finite magnetic field. Our calculations are based on the kinetic theory approach in relaxation time approximation. Repeating the same mathematical steps under finite magnetic field, which is traditionally practiced in the absence of magnetic field, we have obtained two sets of five shear viscosity components, whose final expressions are in good agreements with earlier references, although a difference in methodology or steps can be noticed. In this context, the present work, for the first time, addresses a detailed calculation of relaxation time approximation (RTA)-based kinetic theory calculations of the second set of five shear viscosity components, which was previously done by Denicol et al (Phys. Rev. D 98, 076009 (2018)) in moment method technique. Realising the massless results of viscosity and conductivity for Maxwell–Boltzmann, Fermi–Dirac and Bose–Einstein distribution functions, we have applied them for massless quark gluon plasma and hadronic matter phases, which can provide us a rough order of strength, within which actual results will vary during quark–hadron phase transition. The present work also indicates that the magnetic field might have some role in building perfect fluid nature in RHIC or LHC matter. The lower bound expectation of shear viscosity to entropy density ratio is also discussed. Here, for the first time, we are addressing an analytic expression of temperature- and magnetic field-dependent relaxation time of the massless fluid, for which perpendicular component of shear viscosity to entropy density ratio can reach its lower bound.

Magnetization relaxation dynamics in [Co/Pt]3 multilayers on pico- and nanosecond timescales

We experimentally investigated magnetization relaxation dynamics in the largely unexplored time window extending from few picoseconds up to two nanoseconds following femtosecond laser pulse excitation. We triggered magnetization dynamics in ${[\mathrm{Co}(0.4\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{Pt}(0.7\phantom{\rule{0.16em}{0ex}}\mathrm{nm})]}_{3}$ multilayers and measured the resulting magneto-optic response by recording both transient hysteresis loops as well as transients of magnetization dynamics. We observe that the coercive field of the sample is still strongly suppressed even \ensuremath{\sim}1 ms after the laser excitation, which is three orders of magnitude longer than the recovery time of the magnetization amplitude. In addition, we succeeded to fit the magnetization relaxation data in the entire experimentally observed time window by considering two phenomenological time constants ${\ensuremath{\tau}}_{f}^{*}$ and ${\ensuremath{\tau}}_{s}^{*}$ describing fast (ps) and slow (ns) magnetization relaxation processes, respectively. The fits of the data suggest a magnetic field dependent relaxation slowdown beyond 100 ps after excitation. We observe an explosion of the ${\ensuremath{\tau}}_{f}^{*}$ and ${\ensuremath{\tau}}_{s}^{*}$ values when the magnetization is completely quenched and relaxes intrinsically in the absence of an external magnetic field. We interpret the phenomenological time constants ${\ensuremath{\tau}}_{f}^{*}$ and ${\ensuremath{\tau}}_{s}^{*}$ using an intuitive physical picture based on the Landau-Lifshitz-Bloch model and numerical solutions of the extended three-temperature model [Shim et al., Sci. Rep. 10, 6355 (2020)].

Low Temperature Relaxation of Donor Bound Electron Spins in ^{28}Si:P.

We measure the spin-lattice relaxation of donor bound electrons in ultrapure, isotopically enriched, phosphorus-doped ^{28}Si:P. The optical pump-probe experiments reveal at low temperatures extremely long spin relaxation times which exceed 20h. The ^{28}Si:P spin relaxation rate increases linearly with temperature in the regime below 1K and shows a distinct transition to a T^{9} dependence which dominates the spin relaxation between 2 and 4K at low magnetic fields. The T^{7} dependence reported for natural silicon is absent. At high magnetic fields, the spin relaxation is dominated by the magnetic field dependent single phonon spin relaxation process. This process is well documented for natural silicon at finite temperatures but the ^{28}Si:P measurements validate additionally that the bosonic phonon distribution leads at very low temperatures to a deviation from the linear temperature dependence of Γ as predicted by theory.

A numerical study of field strength and clay morphology impact on NMR transverse relaxation in sandstones

Nuclear magnetic resonance (NMR) relaxometry is a common technique for the petrophysical characterization of sedimentary rocks. The standard interpretation of NMR transverse relaxation responses is based on the assumptions of the fast diffusion limit, dominant surface relaxation, and weak coupling between pores, allowing an interpretation of the NMR response as pore size distribution. In general, three asymptotic relaxation regimes can be defined by comparing dephasing, structural and diffusion length scales. The shortest length scale defines the dominating relaxation regime, which is either the free diffusion, motional averaging, or localization regime. Complex mineralogy and morphology of rocks, especially due to clay minerals, may lead to the co-existence and coupling of multiple relaxation regimes in the presence of surface relaxivity heterogeneity and internal gradient effects.In this work the relationship between morphology of rocks, strength of applied magnetic field, resulting relaxation regimes and observed NMR relaxation responses is studied numerically. Limitations in the discretization of clays typical for micro-CT images are addressed by introducing a fine-scale kaolinite model based on SEM images. The model is utilized to evaluate the field-dependent mean transverse relaxation time and effective diffusion coefficient of clay regions. These effective parameters are incorporated into random-walk simulations on micro-CT images. Relaxation regimes are analysed spatially for three different types of sandstone as function of external magnetic field strength. Increase of paramagnetic clay content, field strength and echo-time increases the fraction of spins relaxing in the localization regime within macro-pores, typically being localised in the regions neighbouring clay pockets and grain surfaces. We demonstrate that a significant contribution of the localization regime to relaxation may lead to incorrect predictions of pore-size distributions and fluid typing. The prefactor of permeability correlations varies significantly due to clay effects. Accounting for these effects should enable more robust petrophysical interpretations.

Magnetic Relaxation Mechanisms in Ho Single Atom Magnets

Surface-supported single atoms with long magnetic lifetime, also called single atom magnets, represent the ultimate limit of downscaling of a magnetic bit. Due to the possibility to write, store and read information in their magnetic states, these atoms are model systems for future ultra-high-density magnetic storage devices. In this review, the properties of the most investigated single atom magnet, namely a Ho atom adsorbed on an ultrathin MgO film, will be presented together with the techniques used to address its quantum level structure and magnetic stability. The temperature and field dependent relaxation mechanisms of this unconventional magnetic system will be discussed based on recent findings. Finally, an overview of the open issues and possible future directions of the research will be provided.