Magnetic Relaxation Mechanisms Research Articles

Ta181 nuclear quadrupole resonance study of the noncentrosymmetric superconductor PbTaSe2

We report on a pure $^{181}$Ta-nuclear quadrupole resonance (NQR) measurement of PbTaSe$_2$ at zero magnetic field, which has the advantage of directly probing the intrinsic superconducting phase and electronic states of the TaSe$_2$ layer. We observed the $^{181}$Ta-NQR spectrum of the intrinsic structure with space group $P6$-$m2$, which agrees well with density functional theory (DFT) calculations. The nuclear spin relaxation rate ($1/T_1$) shows an exponential decrease well below $T_{\rm_c}$, indicating that the superconducting state is fully gapped in the framework of Bardeen-Cooper-Schrieffer (BCS) theory. The gap size obtained by $^{181}$Ta-NQR was smaller than the value in previous reports, which may imply that the Fermi surfaces composed of Ta-5$d$ orbitals, where the average pairing interactions are expected to be weaker than in BCS model, are primarily probed. The temperature dependence of $1/T_1$ below $T_{\rm_c}$ can be reproduced well by the superposition of quadrupole and magnetic relaxation mechanisms, together with the distribution of superconducting gap size inherent to multiple Fermi surfaces theoretically proposed in PbTaSe$_2$.

Magnetic Hyperthermia Experiments with Magnetic Nanoparticles in Clarified Butter Oil and Paraffin: A Thermodynamic Analysis

In Specific Power Absorption (SPA) models for Magnetic Fluid Hyperthermia (MFH) experiments, the magnetic relaxation time of the nanoparticles (NPs) is known to be a fundamental descriptor of the heating mechanisms. The relaxation time is mainly determined by the interplay between the magnetic properties of the NPs and the rheological properties of NPs environment. Although the role of magnetism in MFH has been extensively studied, the thermal properties of the NPs medium and their changes during of MFH experiments have been so far underrated. Here, we show that ZnxFe3-xO4 NPs dispersed through different with phase transition in the temperature range of the experiment: clarified butter oil (CBO) and paraffin. These systems show non-linear behavior of the heating rate within the temperature range of the MFH experiments. For CBO, a fast increase at $306 K$ associated to changes in the viscosity (\texteta(T)) and specific heat (c_p(T)) of the medium below and above its melting temperature. This increment in the heating rate takes place around $318 K$ for paraffin. Magnetic and morphological characterizations of NPs together with the observed agglomeration of the nanoparticles above $306 K$ indicate that the fast increase in MFH curves could not be associated to a change in the magnetic relaxation mechanism, with N\'eel relaxation being dominant. In fact, successive experiment runs performed up to temperatures below and above the CBO melting point resulted in different MFH curves due to agglomeration of NPs driven by magnetic field inhomogeneity during the experiments. Similar effects were observed for paraffin. Our results highlight the relevance of the NPs medium's thermodynamic properties for an accurate measurement of the heating efficiency for in vitro and in vivo environments, where the thermal properties are largely variable within the temperature window of MFH experiments.

Influence of Polymorphism on the Magnetic Properties of Single-Molecule Magnets According to the Data of EPR Spectroscopy in the Terahertz Range

Two earlier described polymorphous modifications of the cobalt(II) (pseudo)clathrochelate are studied by EPR spectroscopy in the terahertz range, where the complex exhibits the properties of a single-molecule magnet (including the record-breaking barrier for magnetization reversal at the moment). Different values of the magnetization reversal barrier found previously for the corresponding crystalline phases by the results of magnetometric measurements in an alternating magnetic field are observed in the EPR spectra in the terahertz range. A combined analysis of these two methods allows one to more precisely estimate the magnetization reversal barrier for two polymorphous modifications and also the contribution of different magnetic relaxation mechanisms to the spin dynamics. This unambiguously confirms that slight changes in the crystalline environment of the molecule of even such structurally rigid metal complexes as cobalt(II) (pseudo)clathrochelates can result in high differences in the magnetization reversal barrier, which is the key characteristic of single-molecule magnets.

Magnetization diffusion in duct flow: The magnetic entrance length and the interplay between hydrodynamic and magnetic timescales

In this work, computational fluid dynamics simulations of a ferrofluid plane Poiseuille flow in the presence of a constant applied magnetic field are performed. The orientation of the field is perpendicular to the direction of the flow. An original numerical methodology for calculating magnetic and hydrodynamic fields is proposed, including an important discussion about an identified magnetization entrance region. Three different magnetization models are considered to calculate the magnetization field. These models are implemented and validated according to analytic and asymptotic theories, including the one developed in this manuscript. Discrepancies between the models are discussed and interpreted physically. An intricate balance between different physical mechanisms is shown to be responsible for a diffusive-like behavior of the magnetization field. This balance is governed by a competition between the flow’s vorticity and the mechanisms of magnetic relaxation. The physical parameters responsible for this non-equilibrium magnetization dynamics are identified and interpreted using the problem’s timescales. It seems that the combination of three different timescales governs the dynamics of non-equilibrium magnetization: the Brownian diffuse timescale, a hydrodynamic (convective) timescale, and a controllable magnetic timescale associated with the intensity of the applied magnetic field. The results indicate toward the possibility of controlling the development of the flow’s magnetization field through the applied magnetic field, particle size distribution, fluid concentration, and flow rate. In addition, several results are presented regarding the fully developed flow, including magnetization profiles and angles between the applied field H and the magnetization field M.

Manipulation of the Coordination Geometry along the C4 Rotation Axis in a Dinuclear Tb3+ Triple-Decker Complex via a Supramolecular Approach.

A supramolecular complex (1⋅C60 ) was prepared by assembling (C60-Ih)[5,6]fullerene (C60 ) with the dinuclear Tb3+ triple-decker complex [(TPP)Tb(Pc)Tb(TPP)] (1: Tb3+ =trivalent terbium ion, Pc2- =phthalocyaninato, TPP2- =tetraphenylporphyrinato) with quasi-D4h symmetry to investigate the relationship between the coordination symmetry and single-molecule magnet (SMM) properties. Tb3+ -Pc triple-decker complexes (Tb2 Pc3 ) have an important advantage over Tb3+ -Pc double-decker complexes (TbPc2 ) since the magnetic relaxation processes correspond to the Zeeman splitting when there are two 4f spin systems. The two Tb3+ sites of 1 are equivalent, and the twist angle (φ) was determined to be 3.62°. On the other hand, the two Tb3+ sites of 1⋅C60 are not equivalent. The φ values for sites Tb1 and Tb2 were determined to be 3.67° and 33.8°, respectively, due to a change in the coordination symmetry of 1 upon association with C60 . At 1.8 K, 1 and 1⋅C60 undergo different magnetic relaxations, and the changes in the ground state affect the spin dynamics. Although 1 and 1⋅C60 relax via QTM in a zero applied magnetic field (H), H dependencies of the magnetic relaxation times (τ) for H>1500 Oe are similar. On the other hand, for H<1500 Oe, the τ values have different behaviors since the off-diagonal terms ( ) affect the magnetic relaxation mechanism. From temperature (T) and H dependences of τ, spin-phonon interactions along with direct and Raman mechanisms explain the spin dynamics. We believe that a supramolecular method can be used to control the magnetic anisotropy along the C4 rotation axis and the spin dynamic properties in dinuclear Ln3+ -Pc multiple-decker complexes.

New Approach to Analyze 2D Map T1–T2

Based on the method of two-dimensional (2D) nuclear magnetic resonance (NMR) relaxometry, a technique was developed for determining the joint distribution of the correlation time $$ \tau_{c} $$ and the Van Vleck second moments $$ \Delta \omega^{2} $$. The field of application is the study of slow molecular motions corresponding to the condition of the ratio of nuclear magnetic relaxation times T1/T2 > 1.05 (the relation of spin–lattice relaxation time T1 to spin–spin relaxation time T2). The technique is based on the use of a priori information about the mechanism of nuclear magnetic relaxation in a system. The technique has used this information in the regularization solution of an inverse problem. In contrast to the known method for calculating 2D maps of the joint distribution P2 (T1, T2), the proposed method for constructing a 2D map of the joint distribution $$ Q_{2} \left( {\tau_{c} ,\Delta \omega^{2} } \right) $$ does not depend on the main characteristic of the NMR relaxometer—the resonance frequency $$ \omega_{0} $$. The technique was used to analyze the characteristics of sorbed water in clay rocks–argillite.

Propeller‐Shaped Fe4 and Fe3M Molecular Nanomagnets: A Journey from Crystals to Addressable Single Molecules

This Microreview covers the preparation and investigation of Fe4 and Fe3M complexes with a propeller‐like structure, most of which function as single‐molecule magnets (SMMs). The magnetic characterization of these highly symmetric and chemically versatile complexes has enabled the establishment of important magneto‐structural correlations regarding magnetic anisotropy and magnetic relaxation mechanisms in SMM materials. Their chemical stability and easy functionalization have been further exploited to process them into thin films, down to monolayers and submonolayers, using solution or vapor‐phase methods. The proof so obtained that surface‐supported molecules can largely retain the rich magnetic behavior of bulk phases has been a turning point in SMM research, which has the integration of SMMs into spintronic devices among its most ambitious goals.

Uncertainty estimates for magnetic relaxation times and magnetic relaxation parameters.

The use of alternating current (AC) magnetometry to measure magnetic relaxation times is one of the most fundamental measurements for characterising single-molecule magnets (SMMs). These measurements, performed as a function of frequency, temperature and magnetic field, give vital information on the underlying magnetic relaxation process(es) occurring in the material. The magnetic relaxation times are usually fitted to model functions derived from spin-phonon coupling theories that allow characterisation of the mechanisms of magnetic relaxation. The parameters of these relaxation models are then often compared between different molecules in order to find trends with molecular structure that may guide the field to the next breakthrough. However, such meta-analyses of the model parameters are doomed to over-interpretation unless uncertainties in the model parameters can be quantified. Here we determine a method for obtaining uncertainty estimates in magnetic relaxation times from AC experiments, and provide a program called CC-FIT2 for fitting experimental AC data as well as the resulting relaxation times, to obtain relaxation parameters with accurate uncertainties. Applying our approach to three archetypal families of high-performance dysprosium(iii) SMMs shows that accounting for uncertainties has a significant impact on the uncertainties of relaxation parameters, and that larger uncertainties appear to correlate with crystallographic disorder in the compounds studied. We suggest that this type of analysis should become routine in the community.

Controlling the dominant magnetic relaxation mechanisms for magnetic hyperthermia in bimagnetic core–shell nanoparticles

We report a simple and effective way to control the heat generation of a magnetic colloid under alternate magnetic fields by changing the shell composition of bimagnetic core-shell Fe3O4/ZnxCo1-xFe2O4 nanoparticles. The core-shell structure constitutes a magnetically-coupled biphase system, with an effective anisotropy that can be tuned by the substitution of Co2+ by Zn2+ ions in the shell. Magnetic hyperthermia experiments of nanoparticles dispersed in hexane and butter oil showed that the magnetic relaxation is dominated by Brown relaxation mechanism in samples with higher anisotropy (i.e., larger concentration of Co within the shell) yielding high specific power absorption values in low viscosity media as hexane. Increasing the Zn concentration of the shell, diminishes the magnetic anisotropy, which results in a change to a Néel relaxation that dominates the process when the nanoparticles are dispersed in a high-viscosity medium. We demonstrate that tuning the Zn contents at the shell of these exchange-coupled core/shell nanoparticles provides a way to control the magnetic anisotropy without loss of saturation magnetization. This ability is an essential prerequisite for most biomedical applications, where high viscosities and capturing mechanisms are present.

Computational Studies on Vibronic Coupling in Single Molecule Magnets: Impact on the Mechanism of Magnetic Relaxation

In this paper we give an overview of our activities on computations of the electronic structure of single molecule magnets with special emphasize of vibronic coupling as revealed by FIR and Raman spectra of two complexes of Co(II) - [CoL2]2- (L2- = 1,2-bis(methanesulfonamido benzoate) (1) and of Co(acac)2(H2O)2 (2) subject to two recent publications (Nature communications 2016 [Ref.14] and 2018 [Ref.15], respectively) in close collaboration with several experimental groups. The implications of spin-vibronic coupling for the field dependence of the magnetic relaxation has been discusses in close relation with our analysis of the spin-vibronic coupling in the considered complexes.

Magneto-Structural Properties and Theoretical Studies of a Family of Simple Heterodinuclear Phenoxide/Alkoxide Bridged MnIIILnIII Complexes: On the Nature of the Magnetic Exchange and Magnetic Anisotropy.

A family of MnIIILnIII strictly dinuclear complexes of general formula [MnIII(μ-L)(μ-OMe)(NO3)LnIII(NO3)2(MeOH)] (LnIII = Gd, Dy, Er, Ho) has been assembled in a one pot synthesis from a polydentate, multipocket aminobis(phenol)ligand [6,6'-{(2-(1-morpholyl)ethylazanediyl)bis(methylene)}bis(2-methoxy-4-methylphenol)], Mn(NO3)2·4H2O, Ln(NO3)3· nH2O, and NEt3 in MeOH. These compounds represent the first examples of fully structurally and magnetically characterized dinuclear MnIIILnIII complexes. Single X-ray diffraction studies reveal that all complexes are isostructural, consisting of neutral dinuclear molecules where the MnIII and LnIII metal ions, which exhibit distorted octahedral MnN2O4 and distorted LnO9 coordination spheres, are linked by phenoxide/methoxide double bridging groups. Static magnetic studies show that the MnIIIGdIII derivative exhibits a weak antiferromagnetic interaction between the metal ions, with a negative axial zero-field splitting D parameter. The MnIIIGdIII complex shows a notable magnetocaloric effect with magnetic entropy change at 5 T and 3 K of -Δ Sm = 16.8 J kg-1 K-1. Theoretical studies were performed to support the sign and magnitude of the magnetic anisotropy of the MnIII ion ( ab initio), to predict the value and nature of JMnGd, to disclose the mechanism of magnetic coupling, and to establish magneto-structural correlations (DFT calculations). The results of these calculations are corroborated by quantum theory of atoms in molecule analysis (QTAIM). Finally, MnIII-DyIII and MnIII-ErIII complexes show field-induced slow relaxation of the magnetization but without reaching a maximum above 2 K in the out-of-phase ac susceptibility. Ab initio calculations were also performed on MnIII-DyIII/HoIII systems to unravel the origin behind the weak SMM characteristics of the molecules possessing two strongly anisotropic ions. The mechanism of magnetic relaxation was developed, revealing a large QTM/tunnel splitting at the single-ion level. Furthermore, the anisotropy axes of the MnIII and LnIII ions were calculated to be noncollinear, leading to reduction of the overall anisotropy in the molecules. Hence, the herein reported complexes demonstrate that a combination of two anisotropic metal ions does not guarantee SMM behavior.

Nuclear magnetic resonance surface relaxation mechanisms of kerogen

Nuclear magnetic resonance (NMR) relaxometry is an excellent tool for probing the interactions between solid pore surface and pore fluids in porous media. Surface relaxation is a key component of NMR relaxation. It is well-known that in conventional rocks, paramagnetic centers contribute most to the surface relaxation phenomenon. However, the interactions between organic pore surfaces and pore fluids, and the mechanism of surface relaxation in organic shale pores, are not well-understood. We tackle the issue using deuterated compounds to adjust the proton density in the liquid phase and monitoring the transverse relaxation rate changes of kerogen-fluid mixtures. With the Barnett and Eagle Ford kerogen isolates, we found that for alkanes, it is intramolecular dipolar coupling that dominates among the magnetic interactions. As a result, the transverse relaxation rate of alkane proton spins is more likely to be dependent on the concentration of active adsorption sites on the kerogen surface, rather than the kerogen proton density. For water inside organic pores, surface relaxation most likely originates from hydrogen bonding and intermolecular dipolar coupling. We also examined the temperature effect on kerogen surface relaxation and found temperature-dependent behavior that is consistent with surface relaxation by hydrogen bonding and homonuclear dipolar coupling interactions.

Determination of the nature of fluctuations using Li8 and Li9β -NMR and spin-lattice relaxation

We report a comparison of the $1/T_1$ spin lattice relaxation rates (SLR) for $^9Li$ and $^8Li$ in Pt and SrTiO$_{3}$, in order to differentiate between magnetic and electric quadrupolar relaxation mechanisms. In Pt, the ratio of the $1/T_{1}$ spin relaxation rates $R_{Pt}$ was found to be 6.82(29), which is close to but less than the theoretical limit of $\sim7.68$ for pure magnetic relaxation. In SrTiO$_{3}$ this ratio was found to be 2.7(3), which is close but larger than the theoretical limit of $\sim2.14$ expected for pure electric quadrupolar relaxation. These results bring new insight into the nature of the fluctuations in the local environment of implanted $^8Li$ observed by $\beta$-NMR.

Evaluation of easy-axis dynamics in a magnetic fluid by measurement and analysis of the magnetization curve in an alternating magnetic field

An understanding of the magnetic relaxation mechanism is critical to the medical application of magnetic nanoparticles. The temporal change in magnetization caused by an applied field can be evaluated by measuring the magnetization curves in the alternating fields. When magnetic nanoparticles are dispersed in a liquid, owing to magnetic torque, the Brownian relaxation influences the magnetization dynamics, in addition to the Néel relaxation. In this study, by evaluating the magnetization curve obtained by subtracting the magnetization curve corresponding to the solid from that of the liquid, the dynamics of the easy axis are observed with respect to the superparamagnetic nanoparticles.

Quenching the Quantum Tunneling of Magnetization in Heterometallic Octanuclear {TMIII4 DyIII4 } (TM=Co and Cr) Single-Molecule Magnets by Modification of the Bridging Ligands and Enhancing the Magnetic Exchange Coupling.

We report the synthesis, structural characterisation, magnetic properties and provide an ab initio analysis of the magnetic behaviour of two new heterometallic octanuclear coordination complexes containing CoIII and DyIII ions. Single-crystal X-ray diffraction studies revealed molecular formulae of [CoIII4 DyIII4 (μ-OH)4 (μ3 -OMe)4 {O2 CC(CH3 )3 }4 (tea)4 (H2 O)4 ]⋅4 H2 O (1) and [CoIII4 DyIII4 (μ-F)4 (μ3 -OH)4 (o-tol)8 (mdea)4 ]⋅ 3 H2 O⋅EtOH⋅MeOH (2; tea3- =triply deprotonated triethanolamine; mdea2- =doubly deprotonated N-methyldiethanolamine; o-tol=o-toluate), and both complexes display an identical metallic core topology. Furthermore, the theoretical, magnetic and SMM properties of the isostructural complex, [CrIII4 DyIII4 (μ-F4 )(μ3 -OMe)1.25 (μ3 -OH)2.75 (O2 CPh)8 (mdea)4 ] (3), are discussed and compared with a structurally similar complex, [CrIII4 DyIII4 (μ3 -OH)4 (μ-N3 )4 (mdea)4 (O2 CC(CH3 )3 )4 ] (4). DC and AC magnetic susceptibility data revealed single-molecule magnet (SMM) behaviour for 1-4. Each complex displays dynamic behaviour, highlighting the effect of ligand and transition metal ion replacement on SMM properties. Complexes 2, 3 and 4 exhibited slow magnetic relaxation with barrier heights (Ueff ) of 39.0, 55.0 and 10.4 cm-1 respectively. Complex 1, conversely, did not exhibit slow relaxation of magnetisation above 2 K. To probe the variance in the observed Ueff values, calculations by using CASSCF, RASSI-SO and POLY_ANISO routine were performed on these complexes to estimate the nature of the magnetic coupling and elucidate the mechanism of magnetic relaxation. Calculations gave values of JDy-Dy as -1.6, 1.6 and 2.8 cm-1 for complexes 1, 2 and 3, respectively, whereas the JDy-Cr interaction was estimated to be -1.8 cm-1 for complex 3. The developed mechanism for magnetic relaxation revealed that replacement of the hydroxide ion by fluoride quenched the quantum tunnelling of magnetisation (QTM) significantly, and led to improved SMM properties for complex 2 compared with 1. However, the tunnelling of magnetisation at low-lying excited states was still operational for 2, which led to low-temperature QTM relaxation. Replacement of the diamagnetic CoIII ions with paramagnetic CrIII led to CrIII ⋅⋅⋅DyIII coupling, which resulted in quenching of QTM at low temperatures for complexes 3 and 4. The best example was found if both CrIII and fluoride were present, as seen for complex 3, for which both factors additively quenched QTM and led to the observation of highly coercive magnetic hysteresis loops above 2 K. Herein, we propose a synthetic strategy to quench the QTM effects in lanthanide-based SMMs. Our strategy differs from existing methods, in which parameters such as magnetic coupling are difficult to control, and it is likely to have implications beyond the DyIII SMMs studied herein.

Rotation of Magnetization Derived from Brownian Relaxation in Magnetic Fluids of Different Viscosity Evaluated by Dynamic Hysteresis Measurements over a Wide Frequency Range.

The dependence of magnetic relaxation on particle parameters, such as the size and anisotropy, has been conventionally discussed. In addition, the influences of external conditions, such as the intensity and frequency of the applied field, the surrounding viscosity, and the temperature on the magnetic relaxation have been researched. According to one of the basic theories regarding magnetic relaxation, the faster type of relaxation dominates the process. However, in this study, we reveal that Brownian and Néel relaxations coexist and that Brownian relaxation can occur after Néel relaxation despite having a longer relaxation time. To understand the mechanisms of Brownian rotation, alternating current (AC) hysteresis loops were measured in magnetic fluids of different viscosities. These loops conveyed the amplitude and phase delay of the magnetization. In addition, the intrinsic loss power (ILP) was calculated using the area of the AC hysteresis loops. The ILP also showed the magnetization response regarding the magnetic relaxation over a wide frequency range. To develop biomedical applications of magnetic nanoparticles, such as hyperthermia and magnetic particle imaging, it is necessary to understand the mechanisms of magnetic relaxation.

Photo-induced Insulator-ferromagnetic Metal Transition and Magnetic Solitons in the Perovskite GdSrMnO

We have discussed the dynamics of photo-induced magnetic solitons in the perovskite GdSrMnO by using quantized massive gauge fields, which are introduced theoretically in the path-integral method. For the first time, we propose the magnetic relaxation mechanism of photo-induced magnetic solitons by using the effective Hamiltonian with the p-magnetic solitons interaction and the Langevin equation.

Finding the true spin–lattice relaxation time for half-integral nuclei with non-zero quadrupole couplings

Measuring true spin–lattice relaxation times T1 of half-integral quadrupolar nuclei having non-zero nuclear quadrupole coupling constants (NQCCs) presents challenges due to the presence of satellite-transitions (STs) that may lie outside the excitation bandwidth of the central transition (CT). This leads to complications in establishing well-defined initial conditions for the population differences in these multi-level systems. In addition, experiments involving magic-angle spinning (MAS) can introduce spin exchange due to zero-crossings of the ST and CT (or possibly rotational resonance recoupling in the case of multiple sites) and greatly altered initial conditions as well. An extensive comparison of pulse sequences that have been previously used to measure T1 in such systems is reported, using the 71Ga (I=3/2) NMR of a Ge-doped h-GaN n-type semiconductor sample as the test case. The T1 values were measured at the peak maximum of the Knight shift distribution. Analytical expressions for magnetization-recovery of the CT appropriate to the pulse sequences tested were used, involving contributions from both a magnetic relaxation mechanism (rate constant W) and a quadrupolar one (rate constants W1 and W2, approximately equal in this case). An asynchronous train of high-power saturating pulses under MAS that is able to completely saturate both CT and STs is found to be the most reliable and accurate method for obtaining the “true T1”, defined here as (2W+2W1,2)−1. All other methods studied yielded poor agreement with this “true T1” value or even resulted in gross errors, for reasons that are analyzed in detail. These methods involved a synchronous train of saturating pulses under MAS, an inversion-recovery sequence under MAS or static conditions, and a saturating comb of pulses on a static sample. Although the present results were obtained on a sample where the magnetic relaxation mechanism dominated the quadrupolar one, the asynchronous saturating pulse train approach is not limited to this situation. The extent to which W1 and W2 are unequal does affect the interpretability of the experiment however, particularly when the quadrupolar mechanism dominates. A numerically approximate solution for the I=3/2 recovery case reveals the quantitative effects of any such inequality.

Probing dynamics and pinning of single vortices in superconductors at nanometer scales.

The dynamics of quantized magnetic vortices and their pinning by materials defects determine electromagnetic properties of superconductors, particularly their ability to carry non-dissipative currents. Despite recent advances in the understanding of the complex physics of vortex matter, the behavior of vortices driven by current through a multi-scale potential of the actual materials defects is still not well understood, mostly due to the scarcity of appropriate experimental tools capable of tracing vortex trajectories on nanometer scales. Using a novel scanning superconducting quantum interference microscope we report here an investigation of controlled dynamics of vortices in lead films with sub-Angstrom spatial resolution and unprecedented sensitivity. We measured, for the first time, the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement, revealing a far more complex behavior than has previously been recognized, including striking spring softening and broken-spring depinning, as well as spontaneous hysteretic switching between cellular vortex trajectories. Our results indicate the importance of thermal fluctuations even at 4.2 K and of the vital role of ripples in the pinning potential, giving new insights into the mechanisms of magnetic relaxation and electromagnetic response of superconductors.

Simultaneous luminescence modulation and magnetic field detection via magneto-optical response of Eu3+-doped NaGdF4 nanocrystals

Magnetic confinement of f electrons wave functions and magnetic field assistant cross relaxation mechanism was firstly built for optical variation.