Time-resolved Circular Dichroism Research Articles

Time-Resolved Circular Dichroism in Molecules: Experimental and Theoretical Advances.

Following changes in chirality can give access to relevant information on the function or reactivity of molecular systems. Time-resolved circular dichroism (TRCD) spectroscopy proves to be a valid tool to achieve this goal. Depending on the class of molecules, different temporal ranges, spanning from seconds to femtoseconds, need to be investigated to observe such chiroptical changes. Therefore, over the years, several approaches have been adopted to cover the timescale of interest, especially based on pump-probe schemes. Moreover, various theoretical approaches have been proposed to simulate and explain TRCD spectra, including linear and non-linear response methods as well as non-adiabatic molecular dynamics. In this review, an overview on both experimental and theoretical advances in the TRCD field is provided, together with selected applications. A discussion on future theoretical developments for TRCD is also given.

Direct Probe of Conical Intersection Photochemistry by Time-Resolved X-ray Magnetic Circular Dichroism.

The direct probing of photochemical dynamics by detecting the electronic coherence generated during passage through conical intersections is an intriguing challenge. The weak coherence signal and the difficulty in preparing purely excited wave packets that exclude coherence from other sources make it experimentally challenging. We propose to use time-resolved X-ray magnetic circular dichroism to probe the wave packet dynamics around the conical intersection. The magnetic field amplifies the relative strength of the electronic coherence signal compared to populations through the magnetic field response anisotropy. More importantly, since the excited state relaxation through conical intersections involves a change of parity, the magnetic coupling matches the symmetry of the response function with the electronic coherence, making the coherence signal only sensitive to the conical intersection induced coherence and excludes the pump pulse induced coherence between the ground state and excited state. In this theoretical study, we apply this technique to the photodissociation dynamics of a pyrrole molecule and demonstrate its capability of probing electronic coherence at a conical intersection as well as population transfer. We demonstrate that a magnetic field can be effectively used to extract novel information about electron and nuclear molecular dynamics.

Microscopic evaluation of spin and orbital moment in ferromagnetic resonance

Time-resolved X-ray magnetic circular dichroism under the effects of ferromagnetic resonance (FMR), known as X-ray ferromagnetic resonance (XFMR) measurements, enables direct detection of precession dynamics of magnetic moment. Here we demonstrated XFMR measurements and Bayesian analyses as a quantitative probe for the precession of spin and orbital magnetic moments under the FMR effect. Magnetization precessions in two different Pt/Ni-Fe thin film samples were directly detected. Furthermore, the ratio of dynamical spin and orbital magnetic moments was evaluated quantitatively by Bayesian analyses for XFMR energy spectra around the Ni L2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_{2,3}$$\\end{document} absorption edges. Our study paves the way for a microscopic investigation of the contribution of the orbital magnetic moment to magnetization dynamics.

Dynamic Observation of the Membrane Interaction Processes of β-Lactoglobulin by Time-Resolved Vacuum-Ultraviolet Circular Dichroism.

The elucidation of protein-membrane interactions is pivotal for comprehending the mechanisms underlying diverse biological phenomena and membrane-related diseases. In this investigation, vacuum-ultraviolet circular dichroism (VUVCD) spectroscopy, utilizing synchrotron radiation (SR), was employed to dynamically observe membrane interaction processes involving water-soluble proteins at the secondary-structure level. The study utilized a time-resolved (TR) T-shaped microfluidic cell, facilitating the rapid and efficient mixing of protein and membrane solutions. This system was instrumental in acquiring measurements of the time-resolved circular dichroism (TRCD) spectra of β-lactoglobulin (bLG) during its interaction with lysoDMPG micelles. The results indicate that bLG undergoes a β-α conformation change, leading to the formation of the membrane-interacting state (M-state), with structural alterations occurring in more than two steps. Global fitting analysis, employing biexponential functions with all of the TRCD spectral data sets, yielded two distinct rate constants (0.18 ± 0.01 and 0.06 ± 0.003/s) and revealed a unique spectrum corresponding to an intermediate state (I-state). Secondary-structure analysis of bLG in its native (N-, I-, and M-states) highlighted that structural changes from the N- to I-states predominantly occurred in the N- and C-terminal regions, which were prominently exposed to the membrane. Meanwhile, transitions from the I- to M-states extended into the inner barrel regions of bLG. Further examination of the physical properties of α-helical segments, such as effective charge and hydrophobicity, revealed that the N- to I- and I- to M-state transitions, which are ascribed to first- and second-rate constants, respectively, are primarily driven by electrostatic and hydrophobic interactions, respectively. These findings underscore the capability of the TR-VUVCD system as a robust tool for characterizing protein-membrane interactions at the molecular level.

Capturing electron-driven chiral dynamics in UV-excited molecules

Chiral molecules, used in applications such as enantioselective photocatalysis1, circularly polarized light detection2 and emission3 and molecular switches4,5, exist in two geometrical configurations that are non-superimposable mirror images of each other. These so-called (R) and (S) enantiomers exhibit different physical and chemical properties when interacting with other chiral entities. Attosecond technology might enable influence over such interactions, given that it can probe and even direct electron motion within molecules on the intrinsic electronic timescale6 and thereby control reactivity7–9. Electron currents in photoexcited chiral molecules have indeed been predicted to enable enantiosensitive molecular orientation10, but electron-driven chiral dynamics in neutral molecules have not yet been demonstrated owing to the lack of ultrashort, non-ionizing and perturbative light pulses. Here we use time-resolved photoelectron circular dichroism (TR-PECD)11–15 with an unprecedented temporal resolution of 2.9 fs to map the coherent electronic motion initiated by ultraviolet (UV) excitation of neutral chiral molecules. We find that electronic beatings between Rydberg states lead to periodic modulations of the chiroptical response on the few-femtosecond timescale, showing a sign inversion in less than 10 fs. Calculations validate this and also confirm that the combination of the photoinduced chiral current with a circularly polarized probe pulse realizes an enantioselective filter of molecular orientations following photoionization. We anticipate that our approach will enable further investigations of ultrafast electron dynamics in chiral systems and reveal a route towards enantiosensitive charge-directed reactivity.

Theoretical study of time-resolved photoelectron circular dichroism in the photodissociation of a chiral molecule.

Photoelectron circular dichroism (PECD), the forward-backward asymmetry of the photoelectron angular distribution when ionizing randomly oriented chiral molecules with circularly polarized light, is an established method to investigate chiral properties of molecules in their electronic ground state. Here, we develop a computational strategy for predicting time-resolved PECD (TRPECD) of chemical reactions and demonstrate the method on the photodissociation of 1-iodo-2-methylbutane. Our approach combines multi-configurational quantum-chemical calculations of the relevant potential-energy surfaces of the neutral and singly ionized molecule with ab initio molecular-dynamics (AIMD) calculations. The PECD parameters along the AIMD trajectories are calculated with the aid of electron-molecule scattering calculations based on the Schwinger variational principle implemented in ePolyScat. Our calculations have been performed for two probe wavelengths (133 and 160 nm) accessible through low-order harmonic generation in gases. Our results show that the TRPECD is a highly sensitive probe of photochemical reaction dynamics. Most interestingly, the TRPECD is found to change sign multiple times along the photodissociation coordinate, in agreement with recent experiments on CHBrFI [Svoboda et al., "Femtosecond photoelectron circular dichroism of chemical reactions," Sci. Adv. 8, eabq2811 (2022)]. The computational protocol introduced in the present work is general and readily applicable to other chiral photochemical processes.

Photocarrier transport of ferroelectric photovoltaic thin films detected by the magnetic dynamics of adjacent ferromagnetic layers

We have observed photocarrier transport behaviors in ${\mathrm{BiFeO}}_{3}/{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{MnO}}_{3}$ (BFO/LSMO) heterostructures by using time-resolved synchrotron x-ray magnetic circular dichroism in reflectivity. The magnetization of LSMO layers was used as a probe of photo-induced carrier dynamics in the photovoltaic BFO layers. During the photo-induced demagnetization process, the decay time of LSMO ($x$=0.2) magnetization strongly depends on the ferroelectric polarization direction of the BFO layer. The variation of decay time should be attributed to the different sign of accumulated photocarriers at the BFO/LSMO interface induced by the photovoltaic effect of the BFO layer. The photocarriers can reach the BFO/LSMO interface and influence the magnetization distribution in the LSMO layers within the timescale of $\ensuremath{\sim}100$ ps. Our results provide a novel strategy to investigate carrier dynamics and mechanisms of optical control of magnetization in thin film heterostructures.

Artifact-free balanced detection for the measurement of circular dichroism with a sub-picosecond time resolution.

Here we present the development of a subpicosecond spectropolarimeter enabling high sensitivity balanced detection of time-resolved circular dichroism (TRCD) signals from chiral sample in solution. The signals are measured with a conventional femtosecond pump-probe set-up using the combination of a quarter-waveplate and a Wollaston prism. This simple and robust method allows access to TRCD signals with improved signal-to-noise ratio and very short acquisition times. We provide a theoretical analysis of the artifacts of such detection geometry and the strategy to eliminate them. We illustrate the potential of this new detection with the study of the [Ru(phen)3]·2PF6 complexes in acetonitrile.

Ab Initio Simulation of the Ultrafast Circular Dichroism Spectrum of Provitamin D Ring-Opening.

We present a method to simulate ultrafast pump-probe time-resolved circular dichroism (TRCD) spectra based on time-dependent density functional theory trajectory surface hopping. The method is applied to simulate the TRCD spectrum along the photoinduced ring-opening of provitamin D. Simulations reveal that the initial decay of the signal is due to excited state relaxation, forming the rotationally flexible previtamin D. We further show that oscillations in the experimental TRCD spectrum arise from isomerizations between previtamin D rotamers with different chirality, which are associated with the helical conformation of the triene unit. We give a detailed description of the formation dynamics of different rotamers, playing a key role in the natural regulation of vitamin D photosynthesis. Going beyond the sole extraction of decay rates, simulations greatly increase the amount of information that can be retrieved from ultrafast TRCD, making it a sensitive tool to unravel details in the subpicosecond dynamics of photoinduced chirality changes.

X-ray magnetic circular dichroism spectroscopy at the Fe L edges with a picosecond laser-driven plasma source

Time-resolved x-ray magnetic circular dichroism (XMCD) enables a unique spectroscopic view on complex spin and charge dynamics in multi-elemental magnetic materials. So far, its application in the soft-x-ray range has been limited to synchrotron-radiation sources and free-electron lasers. By combining a laser-driven plasma source with a magnetic thin-film polarizer, we generate up to 30% circular polarization in the soft-x-ray regime, enabling the first XMCD spectroscopy at the Fe L edges in a laser laboratory, to our knowledge. Our approach can be readily adapted to other transition metal L and rare earth M absorption edges, and with a temporal resolution of <10ps, a wide range of ultrafast magnetization studies can be realized.

Laser induced ultrafast Gd 4f spin dynamics in Co100-xGdx alloys by means of time-resolved XMCD

We have studied the laser induced ultrafast quenching of Gd 4f magnetic order in ferrimagnetic Co100-xGdx alloys to highlight the role of the inter-atomic exchange coupling. We have taken advantage of the ultrashort soft X-ray pulses deliver by the femtoslicing beamline at the BESSY II synchrotron radiation source at the Helmholtz-Zentrum Berlin to perform element- and time-resolved X-ray Magnetic Circular Dichroism spectroscopy.Our results show that the laser induced quenching of Gd 4f magnetic order occurs on very different time-scales for the Co72Gd28, the Co77Gd23 and the Co79Gd21 alloys. Most of the magnetic moment losses occur within the first picosecond (ps) while the electron distribution is strongly out of equilibrium. After the equilibration of the electrons and lattice temperatures (t > 1 ps), the magnetic losses occur on slower rates that depend on the alloy composition: increasing the Co composition speeds up the demagnetization of Gd 4f sublattice. The strength of the inter-atomic exchange coupling which depends on composition, determines the efficiency of the angular momentum flow from the Gd 4f spin towards the lattice. Our results are in qualitative agreements with the predictions of the microscopic three temperatures model for ferrimagnetic alloys.

Time-Resolved Chiral X-Ray Photoelectron Spectroscopy with Transiently Enhanced Atomic Site Selectivity: A Free-Electron Laser Investigation of Electronically Excited Fenchone Enantiomers

Chirality is widespread in nature, playing a fundamental role in biochemical processes and in the origin of life itself. The observation of dynamics in chiral molecules is crucial for the understanding and control of the chiral activity of photoexcited states. One of the most promising techniques for the study of photoexcited chiral systems is time-resolved photoelectron circular dichroism (TR-PECD), which offers an intense and sensitive probe for vibronic and geometric molecular structure as well as electronic structures, and their evolution on a femtosecond timescale. However, the nonlocal character of the PECD effect, which is imprinted during the electron scattering off the molecule, makes the interpretation of TR-PECD experiments challenging. In this respect, core photoionization is known to allow site and chemical sensitivity to photelectron spectroscopy. Here we demonstrate that TR-PECD utilizing core-level photoemission enables probing the chiral electronic structure and its relaxation dynamics with atomic site sensitivity. Following UV pumped excitation to a 3s Rydberg state, fenchone enantiomers (C10H16O) were probed on a femtosecond scale using circularly polarized soft x-ray light pulses provided by the free-electron laser FERMI. C 1s binding energy shifts caused by the redistribution of valence electron density in this 3s-valence-Rydberg excitation allowed us to measure transient PECD chiral responses with an enhanced C atom site selectivity compared to that achievable in the ground state molecule. This chemical-specific, site-specific, and enantiosensitive observation of the electronic structure of a transiently photoexcited chiral molecule is expected to pave the way toward chiral femtochemistry probed by core-level photoemission.Received 2 March 2022Revised 27 September 2022Accepted 2 February 2023DOI:https://doi.org/10.1103/PhysRevX.13.011044Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChiralityElectronic structure of atoms & moleculesPhysical SystemsMoleculesTechniquesPhotoionizationUltrafast femtosecond pump probeX-ray photoelectron spectroscopyAtomic, Molecular & Optical

Time-resolved circular dichroism of excitonic systems: theory and experiment on an exemplary squaraine polymer.

Experimental and theoretical foundations for femtosecond time-resolved circular dichroism (TRCD) spectroscopy of excitonic systems are presented. In this method, the system is pumped with linearly polarized light and the signal is defined as the difference between the transient absorption spectrum probed with left and with right circularly polarized light. We present a new experimental setup with a polarization grating as key element to generate circularly polarized pulses. Herein the positive (negative) first order of the diffracted light is left-(right-)circularly polarized and serves as a probe pulse in a TRCD experiment. The grating is capable of transferring ultrashort broadband pulses ranging from 470 nm to 720 nm into two separate beams with opposite ellipticity. By applying a specific chopping scheme we can switch between left and right circular polarizations and detect transient absorption (TA) and TRCD spectra on a shot-to-shot basis simultaneously. We perform experiments on a squaraine polymer, investigating excitonic dynamics, and we develop a general theory for TRCD experiments of excitonically coupled systems that we then apply to describe the experimental data in this particular example. At a magic angle of 54.7° between the pump-pulse polarization and the propagation direction of the probe pulse, the TRCD and TA signals become particularly simple to analyze, since the orientational average over random orientations of complexes factorizes into that of the interaction with the pump and the probe pulse, and the intrinsic electric quadrupole contributions to the TRCD signal average to zero for isotropic samples. Application of exciton theory to linear absorption and to linear circular dichroism spectra of squaraine polymers reveals the presence of two fractions of polymer conformations, a dominant helical conformation with close interpigment distances that are suggested to lead to short-range contributions to site energy shifts and excitonic couplings of the squaraine molecules, and a fraction of unfolded random coils. Theory demonstrates that TRCD spectra of selectively excited helices can resolve state populations that are practically invisible in TA spectroscopy due to the small dipole strength of these states. A qualitative interpretation of TRCD and TA spectra in the spectral window investigated experimentally is offered. The 1 ps time component found in these spectra is related to the slow part of exciton relaxation obtained between states of the helix in the low-energy half of the exciton manifold. The dominant 140 ps time constant reflects the decay of excited states to the electronic ground state.

Magnet-Free Time-Resolved Magnetic Circular Dichroism with Pulsed Vector Beams.

Magnetic circular dichroism (MCD) is a widely used spectroscopic technique which reveals valuable information about molecular geometry and electronic structure. However, the weak signal and the necessary strong magnets impose major limitations on its application. We propose a novel protocol to overcome these limitations by using pulsed vector beams (VBs), which consist of nanosecond gigahertz pump and femtosecond UV-vis probe pulses. By virtue of the strong longitudinal electromagnetic fields, the MCD signal detected by using the pulsed VBs is greatly enhanced compared to conventional MCD performed with plane waves. Furthermore, varying the pump-probe time delay allows monitoring the ultrafast variation of molecular properties.

Exploring GPR109A Receptor Interaction with Hippuric Acid Using MD Simulations and CD Spectroscopy

Previous research has indicated that various metabolites belonging to phenolic acids (PAs), produced by gut microflora through the breakdown of polyphenols, help in promoting bone development and protecting bone from degeneration. Results have also suggested that G-protein-coupled receptor 109A (GPR109A) functions as a receptor for those specific PAs such as hippuric acid (HA) and 3-(3-hydroxyphenyl) propionic acid (3-3-PPA). Indeed, HA has a molecular structural similarity with nicotinic acid (niacin) which has been shown previously to bind to GPR109A receptor and to mediate antilipolytic effects; however, the binding pocket and the structural nature of the interaction remain to be recognized. In the present study, we employed a computational strategy to elucidate the molecular structural determinants of HA binding to GPR109A and GPR109B homology models in understanding the regulation of osteoclastogenesis. Based on the docking and molecular dynamics simulation studies, HA binds to GPR109A similarly to niacin. Specifically, the transmembrane helices 3, 4 and 6 (TMH3, TMH4 and TMH6) and Extracellular loop 1 and 2 (ECL1 and ECL2) residues of GRP109A; R111 (TMH3), K166 (TMH4), ECL2 residues; S178 and S179, and R251 (TMH6), and residues of GPR109B; Y87, Y86, S91 (ECL1) and C177 (ECL2) contribute for HA binding. Simulations and Molecular Mechanics Poisson-Boltzmann solvent accessible area (MM-PBSA) calculations reveal that HA has higher affinity for GPR109A than for GPR109B. Additionally, in silico mutation analysis of key residues have disrupted the binding and HA exited out from the GPR109A protein. Furthermore, measurements of time-resolved circular dichroism spectra revealed that there are no major conformational changes in the protein secondary structure on HA binding. Taken together, our findings suggest a mechanism of interaction of HA with both GPR109A and GPR109B receptors.

Myoglobin-Pyruvate Interactions: Binding Thermodynamics, Structure-Function Relationships, and Impact on Oxygen Release Kinetics.

Myoglobin (Mb), besides its roles as an oxygen (O2) carrier/storage protein and nitric oxide NO scavenger/producer, may participate in lipid trafficking and metabolite binding. Our recent findings have shown that O2 is released from oxy-Mb upon interaction with lactate (LAC, anerobic glycolysis end-product). Since pyruvate (PYR) is structurally similar and metabolically related to LAC, we investigated the effects of PYR (aerobic glycolysis end-product) on Mb using isothermal titration calorimetry, circular dichroism, and O2-kinetic studies to evaluate PYR affinity toward Mb and to compare the effects of PYR and LAC on O2 release kinetics of oxy-Mb. Similar to LAC, PYR interacts with both oxy- and deoxy-Mb with a 1:1 stoichiometry. Time-resolved circular dichroism spectra revealed that there are no major conformational changes in the secondary structures of oxy- or deoxy-Mb during interactions with PYR or LAC. However, we found contrasting results with respect to binding affinities and substrate preference, where PYR has higher affinity toward deoxy-Mb when compared with LAC (which prefers oxy-Mb). Furthermore, PYR interaction with oxy-Mb releases a significantly lower amount of O2 than LAC. Taken together, our findings support the hypothesis that glycolytic end-products play a distinctive role in the Mb-rich tissues by serving as novel regulators of O2 availability, and/or by impacting other activities related to oxy-/deoxy-Mb toggling in resting vs. exercised or metabolically activated conditions.

Femtosecond photoelectron circular dichroism of chemical reactions.

Understanding the chirality of molecular reaction pathways is essential for a broad range of fundamental and applied sciences. However, the current ability to probe chirality on the time scale of primary processes underlying chemical reactions remains very limited. Here, we demonstrate time-resolved photoelectron circular dichroism (TRPECD) with ultrashort circularly polarized vacuum-ultraviolet (VUV) pulses from a tabletop source. We demonstrate the capabilities of VUV-TRPECD by resolving the chirality changes in time during the photodissociation of atomic iodine from two chiral molecules. We identify several general key features of TRPECD, which include the ability to probe dynamical chirality along the complete photochemical reaction path, the sensitivity to the local chirality of the evolving scattering potential, and the influence of electron scattering off dissociating photofragments. Our results are interpreted by comparison with high-level ab-initio calculations of transient PECDs from molecular photoionization calculations. Our experimental and theoretical techniques define a general approach to femtochirality.

Ultrafast time-evolution of chiral N\xe9el magnetic domain walls probed by circular dichroism in x-ray resonant magnetic scattering

Non-collinear spin textures in ferromagnetic ultrathin films are attracting a renewed interest fueled by possible fine engineering of several magnetic interactions, notably the interfacial Dzyaloshinskii-Moriya interaction. This allows for the stabilization of complex chiral spin textures such as chiral magnetic domain walls (DWs), spin spirals, and magnetic skyrmions among others. We report here on the behavior of chiral DWs at ultrashort timescale after optical pumping in perpendicularly magnetized asymmetric multilayers. The magnetization dynamics is probed using time-resolved circular dichroism in x-ray resonant magnetic scattering (CD-XRMS). We observe a picosecond transient reduction of the CD-XRMS, which is attributed to the spin current-induced coherent and incoherent torques within the continuously varying spin texture of the DWs. We argue that a specific demagnetization of the inner structure of the DW induces a flow of spins from the interior of the neighboring magnetic domains. We identify this time-varying change of the DW texture shortly after the laser pulse as a distortion of the homochiral Néel shape toward a transient mixed Bloch-Néel-Bloch texture along a direction transverse to the DW.

Experimental confirmation of the delayed Ni demagnetization in FeNi alloy

Element-selective techniques are central for the understanding of ultrafast spin dynamics in multi-element materials, such as magnetic alloys. Recently, however, it turned out that the commonly used technique of the transverse magneto-optical Kerr effect (T-MOKE) in the extreme ultraviolet range may have issues with unwanted crosstalk between different elemental signals and energy-dependent non-linear response. This problem can be sizeable, which puts recent observations of ultrafast spin transfer from Fe to Ni sites in FeNi alloys into question. In this study, we investigate the Fe-to-Ni spin transfer in a crosstalk-free time-resolved x-ray magnetic circular dichroism (XMCD) experiment with a reliable time reference. With XMCD near the absorption maxima, we find a very similar Fe and Ni dynamics as with T-MOKE from identical samples. Considering the potential non-linearities of the T-MOKE response, such a good agreement in our findings is remarkable. Our data provide the ongoing discussion about ultrafast spin-transfer mechanisms in FeNi systems with a broader experimental basis.

Photo-induced antiferromagnetic-ferromagnetic and spin-state transition in a double-perovskite cobalt oxide thin film

Investigation of ultrafast dynamic behaviors can provide novel insights about the coupling mechanisms among multiple degrees of freedom in condensed matters, such as lattice, magnetism and electronic structure. Here we investigate both the ferromagnetic (FM) and antiferromagnetic (AFM) dynamics of a strongly correlated oxide system, GdBaCo2O5.5 thin film by time-resolved x-ray magnetic circular dichroism in reflectivity (XMCDR) and resonant magnetic x-ray diffraction (RMXD). A photo-induced AFM-FM transition characterized by an increase of the transient XMCDR (sensitive to FM order) beyond the unpumped value and a decay of RMXD (sensitive to AFM order) was observed. The photon-energy dependence of the transient XMCDR and reflectivity could be interpreted as a concomitant photo-induced spin-state transition (SST). The AFM-FM transition and SST couple with each other in the time domain, resulting in unusual dynamic behaviors of the magnetism.