Many estimates for the magnetic relaxation time of magnetic nanoparticle systems neglect the effect of the applied field strength. This is despite many applications of magnetic nanoparticles involving relaxation dynamics under the influence of applied fields. Here, an analytic approximation for the field-dependent Brownian relaxation time of single-domain, spherical magnetic nanoparticles in an external applied field is developed mathematically. This expression is validated by comparison with existing empirically-derived expressions and by comparison to particle-level simulations that allow particle rotations. Our approximation works particularly well for larger particles. We then use the developed expression to analytically calculate the total magnetic relaxation time when both Brownian and Néel relaxation mechanisms are at play. Again, we show that the results match those found using particle-level simulations, this time with both particle rotations and internal magnetization dynamics allowed. However, for some particle parameters and for large field strengths, our simulations reveal that the Brownian and Néel relaxation mechanisms are decoupled and it is not appropriate to combine these to calculate a total relaxation time.
We investigate the magnetization dynamics of a conducting magnetic nanoparticle weakly coupled to source and drain electrodes, under the assumption that all relaxation comes from exchange of electrons with the electrodes. The magnetization dynamics is characterized by a relaxation time $t_1$, which strongly depends on temperature, bias voltage, and gate voltage. While a direct measure of a nanoparticle magnetization might be difficult, we find that $t_1$ can be determined through a time resolved transport measurement. For a suitable choice of gate voltage and bias voltage, the magnetization pe…
We have carried out in ferritin the Field-Cooling method and data analysis proposed by Mamiya et al. (Phys. Rev. Lett. 88, 67202 (2002) at T = 5 K in order to check the time magnetic relaxation of these antiferromagnetic nanoparticles as a function of the magnetic field. We found that relaxation at T = 5 K in ferritin is faster in the absence of magnetic field, in good agreement with the zero-field Resonant Spin Quantum Tunneling observed previously in ferritin (Phys. Rev. Lett. 79, 1754 (1997).
Graphene on noble-metal nanostructures constitutes an attractive nanocomposite with possible applications in sensors or energy conversion. In this work we study the properties of hybrid graphene/gold nanoparticle structures by Raman spectroscopy and Scanning Probe Methods. The nanoparticles (NPs) were prepared by local annealing of gold thin films using focused laser beam. The method resulted in a patterned surface, with NPs formed at arbitrarily chosen microscale areas. Graphene grown by chemical vapour deposition was transferred onto the prepared, closely spaced gold NPs. While we found that…
Graphene covered metal nanoparticles constitute a novel type of hybrid materials, which provide a unique platform to study plasmonic effects, surface-enhanced Raman scattering (SERS), and metal-graphene interactions at the nanoscale. Such a hybrid material is fabricated by transferring graphene grown by chemical vapor deposition onto closely spaced gold nanoparticles produced on a silica wafer. The morphology and physical properties of nanoparticle-supported graphene is investigated by atomic force microscopy, optical reflectance spectroscopy, scanning tunneling microscopy and spectroscopy (ST…
Subpicosecond wavelength non-degenerate differential transmission (DT) was used to observe the carrier relaxation mechanism in GaN based quantum well (QW) with and without metal nanoparticles (MNPs) in it. The spontaneous emission dominates the stimulated emission for above the GaN band edge excitation energy. We observed long decay times for Au-embedded sample and short decay times for Ag-embedded sample with respect to reference sample.
The specific role played by small gold nanoparticles supported on the rutile TiO2(110) surface in the processes of adsorption and dissociation of H2 is discussed. It is demonstrated that the molecular and dissociative adsorption of H2 on Au_n clusters containing n = 1, 2, 8 and 20 atoms depends on cluster size, geometry structure, cluster flexibility and the interaction with the support material. Rutile TiO2(110) support energetically promotes H2 dissociation on gold clusters. It is demonstrated that the active sites towards H2 dissociation are located at corners and edges on the surface of th…
We investigate slow dynamics of collection of a few antiferromagnetic NiO nanoparticles. The zero-field cooled magnetization exhibits size dependent fluctuations. We find memory effects in field cooled magnetization, as well as aging effects in thermoremenant magnetization of antiferromagnetic nanoparticles. The antiferromagnetic nanoparticles show a stronger memory effect than the corresponding effect in the ferromagnetic particles, when the distribution of particles include very small sizes. The situation reverses for bigger sizes. The relaxation of the magnetization after a sudden cooling, …
The scope of this article is to report very detailed results of the measurements of magnetic relaxation phenomena in the new Cu$_{0.5}$Fe$_{2.5}$O$_{4}$ nanoparticles and known CuFe$_{2}$O$_{4}$ nanoparticles. The size of synthesized particles is (6.5$\pm $1.5)nm. Both samples show the superparamagnetic behaviour, with the well-defined phenomena of blocking of magnetic moment. This includes the splitting of zero-field-cooled and field-cooled magnetic moment curves, dynamical hysteresis, slow quasi-logarithmic relaxation of magnetic moment below blocking temperature. The scaling of the magnetic…
Magnetic single-domain nanoparticles constitute an important model system in magnetism. In particular ensembles of superparamagnetic nanoparticles can exhibit a rich variety of different behaviors depending on the inter-particle interactions. Starting from isolated single-domain ferro- or ferrimagnetic nanoparticles the magnetization behavior of both non-interacting and interacting particle-ensembles is reviewed. A particular focus is drawn onto the relaxation time of the system. In case of interacting nanoparticles the usual Neel-Brown relaxation law becomes modified. With increasing interact…
The aggregation of superparamagnetic iron oxide (SPIO) nanoparticles decreases the transverse nuclear magnetic resonance (NMR) relaxation time T2 of adjacent water molecules measured by a Carr-Purcell-Meiboom-Gill (CPMG) pulse-echo sequence. This effect is commonly used to measure the concentrations of a variety of small molecules. We perform extensive Monte Carlo simulations of water diffusing around SPIO nanoparticle aggregates to determine the relationship between T2 and details of the aggregate. We find that in the motional averaging regime T2 scales as a power law with the number N of nan…
The magnetic properties of Fe$_3$O$_4$ nanoparticle assemblies have been investigated in detail through a combination of vibrating sample magnetometry and muon spin relaxation ($μ$SR) techniques. Two samples with average particle sizes of 5 nm and 20 nm, respectively, were studied. For both samples, the magnetometry and $μ$SR results exhibit clear signatures of the superparmagnetic state at high temperature and the magnetically blocked state at low temperature. The $μ$SR data demonstrate that the transition from the superparamagnetic to the blocked state occurs gradually throughout the sample …
We have measured the relaxation time of a thermally unstable ferromagnetic nanoparticle incorporated into a magnetic tunnel junction (MTJ) as a function of applied magnetic field, voltage V (-0.38 V < V < +0.26 V), and temperatures (283 K< T< 363 K) . By analyzing the results within the framework of a modified Néel-Brown formalism we determine the effective attempt time of the nanoparticle and also the bias dependences of the in-plane and out-of-plane spin torques. There is a significant linear modification of the effective temperature with voltage due to the in-plane torque and a significant …
We report evidence of the magnetization reversal in nanoparticles by surface acoustic waves (SAWs). The experimental system consists of isolated magnetite nanoparticles dispersed on a piezoelectric substrate. Magnetic relaxation from a saturated state becomes significantly enhanced in the presence of the SAW at a constant temperature of the substrate. The dependence of the relaxation on SAW power and frequency has been investigated. The effect is explained by the effective ac magnetic field generated by the SAW in the nanoparticles.
We study the radiative cooling of polar and metallic nanoparticles immersed in a thermal bath close to a partially reflecting surface. The dynamics of relaxation is investigated at different distances from the surface, i.e., in the near-field and far-field zones. We demonstrate the existence of an oscillating behavior for the thermal relaxation time with respect to the separation distance from the surface, an analog of Friedel oscillations in Fermi liquids.
Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for understanding irreversibility and the second law in fundamental chemical and biological processes that are actively driven, thus operating far from thermal equilibrium. Here, we apply the framework of fluctuation theorems to investigate the important case of a system relaxing from a non-equilibrium state towards equilibrium. Using a vacuum-trapped nanoparticle, we …
A model describing spin-polarized current via discrete energy levels of a metallic nanoparticle, which has strongly asymmetric tunnel contacts to two ferromagnetic leads, is presented. In absence of spin-relaxation, the model leads to a spin-accumulation in the nanoparticle, a difference ($Δμ$) between the chemical potentials of spin-up and spin-down electrons, proportional to the current and the Julliere's tunnel magnetoresistance. Taking into account an energy dependent spin-relaxation rate $Ω(ω)$, $Δμ$ as a function of bias voltage ($V$) exhibits a crossover from linear to a much weaker dep…
The results of density functional theory calculations and measurements using X-ray photoelectron spectroscopy of Co-nanoparticles dispersed on graphene/Cu are presented. It is found that for low cobalt thickness (0.02 nm - 0.06 nm) the Co forms islands distributed non-homogeneously which are strongly oxidized under exposure to air to form cobalt oxides. At greater thicknesses up to 2 nm the upper Co-layers are similarly oxidized whereas the lower layers contacting the graphene remain metallic. The measurements indicate a Co2+ oxidation state with no evidence of a 3+ state appearing at any Co t…
The numerous phenomenological equations used in the study of the behaviour of single-domain magnetic nanoparticles are described and some issues clarified by means of qualitative comparison. To enable a quantitative \textit{application} of the model based on the Debye (exponential) relaxation and the torque driving the Larmor precession, we present analytical solutions for the steady states in presence of circularly and linearly polarized AC magnetic fields. Using the exact analytical solutions, we can confirm the insight that underlies Rosensweig's introduction of the "chord" susceptibility f…
We report detailed studies on magnetic properties of Co3O4 nanoparticles of average size 12.5 nm. Temperature and field dependence of magnetization, wait time dependence of magnetic relaxation (aging), memory effects and temperature dependence of specific heat have been investigated to understand the magnetic behavior of these particles. We find that the particles show some features characteristic of nanoparticle magnetism such as bifurcation of field cooled (FC) and zero field cooled (ZFC) susceptibilities and a slow relaxation of magnetization. However, strangely, the temperature at which ZF…
Using the two-level approximation of the energy barrier, we perform extensive kinetic Monte Carlo simulations to probe the relaxation characteristics in a two-dimensional ($L^{}_x\times L^{}_y$) array of magnetic nanoparticle as a function of dipolar interaction strength $h^{}_d$, aspect ratio $A^{}_r=L^{}_y/L^{}_x$, and temperature $T$. In the case of weak dipolar interaction ($h^{}_d\approx0$) and substantial temperature, the magnetic relaxation follows the Néel Brown model as expected. Interestingly, the dipolar interaction of enough strength is found to induce antiferromagnetic coupling in…
We study magnetic relaxation dynamics, memory and aging effects in interacting polydisperse antiferromagnetic NiO nanoparticles by solving a master equation using a two-state model. We investigate the effects of interactions using dipolar, Nearest-Neighbour Short-Range (NNSR) and Long-Range Mean-Field (LRMF) interactions. The magnetic relaxation of the nanoparticles in a time-dependent magnetic field has been studied using LRMF interaction. The size-dependent effects are suppressed in the ac-susceptibility, as the frequency is increased. We find that the memory dip, that quantifies the memory …
The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell--Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases of the temperature profile being continuous or having a jump across the solid-liquid interface. The jump conditions are derived from the sharp-interface limit of a phase-field model that accounts for variations in the thermal properties between the solid and liquid. The Stefan problem is solved using asymptotic and numerical methods. The analysis reveals tha…
In this contribution, we will present a review of our works on the time dependence of magnetization in nanoparticle systems starting from non-interacting systems, presenting a general theoretical framework for the analysis of relaxation curves which is based on the so-called $\svar$ scaling method. We will detail the basics and explain its range of validity, showing also its application in experimental measurements of magnetic relaxation. We will also discuss how it can be applied to determine the energy barrier distributions responsible for the relaxation. Next, we will show how the proposed …
We consider the relaxation of an excited two-level system (TLS) positioned near a spherical plasmonic nanoparticle (NP). The transition frequency of the TLS is assumed to coincide with the frequency of the condensation point of NP plasmonic resonances. We show that the relaxation of the TLS excitation is a two-step process. Following an initial exponential decay, the TLS breaks in to Rabi oscillations. Depending upon the distance between the TLS and NP, the probability of the TLS being in the excited state exhibits either chaotic or nearly regular oscillations. In the latter case, the eigenfre…
Quantizing the electromagnetic vacuum and medium fields of two nanoparticles, we investigate the heat transfer between them. One of the particles has been considered to rotate by angular velocity $ ω_0 $. The effect of rotation on the absorbed heat power by the rotating nanoparticle is discussed. The results for angular velocities much smaller than the relaxation frequency $ Γ$ of the dielectrics are in agreement with the static nanoparticles, however increasing the angular velocity $ ω_0 $ in comparison to the relaxation frequency of the dielectrics $ (ω_0\geqslant Γ) $ generates two sideband…
Based on a microscopic approach, we propose a Lagrangian for the combined system of a rotating dielectric nanoparticle above a plane surface in the presence of electromagnetic vacuum fluctuations. In the framework of canonical quantization, the electromagnetic vacuum field is quantized in the presence of dielectric fields describing the nanoparticle and a semi-infinite dielectric with planar interface. The radiative heat power absorbed by the rotating nanoparticle is obtained and the result is in agreement with previous results when the the rotational frequency of the nanoparticle is zero or m…
We report detailed studies on non-equilibrium magnetic behavior of antiferromagnetic Co_3O_4 nanoparticles. Temperature and field dependence of magnetization, wait time dependence of magnetic relaxation (aging), memory effects and temperature dependence of specific heat have been investigated to understand the magnetic behavior of these particles. We find that the system shows some features characteristic of nanoparticle magnetism such as bifurcation of field cooled (FC) and zero field cooled (ZFC) susceptibilities and a slow relaxation of magnetization. However, strangely, the temperature at …
We propose an explanation for the anomalous behaviour observed in the relaxation dynamics of the differential optical transmission of noble-metal nanoparticles. Using the temperature dependences of the position and the width of the surface plasmon resonance, we obtain a strong frequency dependence in the time evolution of the transmission close to the resonance. In particular, our approach accounts for the slowdown found below the plasmon frequency. This interpretation is independent of the presence of a nearby interband transition which has been invoked previously. We therefore argue that the…
Remote sensing of magnetic nanoparticles has exciting applications for magnetic nanoparticle hyperthermia and molecular detection. We introduce, simulate, and experimentally demonstrate an innovation---a sensing coil that is geometrically decoupled from the excitation field---for magnetic nanoparticle spectroscopy that increases the flexibility and capabilities of remote detection. The decoupling enhances the sensitivity absolutely; to small amounts of nanoparticles, and relatively; to small changes in the nanoparticle dynamics. We adapt a previous spectroscopic method that measures the relaxa…
The concept of quantum plasmonic excitations in plasmonic lattices, which similarly to Frenkel excitons in molecular crystals propagate by hopping from one nanoparticle to another, is introduced. A consistent quantum theory of such plasmonic excitons, beginning with the quantization of localized surface plasmons in a metal nanoparticle and including the radiative relaxation in both 1D and 2D lattices near a reflective substrate surface, is developed. A possible room-temperature Bose-Einstein condensation in the quantum gas of plasmonic excitons is also discussed.
Low-dimensional transition metal dichalcogenide, TMDC, materials are heralding a new era in optoelectronics and valleytronics owing to their unique properties. Photo-induced dynamics in these systems has mostly been studied from the perspective of individual quasi-particles, including excitons, bi-excitons or, even, trions. Their formation, evolution and decay. The role of multi-body and exciton dynamics, the associated collective behaviour, condensation and inter-excitonic interactions remain intriguing and seek attention, especially in room-temperature scenarios which are relevant for device…
We study the relaxation characteristics in the two-dimensional ($l^{}_x \times l^{}_y$) array of magnetic nanoparticles (MNPs) as a function of aspect ratio $A^{}_r=l^{}_y/l^{}_x$, dipolar interaction strength $h^{}_d$ and anisotropy axis orientation using computer simulation. The anisotropy axes of all the MNPs are assumed to have the same direction, $α$ being the orientational angle. Irrespective of $α$ and $A^{}_r$, the functional form of the magnetization-decay curve is perfectly exponentially decaying with $h^{}_d\leq0.2$. There exists a transition in relaxation behaviour at $h^{}_d\appro…
We report on the discovery of a unidirectional continuous orbital motion of a single pair of nanoparticles which occurs spontaneously in room-temperature air and can be manipulated by light. By varying the relative position of two nanoparticles, we demonstrate a phase transition between two Brownian particles and a pair of co-orbiting particles. The orbital motion is sensitive to air pressure and is vanishing at low pressure, suggesting that the orbital motion is supported by air. Our results pave the way for manipulating nanoscale objects on the basis of their cooperative dynamics.
We study electron tunneling through Co nanoparticles in the presence of repeated microwave pulses at 4.2K. While individual pulses are too weak to affect the magnetic switching field, repeated microwave pulses start to reduce the magnetic switching field at 10μs spacing. We use I-V curve as a thermometer to show that the microwave pulses do not heat the sample, showing that magnetization in Co nanoparticles is directly excited by microwave pulses, and the relaxation time of the excitation energy is in the range of microsecond.
We comment on some misleading and biased statements appearing in the manuscript arXiv:1209.0298 ("Thermal fluctuations of magnetic nanoparticles") about the use of the damped Landau-Lifshitz equation and the kinetic Langer theory for the calculation of the relaxation rate of magnetic nanoclusters. We reiterate simple scientific arguments, part of which is well known to the whole community, demonstrating that the authors' criticisms are unfounded and that they overstate the issue of damping in the Landau-Lifshitz equation with no unanimous experimental evidence.
We report studies on magnetization dynamics in NiO nanoparticles of average size 5 nm. Temperature and time dependence of dc magnetization, wait time dependence of magnetic relaxation (aging) and memory phenomena in the dc magnetization are studied with various temperature and field protocols. We observe that the system shows memory and aging in field cooled and zero field cooled magnetization measurements. These experiments show that the magnetic behavior of NiO nanoparticles is similar to spin glasses. We argue that the spin glass behavior originates from the freezing of spins at the surface…
The magnetic relaxation characteristics are investigated in the two-dimensional ($l^{}_x\times l^{}_y$) assembly of nanoparticles as a function of out-of-plane positional disorder strength $Δ(\%)$ using numerical simulations. Such defects are redundantly observed in experimentally fabricated nanostructures, resulting in unusual magnetization dynamics. The magnetization decays exponentially for small and negligible dipolar interaction strength $h^{}_d\leq0.2$. In such a case, the magnetization relaxation does not depend on $Δ$ and aspect ratio $A^{}_r=l^{}_y/l^{}_x$, as expected. In square-like…
Spin-polarized current through an Al nanoparticle in tunnel contact with two ferromagnets is measured as a function of the direction of the applied magnetic field. The nanoparticle filters the spin of injected electrons along a direction specified by the magnetic field. The characteristic field scale for the filtering corresponds to a lower limit of $8ns$ for the spin-dephasing time. Spin polarized current versus applied voltage increases stepwise, confirming that the spin relaxation time is long only in the ground state and the low-lying excited states of the nanoparticle.
To study the magnetic dynamics of superparamagnetic nanoparticles we use scanning probe relaxometry and dephasing of the nitrogen-vacancy (NV) center in diamond, characterizing the spin-noise of a single 10-nm magnetite particle. Additionally, we show the anisotropy of the NV sensitivity's dependence on the applied decoherence measurement method. By comparing the change in relaxation (T 1 ) and dephasing (T 2 ) time in the NV center when scanning a nanoparticle over it, we are able to extract the nanoparticle's diameter and distance from the NV center using an Ornstein-Uhlenbeck model for the …
Nanomaterials based on MoS2 are remarkably versatile; MoS2 nanoparticles are proven catalysts for processes such as hydrodesulphurization and the hydrogen evolution reaction, and transition metal dichalcogenides in general have recently emerged as novel 2D components for nanoscale electronics and optoelectronics. The properties of such materials are intimately related to their structure and dimensionality. For example, only the edges exposed by MoS2 nanoparticles (NPs) are catalytically active, and extended MoS2 systems show different character (direct or indirect gap semiconducting, or metall…
A set of equations describing the motion of a free magnetic nanoparticle in an external magnetic field in a vacuum, or in a medium with negligibly small friction forces is postulated. The conservation of the total particle momentum, i.e. the sum of the mechanical and the total spin momentum of the nanoparticle is taken into account explicitly. It is shown that for the motion of a nanoparticle in uniform magnetic field there are three different modes of precession of the unit magnetization vector and the director that is parallel the particle easy anisotropy axis. These modes differ significant…
Magnetic nanoparticle hyperthermia is an attractive emerging cancer treatment, but the acting microscopic energy deposition mechanisms are not well understood and optimization suffers. We describe several approximate forms for the characteristic time of Néel rotations with varying properties and external influences. We then present stochastic simulations that show agreement between the approximate expressions and the micromagnetic model. The simulations show nonlinear imaginary responses and associated relaxational hysteresis due to the field and frequency dependencies of the magnetization. Th…
In magnetic nanoparticle systems, the variation of the blocking temperature $T_B$ with the measuring frequency $f_m$ is often used to determine the strength of the interparticle interactions (IPI) through a parameter $Φ$ or the Vogel-Fulcher temperature $T_o$. Presence of IPI is inferred if $T_o$$>$0 and $Φ=$$Δ$$T_B$$/$$[T_BΔ$$log_{10}$$f_m]<$0.13 where $Δ$ signifies changes in $T_B$ and $f_m$. Here it is shown that these two parameters are related by the Eq. $Φ=$$Φ_o$$\approx$ 0.11 to 0.15 is a constant of the system depending on the magnitudes of measuring frequency and $Φ=$$Φ_o$$[1-T_o/T_B]…
We perform molecular dynamics (MD) simulations with phonon spectral analysis aiming at understanding the two dimensional (2D) thermal transport in suspended and supported graphene. Within the framework of equilibrium MD simulations, we perform spectral energy density (SED) analysis to obtain the lifetime of individual phonon modes. The per-mode contribution to thermal conductivity is then calculated to obtain the lattice thermal conductivity in the temperature range 300-650 K. In contrast to prior studies, our results suggest that the contribution from out-of-plane acoustic (or ZA) branch to t…
We report magnetic studies on gelatin coated NiO nanoparticles of average size 7 nm. Temperature and time dependence of dc magnetization, wait time dependence of magnetic relaxation (aging), memory effects in the dc magnetization and frequency dependence of ac susceptibility have been investigated. We observe that the magnetic behavior of coated NiO nanoparticles differs substantially from that of bare nanoparticles. The magnetic moment of the particles is highly enhanced and the ZFC magnetization data displays a sharp peak (Tp1 = 15 K) at a low temperature in addition to a usual high temperat…
We describe the synthesis, materials characterization and dynamic nuclear polarization (DNP) of amorphous and crystalline silicon nanoparticles for use as hyperpolarized magnetic resonance imaging (MRI) agents. The particles were synthesized by means of a metathesis reaction between sodium silicide (Na4Si4) and silicon tetrachloride (SiCl4) and were surface functionalized with a variety of passivating ligands. The synthesis scheme results in particles of diameter ~10 nm with long size-adjusted 29Si spin lattice relaxation (T1) times (> 600 s), which are retained after hyperpolarization by low …
The interaction of mass-selected atomic clusters and nanoparticles with surfaces attracts strong interest in view of fundamental research and technological applications. Understanding dynamics of the deposition process is important for controlling structure and functioning of deposited nanoparticles on a substrate, but experimental techniques can usually observe only the final outcome of the deposition process. In this paper, the deposition of 4 nm-sized sodium nanoparticles on an experimentally relevant magnesium oxide substrate is studied by means of classical molecular dynamics simulations.…
119Sn nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rate (1/T1) in SnO2 nanoparticles were measured as a function of temperature and compared with those of SnO2 bulk sample. A 15% loss of 119Sn NMR signal intensity for the nano sample compared to the bulk sample was observed. This is indicative of ferromagnetism from a small fraction of the sample. Another major finding is that the recovery of the 119Sn longitudinal nuclear magnetization in the nano sample follows a stretched exponential behavior, as opposed to that in bulk which is exponential. Further, the 119Sn 1/T1 a…
