Slow Dynamics

In this paper we investigate the superspin glass behavior of a concentrated assembly of interacting maghemite nanoparticles and compare it to that of canonical atomic spin glass systems. ac versus temperature and frequency measurements show evidence of a superspin glass transition taking place at low temperature. In order to fully characterize the superspin glass phase, the aging behavior of both the thermo-remanent magnetization (TRM) and ac susceptibility has been investigated. It is shown that the scaling laws obeyed by superspin glasses and atomic spin glasses are essentially the same, after subtraction of a superparamagnetic contribution from the superspin glass response functions. Finally, we discuss a possible origin of this superparamagnetic contribution in terms of dilute spin glass models.

We use Photon Correlation Imaging, a recently introduced space-resolved dynamic light scattering method, to investigate the spatial correlation of the dynamics of a variety of jammed and glassy soft materials. Strikingly, we find that in deeply jammed soft materials spatial correlations of the dynamics are quite generally ultra-long ranged, extending up to the system size, orders of magnitude larger than any relevant structural length scale, such as the particle size, or the mesh size for colloidal gel systems. This has to be contrasted with the case of molecular, colloidal and granular "supercooled" fluids, where spatial correlations of the dynamics extend over a few particles at most. Our findings suggest that ultra long range spatial correlations in the dynamics of a system are directly related to the origin of elasticity. While solid-like systems with entropic elasticity exhibit very moderate correlations, systems with enthalpic elasticity exhibit ultra-long range correlations due to the effective transmission of strains throughout the contact network.

Today the most studied magnetic materials are the magnetic materials based on the nanoparticles in solid or liquid matrix. The knowledge of the ferrite nanoparticles in high frequency magnetic fields insures the possibility to know the behavior of the magnetic materials based on nanoparticles. The nanocomposites based on ferrite nanoparticles and polymer dielectric matrix can replace successfully the usual high frequency ferrites. This work proposes a study by simulation of the ferrite nanoparticles behavior in high frequency magnetic fields.

The binding of [2,2 0-bipyridyl]-3,3 0-diol (BP(OH) 2) with ionic and n eutral surfactants like cetyltrimethylammonium bromide (CTAB), sodium dodecyl sulfate (SDS), and Triton X-100 (TX-100) has been studied by steady-state and timeresolved fluorescence spectroscopy. The absorption as well as emission spectra of BP(OH) 2 are highly sensitive toward the variation of surfactant concentration and hydrophobicity of the environment. The fluorescent state of the diketo form gains stability in surfactant assemblies, leading to a red-shifted emission spectra. A sharp increase in the fluorescence quantum yield near critical micellar concentration (CMC) is encountered followed by saturation. This indicates a complete encapsulation of BP(OH) 2 in the micelles. The maximum fluorescence quantum yield in anionic SDS is rationalized by the formation of cationic fluorophore at the Stern layer. The increase in quantum yield in neutral TX-100 is attributed to higher microviscosity experienced by the fluorophore in the palisade layer. A direct support in favor of this argument in TX-100 is provided by the viscosity dependence exhibited by the probe in different concentrations of sucrose solutions. CTAB exhibiting only hydrophobic effect shows least increase in qunatum yield of BP(OH) 2 among all the surfactants. Time-resolved fluorescence study of BP(OH) 2 in micelles is used as a tool to monitor the extent of micellization in the lipophilic cavity. An increase in fluorescence quantum yield as well as lifetime of BP(OH) 2 upon micellization indicates an enhanced extent of ESIDPT in hydrophobic medium.

The dynamic properties of nanoparticles suspended in a supercooled glass forming liquid are studied by x-ray photon correlation spectroscopy. While at high temperatures the particles undergo Brownian motion the measurements closer to the glass transition indicate hyperdiffusive behavior. In this state the dynamics is independent of the local structural arrangement of nanoparticles, suggesting a cooperative behavior governed by the near-vitreous solvent.

The relaxation behavior of spin glasses has been analyzed in the framework of the critical fractal-cluster model. It is found that the relaxation rate of the magnetization can be expressed as 8m/81nt «t st'"exp[-(t/zt)~~1'"], where /J, b,z, v are standard static and dynamic critical exponents and i~i s the relaxation time of a characteristic cluster which diverges at the spin-glass freezing temperature T. The expression is valid through T~a nd is found to describe excellently the fundamental features of the relaxation in real spin glasses.

We use Photon Correlation Imaging, a recently introduced space-resolved dynamic light scattering method, to investigate the spatial correlation of the dynamics of a variety of jammed and glassy soft materials. Strikingly, we find that in deeply jammed soft materials spatial correlations of the dynamics are quite generally ultra-long ranged, extending up to the system size, orders of magnitude larger than any relevant structural length scale, such as the particle size, or the mesh size for colloidal gel systems. This has to be contrasted with the case of molecular, colloidal and granular "supercooled" fluids, where spatial correlations of the dynamics extend over a few particles at most. Our findings suggest that ultra long range spatial correlations in the dynamics of a system are directly related to the origin of elasticity. While solid-like systems with entropic elasticity exhibit very moderate correlations, systems with enthalpic elasticity exhibit ultra-long range correlations due to the effective transmission of strains throughout the contact network.

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 effect is about the same as that of non-interacting nanoparticles for the NNSR case. There is a stronger memory-dip for LRMF, and a weaker memory-dip for the dipolar interactions. We have also shown a memory effect in the Zero-field-cooled magnetization for the dipolar case, a signature of glassy behaviour, from Monte-Carlo studies.

In this work we present a new method to calculate the classical magnetic properties of singledomain nanoparticles. Based on the Bethe-Peierls (pair) approximation, we developed a simple system of equations for the classical magnetization of spins at any position within the nanoparticle. Nearest neighbor pair correlations are treated exactly for Ising spins, and the method can be generalized for various lattice symmetries. The master equation is solved for the Glauber dynamics (single-spin-flip) in order to obtain the time evolution of the magnetization. The capabilities of the model are demonstrated through nontrivial calculations of hysteresis loops as well as field cooling (FC) and zero field cooling (ZFC) magnetization curves of heterogeneous non-interacting nanoparticles. The present method automatically incorporates the temperature and could be adapted to describe an ensemble of interacting nanoparticles.

In this work we present a new method to calculate the classical magnetic properties of singledomain nanoparticles. Based on the Bethe-Peierls (pair) approximation, we developed a simple system of equations for the classical magnetization of spins at any position within the nanoparticle. Nearest neighbor pair correlations are treated exactly for Ising spins, and the method can be generalized for various lattice symmetries. The master equation is solved for the Glauber dynamics (single-spin-flip) in order to obtain the time evolution of the magnetization. The capabilities of the model are demonstrated through nontrivial calculations of hysteresis loops as well as field cooling (FC) and zero field cooling (ZFC) magnetization curves of heterogeneous non-interacting nanoparticles. The present method automatically incorporates the temperature and could be adapted to describe an ensemble of interacting nanoparticles.

Extending the framework for multiferroic materials, in which long-range electric and magnetic orderings coexist, we present a novel 'multiglass' concept, where two different glassy states occur simultaneously. It applies to Sr 0.98 Mn 0.02 TiO 3 ceramics, where the Mn 2+ dopant ions are at the origin of both polar and spin glasses. Spin freezing is initiated at the dipolar glass temperature, T g ≈ 38 K. Below T g , both glass phases are independently verified by memory and rejuvenation effects. Strong biquadratic interaction of the Mn 2+ spins with the optic soft mode of the incipient ferroelectric host crystal SrTiO 3 explains the high spin glass temperature and comparably strong higher order magnetoelectric coupling between the polar and magnetic degrees of freedom.

Magnetic nanoparticles are single-domain particles of ferromagnetic or ferrite materials. Recently, magnetic nanoparticles have been applied more and more in technology, such as spintronics, magnetic recording, catalyst, and biomedicine. Therefore, experimental and theoretical studies on their magnetic properties are very important to provide essential information for individual applications. In addition, technical preparations have been developed fast, such as chemical synthesis, sputtering, or lithography. Depending on characters of assemblies, magnetic properties are different, such as two-or three-dimension, metallic or metallic oxide materials, order or disorder arrangement, surrounded by solids (granular solids) or liquids (ferrolfuids), and the magnetic or non-magnetic surrounding matrix. This leads to studying fundamental properties of magnetic nanoparticle assemblies becomes interesting. Among applicable potentials of magnetic nanoparticles, the biomedicine is a promising area, because the magnetic nanoparticles offer some great possibilities (Pankhurst et al., 2003). First, their size ranges from a few nanometers up to tens of nanometers. This means that their size can be smaller than of comparable to the size of biological entities, for example, a cell (10-100 μm), a virus (20-450 nm), a protein (5-50 nm) or a gene (2 nm wide and 10-100 nm long). Thus, they can penetrate easily into these entities. Second, these particles behave magnetic properties, so they can be controlled by an external magnetic field gradient. This opens application including the transport (drug delivery, cell separation) or immobilization (hyperthermia, contrast agent). Third, these particles can strongly resonate to a radio field. This makes them be easily excited by radio field leading, for example, heating in hyperthermia or magnetic resonance in contrast agent. A key quality to study magnetic properties of particle is magnetic anisotropy energy (MAE). However, it is very difficult to exactly observe the MAE of each particle in the assembly. We can just obtain the MAE distribution of the assembly. Usually, the MAE distribution f(E B) is deduced from the size distribution f(V) due to simplest expression of MAE, E B = KV, with K and V as anisotropy constant and volume, respectively, of each particle. However, this way does not describe the exact information of real systems. It is due to some reasons as follow. (i) The size distribution obtains from microscopy images may not coincide with the real sample. (ii) The magnetic anisotropy involves many complexities, such as surface, magnetowww.intechopen.com Applications of Monte Carlo Method in Science and Engineering 496 crystal, or shape. (iii) The orientation of anisotropy axis of particles in the assemblies is random, thus this way can not give the precise response between the size and the energy barrier distribution. A recent review written by Zheng et al. (Zheng et al., 2009) showed that there are some different ways to extract the anisotropy distribution, however, for the dilute sample. The problem becomes much more complex as the inter-particle interactions arise, namely dipolar interaction (for example, Bottoni et al., 1993; Ceylan et al, 2005; Parker et al., 2008) exchange interaction due to the contact between surface of particles or the magnetic surrounding matrix (for recent example, Tamion et al., 2010; Malik et al., 2010). However, the numerical analyses or phenomenal theory has not provided sufficient explanations for the observations of experiments. Therefore, computer simulations, especially Monte Carlo simulation, become efficient. Now, to clearly see the successes of the Monte Carlo (MC) simulation of magnetic nanoparticle assemblies, we will shortly list some the important results. Kechrakos & Trohidou (Kechrakos & Trohidou, 1998) employed the MC simulation to give a general view about the interacting assemblies. Following these results, interacting assemblies possesses the anti-ferromagnetic state (decrease of magnetic responses) and ferromagnetic state (increase of magnetic responses) at low and high temperature, respectively. At the same time, MC method was used to seek the spin-glass (SG) like behavior of interacting systems at the low temperature. While almost results show the SG like behavior (for example,

Magnetic nanoparticles are single-domain particles of ferromagnetic or ferrite materials. Recently, magnetic nanoparticles have been applied more and more in technology, such as spintronics, magnetic recording, catalyst, and biomedicine. Therefore, experimental and theoretical studies on their magnetic properties are very important to provide essential information for individual applications. In addition, technical preparations have been developed fast, such as chemical synthesis, sputtering, or lithography. Depending on characters of assemblies, magnetic properties are different, such as two-or three-dimension, metallic or metallic oxide materials, order or disorder arrangement, surrounded by solids (granular solids) or liquids (ferrolfuids), and the magnetic or non-magnetic surrounding matrix. This leads to studying fundamental properties of magnetic nanoparticle assemblies becomes interesting. Among applicable potentials of magnetic nanoparticles, the biomedicine is a promising area, because the magnetic nanoparticles offer some great possibilities (Pankhurst et al., 2003). First, their size ranges from a few nanometers up to tens of nanometers. This means that their size can be smaller than of comparable to the size of biological entities, for example, a cell (10-100 μm), a virus (20-450 nm), a protein (5-50 nm) or a gene (2 nm wide and 10-100 nm long). Thus, they can penetrate easily into these entities. Second, these particles behave magnetic properties, so they can be controlled by an external magnetic field gradient. This opens application including the transport (drug delivery, cell separation) or immobilization (hyperthermia, contrast agent). Third, these particles can strongly resonate to a radio field. This makes them be easily excited by radio field leading, for example, heating in hyperthermia or magnetic resonance in contrast agent. A key quality to study magnetic properties of particle is magnetic anisotropy energy (MAE). However, it is very difficult to exactly observe the MAE of each particle in the assembly. We can just obtain the MAE distribution of the assembly. Usually, the MAE distribution f(E B) is deduced from the size distribution f(V) due to simplest expression of MAE, E B = KV, with K and V as anisotropy constant and volume, respectively, of each particle. However, this way does not describe the exact information of real systems. It is due to some reasons as follow. (i) The size distribution obtains from microscopy images may not coincide with the real sample. (ii) The magnetic anisotropy involves many complexities, such as surface, magnetowww.intechopen.com Applications of Monte Carlo Method in Science and Engineering 496 crystal, or shape. (iii) The orientation of anisotropy axis of particles in the assemblies is random, thus this way can not give the precise response between the size and the energy barrier distribution. A recent review written by Zheng et al. (Zheng et al., 2009) showed that there are some different ways to extract the anisotropy distribution, however, for the dilute sample. The problem becomes much more complex as the inter-particle interactions arise, namely dipolar interaction (for example, Bottoni et al., 1993; Ceylan et al, 2005; Parker et al., 2008) exchange interaction due to the contact between surface of particles or the magnetic surrounding matrix (for recent example, Tamion et al., 2010; Malik et al., 2010). However, the numerical analyses or phenomenal theory has not provided sufficient explanations for the observations of experiments. Therefore, computer simulations, especially Monte Carlo simulation, become efficient. Now, to clearly see the successes of the Monte Carlo (MC) simulation of magnetic nanoparticle assemblies, we will shortly list some the important results. Kechrakos & Trohidou (Kechrakos & Trohidou, 1998) employed the MC simulation to give a general view about the interacting assemblies. Following these results, interacting assemblies possesses the anti-ferromagnetic state (decrease of magnetic responses) and ferromagnetic state (increase of magnetic responses) at low and high temperature, respectively. At the same time, MC method was used to seek the spin-glass (SG) like behavior of interacting systems at the low temperature. While almost results show the SG like behavior (for example,

Magnetic nanoparticles are single-domain particles of ferromagnetic or ferrite materials. Recently, magnetic nanoparticles have been applied more and more in technology, such as spintronics, magnetic recording, catalyst, and biomedicine. Therefore, experimental and theoretical studies on their magnetic properties are very important to provide essential information for individual applications. In addition, technical preparations have been developed fast, such as chemical synthesis, sputtering, or lithography. Depending on characters of assemblies, magnetic properties are different, such as two-or three-dimension, metallic or metallic oxide materials, order or disorder arrangement, surrounded by solids (granular solids) or liquids (ferrolfuids), and the magnetic or non-magnetic surrounding matrix. This leads to studying fundamental properties of magnetic nanoparticle assemblies becomes interesting. Among applicable potentials of magnetic nanoparticles, the biomedicine is a promising area, because the magnetic nanoparticles offer some great possibilities (Pankhurst et al., 2003). First, their size ranges from a few nanometers up to tens of nanometers. This means that their size can be smaller than of comparable to the size of biological entities, for example, a cell (10-100 μm), a virus (20-450 nm), a protein (5-50 nm) or a gene (2 nm wide and 10-100 nm long). Thus, they can penetrate easily into these entities. Second, these particles behave magnetic properties, so they can be controlled by an external magnetic field gradient. This opens application including the transport (drug delivery, cell separation) or immobilization (hyperthermia, contrast agent). Third, these particles can strongly resonate to a radio field. This makes them be easily excited by radio field leading, for example, heating in hyperthermia or magnetic resonance in contrast agent. A key quality to study magnetic properties of particle is magnetic anisotropy energy (MAE). However, it is very difficult to exactly observe the MAE of each particle in the assembly. We can just obtain the MAE distribution of the assembly. Usually, the MAE distribution f(E B) is deduced from the size distribution f(V) due to simplest expression of MAE, E B = KV, with K and V as anisotropy constant and volume, respectively, of each particle. However, this way does not describe the exact information of real systems. It is due to some reasons as follow. (i) The size distribution obtains from microscopy images may not coincide with the real sample. (ii) The magnetic anisotropy involves many complexities, such as surface, magnetowww.intechopen.com Applications of Monte Carlo Method in Science and Engineering 496 crystal, or shape. (iii) The orientation of anisotropy axis of particles in the assemblies is random, thus this way can not give the precise response between the size and the energy barrier distribution. A recent review written by Zheng et al. (Zheng et al., 2009) showed that there are some different ways to extract the anisotropy distribution, however, for the dilute sample. The problem becomes much more complex as the inter-particle interactions arise, namely dipolar interaction (for example, Bottoni et al., 1993; Ceylan et al, 2005; Parker et al., 2008) exchange interaction due to the contact between surface of particles or the magnetic surrounding matrix (for recent example, Tamion et al., 2010; Malik et al., 2010). However, the numerical analyses or phenomenal theory has not provided sufficient explanations for the observations of experiments. Therefore, computer simulations, especially Monte Carlo simulation, become efficient. Now, to clearly see the successes of the Monte Carlo (MC) simulation of magnetic nanoparticle assemblies, we will shortly list some the important results. Kechrakos & Trohidou (Kechrakos & Trohidou, 1998) employed the MC simulation to give a general view about the interacting assemblies. Following these results, interacting assemblies possesses the anti-ferromagnetic state (decrease of magnetic responses) and ferromagnetic state (increase of magnetic responses) at low and high temperature, respectively. At the same time, MC method was used to seek the spin-glass (SG) like behavior of interacting systems at the low temperature. While almost results show the SG like behavior (for example,

Magnetic nanoparticles are single-domain particles of ferromagnetic or ferrite materials. Recently, magnetic nanoparticles have been applied more and more in technology, such as spintronics, magnetic recording, catalyst, and biomedicine. Therefore, experimental and theoretical studies on their magnetic properties are very important to provide essential information for individual applications. In addition, technical preparations have been developed fast, such as chemical synthesis, sputtering, or lithography. Depending on characters of assemblies, magnetic properties are different, such as two-or three-dimension, metallic or metallic oxide materials, order or disorder arrangement, surrounded by solids (granular solids) or liquids (ferrolfuids), and the magnetic or non-magnetic surrounding matrix. This leads to studying fundamental properties of magnetic nanoparticle assemblies becomes interesting. Among applicable potentials of magnetic nanoparticles, the biomedicine is a promising area, because the magnetic nanoparticles offer some great possibilities (Pankhurst et al., 2003). First, their size ranges from a few nanometers up to tens of nanometers. This means that their size can be smaller than of comparable to the size of biological entities, for example, a cell (10-100 μm), a virus (20-450 nm), a protein (5-50 nm) or a gene (2 nm wide and 10-100 nm long). Thus, they can penetrate easily into these entities. Second, these particles behave magnetic properties, so they can be controlled by an external magnetic field gradient. This opens application including the transport (drug delivery, cell separation) or immobilization (hyperthermia, contrast agent). Third, these particles can strongly resonate to a radio field. This makes them be easily excited by radio field leading, for example, heating in hyperthermia or magnetic resonance in contrast agent. A key quality to study magnetic properties of particle is magnetic anisotropy energy (MAE). However, it is very difficult to exactly observe the MAE of each particle in the assembly. We can just obtain the MAE distribution of the assembly. Usually, the MAE distribution f(E B) is deduced from the size distribution f(V) due to simplest expression of MAE, E B = KV, with K and V as anisotropy constant and volume, respectively, of each particle. However, this way does not describe the exact information of real systems. It is due to some reasons as follow. (i) The size distribution obtains from microscopy images may not coincide with the real sample. (ii) The magnetic anisotropy involves many complexities, such as surface, magnetowww.intechopen.com Applications of Monte Carlo Method in Science and Engineering 496 crystal, or shape. (iii) The orientation of anisotropy axis of particles in the assemblies is random, thus this way can not give the precise response between the size and the energy barrier distribution. A recent review written by Zheng et al. (Zheng et al., 2009) showed that there are some different ways to extract the anisotropy distribution, however, for the dilute sample. The problem becomes much more complex as the inter-particle interactions arise, namely dipolar interaction (for example, Bottoni et al., 1993; Ceylan et al, 2005; Parker et al., 2008) exchange interaction due to the contact between surface of particles or the magnetic surrounding matrix (for recent example, Tamion et al., 2010; Malik et al., 2010). However, the numerical analyses or phenomenal theory has not provided sufficient explanations for the observations of experiments. Therefore, computer simulations, especially Monte Carlo simulation, become efficient. Now, to clearly see the successes of the Monte Carlo (MC) simulation of magnetic nanoparticle assemblies, we will shortly list some the important results. Kechrakos & Trohidou (Kechrakos & Trohidou, 1998) employed the MC simulation to give a general view about the interacting assemblies. Following these results, interacting assemblies possesses the anti-ferromagnetic state (decrease of magnetic responses) and ferromagnetic state (increase of magnetic responses) at low and high temperature, respectively. At the same time, MC method was used to seek the spin-glass (SG) like behavior of interacting systems at the low temperature. While almost results show the SG like behavior (for example,

Magnetic nanoparticles are single-domain particles of ferromagnetic or ferrite materials. Recently, magnetic nanoparticles have been applied more and more in technology, such as spintronics, magnetic recording, catalyst, and biomedicine. Therefore, experimental and theoretical studies on their magnetic properties are very important to provide essential information for individual applications. In addition, technical preparations have been developed fast, such as chemical synthesis, sputtering, or lithography. Depending on characters of assemblies, magnetic properties are different, such as two-or three-dimension, metallic or metallic oxide materials, order or disorder arrangement, surrounded by solids (granular solids) or liquids (ferrolfuids), and the magnetic or non-magnetic surrounding matrix. This leads to studying fundamental properties of magnetic nanoparticle assemblies becomes interesting. Among applicable potentials of magnetic nanoparticles, the biomedicine is a promising area, because the magnetic nanoparticles offer some great possibilities (Pankhurst et al., 2003). First, their size ranges from a few nanometers up to tens of nanometers. This means that their size can be smaller than of comparable to the size of biological entities, for example, a cell (10-100 μm), a virus (20-450 nm), a protein (5-50 nm) or a gene (2 nm wide and 10-100 nm long). Thus, they can penetrate easily into these entities. Second, these particles behave magnetic properties, so they can be controlled by an external magnetic field gradient. This opens application including the transport (drug delivery, cell separation) or immobilization (hyperthermia, contrast agent). Third, these particles can strongly resonate to a radio field. This makes them be easily excited by radio field leading, for example, heating in hyperthermia or magnetic resonance in contrast agent. A key quality to study magnetic properties of particle is magnetic anisotropy energy (MAE). However, it is very difficult to exactly observe the MAE of each particle in the assembly. We can just obtain the MAE distribution of the assembly. Usually, the MAE distribution f(E B) is deduced from the size distribution f(V) due to simplest expression of MAE, E B = KV, with K and V as anisotropy constant and volume, respectively, of each particle. However, this way does not describe the exact information of real systems. It is due to some reasons as follow. (i) The size distribution obtains from microscopy images may not coincide with the real sample. (ii) The magnetic anisotropy involves many complexities, such as surface, magnetowww.intechopen.com Applications of Monte Carlo Method in Science and Engineering 496 crystal, or shape. (iii) The orientation of anisotropy axis of particles in the assemblies is random, thus this way can not give the precise response between the size and the energy barrier distribution. A recent review written by Zheng et al. (Zheng et al., 2009) showed that there are some different ways to extract the anisotropy distribution, however, for the dilute sample. The problem becomes much more complex as the inter-particle interactions arise, namely dipolar interaction (for example, Bottoni et al., 1993; Ceylan et al, 2005; Parker et al., 2008) exchange interaction due to the contact between surface of particles or the magnetic surrounding matrix (for recent example, Tamion et al., 2010; Malik et al., 2010). However, the numerical analyses or phenomenal theory has not provided sufficient explanations for the observations of experiments. Therefore, computer simulations, especially Monte Carlo simulation, become efficient. Now, to clearly see the successes of the Monte Carlo (MC) simulation of magnetic nanoparticle assemblies, we will shortly list some the important results. Kechrakos & Trohidou (Kechrakos & Trohidou, 1998) employed the MC simulation to give a general view about the interacting assemblies. Following these results, interacting assemblies possesses the anti-ferromagnetic state (decrease of magnetic responses) and ferromagnetic state (increase of magnetic responses) at low and high temperature, respectively. At the same time, MC method was used to seek the spin-glass (SG) like behavior of interacting systems at the low temperature. While almost results show the SG like behavior (for example,

The finite size and surface roughness effects on the magnetization of NiO nanoparticles is investigated. A large magnetic moment arises for an antiferromagnetic nanoparticle due to these effects. The magnetic moment without the surface roughness has a non-monotonic and oscillatory dependence on $R$, the size of the particles, with the amplitude of the fluctuations varying linearly with $R$. The geometry of the particle also matters a lot in the calculation of the net magnetic moment. An oblate spheroid shape particle shows an increase in net magnetic moment by increasing oblateness of the particle. However, the magnetic moment values thus calculated are very small compared to the experimental values for various sizes, indicating that the bulk antiferromagnetic structure may not hold near the surface. We incorporate the surface roughness in two different ways; an ordered surface with surface spins inside a surface roughness shell aligned due to an internal field, and a disordered sur...

We measure the field dependence of spin glass free energy barriers in a thin amorphous Ge:Mn film through the time dependence of the magnetization. After the correlation length ξ(t, T) has reached the film thickness L = 155Å so that the dynamics are activated, we change the initial magnetic field by δH. In agreement with the scaling behavior exhibited in a companion Letter, we find the activation energy is increased when δH < 0. The change is proportional to (δH) 2 with the addition of a small (δH) 4 term. The magnitude of the change of the spin glass free energy barriers is in near quantitative agreement with the prediction of a barrier model.

We probe the effects of different initial conditions on the process of aging in spin glasses arising from alternative temperature quenching protocols for the canonical and representative Cu:Mn (6 at.%) dilute magnetic alloy. The effects of these changes are observed through the decay of the thermoremanent magnetization, M TRM (t). We find significant changes in the initial state as a consequence of the different cooling processes, reflected through an effective waiting time, t eff w. The effective waiting time shortens as the time spent above the measuring temperature in the cooling protocol is reduced, reaching a minimum when the temperature is not allowed to rise above the final measurement temperature after the initial quench. This behavior is consistent with the picture of a rapid temperature dependence of the barrier heights separating metastable states.

Discontinuous magnetic multilayers [Co 80 Fe 20 (t)/Al 2 O 3 (3nm)] 10 with t = 0.9 and 1.0nm are studied by SQUID magnetometry and ac susceptibility. Owing to dipolar interaction the superparamagnetic cluster systems undergo collective glass-like freezing upon cooling. While both samples exhibit very similar glass temperatures T g ≈ 45 K and critical exponents zν ≈ 10 and γ ≈ 1.4 as obtained from the temperature dependencies of the relaxation time, τ, and the nonlinear susceptibility, χ 3 , dynamical scaling reveals different critical exponents, β(0.9nm) ≈1.0 and β(1.0nm) ≈ 0.6, respectively.

Aging dynamics of a reentrant ferromagnet stage-2 Cu0.8Co0.2Cl2 graphite intercalation compound has been studied using DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures Tc (≈ 8.7 K) and TRSG (≈ 3.3 K). The relaxation rate SZF C (t) exhibits a characteristic peak at tcr below Tc. The peak time tcr as a function of temperature T shows a local maximum around 5.5 K, reflecting a frustrated nature of the ferromagnetic phase. It drastically increases with decreasing temperature below TRSG. The spin configuration imprinted at the stop and wait process at a stop temperature Ts (< Tc) during the field-cooled aging protocol, becomes frozen on further cooling. On reheating, the memory of the aging at Ts is retrieved as an anomaly of the thermoremnant magnetization at Ts. These results indicate the occurrence of the aging phenomena in the ferromagnetic phase (TRSG < T < Tc) as well as in the reentrant spin glass phase (T < TRSG).

Using Monte Carlo techniques, we show that the recently experimentally observed transitionlike phenomena in the transverse spin-ordering close to the anomalies in the antiferromagnetic phase of FeBr2 (Petracic et al. [Phys. Rev. B 57, R11051 (1998)]) may result from the quantum nature of the S=1 spins and an off-diagonal exchange between axial and planar spin components.

Magnetic nanoparticles are single-domain particles of ferromagnetic or ferrite materials. Recently, magnetic nanoparticles have been applied more and more in technology, such as spintronics, magnetic recording, catalyst, and biomedicine. Therefore, experimental and theoretical studies on their magnetic properties are very important to provide essential information for individual applications. In addition, technical preparations have been developed fast, such as chemical synthesis, sputtering, or lithography. Depending on characters of assemblies, magnetic properties are different, such as two-or three-dimension, metallic or metallic oxide materials, order or disorder arrangement, surrounded by solids (granular solids) or liquids (ferrolfuids), and the magnetic or non-magnetic surrounding matrix. This leads to studying fundamental properties of magnetic nanoparticle assemblies becomes interesting. Among applicable potentials of magnetic nanoparticles, the biomedicine is a promising area, because the magnetic nanoparticles offer some great possibilities (Pankhurst et al., 2003). First, their size ranges from a few nanometers up to tens of nanometers. This means that their size can be smaller than of comparable to the size of biological entities, for example, a cell (10-100 μm), a virus (20-450 nm), a protein (5-50 nm) or a gene (2 nm wide and 10-100 nm long). Thus, they can penetrate easily into these entities. Second, these particles behave magnetic properties, so they can be controlled by an external magnetic field gradient. This opens application including the transport (drug delivery, cell separation) or immobilization (hyperthermia, contrast agent). Third, these particles can strongly resonate to a radio field. This makes them be easily excited by radio field leading, for example, heating in hyperthermia or magnetic resonance in contrast agent. A key quality to study magnetic properties of particle is magnetic anisotropy energy (MAE). However, it is very difficult to exactly observe the MAE of each particle in the assembly. We can just obtain the MAE distribution of the assembly. Usually, the MAE distribution f(E B) is deduced from the size distribution f(V) due to simplest expression of MAE, E B = KV, with K and V as anisotropy constant and volume, respectively, of each particle. However, this way does not describe the exact information of real systems. It is due to some reasons as follow. (i) The size distribution obtains from microscopy images may not coincide with the real sample. (ii) The magnetic anisotropy involves many complexities, such as surface, magnetowww.intechopen.com Applications of Monte Carlo Method in Science and Engineering 496 crystal, or shape. (iii) The orientation of anisotropy axis of particles in the assemblies is random, thus this way can not give the precise response between the size and the energy barrier distribution. A recent review written by Zheng et al. (Zheng et al., 2009) showed that there are some different ways to extract the anisotropy distribution, however, for the dilute sample. The problem becomes much more complex as the inter-particle interactions arise, namely dipolar interaction (for example, Bottoni et al., 1993; Ceylan et al, 2005; Parker et al., 2008) exchange interaction due to the contact between surface of particles or the magnetic surrounding matrix (for recent example, Tamion et al., 2010; Malik et al., 2010). However, the numerical analyses or phenomenal theory has not provided sufficient explanations for the observations of experiments. Therefore, computer simulations, especially Monte Carlo simulation, become efficient. Now, to clearly see the successes of the Monte Carlo (MC) simulation of magnetic nanoparticle assemblies, we will shortly list some the important results. Kechrakos & Trohidou (Kechrakos & Trohidou, 1998) employed the MC simulation to give a general view about the interacting assemblies. Following these results, interacting assemblies possesses the anti-ferromagnetic state (decrease of magnetic responses) and ferromagnetic state (increase of magnetic responses) at low and high temperature, respectively. At the same time, MC method was used to seek the spin-glass (SG) like behavior of interacting systems at the low temperature. While almost results show the SG like behavior (for example,

Using a series of fast cooling protocols we have probed aging effects in the spin glass state as a function of temperature. Analyzing the logarithmic decay found at very long time scales within a simple phenomenological barrier model, leads to the extraction of the fluctuation time scale of the system at a particular temperature. This is the smallest dynamical timescale , defining a lower-cut off in a hierarchical description of the dynamics. We find that this fluctuation time scale, which is approximately equal to atomic spin fluctuation time scales near the transition temperature, follows a generalized Arrhenius law. We discuss the hypothesis that, upon cooling to a measuring temperature within the spin glass state, there is a range of dynamically in-equivalent configurations in which the system can be trapped, and check within a numerical barrier model simulation, that this leads to sub-aging behavior in scaling aged TRM decay curves, as recently discussed theoretically [1].

The crossover between quasiequilibrium and nonequilibrium spin-glass dynamics has been studied in Monte Carlo simulations of twoand three-dimensional short-range Ising spin-glass systems. The spin system was quenched in zero field to a low temperature T. After equilibrating for a time t, a weak magnetic field was applied and the time dependence of the magnetization M(t) and the spin autocorrelation function q(t) was studied. Our results show that the relaxation rate S(t)=8M(t)/Bloglo(t) exhibits a maximum at t =t. If the temperature is lowered or raised, immediately prior to the field application, the apparent age (t,) of the system, as defined by the maximum in relaxation rate, is shifted to longer or shorter time scales, respectively. No significant differences between the aging behavior in two and three dimensions are found. The relation y(t)=[1 q(t)-)iT holds only for short time scales (t « t), clear deviations are found at longer time scales (t) t). Since this relation should according to the fluctuation-dissipation theorem hold for a system in equilibrium, this result is interpreted as an indication of a crossover between equilibrium and nonequilibrium dynamics. Our results are qualitatively in agreement with experiments as we11 as with theoretical models for the nonequilibrium spin-glass dynam-1cs.

The low-field time-dependent magnetic susceptibility of the amorphous metallic spin glass (Feo~5Nio 85)75P]686A13 has been studied in a superconducting-quantum-interference-device magnetometer. Both ac susceptibility and zero-field-cooled susceptibility measurements have been utilized to cover more than ten decades in time, 3& 10-10' sec. At short observation times the equilibrium relaxation is observed, while at long observation times the influence of the aging process dominates the relaxation. The aging behavior is shown to persist through the spin-glass freezing temperature and it remains to have a vital influence on the relaxation until the spin system has been allowed to age for times comparable to the longest relaxation time of the system. The functional form of the time-dependent susceptibility is also illuminated.

The time decay of the saturated remanent magnetization (M,) has been studied in the amorphous metallic spin glass (Fep|SNip85)75P|6B6A13. This relaxation, which by nature is different from the zero-field equilibrium relaxation, shows at low temperatures (T/Ts & 0.98) a time variation accurately described by a pure power law. At temperatures in the immediate vicinity of Tg, the experimental time decay can be described by a power law times a stretched exponential functional form: M, Mpt exp[-(t/rr)' "l. Spin glasses are known to exhibit slow, nonexponential relaxation. This kind of dynamical behavior is a characteristic feature of disordered, strongly interacting systems of condensed matter. The response function of dielectrics, ' glasses, and glassy polymers resembles that of spin glasses. In particular, it has been experimentally shown that spin glasses display aging phenomena, a behavior that is well known from other glassy materials. This implies that the spin-glass "phase" is a thermodynamic nonequilibrium state. In spin glasses aging is revealed by a dependence of the response function on the wait-time t

The effect of applied magnetic fields on the collective nonequilibrium dynamics of a strongly interacting Fe-C nanoparticle system has been investigated. It is experimentally shown that the magnetic aging diminishes to finally disappear for fields of moderate strength. The field needed to remove the observable aging behavior increases with decreasing temperature. The same qualitative behavior is observed in an amorphous metallic spin glass (Fe 0.15 Ni 0.85) 75 P 16 B 6 Al 3 .

The dynamics of a magnetic particle system consisting of ultrafine Fe-C particles of monodisperse nature has been investigated in a large time window, 10 29 10 4 s, using Mössbauer spectroscopy, ac susceptibility, and zero field cooled magnetic relaxation measurements. By studying two samples from the same dilution series, with concentrations of 5 and 6 3 10 23 vol %, respectively, it has been found that dipole-dipole interaction increases the characteristic relaxation time of the particle system at all temperatures investigated. The results for the most concentrated particle assembly are indicative of collective magnetic dynamics and critical slowing down at a finite temperature, T g ഠ 40 K. Close to and below the transition temperature, an aging phenomenon is observed, another manifestation of collective magnetic dynamics. [S0031-9007(97)04826-6]

The non-equilibrium dynamics in a Fe}C nano-particle sample, showing a low-temperature spin-glass-like phase, have been studied by low-frequency AC-susceptibility experiments. A temporary stop in the cooling during an AC-susceptibility measurement yields a decrease of with time. Upon the following reheating traces the previous curve with a dip at the temperature where the stop occurred. This e!ect has recently been discovered and discussed for di!erent spin-glass systems, but has never been detected before in a nano-particle system.

Effects of dipole-dipole interactions on the magnetic relaxation have been investigated for three Fe-C nanoparticle samples with volume concentrations of 0.06, 5 and 17 vol%. While both the 5 and 17 vol% samples exhibit collective behavior due to dipolar interactions, only the 17 vol% sample displays critical behavior close to its transition temperature. The behaviour of the 5 vol% sample can be attributed to a mixture of collective and single particle dynamics.

The nonequilibrium character of the spin glass dynamics has been studied in Monte Carlo simulations of two-and three-dimensional short-range lsing spin glass systems. The spin system was quenched in zero field to a temperature T. After equilibrating for a waiting time t,, a weak magnetic field was applied and the time dependence tff the magnetization M(t } was studied. Our results show that the relaxation rate, S(t } = aM(t)/alog t, exhibits a maximum at a time t = t,,. which is consistent with results from experiments. If the temperature is increased or decreased prior to the field application, the apparent age t,, of the system, as defined by the maximum in relaxation rate. is changed. The results are qualitatively in agreement with experinaents as well as with theoretical models for the nonequilibrium spin glass dynamics.

The time decay of the saturated remanent magnetization (M,) has been studied in the amorphous metallic spin glass (Fep|SNip85)75P|6B6A13. This relaxation, which by nature is different from the zero-field equilibrium relaxation, shows at low temperatures (T/Ts & 0.98) a time variation accurately described by a pure power law. At temperatures in the immediate vicinity of Tg, the experimental time decay can be described by a power law times a stretched exponential functional form: M, Mpt exp[-(t/rr)' "l. Spin glasses are known to exhibit slow, nonexponential relaxation. This kind of dynamical behavior is a characteristic feature of disordered, strongly interacting systems of condensed matter. The response function of dielectrics, ' glasses, and glassy polymers resembles that of spin glasses. In particular, it has been experimentally shown that spin glasses display aging phenomena, a behavior that is well known from other glassy materials. This implies that the spin-glass "phase" is a thermodynamic nonequilibrium state. In spin glasses aging is revealed by a dependence of the response function on the wait-time t

The effect of applied magnetic fields on the collective nonequilibrium dynamics of a strongly interacting Fe-C nanoparticle system has been investigated. It is experimentally shown that the magnetic aging diminishes to finally disappear for fields of moderate strength. The field needed to remove the observable aging behavior increases with decreasing temperature. The same qualitative behavior is observed in an amorphous metallic spin glass (Fe0.15Ni0.85)75P16B6Al3.

Effects of dipole-dipole interactions on the magnetic relaxation have been investigated for three Fe-C nanoparticle samples with volume concentrations of 0.06, 5 and 17 vol%. While both the 5 and 17 vol% samples exhibit collective behavior due to dipolar interactions, only the 17 vol% sample displays critical behavior close to its transition temperature. The behaviour of the 5 vol% sample can be attributed to a mixture of collective and single particle dynamics.

Nanoparticles of iron and iron oxide are widely explored in several biomedical and technological applications. We report on the magnetic properties of amorphous Fe/Fe-O core/shell nanoparticles compared to those of a reference system with crystalline Fe-O nanoparticles. These nanoparticles are prepared by thermal decomposition of iron precursor, where the amorphous and crystalline nature of core and shell is determined by the choice and concentration of the ligand. The crystalline system exhibits a blocking temperature higher than 300 K and negligible exchange bias effect. In contrast, the amorphous systems display large exchange bias, and collective magnetic behavior at low temperatures, with features of magnetic frustration and disorder reminiscent of those observed in spin glass and superspin glass systems. We discuss the origin of the dynamical magnetic behavior of the amorphous particles and study the dependence of the exchange bias field on the cooling field.

The magnetic properties of Mg 0.95Mn 0.05Fe 2O 4 ferrite samples with an average particle size of ˜6.0±0.6 nm have been studied using X-ray diffraction, Mössbauer spectroscopy, dc magnetization and frequency dependent real χ'(T) and imaginary χ″(T) parts of ac susceptibility measurements. A magnetic transition to an ordered state is observed at about 195 K from Mössbauer measurements. The zero-field-cooled (ZFC) and field-cooled (FC) magnetization have been recorded at low field and show the typical behavior of a small particle system. The ZFC curve displays a broad maximum at T=195±5 K, a temperature which depends upon the distribution of particle volumes in the sample. The FC curve was nearly flat below T, as compared with monotonically increasing characteristics of non-interacting superparamagnetic systems indicating the existence of strong interactions among the nanoparticles. A frequency-dependent peak observed in χ'(T) is well described by Vogel-Fulcher law, yielding a relaxation time τ0=5.8×10-12 s and an interaction parameter T0=195±3 K. Such values show the strong interactions and rule out the possibility of spin-glass (SG) features among the nanoparticle system. On the other hand fitting with the Néel-Brown model and the power law yields an unphysical large value of τ0 (˜6×10 -69 and 1.2×10 -22 s respectively).

Magnetic fluids based on manganese ferrite nanoparticles were studied from the structural point of view through small angle x-rays scattering (SAXS) and from the magnetic point of view through zero-field cooling and field cooling (ZFC-FC) and ac susceptibility measurements (MS). Three different colloids with particles mean diameters of 2.78, 3.42, and 6.15 nm were investigated. The size distribution obtained from SAXS measurements follows a log-normal behavior. The ZFC-FC and MS results revealed the presence of an important magnetic interaction between the nanoparticles, characterized by a magnetic correlation distance . The colloidal medium can be pictures as composed by magnetic cluster constituted by N interacting particles. These magnetic clusters are not characterized by a physical aggregation of particles. The energy barrier energy obtained is consistent with the existence of this magnetic clusters. Besides the magnetic interaction between particles, confinement effects must be included to account for the experimental values of the magnetic energy barrier encountered.

Measurements of the complex susceptibility, χ(ω) = χ (ω) − iχ (ω), as a function of the frequency (100 Hz–18 GHz) and polarizing field (0–90 kA m −1) at room temperature together with static magnetic measurements over the temperature range 4–300 K, are reported for a colloidal suspension of cobalt nanoparticles. The transition of the cobalt particles to the superparamagnetic state are supported by the temperature dependencies of field cooling (FC) and zero field cooling (ZFC) magnetization measurements. From these measurements, which show a typical blocking behaviour of an assembly of super-paramagnetic particles with a wide distribution of blocking temperatures, the exponential pre-factor τ0 of Brown's equations for Néel relaxation, is found to be equal to 9.2 × 10 −10 s. Measurement of the complex susceptibility χ(ω) over this broad frequency range, with an upper frequency value corresponding to three times that previously reported in our measurements on cobalt, has enabled the presence of both resonance and Néel relaxation mechanisms to be identified. From the Néel component, a further value for τ0 was evaluated and shown to be in close agreement with that obtained from the ZFC data. Data on the after-effect function, realised by Fourier transformation of the χ (ω) component, is also presented.

The field-cooled (FC) process on an Ising spin-glass model is investigated by a standard Monte Calro (MC) method on one hand, and the equilibrium magnetization of the same system is evaluated by the exchang MC method on the other hand. The two types of simulation reveal intriguing glassy (nonequilibrium) dynamic properties of the FC magnetization (FCM) of the system. Particularly, the FCM decrease is observed when the FC process is halted at a low temperater, although its value is smaller than the corresponding equilibrium value. We present a comprehensive interpretation of such peculiar phenomena based on the scenario for the FCM process recently propsed by Jönsson and one of us (HT).

A new protocol of the zero-field-cooled (ZFC) magnetization process is studied experimentally on an Ising spin-glass (SG) Fe0.50Mn0.50TiO3 and numerically on the Edwards-Anderson Ising SG model. Although the time scales differ very much between the experiment and the simulation, the behavior of the ZFC magnetization observed in the two systems can be interpreted by means of a common scaling expression based on the droplet picture. The results strongly suggest that the SG coherence length, or the mean size of droplet excitations, involved even in the experimental ZFC process, is about a hundred lattice distances or less.

The non-equilibrium dynamics in a Fe}C nano-particle sample, showing a low-temperature spin-glass-like phase, have been studied by low-frequency AC-susceptibility experiments. A temporary stop in the cooling during an AC-susceptibility measurement yields a decrease of with time. Upon the following re-heating traces the previous curve with a dip at the temperature where the stop occurred. This e!ect has recently been discovered and discussed for di!erent spin-glass systems, but has never been detected before in a nano-particle system.

The dynamics of a magnetic particle system consisting of ultrafine Fe-C particles of monodisperse nature has been investigated in a large time window, 10 29 10 4 s, using Mössbauer spectroscopy, ac susceptibility, and zero field cooled magnetic relaxation measurements. By studying two samples from the same dilution series, with concentrations of 5 and 6 3 10 23 vol %, respectively, it has been found that dipole-dipole interaction increases the characteristic relaxation time of the particle system at all temperatures investigated. The results for the most concentrated particle assembly are indicative of collective magnetic dynamics and critical slowing down at a finite temperature, T g ഠ 40 K. Close to and below the transition temperature, an aging phenomenon is observed, another manifestation of collective magnetic dynamics. [S0031-9007(97)

The non-equilibrium dynamics in a Fe}C nano-particle sample, showing a low-temperature spin-glass-like phase, have been studied by low-frequency AC-susceptibility experiments. A temporary stop in the cooling during an AC-susceptibility measurement yields a decrease of with time. Upon the following re-heating traces the previous curve with a dip at the temperature where the stop occurred. This e!ect has recently been discovered and discussed for di!erent spin-glass systems, but has never been detected before in a nano-particle system.

Experimental results on the relaxation of the magnetization of spin glasses at temperatures below the spin glass freezing temperature Tg show very similar behaviour for different spin glass materials. Some data on relaxation are presented and discussed in the context of a droplet scaling theory for the spin glass phase elaborated by Fisher and Huse (Phys Rev. B, in print).

The nonequilibrium character of the spin glass dynamics has been studied in Monte Carlo simulations of two-and three-dimensional short-range lsing spin glass systems. The spin system was quenched in zero field to a temperature T. After equilibrating for a waiting time t,, a weak magnetic field was applied and the time dependence tff the magnetization M(t } was studied. Our results show that the relaxation rate, S(t } = aM(t)/alog t, exhibits a maximum at a time t = t,,. which is consistent with results from experiments. If the temperature is increased or decreased prior to the field application, the apparent age t,, of the system, as defined by the maximum in relaxation rate. is changed. The results are qualitatively in agreement with experinaents as well as with theoretical models for the nonequilibrium spin glass dynamics.