Magnetic relaxation in finite two-dimensional nanoparticle ensembles

Denisov, S. I.; Lyutyy, T. V.; Trohidou, K. N.

doi:10.1103/physrevb.67.014411

Cited by 37 publications

(35 citation statements)

References 29 publications

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“…(18) exhibits logarithmic singularities. To prevent this nonphysical behavior of T Ω the regularity condition dT Ω /dθ ′ | θ ′ =π(1−Ω)/2 = 0 must hold [23]. In order to derive the boundary condition for eq.…”

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Mean first-passage times for an ac-driven magnetic moment of a nanoparticle

et al. 2006

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PACS. 05.10.Gg -Stochastic analysis methods. PACS. 75.60.Jk -Magnetization reversal mechanisms. PACS. 75.50.Tt -Fine-particle systems; nanocrystalline materials.Abstract. -The two-dimensional backward Fokker-Planck equation is used to calculate the mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle driven by a rotating magnetic field. It is shown that a magnetic field that is rapidly rotating in the plane perpendicular to the easy axis of the nanoparticle governs the MFPTs just in the same way as a static magnetic field that is applied along the easy axis. Within this framework, the features of the magnetic relaxation and net magnetization of systems composed of ferromagnetic nanoparticles arising from the action of the rotating field are revealed.Introduction. -The mean first-passage time (MFPT), i.e., the average time that elapses until a stochastic process reaches a prescribed domain, is an important characteristic of the considered process. It is widely used for describing various dynamic features such as exit problems, activation rates, lifetimes of metastable states and other noise induced phenomena [1,2]. The class of stochastic processes for which the MFPT can be calculated explicitly is rather limited [1]. In fact, the most general analytical results were obtained for continuous one-dimensional Markov processes within an approach based on the backward Fokker-Planck equation [3][4][5][6][7]. It is important to note that most of the exactly known results are restricted to Markov processes that are homogeneous in time.However, Markov processes that describe time-dependent systems usually cannot be approximated by homogeneous processes. Well-known examples are, the phenomenon of Stochastic Resonance [8][9][10] and directed transport in ratchet-like systems [11] where external timedependent fields play a crucial role. Since the above-mentioned method is no longer applicable, the development of new approaches for calculating MFPTs in periodically driven systems presents an important challenge. For slowly varying external driving forces adiabatic and semiadiabatic approximations are available [12,13]. The path integral formulation of the conditional probability provides a convenient basis for approximations if the noise is weak [14].In this Letter we present an analytical approach to the two-dimensional MFPT problem for a rapidly driven magnetic moment of a ferromagnetic nanoparticle. It is based on the backward Fokker-Planck equation in a rotating coordinate system, which describes the homogeneous

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Mean first-passage times for an ac-driven magnetic moment of a nanoparticle

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“…r H i l (for brevity, we omitted the arguments i and l). Next, defining p i i; l t i i; l = t 1 i; l t ÿ1 i; l and using the numerical procedure developed in [16], we performed a Monte Carlo simulation of the magnetization h t i induced by the rotating field in two-dimensional systems of dipolar interacting nanoparticles.…”

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Magnetization of Nanoparticle Systems in a Rotating Magnetic Field

2006

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The investigation of a sizable thermal enhancement of magnetization is put forward for uniaxial ferromagnetic nanoparticles that are placed in a rotating magnetic field. We elucidate the nature of this phenomenon and evaluate the resonant frequency dependence of the induced magnetization. Moreover, we reveal the role of magnetic dipolar interactions, point out potential applications, and reason the feasibility of an experimental observation of this effect. DOI: 10.1103/PhysRevLett.97.227202 PACS numbers: 75.50.Tt, 05.40.ÿa, 75.60.Jk Presently, the study of magnetic nanoparticles and their structures is one of the most important research areas in nanoscale physics. The first reason is that such nanoparticles increasingly find numerous applications that range from medicine to nanotechnology. Another reason is that these systems exhibit a number of remarkable physical phenomena, such as quantum tunneling of magnetization [1], giant magnetoresistance [2], exchange bias [3], and finite-size and surface effects [4], to name but a few. Moreover, the study of fundamentals of magnetic behavior in these systems is also an important issue, especially for high-density data storage devices [5].From a practical point of view, the lifetime of stored data and the switching time (i.e., the time during which the reversal of the nanoparticle magnetic moments occurs) are salient characteristics of such devices. Now, thanks to the experimental discovery of fast switching of magnetization [6], the switching time reaches the fundamental (picosecond) limit for field-induced magnetization reversal. On the contrary, a feasible lifetime must cover up to 10 yr and beyond. Its value is usually limited by the superparamagnetic effect [7] and is defined by the probabilities p that the nanoparticle magnetic moment m stays in the up ( 1) and down ( ÿ1) equilibrium directions. These probabilities, which are also responsible for other thermal effects in such systems including magnetic relaxation [8], are very sensitive to small perturbations that change the static states of the magnetic moments. Namely, according to the Arrhenius law [9] the ratio p 1 =p ÿ1 is approximately given by exp E=kT , where E E 1 ÿ E ÿ1 , E is the potential barrier for the reorientation ! ÿ , k is the Boltzmann constant, and T is the absolute temperature. Therefore, if without perturbations E 0, then p 1 =p ÿ1 1 and the nanoparticle system is demagnetized. But due to the exponential dependence on E and T, the ratio p 1 =p ÿ1 can drastically be changed by small perturbations. In particular, a static magnetic field H applied along the nanoparticle easy axis of magnetization yields E 2Hm (m jmj), and so p 1 strongly differs from p ÿ1 if jHj=H a 1=4a, where a H a m=2kT and H a is the anisotropy field. This means that even small magnetic fields (in comparison with H a ) almost fully magnetize the nanoparticle systems when a 1. In the case of time-periodic perturbations the situation is not settled yet and far less researched. On the one hand, these perturbations generate ...

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“…5 is that it does not use the Monte Carlo approach, so the last complicated problem does not appear. This feature of the method and its applicability to the study of magnetic relaxation over ten decades of time 5 make it a very useful tool in this domain.…”

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“…5 to study the magnetic relaxation in 2D ensembles of dipolar interacting nanoparticles subjected to a bias magnetic field. We have demonstrated its efficiency for the analysis of the relaxation law features arising from the mutual action of the dipolar correlations and bias field for different ensembles of Co nanoparticles and we have shown that the correlation effects play an important role in magnetic relaxation on all times.…”

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“…To study the features of magnetic relaxation in such ensembles, which are conditioned by the correlation effects, we have developed a method for its numerical simulation at zero bias field. 5 Usually, magnetic relaxation in ensembles of dipolar interacting nanoparticles is simulated either by the conventional Monte Carlo method, 6,7 where the role of time plays the Monte Carlo steps, or by the improved Monte Carlo methods, [8][9][10][11] that use the short-time stochastic behavior of the nanoparticle magnetic moments to convert the Monte Carlo steps to real time units. The main advantage of the method proposed in Ref.…”

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Dipolar interaction effects on the thermally activated magnetic relaxation of two-dimensional nanoparticle ensembles

Denisov

Lyutyy

Trohidou

2004

Applied Physics Letters

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The thermally activated magnetic relaxation in two-dimensional lattices of dipolar interacting nanoparticles with large uniaxial perpendicular anisotropy is studied by a numerical method and within the mean-field approximation for comparison. The role that the correlation effects play in magnetic relaxation and the influence of lattice structure and bias magnetic field on the relaxation process are revealed. The correlations of the nanoparticle magnetic moments enhance relaxation on small times, delay it on large times, and reduce the steady-state absolute magnetization at nonzero bias fields. In a hexagonal lattice, magnetic relaxation on small times occurs faster and the steady-state absolute magnetization has the larger magnitude than in a square lattice with the same lattice spacing. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1759782͔The two-dimensional ͑2D͒ ensembles of uniaxial ferromagnetic nanoparticles, whose easy axes of magnetization are perpendicular to the nanoparticles' plane, represent an important class of perpendicular magnetic recording media. 1 From a technological point of view, the main characteristic of these media is the average time of data storage, which is one of the numerical parameters that describe the thermally activated magnetic relaxation. Due to the dipolar interaction between nanoparticles, its analytical description in such ensembles is a very complicated problem, which was solved only within the mean-field 2,3 and fluctuating 4 theories of magnetic relaxation. The former deals with the mean component of the dipolar field acting on the nanoparticles, and the latter accounts of both the mean and fluctuation components. However, the correlations of the nanoparticle magnetic moments, arising from the dipolar interaction, also play an important role, especially on the final phase of magnetic relaxation. To study the features of magnetic relaxation in such ensembles, which are conditioned by the correlation effects, we have developed a method for its numerical simulation at zero bias field. 5 Usually, magnetic relaxation in ensembles of dipolar interacting nanoparticles is simulated either by the conventional Monte Carlo method, 6,7 where the role of time plays the Monte Carlo steps, or by the improved Monte Carlo methods, [8][9][10][11] that use the short-time stochastic behavior of the nanoparticle magnetic moments to convert the Monte Carlo steps to real time units. The main advantage of the method proposed in Ref. 5 is that it does not use the Monte Carlo approach, so the last complicated problem does not appear. This feature of the method and its applicability to the study of magnetic relaxation over ten decades of time 5 make it a very useful tool in this domain.In this letter, we extend our method to the case of nonzero bias magnetic fields, and we present results obtained within its framework, which clarify the role that the correlation effects, bias field, and lattice structure play in the magnetic relaxation. We consider the 2D ensembles of spherical nanoparticl...

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Magnetic relaxation in finite two-dimensional nanoparticle ensembles

Cited by 37 publications

References 29 publications

Mean first-passage times for an ac-driven magnetic moment of a nanoparticle

Mean first-passage times for an ac-driven magnetic moment of a nanoparticle

Magnetization of Nanoparticle Systems in a Rotating Magnetic Field

Dipolar interaction effects on the thermally activated magnetic relaxation of two-dimensional nanoparticle ensembles

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