Pseudocritical behavior of ferromagnetic pure and random diluted nanoparticles with competing interactions: Variational and Monte Carlo approaches

Velásquez, E. A.; Mazo-Zuluaga, J.; Restrepo, Juan Pablo; Iglesias, Òscar

doi:10.1103/physrevb.83.184432

Cited by 11 publications

(13 citation statements)

References 61 publications

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“…In agreement with the work of Velásquez et al [44], the authors found that the critical temperature decreases proportionally to the inverse of the radius of the cluster. Recently [46], the Ising model on a simple-cubic lattice was used to analyze the main concepts of nanothermodynamics applied to Monte Carlo simulations.…”

Section: Introductionsupporting

confidence: 80%

“…In the last few years, the Ising model has been adopted as a prototype for studying the magnetic properties of systems far away from the TL [44][45][46]. In [44], Velásquez et al studied the magnetic properties and pseudocritical behavior of ferromagnetic pure and metallic nanoparticles in the presence of atomic disorder, dilution and competing interactions.…”

Section: Introductionmentioning

confidence: 99%

“…In [44], Velásquez et al studied the magnetic properties and pseudocritical behavior of ferromagnetic pure and metallic nanoparticles in the presence of atomic disorder, dilution and competing interactions. Using variational and Monte Carlo methods, the authors reported the particle size dependence of the ordering temperature for pure and random diluted particles.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamics of Small Magnetic Particles

Vogel

Vargas

Saravia

et al. 2017

Entropy

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Abstract:In the present paper, we discuss the interpretation of some of the results of the thermodynamics in the case of very small systems. Most of the usual statistical physics is done for systems with a huge number of elements in what is called the thermodynamic limit, but not all of the approximations done for those conditions can be extended to all properties in the case of objects with less than a thousand elements. The starting point is the Ising model in two dimensions (2D) where an analytic solution exits, which allows validating the numerical techniques used in the present article. From there on, we introduce several variations bearing in mind the small systems such as the nanoscopic or even subnanoscopic particles, which are nowadays produced for several applications. Magnetization is the main property investigated aimed for two singular possible devices. The size of the systems (number of magnetic sites) is decreased so as to appreciate the departure from the results valid in the thermodynamic limit; periodic boundary conditions are eliminated to approach the reality of small particles; 1D, 2D and 3D systems are examined to appreciate the differences established by dimensionality is this small world; upon diluting the lattices, the effect of coordination number (bonding) is also explored; since the 2D Ising model is equivalent to the clock model with q = 2 degrees of freedom, we combine previous results with the supplementary degrees of freedom coming from the variation of q up to q = 20. Most of the previous results are numeric; however, for the case of a very small system, we obtain the exact partition function to compare with the conclusions coming from our numerical results. Conclusions can be summarized in the following way: the laws of thermodynamics remain the same, but the interpretation of the results, averages and numerical treatments need special care for systems with less than about a thousand constituents, and this might need to be adapted for different properties or devices.

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Section: Introductionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermodynamics of Small Magnetic Particles

Vogel

Vargas

Saravia

et al. 2017

Entropy

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“…At a large field of 10 000 Oe, a deviation from the AT line is observed in agreement with what has been reported that deviations from the AT line may happen in some spin glasses under large magnetic fields. 53,54 Thus, the hump at T a should stem from a spin-glass-like freezing process. The downshift in T a with increasing magnetic fields makes sense because higher magnetic fields suppress the energy barriers and, thus, reduce the freezing temperature.…”

Section: B DC Magnetizationmentioning

confidence: 99%

Coexistence of magnetic order and spin-glass-like phase in the pyrochlore antiferromagnet Na3Co(CO3)2Cl

Zheng

Xiao

et al. 2013

Phys. Rev. B

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We present comprehensive investigations on a pyrochlore antiferromagnet Na 3 Co(CO 3 ) 2 Cl. Performed dc magnetization indicates a broad maximum at around 4 K. The field dependence of the peak temperature of this maximum follows the de Almeida-Thouless line, suggesting a spin-glass-like phase transition. The ac susceptibility measurements determine the glassy transition temperature to be 4.5 K and reveal a frequencyindependent peak at 17 K. The temperature dependence of the specific heat shows a sharp peak at 1.5 K and a broad hump at around 5 K, which are attributed to a long-range magnetic phase transition and a spin-glass-like freezing process, respectively. The average crystallographic structure of Na 3 Co(CO 3 ) 2 Cl has been determined using neutron-powder diffraction. No obvious site disorder has been detected within the experimental resolution. The diffuse neutron scattering with polarization analysis indicates short-range spin correlations characterized by dominating antiferromagnetic coupling between nearest neighbors and weak ferromagnetic coupling between next-nearest neighbors. The long-range magnetic order below 1.5 K is evidenced by the magnetic reflections observed at 50 mK and can be well explained with an all-in-all-out spin configuration. Inelastic neutron scattering of Na 3 Co(CO 3 ) 2 Cl exhibits collective magnetic excitations at 3.5 K, suggesting that the spin-glass-like transition temperature T g = 4.5 K does not correspond to a complete spin-glass freezing as expected in canonical spin glasses. The peak observed in magnetic susceptibility at 17 K is attributed to the onset of an intermediate partially ordered phase transition, qualitatively consistent with the theoretical predictions for pyrochlore antiferromagnets with weak ferromagnetic next-nearest-neighbor interactions.

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“…The fluctuations in m becomes dominant in bulk ferromagnets only at high temperatures. On the other hand, due to enhanced relative fluctuations in small ferromagnetic domains, e.g., in a macrospin, the transition temperatures get largely suppressed with reduction of system size [12,13], enhancing the fluctuations in m even at room temperature. Recently, a generalized Langevin spin dynamics has been proposed that captures longitudinal fluctuations in the spin magnitude, as well as the stochastic rotation dynamics of its orientation [14].…”

Section: Introductionmentioning

confidence: 99%

Stochastic thermodynamics of macrospins with fluctuating amplitude and direction

2015

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We consider stochastic energy balance and entropy production (EP) in a generalized Langevin dynamics of macrospins, allowing for both amplitude and direction fluctuations, under external magnetic field. EP is calculated using Fokker-Planck equation, distinguishing between reversible and irreversible parts of probability currents. The system entropy increases due to irreversible non-equilibrium processes, and reduces as heat dissipates to surrounding environment. Using path probability distributions of time-forward trajectories and conjugate trajectories under time reversal, we obtain fluctuation theorems (FT) for total stochastic EP. We show that the choice of conjugate trajectories is crucial in obtaining entropy like quantities that obey FTs.

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Pseudocritical behavior of ferromagnetic pure and random diluted nanoparticles with competing interactions: Variational and Monte Carlo approaches

Cited by 11 publications

References 61 publications

Thermodynamics of Small Magnetic Particles

Thermodynamics of Small Magnetic Particles

Coexistence of magnetic order and spin-glass-like phase in the pyrochlore antiferromagnet Na3Co(CO3)2Cl

Stochastic thermodynamics of macrospins with fluctuating amplitude and direction

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