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Register a new userNonmagnetic impurities and roughness effects on the finite temperature magnetic properties of core-shell spherical nanoparticles
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Being inspired by a recent study [V. Dimitriadis et al. Phys. Rev. B textbf{92}, 064420 (2015)], we study the finite temperature magnetic properties of the spherical nanoparticles with core-shell structure including quenched (i) surface and (ii) interface nonmagnetic impurities (static holes) as well as (iii) roughened interface effects. The particle core is composed of ferromagnetic spins, and it is surrounded by a ferromagnetic shell. By means of Monte Carlo simulation based on an improved Metropolis algorithm, we implement the nanoparticles using classical Heisenberg Hamiltonians. Particular attention has also been devoted to elucidate the effects of the particle size on the thermal and magnetic phase transition features of these systems. For nanoparticles with imperfect surface layers, it is found that bigger particles exhibit lower compensation point which decreases gradually with increasing amount of vacancies, and vanishes at a critical value. In view of nanoparticles with diluted interface, our Monte Carlo simulation results suggest that there exists a region in the disorder spectrum where compensation temperature linearly decreases with decreasing dilution parameter. For nanoparticles with roughened interface, it is observed that the degree of roughness does not play any significant role on the variation of both the compensation point and critical temperature. However, the low temperature saturation magnetizations of the core and shell interface regions sensitively depend on the roughness parameter.
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A detailed analysis of the finite-size effects on the bulk critical behaviour of the $d$-dimensional mean spherical model confined to a film geometry with finite thickness $L$ is reported. Along the finite direction different kinds of boundary conditions are applied: periodic $(p)$, antiperiodic $(a)$ and free surfaces with Dirichlet $(D)$, Neumann $(N)$ and a combination of Neumann and Dirichlet $(ND)$ on both surfaces. A systematic method for the evaluation of the finite-size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary $d$. It is found, for $2<d<4$, that the singular part of the free energy has the required finite-size scaling form at the bulk critical temperature only for $(p)$ and $(a)$. For the remaining boundary conditions the standard finite-size scaling hypothesis is not valid. At $d=3$, the critical amplitude of the singular part of the free energy (related to the so called Casimir amplitude) is estimated. We obtain $Delta^{(p)}=-2zeta(3)/(5pi)=-0.153051...$, $Delta^{(a)}=0.274543...$ and $Delta^{(ND)}=0.01922...$, implying a fluctuation--induced attraction between the surfaces for $(p)$ and repulsion in the other two cases. For $(D)$ and $(N)$ we find a logarithmic dependence on $L$.
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