Boundary and finite-size effects in small magnetic systems

We study the effect of free boundaries in finite magnetic systems of cubic shape on the field and temperature dependence of the magnetization within the isotropic model of D-component spin vectors in the limit D \to \infty. This model is described by a closed system of equations and captures the Goldstone-mode effects such as global rotation of the magnetic moment and spin-wave fluctuations. We have obtained an exact relation between the intrinsic (short-range) magnetization M = M(H,T) of the system and the supermagnetization m = m(H,T) which is induced by the field. We have shown, analytically at low temperatures and fields and numerically in a wide range of these parameters, that boundary effects leading to the decrease of M with respect to the bulk value are stronger than the finite-size effects making a positive contribution to M. The inhomogeneities of the magnetization caused by the boundaries are long ranged and extend far into the depth of the system.Comment: 15 pages, 5 figures, To appear in Physica

Magnetic free energy at elevated temperatures and hysteresis of magnetic particles

We derive a free energy for weakly anisotropic ferromagnets which is valid in the whole temperature range and interpolates between the micromagnetic energy at zero temperature and the Landau free energy near the Curie point T_c. This free energy takes into account the change of the magnetization length due to thermal effects, in particular, in the inhomogeneous states. As an illustration, we study the thermal effect on the Stoner-Wohlfarth curve and hysteresis loop of a ferromagnetic nanoparticle assuming that it is in a single-domain state. Within this model, the saddle point of the particle's free energy, as well as the metastability boundary, are due to the change in the magnetization length sufficiently close to T_c, as opposed to the usual homogeneous rotation process at lower temperatures.Comment: 16 pages, 4 figure

Finite-size versus Surface effects in nanoparticles

We study the finite-size and surface effects on the thermal and spatial behaviors of the magnetisation of a small magnetic particle. We consider two systems: 1) A box-shaped isotropic particle of simple cubic structure with either periodic or free boundary conditions. This case is treated analytically using the isotropic model of D-component spin vectors in the limit $D\to \infty$, including the magnetic field. 2) A more realistic particle ($\gamma$-Fe$_{2}$O$_{3}$) of ellipsoidal (or spherical) shape with open boundaries. The magnetic state in this particle is described by the anisotropic classical Dirac-Heisenberg model including exchange and dipolar interactions, and bulk and surface anisotropy. This case is dealt with by the classical Monte Carlo technique. It is shown that in both systems finite-size effects yield a positive contribution to the magnetisation while surface effects render a larger and negative contribution, leading to a net decrease of the magnetisation of the small particle with respect to the bulk system. In the system 2) the difference between the two contributions is enhanced by surface anisotropy. The latter also leads to non saturation of the magnetisation at low temperatures, showing that the magnetic order in the core of the particle is perturbed by the magnetic disorder on the surface. This is confirmed by the profile of the magnetisation.Comment: 6 pages of RevTex including 4 Figures, invited paper to 3rd EuroConference on Magnetic Properties of Fine Nanoparticles, Barcelona, October 9

Dipolar ordering in crystals of Mn12 Ac

Ordering in realistic elongated box-shape crystals of the molecular magnet Mn_12 Ac is investigated with the site-resolved mean-field approximation that does not assume a uniform ordering. It is shown that ferromagnetic ordering should not occur in crystals with the aspect ratio up to 12. Instead, for the aspect ratio about 6, the inner and outer regions of the crystal order in different directions, uniformly along its length. Finding ordering temperature by extrapolating the inverse susceptibility curve does not provide a correct T_C.Comment: 4 Phys. Rev. pages, 3 figures, submitted to PR

Turbulent fronts of quantum detonation in molecular magnets

Dipolar-controlled quantum deflagration going over into quantum detonation in the elongated Mn_12 Ac molecular magnet in a strong transverse field has been considered within the full 3d model. It is shown that within the dipolar window around tunneling resonances the deflagration front is non-flat. With increasing bias, dipolar instability makes the front turbulent, while its speed reaches sonic values, that is a signature of detonation.Comment: 4 PR pages, 5 figure

Susceptibilities and Correlation Functions of the Anisotropic Spherical Model

The static transverse and longitudinal correlation functions (CF) of a 3-dimensional ferromagnet are calculated for the exactly solvable anisotropic spherical model (ASM) determined as the limit D \to \infty of the classical D-component vector model. The results are nonequivalent to those for the standard spherical model of Berlin and Kac even in the isotropic case. Whereas the transverse CF has the usual Ornstein-Zernike form for small wave vectors, the longitudinal CF shows a nontrivial behavior in the ordered region caused by spin-wave fluctuations. In particular, in the isotropic case below T_c one has S_{zz}(k) \propto 1/k (the result of the spin-wave theory) for k \lsim \kappa_m \propto T_c-T.Comment: 6 pages, 4 figure