JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS, Vol. 11, No. 4, April 2009, p. 369 - 379 Band ferromagnetism in systems of variable dimensionality II: the two-dimensional finite-temperature case G. A. LUNGU * , C. M. TEODORESCU National Institute of Materials Physics, P.O. box MG-7, Bucharest-Magurele, Ilfov, 077125, Romania In a previous paper [C.M. Teodorescu and G.A. Lungu, J. Optoelectron. Adv, Mater. 10, 3058 (2008)] we studied the zero temperature problem of the occurence of band ferromagnetism and of the derivation of the Stoner criterion for systems of variable dimensionality: 1D, 2D, 3D. The dimensionality of the system is reflected by a different shape of the density of states. For ideal 2D systems, the density of states is a constant and this seems to be the simplest case to be modelled. In this paper we integrate to this simplest model of constant density of states the influence of temperature, in order to analyse temperature-dependent ferromagnetism in two-dimensional systems, such as magnetic surfaces. Some surprising results are obtained, namely: (i) in contrast to the common belief, in this case the influence of the temperature is to favour, not to inhibit ferromagnetism, i.e. in some conditions ferromagnetism may be obtained at finite temperature, even for systems where the zero temperature Stoner criterion is not satisfied; (ii) for a careful choice of the ratio between the Hubbard energy parameter and the equilibrium zero-temperature Fermi level value , systems nonmagnetic at low temperature which become magnetic at higher temperature may be possible. A short review of the experimental data which may be interpreted within the present formalism is also given. (Received March 25, 2009; after revision April 24, 2009; accepted April 25, 2009) Keywords: Low-dimensional systems, Ferromagnetism, Stoner criterion, Surfaces 1. Introduction Since the original paper of Stoner [1], many studies treated the band ferromagnetism, since it is a resonable alternate model to magnetism of localized moments for explaining magnetism in metals. Nowadays, these studies are revigorated, especially dealing with magnetism in low- dimensional systems of delocalized electrons, mainly because of recent achievements in the experimental synthesis of such systems [2,3]. We note the quite recent report on the experimental evidence of ferromagnetic order in nickel single atomic layers on Cu(001) [4], and of linear decrease of magnetisation with temperature, which was treated in a model of 2D spin waves. Recent studies of surface magnetism revealed exciting trends, mainly the possibility of synthesis of ferromagnetic surfaces from materials which are not ferromagnetic in the bulk. In 2000, the synthesis of magnetic hcp chromium grown on Ru(0001) was reported [5]. In 2001, the long- standing problem of the magnetism of the c(2×2) Mn grown on Cu(001) was shown to exhibit ferromagnetism [6], and in 2003 magnetic vanadium was synthesized on Cu(001) in the form of small aggregates grown at very low temperature [7]. The generic affirmation that "the Stoner criterion is satisfied in surfaces, whereas it is not satisfied in the bulk material" is somehow misleading, in the absence of a detailed knowledge of the density of states of the above mentioned surfaces. In this work, we intend to systematically investigate the occurence of ferromagnetism as function on temperature in metal surfaces and to compare the theoretical findings with recent available experimental data. In a previous paper [8], we treated the zero temperature case for the occurence of band ferromagnetism in systems of variable dimensionality. The dimensionality of the system is taken into accont via the energy dependence of the equilibrium density of states for 3D, for 2D, and for 1D. The ferromagnetic interaction occurs via the Hubbard energy term , where is the polarization fraction: electrons per unit volume passed from the minority spin sub-band to the majority spin sub-band (where is the total electron density). Therefore, the Fermi levels will be different for the majority and for the minority sub-bands and , functions on . This allows to compute the kinetic energy increase due to the spin polarization and then the total energy variation . Stable states are obtained when exhibits a minimum. The Stoner criterion examines the stability of the paramagnetic state ; indeed, it may be shown that the energy always exhibits an extremum at , but, in order to obtain ferromagnetism, this extremum must be a maximum, i.e. must be negative. This inequality is readily transformed in a condition between the relevant parameters of the model (e.g. Hubbard energy, equilibrium Fermi level), which is called the Stoner criterion [1].