Ferromagnetism in the Hubbard model on fcc-type lattices

Abstract

The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges. PACS numbers: 71.27.+a, 75.10.Lp, 75.30.Kz More than 30 years ago, the Hubbard model was introduced to describe band magnetism in transition metals, in particular the ferromagnets Fe, Co and Ni [1][2][3]. However, for a long time it appeared to be a generic model rather for anti-ferromagnetism than for ferromagnetism. At half filling (one electron per site) on bipartite lattices antiferromagnetism emerges in both weak and strong coupling perturbational approaches and, in particular, antiferromagnetism is tractable by renormalization group methods [4]. By contrast, ferromagnetism is a non-trivial strong coupling phenomenon which cannot be investigated by any standard perturbation theory. In fact, our knowledge on the possibility of ferromagnetism in the Hubbard model is still very limited. Only in a few special cases was the Hubbard model proven to have ferromagnetic order. The first rigorous result showing a fully polarized ground state, the theorem by Nagaoka [5], is only valid for a single hole added to the half filled band in the limit of infinite on-site repulsion. In the limit of low electronic density a saturated ferromagnetic ground state has been found recently in the one dimensional Hubbard model on zigzag chains [6,7]. Further, the existence of a ground state with net polarization has been proven for the half filled band case on bipartite lattices with asymmetry in the number of sites per sublattice [8], and in 'flat-band' systems [9].Due to the development of new numerical algorithms and powerful computers the problem of ferromagnetism in the Hubbard model has recently become accessible to numerical investigations of finite systems, at least in reduced dimensions (d = 1, 2). In the presence of a next nearest neighbor hopping, polarized ground states were found very recently in d = 1 [10] and on square lattices in the case of a van Hove singularity at the Fermi energy [11].The rigorous and numerical results mentioned above show that the stability of ferromagnetism is intimately linked with the structure of the underlying lattice and the kinetic energy (i.e. the hopping) of the electrons. This fact has also been observed by exact variational bounds for the stability of saturated ferromagnetism [12][13][14][15], and within approximative methods [16]. Generally, lattices with closed loops and with frustration of the competing antiferromagnetism (non-bipartite lattices) are expected to support ferromagnetism. Non-bipartite lattices have an asymmetric density of states (DOS) and thus a peak away fro...

Ferromagnetism in the periodic Anderson model. A comparison of spectral density approximation (SDA), modified alloy analogy (MAA) and modified perturbation theory (MPT)

“…For the Hubbard model [14,50,51], the existence of a ferromagnetic phase in the strong-coupling regime was confirmed in the limit of infinite dimensions [52,53]. The mechanism driving this transition is simply based on a gain of kinetic energy [54,49].…”

Metallic Ferromagnetism — An Electronic Correlation Phenomenon

“…However, already a small contribution of t ′ -hopping (which is present in any real system) is enough to stabilize a large region of metallic ferromagnetism in addition to an antiferromagnetic phase (which is absent in d = ∞), close to half filling (Fig. 3a) [35]. This shows the strong and subtle dependence of the stability on the dispersion and the distribution of spectral weight in the DOS.…”

“…Thereby one can construct the T vs. n phase diagram for different values of U . The region of stability increases with U [35].…”

Magnetic phases in the correlated Kondo-lattice model

“…A possible reason for the tendency of both finite U and negative J to stabilize ferromagnetism is the strong asymmetry induced by U and J 55,56 . As can be seen from Fig.…”