Role of inter-site exchange and hybrid interactions in itinerant ferromagnetism

Abstract

We study role of inter-site hybrid interactions in deciding ferromagnetic state in the itinerant electron (narrow band) systems like some of the transition metals. We have considered Hubbard like tight binding model alongwith exchange and hybrid interactions. All interactions have been treated within mean-field approximation. It is found here that hybrid interactions play significant role at zero as well as infinite temperatures in deciding on-set of ferromagnetic state. We have studied variation of effective mass of up and down spin electrons in ferromagnetic state as a function of temperature. Also studied are magnetic susceptibility, optical conductivity and magnetoresistance as a function of temperature.Suggested PACS Numbers: 71.28.+d, 75.10.Lp,

Ferromagnetism in Monatomic Chains: Spin-Dependent Bandwidth Narrowing/Broadening

“…The effective mass ratio is defined as the inverse of bandwidth ratio ( m */ m = W / W *), , where W * is the bandwidth after inclusion of off-diagonal elements. In the paramagnetic region, the effective mass ratio is the same for both spins.…”

“…The Hubbard model has been used to study the itinerant ferromagnets for quite a long time. It was investigated by Hirsch and thereafter by Dua et al , that the inclusion of off-diagonal elements of the Coulomb interaction in the Hamiltonian introduces band narrowing/broadening, and it is the key concept for a system to become ferromagnetic. The Hamiltonian, which includes all the off-diagonal matrix elements of Coulomb interaction, is given by In eq h.c. denotes Hermitian conjugate, and c i σ † / c i σ creates/destroys an electron of spin σ at site “ i ”.…”

“…To obtain the quasi-particle energy, we use the Green’s function method with mapping the Coulomb interactions into the perturbation to the noninteracting electron kinetic energy ε k = − t ∑ δ e – ikδ (see Supporting Information for details). The energy of the quasi-particle for the nondegenerate extended Hubbard model within the mean field approximation is , where M = n ↑ – n ↓ is the magnetization per site; W = 2 zt is the bandwidth; and “ z ” is the number of nearest neighbors. In the absence of off-diagonal elements of Coulomb interaction (i.e., when V , P , J , and K vanish), only band splitting is present, while the inclusion of off-diagonal elements introduces band narrowing/broadening in addition to band splitting.…”

“…In To obtain the quasi-particle energy, we use the Green's function method 76 with mapping the Coulomb interactions into the perturbation to the noninteracting electron kinetic energy ε k = −t∑ δ e −ikδ (see Supporting Information for details). The energy of the quasi-particle for the nondegenerate extended Hubbard model within the mean field approximation is 66,67 ε ε…”

“…Despite a number of Hubbard model studies on ferromagnetic NWs, − such a Hubbard model has not been well tested by using DFT. Thus, addressing the techniques used for qualitative derivation of variation of bandwidth with magnetization based on the Hubbard model in the Supporting Information, we report a quantitative description of results obtained from DFT calculations.…”