Nesting-driven ferromagnetism of itinerant electrons

TL;DR

The paper investigates a nesting driven mechanism for ferromagnetism in a model of itinerant electrons and holes with repulsive interactions, incorporating electron-lattice coupling to stabilize density wave states. Using a mean-field approach, it shows that the undoped system forms insulating SDW or CDW order, while finite doping induces a ferromagnetic, half-metallic state with spin flavor polarization, distinct from the Stoner scenario. A detailed phase diagram is constructed, highlighting how the lattice coupling and doping control the competition between SDW and CDW order and the emergence of half-metallicity, including first order transitions and cone-like spin textures. The work discusses limitations of mean-field and weak-coupling assumptions and suggests experimental platforms such as graphene multilayers and hexaborides where nesting driven order and doping induced ferromagnetism may be realized.

Abstract

We theoretically investigate a model with electrons and holes whose Fermi surfaces are perfectly nested. The fermions are assumed to be interacting, both with each other and with the lattice. To suppress inhomogeneous states, a sufficiently strong long-range Coulomb repulsion is included into the model. Using the mean field approximation, one can demonstrate that in the absence of doping, the ground state of such a model is insulating and possesses a density-wave order, either SDW, or CDW. Upon doping, a finite ferromagnetic polarization emerges. It is argued that the mechanism driving the ferromagnetism is not of the Stoner type. A phase diagram of the model is constructed, and various properties of the ordered phases, such as half-metallicity and cone magnetic structure, are studied.

Figures (8)

• Figure 1: Single-fermion dispersion schematics. (a) The congruence of electron and hole cross sections of $\varepsilon_{a,b}$ - curves clearly demonstrate the nested Fermi surfaces separated by the nesting vector $\mathbf{Q}$. (b) The finite doping ($\mu$) destroys the ideal nesting of Fermi surfaces (unequal cross-sections).
• Figure 2: Dispersion curves $E_{\sigma,\pm}$, see Eq.(21), modified to account for finite doping. The electron mass $m_a$ is larger than the hole mass $m_b$. To simplify the drawing, we assumed that the nesting vector ${\bf Q}$ is zero. Vertical axis represents energy, horizontal axis is momentum $p$. The chemical potential level is shown by the horizontal dashed line. Two sectors are doped differently: one is empty (the corresponding dispersion curve lies above $\mu$), the other one contains all extra charges accumulated between $p_-$ and $p_+$. The momentum $p_c$ corresponding to the minimum of the conduction band differs from the momentum $p_v$ corresponding to the maximum of the valence band marking the indirect gap [see the discussion after Eq. \ref{['gap0']}].
• Figure 3: Magnetization vector behavior for different orientation of nesting vector $\mathbf{Q}$ as radius vector $\mathbf{r}$ moves along $\mathbf{Q}$. For illustrative purposes, we choose $|\Delta_\downarrow|/ |\Delta_\uparrow|=2$ and $S_z = 1.3 |\Delta_\uparrow|/g$. (a) The magnetic polarization vectors (laid off from the same point) sweeping out a conical shape, as the radius vector $\mathbf{r}$ moves along the nesting vector $\mathbf{Q}$. (b-d): the behavior of magnetization vector in coordinate space. (b) $\mathbf{Q}$ is oriented in $y$ direction. (c) $\mathbf{Q}$ direction is shown with the dashed line, $\mathbf{Q} \propto [0, 1/\sqrt{5},2/\sqrt{5}]$. (d) $\mathbf{Q} \propto [0, 0, 1]$, the helical structure is clearly pronounced.
• Figure 4: The region of existence of the CDW half-metal. The asymmetric solution of \ref{['self2']} exists in the shaded (blue) area. When dimensionless doping exceeds the critical value $X_c$, the consistency relation (\ref{['cons']}) is violated, implying the disappearance of the half-metallic phase. The curve $X_c = X_c (|W|)$ is parametrically determined by Eq. (\ref{['curve']}). Asymptotically, at $|W|\gg1$, it becomes a simple hyperbola $X=|W|^{-1}$.
• Figure 5: (a) Dimensionless chemical potential as a function of dimensionless particle number $X$ and coupling constant $W$ for the asymmetric CDW state. Only the ${\bar{\sigma}}$ sector is doped. The corner-like shape $\nu = 1/2+|X-1/2|$ is clearly pronounced at zero coupling $W=0$. (b) Dimensionless order parameter $\delta_{\bar{\sigma}}$ as a function of the same parameters. A simple solution of system \ref{['self2']} is clearly evident at $W=0$, where $\delta_{\bar{\sigma}} = \sqrt{1-2X},\ X<1/2$, and the gap closes ($\delta_{\bar{\sigma}} = 0$), at $X>1/2$.