Breakdown of Stoner Ferromagnetism by Intrinsic Altermagnetism

Abstract

The Stoner criterion for ferromagnetism arises from interaction-driven asymmetric filling of spin bands, requiring that the spin susceptibility: (i) peaks dominantly at $\mathbf{Q}=\bm{0}$; and (ii) diverges at a critical interaction strength. Here, we demonstrate that this Stoner mechanism breaks down due to competition with altermagnetic orders, even when both conditions are met. Altermagnetism in solids is characterized by collinear antiparallel spin alignment that preserves translational symmetry, and inherently fulfills these requirements. As a proof of concept, we study a two-orbital Hubbard model with electron filling near Van Hove singularities at high-symmetry momenta. Our results reveal that orbital-resolved spin fluctuations, amplified by strong inter-orbital hopping, stabilize intrinsic altermagnetic order. A quantum phase transition from altermagnetism to ferromagnetism occurs at critical Hund's coupling $J_H$. We further propose directional spin conductivity anisotropy as a detectable signature of this transition via non-local spin transport. This work establishes the pivotal role of altermagnetism in correlated systems.

Figures (4)

• Figure 1: Breakdown of Stoner FM. (a) First Stoner condition: dominant spin susceptibility at $\bm{q}=\bm{0}$. (b) Second Stoner condition: susceptibility divergence at critical $U_c$. (c) Illustration for the competition between FM and AM in the $t$-$J_H$ phase diagram. (d) Dual breakdown mechanisms of Stoner FM: (i) FM $\to$ Néel AFM transition when $\chi_{\text{spin}}^{\text{RPA}}(\bm{q}) > \chi_{\text{spin}}^{\text{RPA}}(\bm{0})$ (established mechanism moriya2012spincoleman2015introduction); and (ii) FM $\to$ AM transition when $\chi_{\text{AM}}^{\text{RPA}}(\bm{0}) > \chi_{\text{FM}}^{\text{RPA}}(\bm{0})$ (this work). A complete theory of Stoner FM must account for both breakdown channels.
• Figure 2: Fermi surface, band structure and $\chi ^{(0)}(\bm{k})$ in the two-orbital square lattice model. (a) Band structure and the corresponding density of states (DOS) distribution. (b) Fermi surface in the first Brillouin zone, showing density-of-states "hot spots" near high-symmetry points $\textbf{X}$ and $\textbf{Y}$ due to VHS. (c) Corresponding schematic band structure near the Fermi level. The nesting vector $\bm{Q}_1=(0,0)$, $\bm{Q}_2=(\pi,\pi)$. (d) Real-space configurations of ferromagnetic order and $\tau_z$-type altermagnetic order. (e) Bare susceptibilities in the $\tau_z$-type altermagnetic and ferromagnetic channels along the high-symmetry paths in the first Brillouin zone.
• Figure 3: Comparison of susceptibilities between different magnetic orders and the corresponding interaction phase diagram at the RPA level. (a) High-symmetry-line plots of $\tau_z$-type AM ($\text{AM}_z$) and FM susceptibilities with $J_H/U=0.05$ and $U=2$. (b) Same as (a) for $J_H/U=0.2$. (c) Phase diagram showing three distinct regimes: the altermagnetic phase ($\text{AM}_z$,blue), ferromagnetic phase (FM, gray), and non-magnetic phase (white). The magnetic-to-non-magnetic boundary is marked by the critical $U_c$ (solid black curve), while the dashed line ($J_H/U=0.092$) separates the $\tau_z$-type AM and FM phases. (d) The two dominant eigenvalues of the susceptibility matrix $[\chi^{\text{RPA}}_\text{spin}(0)]^{l_1l_1}_{l_2l_2}$ correspond to two magnetic phases: $\text{AM}_z$ and FM. Their eigenvalues $\lambda$ evolve with the ratio $J_H/U$, tracking the transition at $J_H/U=0.092$ between these two phases. (e) The divergent behavior of ${\chi}^{\text{RPA}}_{\Gamma,\text{AM}_z}-{\chi}^{\text{RPA}}_{\Gamma,\text{FM}}$ as $U$ approaches $U_c$, where $U=(1-1/N_r)U_c$ with $N_r$ increasing from $0$ to $200$. Results are shown for $J_H/U=0.05$ and $J_H/U=0.2$. All calculations use the same parameters as in Fig. \ref{['Lattice']}(a). (f) Phase diagram in the $t_2$–$J_H$ plane calculated at $U = 2$ with band parameters $\{t_0, t_1, t^{\prime}_1, t_2, \mu\} = \{1, 0.15, 0.6, 0.77, -0.625\}$.
• Figure 4: Spin conductivity anisotropy as a probe of quantum phase transition. (a) Fermi surface with $d$-wave spin splitting induced by the $\tau_z$-type AM order with $\Delta_{\text{AM}}=0.2$. (b) Fermi surface with isotropic spin splitting from the ferromagnetic order with $\Delta_{\text{FM}}=0.2$. (c) Anisotropic spin conductivity $\sigma_{\parallel}(\theta)$ for $\tau_z$-type AM, following $\sigma_{\parallel}(\theta)=\sigma^z_{xx}\cos(2\theta)$ with $\sigma^z_{xx}=-\sigma^z_{yy}=8.83$, characteristic of $d$-wave symmetry. (d) Nearly isotropic spin conductivity for FM, demonstrating distinct transport signatures between phases. All calculations use the same parameters as in Fig. \ref{['Lattice']}(b).