Van Hove singularity-induced multiple magnetic transitions in multi-orbital systems

Abstract

Van Hove singularities (VHSs) amplify electronic correlations, providing a crucial platform for discovering novel quantum phase transitions. Here, we show that VHSs in multi-orbital systems can stabilize a variety of competing $\bm{Q}=0$ magnetic orders, including intrinsic altermagnetism emerging from spontaneous orbital antiferromagnetism. This intrinsic phase, in which antiparallel spins reside on distinct orbitals, is realized across all four 2D Bravais lattices. It is driven by orbital-resolved spin fluctuations enhanced by inter-orbital hopping and favors suppressed Hund's coupling $J_H$, strong inter-orbital hybridization, and filling near a VHS from quadratic band touching. Through Hubbard-$U$-$J_H$ phase diagrams we map several magnetic phase transitions: (i) ferrimagnet to $d$-wave extrinsic altermagnet, (ii) $d$-wave intrinsic altermagnet to ferromagnet, and (iii) $g$-wave extrinsic altermagnet to either $d$-wave extrinsic altermagnet or ferromagnet. Our work identifies VHSs as a generic route to altermagnetism in correlated materials.

Figures (7)

• Figure 1: Competing magnetic orders in a two-orbital square lattice model. (a) Schematic of the square lattice with two orbitals ($d_{xz}$, $d_{yz}$) and $A$ (orange) and $B$ (green) sublattices. Hopping parameters include intra-orbital terms ($t_0, t_1, t_2$) and and inter-orbital terms ($t_3, t_5$). (b) Tight-binding band structure with parameters $\{t_0,t_1,t_2,t_3,t_5\}=\{ 1,0.05,0.05,0.48,0.29\}$. Gray line is $\mu=-0.19$. (c) Tight-binding band structure with parameters $\{t_0,t_1,t_2,t_3,t_5\}=\{ 1,0.1,0.05,0.32,0.13\}$. Gray line is $\mu=-0.3$. (d) Six possible $\bm{Q}=\bm{0}$ magnetic order configurations within a unit cell, where blue ($\color{blue}\uparrow$) and red ($\color{red}\downarrow$) arrows represent the spin polarization of magnetic moments.
• Figure 2: Momentum-space distribution of RPA susceptibilities $\chi^{\text{RPA}}_{\alpha}(\bm{k})$. (a-f) Calculated susceptibility $\chi^{\text{RPA}}_{1 \to 6}(\bm{k})$ for $U=1$ and $J_H=0.2$. The ${\cal O}_4$ phase (panel d) exhibits the strongest susceptibility with pronounced peaks at the $\Gamma$ point (slightly exceeding that of the ${\cal O}_3$ phase in panel (c). All calculations use the same parameters as in Fig. \ref{['Lattice']}(c).
• Figure 3: The phase diagram with $d$-wave extrinsic altermagnetic phase [Case I]. (a) The $U$–$J_H$ phase diagram for parameters used in Fig. \ref{['Lattice']}(c) shows: extrinsic $d$-wave altermagnetic phase (${\cal O}_4$, purple), ferrimagnetic phase (${\cal O}_3$, green), and non-magnetic phase (white). The magnetic-to-non-magnetic boundary is marked by the critical $U_c$ (solid black curve); the dashed line at $J_H/U=0.114$ separates the $\mathcal{O}_3$ and $\mathcal{O}_4$ phases. (b) The two largest eigenvalues of the susceptibility matrix correspond to the ${\cal O}_3$ and ${\cal O}_4$ phases. (c,d) Divergence of the susceptibility difference ${\chi}^{\text{RPA}}_{\Gamma,1}-{\chi}^{\text{RPA}}_{\Gamma,6}$ as $U$ approaches $U_c$, with $U=(1-1/N_r)U_c$ and $N_r$ running from $0$ to $200$. Results are shown for $J_H/U=0.05$ (c) and $J_H/U=0.2$ (d). All calculations employ the band parameters of Fig. \ref{['Lattice']}(c). (e) The transition between ${\cal O}_3$ and ${\cal O}_6$ occurs at $J_H/U=0.047$. Parameters: $\{ t_0,t_1,t_2,t_3,t_5,\mu\} = \{1,0.42,0.08,0.7,0.49,-1\}$.
• Figure 4: The phase diagram with $d$-wave intrinsic altermagnetic phase [Case II]. (a) The phase diagram for parameters used in Fig. \ref{['Lattice']}(b) shows: intrinsic $d$-wave altermagnetic phase (${\cal O}_1$, blue), ferromagnetic phase (${\cal O}_6$, gray), and non-magnetic phase (white). The dashed line separates the ${\cal O}_1$ and ${\cal O}_6$ phases at $J_H/U=0.098$. The parameters are the same as Fig. \ref{['Lattice']}(b). (b) Similarly, using another set of band parameters leads to the other intrinsic altermagnetic phase (${\cal O}_2$, red). The phase boundary between $\mathcal{O}_2$ and $\mathcal{O}_6$ is $J_H/U = 0.144$. Parameters: $\{t_0,t_1,t_2,t_3,t_5,\mu \}=\{ 1,0.25,0.25,0.17,0.07,-1\}$.
• Figure 5: The phase diagram with $g$-wave extrinsic altermagnetic phase [Case III]. (a) Phase diagram includes extrinsic $g$-wave altermagnetic phase (${\cal O}_5$, brown), extrinsic $d$-wave altermagnetic phase (${\cal O}_4$, purple), and non-magnetic phase (white). The transition between ${\cal O}_5$ and ${\cal O}_4$ occurs at $J_H/U=0.1$. Parameters: $\{ t_0,t_1,t_2,t_3,t_5,\mu\} = \{1,0.1,0.05,0.14,0.2,-0.26\}$. (b) shows the transition from ${\cal O}_5$ to ${\cal O}_6$ at $J_H/U=0.126$. Parameters: $\{ t_0,t_1,t_2,t_3,t_5,\mu \} = \{1,0.1,0.05,0.36,0.32,-0.08 \}$.