Spontaneous Fully Compensated Ferrimagnetism

Abstract

We propose a general mechanism for the spontaneous emergence of filling-enforced fully compensated ferrimagnetism (fFIM), characterized by zero net magnetization yet ferromagnetic-like spin-split band structures. Using Hartree-Fock mean-field calculations of the Hubbard model, we map out the stability regime of spontaneous fFIM over a broad parameter space of interaction strength and staggered potential. We show the unique quantum-geometry-governed optical selection rules and the abundant valley- and spin-related physics of electronics and optics arising from the emergence of fFIM order, with tunable spin-polarized and valley-contrasting charge and spin currents. Furthermore, based on our theory, we demonstrate that spontaneous fFIM can be realized in nominally nonmagnetic graphene via defect engineering. Our results establish a unified framework for the mechanism, emergent properties, and materials realization of spontaneous fFIM, opening new opportunities for spintronic, valleytronic, and optoelectronic applications.

Figures (3)

• Figure 1: Spontaneous fully compensated ferrimagnetism in Hubbard models. (a) Honeycomb lattice model. The honeycomb lattice vectors are defined as $\boldsymbol{a_{1}}=(1/2,\sqrt{3}/2)$ and $\boldsymbol{a_{2}}=(1,0)$. (b) Square lattice model. The square lattice model are defined as $\boldsymbol{b_{1}}=1/\sqrt{2}(1,1)$ and $\boldsymbol{b_{2}}=1/\sqrt{2}(1,-1)$. The onsite energies $u_A$ and $u_B$ are applied on sublattices A and B. (c)-(d) The Hartree-Fock mean-field phase diagrams in the $U/t$-$\Delta/t$ plane for (c) honeycomb lattice and (d) square lattice at half-filling. AFM, fFIM, NM denote conventional antiferromagnetism, filling-enforced fully compensated ferrigmanetism and non-magnetism, respectively. (e1)-(e2) Band spectra of half-metallic and gapped fFIM honeycomb model. The parameters are chosen to be $U=5t$, $\Delta=3.89t$ in (e1) and $U=5t$, $\Delta=4.1t$ in (e2). (f1)-(f2) Band spectra of AFM and fFIM square lattice. The parameters are chosen to be $U=3.2t$, $\Delta=0$ in (f1) and $U=5t$, $\Delta=t$ in (f2). The red and blue colors represent the spin-up and spin-down components, respectively.
• Figure 2: Circular and linear polarized optical selection rules in spontaneous fFIMs. (a) Degrees of circular polarization in the honeycomb lattice. (b) Degrees of linear polarization in the square lattice. In this case, additional next nearest neighbor hopping is included, which induces two valleys in the energy spectrum. (c) Valley-contrasted selection rules of circularly polarized light in $K_{+}$ and $K_{-}$ valleys. The Berry curvatures of the two valleys are opposite in sign, leading to opposite circular polarization selectivity. Excited electrons exhibit the same longitudinal and opposite transverse currents. Reversing the staggered potential switches spin polarization and the valley selection for a specific circular polarization of light. (d) Valley-contrasted selection rules of linearly polarized light. X and Y denote two valleys with opposite quantum metric. The Berry curvatures are zero, with zero transverse current. The spin-up and spin-down in the band structure are labeled in red and blue. Holes alongside the excited electrons, possessing both opposite velocity and opposite spin relative to their electronic counterparts. The parameters are taken as $U=4t$ and $\Delta=2t$ for (a) and $U=4.8t$ and $\Delta=0.7t$ for (b).
• Figure 3: Spontaneous fFIM in graphene with vacancies. (a) The 6$\times$6 graphene supercell with two pairs of vacancies. The red regions represent spin-up components, and the blue regions represent spin-down components. (b) Illustration of magnetic distribution. Magnetic moments are predominantly localized on the carbon atoms containing an unpaired $\pi$-electron. (c) Band structure. (d) Density of states (DOS) and integrated density of states (IDOS). From the DOS, we can see that the Fermi energy level lies in the gap. The IDOS diagram reveals that the spin-up and spin-down electronic states at the Fermi level exhibit full compensation.