Spin Seebeck effect in magnetic junctions with a compensated ferrimagnet

Technical Summary: Spin Seebeck Effect in Magnetic Junctions with a Compensated Ferrimagnet

Problem Statement
The paper addresses the challenge of generating efficient thermal spin currents in magnetically compensated systems (those with zero net magnetization). While recent studies have established that collinear antiferromagnets with sublattice-dependent environments can exhibit spin splitting, the mechanisms and magnitudes of spin transport vary significantly between system classes. Specifically, "altermagnets" exhibit anisotropic, momentum-dependent splitting, whereas "compensated ferrimagnets" (CFs) can exhibit nearly isotropic splitting. Previous theoretical work on CFs focused on mechanisms driven by unequal single-ion anisotropies, which typically yield spin Seebeck effect (SSE) signals orders of magnitude smaller than those in ferromagnetic junctions. Furthermore, single-ion anisotropies are often small and difficult to tune experimentally, particularly in organic materials and van der Waals heterostructures. The authors aim to investigate whether an alternative mechanism—exchange-coupling asymmetry—can produce robust, ferromagnet-like spin currents in CFs without relying on a finite anisotropy gap.

Methodology
The study employs a theoretical framework based on a quantum Heisenberg model defined on a square lattice with a four-sublattice unit cell.

• Model Construction: The compensated ferrimagnet is modeled with antiferromagnetic exchange interactions ($J > 0$) and two distinct ferromagnetic exchange interactions ($J_1, J_2 < 0$). The inequivalence of sublattices arises from the condition $J_1 \neq J_2$, rather than single-ion anisotropy. This setup creates an intrinsically compensated state with zero net magnetization at zero temperature.
• Spin-Wave Approximation: The Hamiltonian is linearized using the Holstein–Primakoff transformation to describe magnon excitations. A Bogoliubov transformation is applied to diagonalize the Hamiltonian, yielding magnon dispersion relations ($\varepsilon_{j\mathbf{k}}$).
• Transport Formalism: The spin current flowing from the CF into an adjacent normal metal (NM) is calculated using the nonequilibrium Green's function (NEGF) method within the Keldysh formalism. The calculation is performed to the second order in the interfacial exchange coupling ($J_{int}$), assuming configurational averaging over interface disorder.
• Comparative Analysis: The derived expressions for the SSE in CF/NM junctions are benchmarked against standard ferromagnetic insulator (FI)/NM junctions and altermagnet (AM)/NM junctions. The altermagnet case is analyzed using a two-sublattice model with a paraunitary Bogoliubov transformation to test the effect of anisotropic splitting.

Key Contributions and Results

1. Isotropic Magnon Splitting: The four-sublattice model with exchange-coupling asymmetry ($J_1 \neq J_2$) generates isotropic (s-wave-like) magnon splitting across the Brillouin zone. Unlike altermagnets, where splitting is anisotropic (d-wave-like) and vanishes along nodal lines, the CF model maintains a finite energy difference between magnon branches ($\varepsilon_1 \neq \varepsilon_2$) throughout the zone (except at the $\Gamma$ point).
2. Robust Spin Current Magnitude: The numerical evaluation of the thermally driven spin current ($I_S^{SSE}$) reveals that the signal in CF/NM junctions is comparable in magnitude to that of standard ferromagnetic junctions. This stands in stark contrast to the anisotropy-based CF model studied previously, where the signal was approximately two orders of magnitude smaller. The authors attribute this enhancement to the energy scale of the splitting: in the exchange-coupling model, the splitting is governed by $|J_1 - J_2|$, which can be of the same order as the exchange coupling $J$, whereas anisotropy-based splitting is limited by the much smaller single-ion anisotropy energy.
3. Vanishing Signal in Altermagnets: The study demonstrates that under uniform interfacial coupling, the spin Seebeck effect vanishes identically in altermagnet/NM junctions. The anisotropic nature of the splitting causes the momentum summation over the Brillouin zone to cancel out the contributions, resulting in zero net spin current.
4. Thermally Induced Magnetization: While the net magnetization is zero at $T=0$, the model predicts a finite, temperature-induced magnetization at $T > 0$ due to the asymmetric thermal population of the split magnon branches. However, the authors note that this induced magnetization is too small to explain the observed spin current via conventional mechanisms, confirming that the SSE in this system is an intrinsic property of the compensated ferrimagnet's spin-splitting structure.

Significance
The paper establishes that compensated ferrimagnets with exchange-coupling asymmetry are uniquely suited for thermal spin-current generation among magnetically compensated systems. By leveraging exchange-coupling asymmetry—a mechanism naturally present in organic antiferromagnets and van der Waals heterostructures—the system achieves ferromagnet-like spin transport efficiency without the drawbacks of stray magnetic fields. The results provide a theoretical basis for utilizing these materials as stray-field-free spin-current sources in spintronic devices, distinguishing them from both conventional antiferromagnets and altermagnets, which yield vanishing or negligible signals under similar interface conditions.