Altermagnetism in exactly solvable model: the Ising-Kondo lattice model

TL;DR

This work demonstrates the emergence of altermagnetism (AM) in an exactly solvable Ising-Kondo lattice model on a square lattice with alternating next-nearest-neighbor hopping. By mapping the model to an effective Falicov-Kimball-like problem and solving it with lattice Monte Carlo, the authors identify a robust d-wave AM phase near half filling, characterized by spin-split quasiparticle bands and spin-resolved spectral functions. They map out ground-state and finite-temperature phase diagrams, show AM persists across a broad range of $J$, doping, and NNNH strength, and confirm the $d$-wave symmetry via impurity and transport analyses. The study also discusses impurity effects and observables, including a sizable spin-polarized conductivity in AM, offering a solid theoretical platform for exploring AM-like phases in heavy-fermion materials.

Abstract

Altermagnet (AM), a recently identified class of collinear magnet, has garnered significant attention due to its unique combination of zero net magnetization and spin-split energy bands, leading to a variety of novel physical phenomena. Using numerically exact lattice Monte Carlo simulations, we investigate AM-like phases within the Ising-Kondo lattice model which is commonly employed to describe heavy-fermion materials. By incorporating an alternating next-nearest-neighbor hopping (NNNH) term, which arises from the influence of non-magnetic atoms in altermagnetic candidate materials, our results reveal key signatures of AM-like states, including spin-splitting quasiparticle bands and spectral functions, and demonstrate that d-wave AM remains stable across a broad range of interaction strengths, doping levels, NNNH amplitudes and temperatures, highlighting its robustness. Furthermore, through an analysis of non-magnetic impurity effects, we further confirm the d-wave symmetry of the AM phase. These findings establish a solid theoretical foundation for exploring AM-like phases in f-electron compounds, paving the way for future investigations into their exotic magnetic and electronic properties.

Figures (16)

• Figure 1: The Ising-Kondo lattice model on a square lattice with alternating next-nearest-neighbor-hopping (NNNH), $t_{+}$ and $t_{-}$. The lower layer denotes local spin moments of $f$-electron, which interact with the conduction electron in the upper layer via only longitudinal Kondo exchange.
• Figure 2: (a) The schematic ground state phase diagram of the Ising-Kondo lattice model as a function of NNNH $t_{-}-t_{+}$ and chemical potential $\mu$. There exist three distinct states, i.e., altermagnet (AM), normal antiferromagnet (NAF, corresponding to $t_{-}-t_{+}=0$, i.e., the dashed line with pentagram) and the spin density wave (SDW). (b) the range of electron density for part (a) with varying $t_{-}-t_{+}$ and $\mu$. Only when $n_{c}$ is in the vicinity of half filling and $t_{-}\neq t_{+}$, AM occurs. The other parameters are $J=3$ and $t_{+}$=0.3.
• Figure 3: (a) Spin-splitting bands in the AM state ($t_{-}-t_{+}=-0.2$). The $C_{4z}$ symmetry of bands indicates a d-wave AM state. (b) Spin-degenerated bands in the NAM state ($t_{-}-t_{+}=0$). The other parameters are $J=3$, $t_{+}=0.3$ and $n_{c}=1$.
• Figure 4: The spectral function $A(k,\omega)$ for $t_{-}-t_{+}=-0.2$. (a) and (b) correspond to the cases for spin-up and spin-down, respectively, with $\mu=0.22$ (half filling) in AM; (c) and (d) correspond to the cases for $\mu=1.1$ (far away from half-filling) in SDW. The other parameters are $t_{+}=0.3$ and $J=3$.
• Figure 5: The first derivative of energy $E$ with respect to the chemical potential $\mu$ in the Ising-Kondo lattice model, $dE/d\mu$, for different values of $t_{-}-t_{+}$. The other parameters are $J=3$ and $t_{+}=0.3$.