CeCo$_2$P$_2$: a unique Co-antiferromagnetic topological heavy-fermion system with $P\cdot T$-protected Kondo effect and nodal-line excitations

Abstract

Based on high-throughput screening and experimental data, we find that CeCo$_2$P$_2$ is unique in heavy-fermion materials: it has a Kondo effect at a high temperature which is nonetheless below a Co-antiferromagnetic ordering temperature. This begs the question: how is the Kondo singlet formed? \emph{All} other magnetic Kondo materials do not first form magnetism on the atoms whose electrons are supposed to screen the local moments. We theoretically explain these observations and show the multifaceted uniqueness of CeCo$_2$P$_2$: a playground for Kondo, magnetism, flat band, and topological physics. At high temperatures, the itinerant Co $c$ electrons of the system form non-atomic bands with a narrow bandwidth, leading to a high antiferromagnetic transition temperature. We show that the quantum geometry of the bands promotes in-plane ferromagnetism, while the weak dispersion along the $z$ direction facilitates out-of-plane antiferromagnetism. At low temperatures, we uncover a novel phase that manifests the coexistence of Co-antiferromagnetism and the Kondo effect, linked to the $P\cdot T$-protected Kramers' doublets and the filling-enforced metallic nature of $c$ electrons in the antiferromagnetic phase. Subsequently, the emergence of the Kondo effect, in cooperation with glide-mirror-$z$ symmetry, creates nodal-line excitation near the Fermi energy. Our results emphasize the importance of lattice symmetry and quantum geometry, Kondo physics, and magnetism in the understanding of the correlation physics of this unique compound. We also test our theory on the structurally similar compound LaCo$_2$P$_2$ and show how we are able to understand its vastly different phase diagram.

Figures (31)

• Figure 1: Theoretical and experimental phase diagram of the system.
• Figure 2: (a) DFT band structures in the primitive cell and density of states of PM phase. Green dot marks the weight of Co $(d_{z^2},d_{x^2-y^2})$ orbitals. (b) Comparison between band structures of two-orbital model (red lines) and DFT model (dashed black lines). The two-orbital model successfully reproduces the narrow bands near the Fermi energy. (c) DFT band structures of AFM phase. Green dot marks the weight of Co $(d_{z^2},d_{x^2-y^2})$ orbitals. The yellow-shaded region marks the narrow bands. (d) Magnetic structure of the system.
• Figure 3: (a) Illustration of Kondo-singlet formation in the AFM phase. The spin $\uparrow$$c$ electrons of Co-P layer $I$ (green) and spin $\downarrow$$c$ electrons of Co-P layer $II$ (blue) are degenerate and form the Kondo singlet with the $f$ local moments of Ce (orange). (b) Evolution of the $fc$ hybridization strength $\chi\sim \langle f^\dag c\rangle$ at different strength of Co magnetic orders ($U_dm$) and temperatures $T$. We observe the stability of the Kondo phase, even in the presence of strong magnetic ordering. We can observe the Kondo temperature tends to saturate as we increase $U_d m$. (c) Spectrum of the Kondo phase obtained from embedded DMFT (DFT+DMFT) calculations. Different colors indicate the spectral weight contributions from various electronic components. (d) Band structures of the Kondo phase in a smaller energy window (obtained from large-$N$ calculations). Red and blue mark the bands with opposite glide-mirror-$z$ eigenvalues. We can observe the formation of the nodal line as marked by green dots.
• Figure S4: Lattice structures and magnetic structures.
• Figure S5: DFT-calculated band structure and density of states (DOS) of PM phase where $f$ electrons have been treated as core states.