Spectroscopic evidence of Kondo resonance in 3$d$ van der Waals ferromagnets

TL;DR

The paper investigates how localized moments and itinerant electrons interact in a 3d van der Waals ferromagnet by studying Co-doped Fe$_3$GeTe$_2$ using temperature-dependent high-resolution photoemission spectroscopy and DFT+DMFT. They observe a Kondo resonance near $E_F$ at low $T$ that strengthens with increasing Co content, and they quantify a Kondo temperature $T_K$ that rises from approximately $190$ K to about $730$ K, signaling approach to a quantum critical point. Core-level and valence-band spectra show minimal changes across the magnetic transition, while DFT+DMFT reproduces spin-split bands persisting above $T_C$, supporting a non-Stoner, correlated-electron scenario. Together, these results establish a tunable route to explore heavy-fermion-like behavior and quantum criticality in a 3d vdW magnet.

Abstract

Two-dimensional van der Waals (vdW) ferromagnets drive the advancement in spintronic applications and enable the exploration of exotic magnetism in low-dimensional systems. The entanglement of dual $-$ localized and itinerant $-$ nature of electrons lies at the heart of the correlated electron systems giving rise to exotic ground state properties such as complex magnetism, heavy fermionic behavior, Kondo lattice formation, \textit{etc}. Through temperature-dependent electronic structure of vdW ferromagnets, (Co$_{x}$Fe$_{1-x}$)$_{3}$GeTe$_{2}$, probed using high-resolution photoemission spectroscopy and density functional theory combined with dynamical mean field theory (DFT+DMFT), we provide direct evidence of the emergence of Kondo resonance peak driven by complex interplay between localized and itinerant electrons. In overall agreement with experimental electronic structure and magnetic properties, DFT+DMFT also reveals finite spin band splitting well beyond $T_{C}$. Core levels, valence band photoemission spectra together with DFT+DMFT spectral functions reveal insignificant change across $T_{C}$ indicating non-Stoner magnetism in (Co$_{x}$Fe$_{1-x}$)$_{3}$GeTe$_{2}$. Our results provide a way forward to the understanding of complex interplay between electronic structure, exotic magnetism and heavy fermionic behavior leading to Kondo scenerio in 3$d$ vdW ferromagnets.

Figures (5)

• Figure 1: Photoemission spectra of (a) Co 2$p$ and (b) Fe 2$p$ core levels, and (c) valence band, collected at 300 K (black symbols) and 30 K (red lines) using Al $K_{\alpha}$ for Co$_{x}$FGT (x = 0.35, 0.45 and 0.55), in vertically stacked order. Shaded regions in (a) and (b) schematically depicts intensity of Fe and Co Auger, respectively. Inset of (c) shows the comparison of valence band spectra in the vicinity of $E_{F}$ at 300 K for Co$_{x}$FGT (x = 0, 0.35, 0.45 and 0.55).
• Figure 2: DFT+DMFT results. (a) Total spectral functions for Co$_{x}$FGT (x = 0, 0.35, 0.45 and 0.55) in PM phase. (b) Comparison of total spectral function for Co$_{0.55}$FGT in the PM and FM phases. (c) Spin-up (solid lines) and spin-down (dot-dash lines) spectral functions of Fe/Co in FM phase. (d) Magnetic moment at various $T$ within FM phase.
• Figure 3: $k$-resolved spectral functions for (a) spin-up and (b) spin-down, along high symmetry directions at T = 50 K obtained using FM DFT+DMFT calculations for Co$_{x}$FGT (x = 0.35, 0.45, and 0.55). (c) $\varGamma$/k$_{B}T$ for d$_{z^2}$, $d_{{{x}^{2}}-{{y}^{2}}}$/$d_{xy}$ and $d_{xz}$/$d_{yz}$ orbitals (top to bottom) for both the spin channels and for both the non-degenerate Fe/Co sites at various T for Co$_{x}$FGT. Spin-up and spin-down are shown in closed markers and open markers, respectively for Fe/Co I (brown) and Fe/Co II (green).
• Figure 4: (a-c) $T$-dependent high-resolution valence band spectra of Co$_{x}$FGT for (a) x = 0.35, (b) x= 0.45, and (c) x = 0.55, while the insets show the comparison of 30 K spectra with resolution broadened FD function around $E_{F}$. (d-f) Corresponding SDOS has been shown (upto 5$k_BT$) in (d), (e), and (f), respectively. SDOS for T = 250 K is overlaid (grey lines) with SDOS for T = 30 K for all x. The inset in (d) shows the $T$-dependent spectra of Silver as a reference.
• Figure 5: (a)-(c) Schematic representation of T-dependent evolution of the Kondo lattice along with DFT+DMFT spectral functions for Co$_{0.55}$FGT. Red and blue sheets represent up spin and down spin itinerant electrons and thick arrows represent localized moments. (d) Effective local moment, $\mu_{eff}^2$ obtained from DFT+DMFT for Co$_{x}$FGT (where, $x$ = 0, 0.35, 0.45 and 0.55) at various $T$. The $T_K$ is obtained from the fit to the universal dependence for the Kondo model (KM, grey dash lines) PhysRevB.21.1003.