Strong electron correlations can give rise to many exotic properties in materials, such as high temperature superconductivity, heavy fermions, quantum spin liquids, etc.^[1–3] Understanding the effect has been a grand challenge in condensed matter physics. An example of a strongly correlated electron system under extensive study is the Kondo lattice, in which a dense array of local magnetic moments interact with itinerant conduction electrons via the so-called Kondo effect. The competition between the Kondo effect, which results in screening of the local moment, and the Ruderman–Kittel–Kasuya–Yoshida (RKKY) interaction, which promotes ordering of the moment, leads to a variety of ground states, e.g., a Kondo insulator, an antiferromagnet, and a heavy fermion superconductor.^[2,4–13]

Note that the key ingredients of a Kondo lattice include local moments and itinerant electrons. A naive idea to design such a material is to embed an array of moments in a conductive material. Here, we demonstrate that this simple route is feasible by introducing the Kondo effect into a nonmagnetic van der Waals layered material via intercalation with local moments. We study V₅S₈ (or V_1/4VS₂), a self-intercalated compound of VS₂. The magnetic susceptibility, specific heat, electrical and thermoelectric transport studies coherently suggest Kondo physics at work and the consequent enhancement of electron correlation in V₅S₈. Intercalation of van der Waals materials has been well studied, for instance, in graphite and transition metal chalcogenides.^[14–16] Various chemical species with very different properties can be intercalated. Given a large body of van der Waals materials, we believe that this technique can be a versatile means to introduce a class of Kondo lattices. Moreover, the same idea can be applied to two-dimensional materials, too.^[17,18]

V₅S₈ bulk single crystals were grown by a chemical vapor transport method, using vanadium and sulfur powders as precursors and iodine as a transport agent. These species were loaded into a silica ampule under argon. The ampule was then evacuated, sealed, and heated gradually in a two-zone tube furnace to a temperature gradient of 1000 °C to 850 °C. After two weeks, single crystals with regular shapes and shiny facets can be obtained. X-ray experiments on grown crystals indicate a pure V₅S₈ phase. The crystallographic structure of the single crystal was further confirmed by high-angle annular dark field scanning transmission electron microscope (HAADF-STEM). Transport properties were measured using a standard lock-in method in an Oxford variable temperature cryostat from 1.5 K to 300 K. Heat capacity was measured in a Quantum Design physical properties measurement system. A Quantum Design SQUID magnetometer was employed to measure the magnetic susceptibility. Thermopower of bulk single crystals was measured using a standard four-probe steady-state method with a Chromel/AuFe(0.07%) thermocouple.

V₅S₈ can be seen as a van der Waals layered material VS₂ self-intercalated with V, i.e., V_1/4VS₂. It crystallizes in a monoclinic structure, space group C2/m. V atoms lie on three inequivalent sites. Intercalated V atoms take the V^I site, while V atoms in the VS₂ layer take V^II and V^III sites. Each V^I atom is surrounded by six S atoms, forming a distorted octahedron, shown in Fig. 1(b). The resultant crystal field is believed to be intricately related to the local magnetic moment of V atoms.^[19,20] Figure 1(a) shows a HAADF-STEM image of a single crystal, in which both V and S atoms can be clearly seen, as well as the rectangular arrangement of the intercalated V^I atoms. Images have been taken at various spots. All of them show high crystallinity and the same lattice orientation, indicating uniform V intercatlation (see Fig. A1 in Appendix A). A zoom-in and color-enhanced image is shown in the lower right of Fig. 1(a), which is in excellent accordance with the in-plane atomic model of V₅S₈. The lattice constants, a = 11.65v Å and b = 6.76 Å, are determined from a fast Fourier transformation (FFT) image shown in the upper right of Fig. 1(a).

VS₂ is a non-magnetic layered TMD.^[21] V₅S₈, however, becomes an antiferromagnetic (AFM) metal because of the local moment of the intercalated V ion. The magnetic susceptibility of V₅S₈ displays a paramagnetic behavior which follows the Curie–Weiss (CW) law at high temperatures and undergoes an antiferromagnetic transition at about 32 K, shown in Fig. 1.^[22] The high temperature CW behavior indicates local moments. Fitting of the paramagnetic susceptibility to the CW law, χ=χ0+CT−θCW, yields a positive CW temperature θ_CW ≈ 8.8 K despite the AFM order and an effective magnetic moment of μ_eff = 2.43μ_B per V₅S₈ formula unit (f.u.). This value is consistent with the reported ones, ranging from 2.12μ_B to 2.49μ_B.^[22–24] It is generally believed that only V^I ions carry a local magnetic moment.^[19,20,25] So, the measured moment is close to the theoretical value 2.64μ_B for V³⁺(3 d²).^[19,22,26] Below the Néel temperature, the moments point in the direction of 10.4° away from the c axis toward the a axis. They align as ↑↑↓↓ along the a axis, while ferromagnetically aligned along the b and c axes.^[19] Consequently, the in-plane (B ∥ ab plane) susceptibility is larger than the out-of-plane one. The field dependence of the out-of-plane magnetization displays a sudden change of the slope at about 4.5 T, seen in the inset of Fig. 1(c). This is caused by a metamagnetic spin-flop transition.^[22] Taking the measured paramagnetic moment of 2.43μ_B, S ≈ 0.8 is obtained, close to the expected value 2S = 1.7.^[27] However, below T_N, this moment was found to be smaller than expected, 0.7μ_B by neutron scattering or 0.22μ_B by nuclear magnetic resonance.^[25,28] This discrepancy has been an unresolved puzzle. We would also like to point out that the susceptibility deviates from the CW law below 140 K. In the following, we are going to show that this puzzle and the deviation can be explained in terms of hybridization of the local d-electrons on V^I with the conduction electrons in the VS₂ plane, a correlation effect known as the Kondo effect.

There have already been indications for interactions between the localized d-electrons and the conduction electrons in this system. Anomalous Hall effect, due to skew scattering of conduction electrons off from local moments, has been observed in V₅S₈.^[29] Photoemission-spectroscopy study has shown both local-moment-like and band-like features for V 3d electrons. To understand the discrepancy, it was thus postulated that the 3d electron that provides the local moment becomes partially itinerant at low temperatures.^[20] Recently, the Kondo effect has been observed in similar compounds, VSe₂ with dilute V intercalation^[30] and VTe₂ nanoplate.^[31] In V₅S₈, where local moments of V^I atoms arrange in a periodic array, a Kondo lattice may even emerge. It is expected that the effective mass of the conduction electron will be enhanced by the electron correlation. We have carried out specific heat measurements. The data of a 3.18 mg bulk single crystal are presented in Fig. 2(a). A sizeable jump at T_N = 32 K manifests the AFM transition. In the inset of Fig. 2(a), C(T)/T is plotted as a function of T². By a linear fit to C/T = γ + β T², the electronic Sommerfeld coefficient, γ = 74 mJ⋅K⁻² per mole of V^I atoms, is obtained, as is commonly done.^[2,6,32,33]

Since the system exhibits an antiferromagnetic order, to obtain γ more accurately, one needs to consider the contribution from spin waves. So, the total specific heat at low temperatures consists of three parts,

$$ \begin{eqnarray}C=\gamma T+\beta {T}^{3}+B\sqrt{T}{{\rm{e}}}^{-\varDelta /T},\end{eqnarray}$$ (1)

$$ \begin{eqnarray}{C}_{{\rm{la}}}=9NR{\left(\displaystyle \frac{T}{{\theta }_{{\rm{D}}}}\right)}^{3}\displaystyle {\int }_{0}^{{\theta }_{{\rm{D}}}/T}\displaystyle \frac{{x}^{4}{{\rm{e}}}^{x}}{{({{\rm{e}}}^{x}-1)}^{2}}{\rm{d}}x,\end{eqnarray}$$ (2)

Once β is determined, C at low temperatures is fitted to Eq. (1). In Fig. 2(b), we plot the three contributions to the total specific heat according to the fitting results. The fitted γ is 64 mJ⋅K⁻²⋅mol⁻¹, close to the one by the fit to C/T = γ + β T². Though much smaller than those in some f-electron heavy-fermion systems,^[6] the γ value is still comparable to that of some strongly correlated materials.^[32,33] The suppression of the Sommerfeld coefficient by magnetic ordering is typical in heavy fermion systems that order magnetically at low temperatures.^[6,32] This is because of the competition between the Kondo coupling and the RKKY interaction.^[4]

Such competition is reflected in the observed negative correlation between γ and T_N. In Fig. 2(c), the specific heat analysis has been carried out for three samples. These samples display a variation of T_N, likely due to different intercalation levels.^[22] As T_N decreases, the spin-wave gap Δ is gradually reduced, but γ increases from 64 mJ⋅K⁻²⋅mol⁻¹ to 158 mJ⋅K⁻²⋅mol⁻¹. Such a negative correlation is illustrated in the Doniach phase diagram of heavy fermion systems, indicating approaching to the quantum critical point.^[4] Similar behavior has been observed in Kondo systems with a magnetic order.^[41,42]

In order to better understand the Kondo scale in this system, we estimate the Kondo temperature T_K by the jump of the specific heat (δC) at the Néel temperature T_N. According to the mean field theory, without Kondo coupling, the discontinuity in the specific heat δC at T_N is^[43,4]

$$ \begin{eqnarray}\delta C=\displaystyle \frac{5S(S+1)}{2{S}^{2}+2S+1}{N}_{{\rm{A}}}{k}_{{\rm{B}}},\end{eqnarray}$$ (3)

Given the key effect of intercalated V atoms in introducing the Kondo effect, it would be informative to compare the intercalate V_1/4VS₂ and the host compound VS₂. However, it is challenging to grow VS₂ because of self intercalation and contradicting properties have been observed so far.^[46] Consequently, we have measured the specific heat of VSe₂ instead, an isoelectronic and isostructural compound of VS₂, shown in Appendix A. The Sommerfeld coefficient is found to be 46 mJ⋅K⁻² per mol of V₄Se₈, smaller than that of V₅S₈. This difference offers additional evidence for enhanced electronic correlation by the Kondo coupling.

To get an idea of the strength of the electron correlation, we estimate the effective quasiparticle mass enhanced by the correlation by comparing the experimental Sommerfeld coefficient to that calculated from the Kohn–Sham model to density functional theory (DFT).^[47] Within such a non-interacting electron model, the Sommerfeld coefficient can be estimated as γ=13π2kB2N(εF), where k_B is the Boltzmann constant and N(ε_F) is the density of states (DOS) per f.u. at the Fermi level ε_F. Our DFT calculation for the antiferromagetic phase of V₅S₈ yields an electronic DOS of 6.6 states/eV/f.u., which translates to a Sommerfeld coefficient of only 16.8 mJ⋅K⁻²⋅mol⁻¹. To understand the difference between the experimental value and the calculated one here, it is necessary to first take into account the electron–phonon coupling which can enhance the Sommerfeld coefficient by a factor of (1 + λ_ep), where λ_ep is the mass enhancement factor due to the electron–phonon coupling.^[48] A reasonable estimate of λ_ep is 1.19,^[49] which was obtained in V metal. This leads to an enhanced Sommerfeld coefficient of 36.8 mJ⋅K⁻²⋅mol⁻¹. Thus, one can see that, even after accounting for the electron–phonon coupling effect, the theoretical value estimated from a quasiparticle picture is still markedly smaller than the experimental one. We attribute the remaining discrepancy to the mass enhancement effect due to electron correlations. That is, electron correlations give rise to an enhanced effective mass of 1.58 m_e with m_e being the bare electron mass. The details of our DFT calculation for the electronic DOS can be found in Appendix B.

The temperature dependent resistivity of many metallic Kondo lattice materials exhibits characteristic features, such as a maximum, stemming from the Kondo scattering.^[6,50] Figure 3 shows the resistivity for three V₅S₈ single crystal samples A1, A2, and A3 grown from the same batch as sample A0. At 32 K, the resistivity exhibits a kink, which results from the antiferromagnetic transition. Above this temperature, there is an apparent hump at about 140 K, in stark contrast to a linear dependence commonly seen in metals.

In fact, VSe₂ displays a typical metallic resistivity linear in T. We tentatively subtract the resistivity of VSe₂ from that of V₅S₈ to highlight the effect of intercalated atoms. As shown in the inset of Fig. 3(a), the broad maximum is evident. This feature has been observed in Kondo lattices and believed to originate from coherent Kondo scattering.^[6,12,32,50] Although the crystal field may play a role, it often indicates collective local-moment deconfinement,^[9,51,52] The deconfinement also manifests as a deviation from the Curie–Weiss behavior, which is observed at almost the same temperature in our experiments, see Fig. 1(d). On the high temperature side of the maximum, the resistivity roughly follows a – lnT dependence, consistent with the effect of incoherent Kondo scattering.

We now turn to the low temperature resistivity in the AFM state. In the magnetically ordered state, the strong decrease of the resistivity below T_N is caused by the reduction of spin-disorder scattering. In this case, the resistivity consists of both the electronic contribution and the magnon scattering term, and takes the form

$$ \begin{eqnarray}\rho (T)={\rho }_{0}+A{T}^{2}+b\displaystyle \frac{T}{\varDelta }\left(1+2\left(\displaystyle \frac{T}{\varDelta }\right)\right){{\rm{e}}}^{-\varDelta /T},\end{eqnarray}$$ (4)

In strongly correlated systems, it has been found that the Kadowaki–Woods ratio, r_KW = A/γ², is significantly enhanced, around a₀ = 1.0 × 10⁻⁵ μΩ⋅cm(mol⋅K/mJ)².^[59] Using the obtained Sommerfeld coefficient γ = 64 mJ⋅K⁻²⋅mol⁻¹ and A ∼ 0.008 μΩ⋅cm⋅K⁻², we obtain r_KW = 0.20a₀. This value is comparable to those in d-electron strongly correlated systems such as LiV₂O₄, V₂O₃, Sr₂RuO₄, Na_0.7CoO₂, etc.^[33,60–63] and much larger than 0.04a₀ in transition metals.^[64]

The magnetoresistance shows features in agreement with the Kondo lattice. Figure 4(a) shows the magnetoresistance MR=ρ(B)−ρ(0)ρ(0)×100% at different temperatures. Below T_N, MR displays a sudden drop at the spin-flop transition, while in the high temperature paramagnetic state, MR follows a B² dependence, consistent with the spin fluctuation scattering.^[29] Moreover, MR data in the paramagnetic state collapse onto a single curve when the field is scaled by T + T^*, where T^* is a characteristic temperature, as shown in Fig. 4(b). It is known that in a Kondo impurity model, the magnetoresistance follows the Schlottmann’s relation ρ(B)ρ(0)=f[B/(T+T*)].^[65] The scaling behavior confirms the Kondo effect and has been observed in many Kondo lattices.^[12,50,66] However, the best scaling of our data yields a negative T^* = –6 K. This sign is consistent with the positive CW temperature. Both the positive CW temperature and the negative T^* indicate the presence of ferromagnetic correlations.^[12,50,66] A negative T^* has been reported in other antiferromagnetic heavy fermion compounds, such as CeNiGe₃,^[50] CeBi₂,^[66] and YbPtSn.^[67]

The thermoelectric properties of heavy fermion compounds share some common features.^[68] Figure 5 shows the temperature-dependent thermopower S for V₅S₈ bulk single crystal. Instead of a linear T dependence as expected for ordinary metals, S shows a sign change at about 140 K, as well as a negative S minimum around 60 K. A change of sign is generally associated with a change of carrier type. However, this explanation is inconsistent with hole conduction inferred from Hall measurement in the whole temperature range (see Appendix A for details). In a Kondo lattice system, the interplay between the Kondo and crystal field effects gives rise to a broad peak in thermopower S at high temperatures. More prominently, with decreasing temperature, S changes its sign at T = α T_K, where roughly α = 2.5–10. After that, S displays an extremum and may change sign again in some compounds.^[42,68–70] Our data agree with some of these essential features, e.g., a sign change and a negative peak. It is worth mentioning that the temperature of 140 K, at which S changes its sign, is very close to the temperature obtained from the resistivity maximum and deviation of the magnetic susceptibility from the CW law.

Based on these observations, we conclude that itinerant electrons in V₅S₈ interact with intercalated local moments through the Kondo effect, giving rise to the enhancement of electron correlation. Under this picture, the magnetic susceptibility can be understood. The deviation from the CW law beginning at 140 K results from local-moment deconfinement by Kondo coupling, which has been seen in other heavy fermion compounds.^{[9,12,32,50–52,71,72]} The reduction of the magnetic local moment at low temperatures is due to the Kondo screening, which, though strongly suppressed, persists in the AFM state.^[6,10]

Our experiments strongly suggest that itinerant electrons in the intercalated material V₅S₈ are correlated. The results have demonstrated a means that can potentially bring a class of materials into the category of correlated electronic systems.