Unusual d-electron heavy-fermion behaviour in f-electron ferromagnetic antiperovskite Gd3SnC

doi:10.21203/rs.3.rs-336915/v1

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Unusual d-electron heavy-fermion behaviour in f-electron ferromagnetic antiperovskite Gd₃SnC

https://doi.org/10.21203/rs.3.rs-336915/v1

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Inverted structures of common crystal lattices, referred to as antistructures, are rare in nature due to their thermodynamic constraints imposed by the switched cation and anion positions in reference to the original structure. However, a stable antistructure formed with mixed bonding characters of constituent elements in unusual valence states can provide unexpected material properties. Here, we report a heavy-fermion behaviour of ferromagnetic gadolinium lattice in Gd₃SnC antiperovskite, contradicting the common belief that ferromagnetic gadolinium cannot be a heavy-fermion system. The specific heat shows an unusually large Sommerfeld coefficient of ~ 1114 mJ⋅mol^− 1⋅K^− 2 with a logarithmic behaviour of non-Fermi-liquid state. We demonstrate that the heavy-fermion behaviour in the non-Fermi-liquid state appears to arise from the hybridized electronic states of gadolinium 5d-electrons participating in metallic Gd–Gd and covalent Gd–C bonds. These results accentuate unusual chemical bonds in CGd₆ octahedra with the dual characters of gadolinium 5d-electrons for the emergence of heavy-fermions.

Magnetics Materials and Devices

Soft Condensed-matter Physics

Hard Condensed-matter Physics

stable antistructures

heavy-fermion behaviour

ferromagnetic gadolinium lattice

Gd3SnC antiperovskite

The crystal structure constructed with chemical bonds of constituent elements determines the electronic structure of a material and its properties. In a fixed symmetry, electronically inverted structures with switched crystallographic positions of cations and anions from the original structure often have a reversed compositional ratio, which necessarily forms a different coordinated substructure with additional bonding characters and can lead to an exotic electronic structure. However, in general, such antistructures composed of the same constituent elements in the reversed compositional ratio are thermodynamically unstable. Indeed, due to the thermodynamic constraints, antistructures found in several classes of materials are constructed by subsidiary chemical bonds of different constituent elements from original structures. This appears, for example, in the Cd-deficient Cd₃As₂ antifluorite¹, which has a strong covalent bonding nature in a reversed compositional ratio from the ionic CaF₂ fluorite. It is noteworthy that the Cd₃As₂ antifluorite exhibits exotic properties: a three-dimensional topological Dirac band^1–3 along with negative magnetoresistance⁴, anomalous Hall effect⁵, and pressure-induced superconductivity⁶.

ABX ₃ perovskites, as the largest family of crystalline materials, also have their counterpart antistructures, A₃BX antiperovskites⁷. In contrast to the perovskite compounds constructed by the ionic bonds of constituent elements in stable valence states, the antiperovskites have mixed bonding characters with ionic, covalent, and metallic bonds in unusual valence states⁸. However, oxide antiperovskites (A₃BO), antistructures of common oxide perovskites (ABO₃), are hardly stabilized in ambient conditions as oxygen tends to form ionic bonds with counter-cationic A and B elements due to its large ionicity⁹. This constraint may be lifted for s-block and transition metal-based antiperovskites, in which additional covalent and metallic bonds come into play for their crystallographic stability^7,10. The boundary for such stable antiperovskite compounds can be extended to f-block lanthanides, which form a crystal with various elemental groups of d-block transition metals and p-block post-transition metals⁷. Those compounds may exhibit diverse electronic properties because of the multiple bonding characters with enhanced covalency and/or metallicity. Furthermore, considering the fact that f-electrons often contribute to strongly correlated electronic properties, a variety of unconventional quantum phenomena may be anticipated in f-block antiperovskites, which can exhibit exotic electronic band structures arising from the mixed chemical bonds. However, thermodynamically stable f-block element-based antiperovskites and their novel properties have been hardly demonstrated up to now^7,11. Herein, we demonstrate the unprecedented heavy-fermion behaviour of the ferromagnetic (FM) gadolinium lattice in the Gd₃SnC antiperovskite structure and verify the crucial role of the metallic Gd–Gd and covalent Gd–C bonds of CGd₆ octahedral skeleton on an unusually hybridized Gd 5d-electrons responsible for the emergent heavy-fermions.

Synthesis and structural analysis. Figure 1a shows that the Gd₃SnC crystallizes in the antiperovskite structure (space group: Pm\(\stackrel{-}{3}\)m) with face-centred Gd and body-centred C atoms in a Sn cubic lattice, as confirmed by Rietveld analysis of powder X-ray diffraction (XRD) pattern (Supplementary Table 1). Single-phase bulk Gd₃SnC was synthesized via the melt-solidification process at one atmosphere. This indicates the thermodynamic stability of Gd₃SnC antiperovskite, which gets additional support from the calculated phonon dispersions having no imaginary frequency (Supplementary Fig. 1). In contrast to the ABX₃ perovskite, which has cation-centred BX₆ octahedra with ionic bonds, Gd₃SnC has anion-centred CGd₆ octahedra with strong covalent Gd–C and metallic Gd–Gd bonds. This mixed bonding character of Gd bonds in CGd₆ octahedra results in different Gd orbital levels from those of the Gd element and its ionic compounds. As shown in Fig. 1b, while Gd metal and Gd₂O₃ have ordinary Gd orbital levels of Gd–Gd metallic and Gd–O ionic bonds, respectively, Gd₃SnC has unusual energy levels for Gd orbitals due to the coexistence of metallic and covalent bonds. Considering the shorter Gd–Gd bond length (3.48 Å) in CGd₆ octahedra compared to that of Gd metal (~ 3.6 Å), one expects an enhanced metallicity and thus additional Fermi level (E_F) crossings for Gd bands in Gd₃SnC. On the other hand, the electronegativity difference between Gd and C is much smaller than that between Gd and O, resulting in the formation of covalent bonds between Gd and C. The energy difference between bonding and antibonding states of the covalent bonds is expected to be significantly smaller than that of ionic bonds between Gd and O. These mixed bonding characters of Gd valence orbitals in CGd₆ octahedra can lead to a peculiar molecular orbital diagram with both metallic and covalent bonds as shown in Fig. 1b. Such observation indicates that Gd₃SnC antiperovskite may exhibit unusual physical properties that are hardly found in elemental Gd and conventional Gd-related compounds.

Tricritical ferromagnetic behaviour. Figure 2a shows the FM phase transition of Gd₃SnC with a Curie temperature (T_C) of 100 K under a low magnetic field (H) of 0.1 kOe. In comparison to the itinerant FM in Gd metal with a T_C of 297 K, different aspects of the FM order are observed¹². A sharp increase in the magnetization (M) near the T_C indicates a first-order transition, which is further evidenced by the hysteresis in the temperature(T) dependence of electrical resistivity (ρ) (Fig. 2e) and the negative slope in the M² dependence of H/M (Supplementary Fig. 2e). In addition, no structural phase transition is observed around the T_C, indicating that the FM ordering occurs while preserving the antiperovskite structure (Supplementary Fig. 3). We confirm the saturation magnetic moment of ∼6.8 µ_B per Gd obtained from the M–H curve (Fig. 2b), indicating this FM state comes mostly from the seven Gd 4f-electrons. A notable aspect of M (T) is a slight decrease in the ZFC curve below ~ 20 K (inset of Fig. 2a), which suggests a possible formation of singlets such as Kondo singlet^13,14, as will be discussed in the following sections. This unusual behaviour in M indicates that the near E_F states of Gd, which do not have contributions from fully localized f-orbitals, may be different from those of the familiar FM Gd metal and Gd-based compounds^12,15.

The most peculiar aspect of the FM state in Gd₃SnC is the tricritical behaviour that appears near the boundary between the first- and the second-order phase transitions¹⁶. Figure 2c shows a modified Arrott plot¹⁷ of the tricritical mean-field model for the FM order with β_Arrott = 0.25 and γ_Arrott = 1 in (H/M)^1/γArrott and M^1/βArrott, respectively. Compared to other magnetic ordering models, it is apparent from the relative slopes (dashed red lines in Fig. 2c and Supplementary Fig. 2a–d) that the FM transition belongs to the universality class of the tricritical mean-field model (Fig. 2d). A clear crossover from a first-order to second-order transition is seen in the T dependent ρ and M curves under different H as shown in Fig. 2e,f, respectively. Three representative features in the data verify the crossover between FM orders: (i) disappearance of the peak in ρ at T_C, (ii) suppression of the hysteresis in the ρ–T curve during a thermal cycle (insets of Fig. 2e), and (iii) smooth increase of M upon cooling (Fig. 2f). Such tricritical behaviour often emerges in heavy-fermion systems such as UGe₂¹⁸ and YbRh₂Si₂¹⁹ due to the competition between Kondo coupling (T_K) and Ruderman–Kittel–Kasuya–Yosida interaction²⁰.

Heavy-fermions with non-Fermi liquid behaviour. More unusual properties of Gd₃SnC may be found in the heat capacity (C) measurement results (Fig. 3). As a way to determine the unexpected behaviour, we compare the C of Gd₃SnC to those of FM Gd metal and non-magnetic La₃SnC antiperovskite, as shown in Fig. 3a. In contrast to the small C values of Gd metal and La₃SnC antiperovskite in the low-T region, an extremely large C value with a Sommerfeld coefficient (γ) of ~ 1114 mJ mol^− 1 K^− 2 at 90 mK is observed for the Gd₃SnC. The dramatic low-T rise of C is reminiscent of a nuclear Schottky anomaly, most likely from the Sn nucleus (the natural abundance for non-zero nuclear spin ¹³C is below 1%). However, our modelling, which considers 16 % natural abundance of ¹¹⁷Sn and ¹¹⁹Sn, rules out the Schottky anomaly by showing that the required internal field is about − 1287 kOe, a value much larger than any reported values^21–23 (Supplementary Fig. 4d). In addition, the Gd nuclear spin cannot be the culprit as we do not see a similar rise in C for Gd metal. Therefore, we attribute the logarithmic rise of C for Gd₃SnC below ~ 0.13 K (Supplementary Fig. 4a) to a non-Fermi-liquid (NFL) behaviour of itinerant conduction electrons^24–26 (inset of Fig. 3a). A T-linear dependence of ρ in the low-T region also supports the NFL behaviour of itinerant conduction electrons in Gd₃SnC (left panel in Fig. 3b). The transition from T-linear to T² behaviour of ρ upon applying 140 kOe (right panel in Fig. 3b and Supplementary Fig. 5) is suggestive of a magnetic origin of the NFL behaviour^27,28. Thus, we assume that an exotic quantum phenomenon coupled with a correlation between itinerant and localized electrons in the Gd₃SnC antiperovskite appears as heavy fermions.

As Gd f-electron levels locate deep in the binding energy, the heavy-fermion with the NFL behaviour should originate from the electrons of other orbitals, which is revealed from the analysis of the C of FM Gd₃SnC. The magnetic contribution (C_mag) to the C of FM Gd₃SnC is obtained by subtracting the C of non-magnetic La₃SnC without 4f-electrons (La metal with the configuration of [Xe]4f⁰5d¹6s²) from those of Gd₃SnC with seven 4f-electrons (Gd metal with the configuration of [Xe]4f⁷5d¹6s²). We find two distinct features in C_mag: a large C_mag in the high-T region (C_mag,high, Fig. 3c) and a small C_mag in the low-T region (C_{mag, low}, inset of Fig. 3c). While the C_mag,high is attributed to the FM order of 4f⁷-electrons, which agrees well with the prediction of the renormalization-group approach²⁹ in the scheme of tricritical ferromagnetism (Supplementary Fig. 2f), the origin of C_mag,low is ambiguous. From the T-dependent magnetic entropy (ΔS) obtained by integrating C_mag (T) (Supplementary Fig. 4b), we can assign which electrons are responsible for C_mag,low. Figure 3d shows a large difference in ΔS between the high- and low-T regions: 0.5Rln8 and 0.05Rln2, respectively. Since 0.5Rln8 reflects the contribution from seven 4f-electrons (4f⁷) involved in FM ordering, one may notice that the much smaller value of 0.05Rln2 has no correlation with 4f-electrons but is ascribed to 5d-electrons, which are responsible for the heavy-fermion with the NFL behaviour.

Dual character of Gd 5d electrons. This unconventional and anomalous d-electron heavy-fermion state in f-block Gd-based Gd₃SnC is, if true, the first case of FM-assisted heavy-fermion behaviour in 5d-electron systems. Density functional theory (DFT) calculations along with angle-resolved photoemission spectroscopy (ARPES) measurements provide a clear picture for the formation of the heavy-fermion state, which is induced not by 4f-electrons but by 5d-electrons of Gd element in the context of mixed bonding characters of the antiperovskite structure. Figure 4a shows ARPES data along the Γ–X–Γ direction taken above (125 K) and below (90 and 13 K) the T_C. The 125 K data shows a fast-dispersing band centred at the X point. As the T is lowered to 90 K, the band shifts down due to the exchange splitting of both 4f- and 5d-electrons (Supplementary Fig. 6d). In addition to the fast-dispersing band (green curve), there is a weakly dispersing band near E_F (red curve in Fig. 4a, Supplementary Fig. 6a–c). Upon cooling to 13 K, the fast-dispersing band shifts further down, and the weakly dispersing band near E_F disappears. These changes in the electronic structure might be related to the hybridization of fast and weakly dispersing bands below 20 K. The T-dependent electronic structure change is also seen in the k_x–k_y plane of Fermi surface maps in Fig. 4b; the Fermi surface pocket becomes larger as the T decreases. This enlarged Fermi surface is a typical phenomenon as found in various heavy-fermion systems^27,30−32. The calculated partial density of states (DOS) clearly demonstrates that the Gd 5d-orbitals are almost solely responsible for the states near E_F, while Sn 5p and C 2p derived states are located away from E_F (Fig. 4c). Meanwhile, we confirm that the contribution of Gd 4f-orbitals into the band structure near E_F is negligible but responsible for the FM ordering (Supplementary Fig. 7).

We note that the calculated band structure shows an anomalous flat band feature near E_F, which is also a signature of heavy-fermion behaviour (Fig. 4d,e). The experimentally observed flatness of the fast-dispersing band at the X point (13 K in Fig. 4a) is indeed well-reproduced by band calculations (highlighted as yellow colour in Fig. 4e). The fat band analysis reveals that the band hybridization triggers the appearance of a flat band feature near E_F. Importantly, the two hybridized bands originate from the only Gd 5d-orbitals: t_2g bands from the Gd–Gd bonds (red curves) and e_g bands from the mostly Gd–C bonds (green curves). Thus, we believe that the flat t_2g band observed at 90 K (Fig. 4a) is lifted above E_F after the band hybridization process (Supplementary Fig. 6e). Finally, we emphasize the importance of antiperovskite structure with mixed bonding nature, which is the key to imparting the unusual heavy-fermion behaviour to Gd₃SnC. The crystal orbital Hamiltonian population (COHP) analysis (Fig. 4f) explains how the chemical bonds of CGd₆ octahedra in antiperovskite structure can induce the unusual band structure. The COHP analysis suggests two types of orbital overlap: a small orbital overlap in metallic Gd–Gd bond responsible for the t_2g bands near E_F (− ICOHP ~ 0.5 eV/bond, Supplementary Table 2) and large orbital overlap in covalent Gd–C bond for the e_g bands below E_F (− ICOHP ~ 1.5 eV/bond). This mixed bonding nature with the different degrees of orbital overlap leads to the unusual band dispersion of Gd 5d-electrons, as illustrated in Fig. 4g − i. Thus, the duality of Gd 5d-electrons participating in the mixed chemical bonds in CGd₆ octahedra of the Gd₃SnC antiperovskite structure is a key factor that determines the unusual physical properties.

In summary, we discovered the d-electron heavy-fermion state in the f-electron FM Gd₃SnC antiperovskite. The mixed bonding nature of the antiperovskite structure, composed of metallic Gd–Gd bonds and covalent Gd–C bonds, is found to be the key ingredient for realizing the heavy-fermions of Gd 5d-electrons. The present findings are against the knowledge that the FM lanthanide elements are not suitable for heavy-fermion states, implying that the properties of the elements in the common crystal structure can be completely changed by adopting the antistructured lattice framework. This work will trigger further exploratory studies on the antistructures to challenge the common knowledge in the elemental properties of materials.

Crystal growth and structural analysis. Stoichiometric Polycrystalline Gd₃SnC ingot rods were used for the single-crystal growth by the floating zone (FZ) melting method. We mixed Gd, Sn metals, and graphite chips in a 3:1:1 molar ration to fabricate a polycrystal ingot rod. The mixed sample was melted using the arc melting furnace in a high purity argon atmosphere (Ar > 99.9999%). The single crystal was grown by four-mirror FZ melting method with the rod-shaped ingots under high purity argon (Ar > 99.9999%) with pressurized conditions in 0.3 MPa. The feed and the seed rod were rotated at 50 rpm, and the growing speed was 2 mm per hour. The crystal structure was determined using the high-resolution X-ray diffractometer and Rietveld analysis using the GSAS-II program.

Physical property measurements. ρ, M, and C measurements were performed using a physical property measurement system (PPMS). The ρ and C at ambient pressure were measured down to 0.06 K using a diluted helium-3 refrigerator. To measure the electrical properties of samples, the electrical contacts in the four-probe configuration were adopted that made by Ag epoxy onto a sample. To prevent movement of samples by H (up to 140 kOe) in the chamber, samples were fixed using torr seal epoxy onto the PPMS puck. To measure the M of the sample, a vibrating sample magnetometer (VSM) was used. For C measurement, the standard relaxation method was adopted. Every process was performed in an Ar-filled glove box, and N-grease covered samples for ρ and C measurements to prevent degradation of Gd₃SnC under ambient oxygen and water vapour atmosphere. T-dependent ARPES measurements were performed at the MERLIN beamline 4.0.3 of the Advanced Light Source, Lawrence Berkeley National Laboratory using both linearly horizontal (π) and vertical (σ) polarization from an elliptically polarized undulator. Spectra were acquired with a Scienta R8000 (BL 4.0.3) electron analyser. Cleaving of the samples was conducted at 13 K in an ultra-high vacuum better than 5 × 10^− 11 Torr. The total energy resolution of approximately 15 meV was used for measurements at hν = 142 eV.

DFT Calculations. First-principles DFT calculations were performed using the generalized gradient approximation with the Perder-Burke-Ernzerhof functional with spin-orbit coupling (SOC) and the projector augmented plane-wave method implemented in the Vienna ab initio simulation program code^33–35. The 4f-, 5s-, 5p-, 5d- and 6s-electrons of Gd, the 5s- and 5p-electrons of Sn, and the 2s- and 2p-electrons of C were used as valence electrons. The plane-wave-basis cut-off energy was set to 600 eV. On-site Coulomb interaction values of U = 3 eV were used for the Gd 5d-electrons (Supplementary Fig. 7). Self-consistency was carried out using an a × b × c unit cell containing 5 atoms, and a 12 × 12 × 12 k-point mesh was used. Structural relaxation was performed until the Hellmann-Feynman forces were less than 1 × 10^− 5 eV Å⁻¹, respectively. The crystal structures and charge density distribution were visualized with the Visualization for Electronic and Structural Analysis code³⁶.

Data Availability

The data that support the plots in this paper and other findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

This work was supported by the Institute for Basic Science (IBS-R011-D1, IBS-R009-G2) and the National Research Foundation of Korea (NRF) grant funded by the Korean government (Ministry of Science, ICT & Future Planning) (No. 2015M3D1A1070639, NRF-2019R1I1A1A01061913) and. We acknowledge Dr. Filip Ronning (Los Alamos National Laboratory) for valuable discussions.

Author Contributions

S.W.K. conceived the idea and organized the research. J.P. synthesized samples and measured physical properties. M.K and C.K. performed ARPES measurements. J.B, J.P, and K.L. analysed the structural and physical properties. J.B carried out computational studies. All the authors discussed the results and wrote the manuscript.

Competing interests

The authors declare no competing interests.

Additional Information

Supplementary information is available for this paper at https://doi.org/xxxxx.

Correspondence and requests for materials should be addressed to S.W.K.

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Unusual d-electron heavy-fermion behaviour in f-electron ferromagnetic antiperovskite Gd₃SnC

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