Introduction

Topological kagome materials have attracted tremendous attention in the past decades, serving as a fundamental platform to investigate the quantum interactions between geometry, topology, spin, and correlation1. From Heisenberg’s view2, magnetic ions on the kagome lattice with antiferromagnetic interaction would exhibit geometrical frustration3, resulting in possible quantum-spin-liquid states4, fractionalized excitations5, and the absence of ordinary magnetic order6,7. When focusing on the electronic structure of kagome lattices with magnetic ions, the strong electron correlation originating from the flat band would stabilize a ferromagnetic (FM) ground state8. Moreover, with Dirac fermions and van Hove singularities in the electronic structure, kagome lattices would show nontrivial topological properties9,10 and multiple long-range orders with instabilities of Fermi surface11. By introducing the magnetic degree of freedom, correlated topological band structures can be realized in kagome lattices with magnetic ions, known as topological kagome magnets. Theoretically, the inclusion of spin-orbit coupling in the kagome lattice would open gaps at the Dirac point and the touching point connecting the flat band and the quadratic band, making the nonmagnetic kagome lattice a quantum spin Hall insulator with nontrivial Z2 topological invariants12,13. Thus, a kagome lattice with magnetic ions showing out-of-plane FM ordering would become a Chern insulator with chiral edge states, which usually exhibits exotic quantum properties such as quantized anomalous Hall effect14 and giant anomalous Hall conductance15,16. Moreover, a large in-plane magnetization would close the gaps in topological kagome magnets, acting as a tuning parameter for topological phases1. Considering the strong or weak interlayer interaction, Weyl point17,18,19 or three-dimensional quantum anomalous Hall effect20 is anticipated to appear in topological kagome magnets. Due to these exotic quantum properties, topological kagome magnets have great potential applications for next-generation electronics, and it is essential to explore more topological kagome magnets and investigate their properties.

Experimentally, there are two strategies to introduce magnetism into kagome materials, placing magnetic ions on the kagome lattice or intercalating magnetic ions between stacked kagome lattices. Plenty of topological kagome magnets have been reported with magnetic transition metal ions on the kagome lattice, such as Mn3X (X = Sn, Ge) with a manganese-kagome lattice21,22,23, Co3Sn2S224,25,26 and CoSn27,28 with a cobalt-kagome lattice, Fe3Sn216,29,30 and FeSn31,32,33 with an iron-kagome lattice, most of which have strong in-plane magnetization. In REMn6Sn6 (RE = Gd-Tm, Lu) with manganese-kagome lattice, various magnetic states can be realized by substitution of rare-earth atoms, named rare-earth engineering, which leads to quite different quantum transport behaviors34,35. In particular, TbMn6Sn6 shows an out-of-plane magnetization and stands out as a Chern insulator with zero-field anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects10,35,36,37. For REV6Sn6 compounds with similar crystal structure yet featuring a nonmagnetic vanadium-kagome lattice, weak magnetic couplings among the local 4 f moments of various rare-earth atoms not only result in various magnetic orderings38,39,40, but also in topologically nontrivial Dirac surface states (GdV6Sn6 and HoV6Sn641,42,43), quantum oscillations (YV6Sn642), quantum critical behavior (YbV6Sn644), and charge density waves (ScV6Sn645,46,47). The close relationship between rare-earth magnetism and topological electronic structure underscores that rare-earth engineering is an effective way to tune the exotic topological phases35,48,49,50.

Recently, the nonmagnetic AM3X5 family (A = K, Rb, and Cs; M = Ti, V; X = Sb, Bi) with vanadium/titanium-kagome lattices51,52 has aroused great interest due to the combined charge density wave states, superconductivity, orbital-selective nematic order or electronic nematicity, and nontrivial band topology53,54,55,56,57,58,59,60. By intercalating RE ions between VSb layers, vanadium-based kagome metals with multiple magnetic states emerge61, such as a FM-like ground state in EuV3Sb4. In contrast, there is a lack of systematic investigation into titanium-based kagome metals with magnetism, only LaTi3Bi4, CeTi3Bi462, and EuTi3Bi463 have been briefly reported.

By using rare-earth engineering, we report the synthesis and physical properties of three discovered titanium-based kagome metals, RETi3Bi4 (RE = Yb, Pr, and Nd). Compared with AM3X5, the titanium-kagome lattice in RETi3Bi4 is slightly distorted, and zig-zag RE chains are formed in REBi bilayers, enabling the exhibition of various magnetic states with different RE atoms. The combined measurements of magnetism, resistivity, and specific heat capacity show an evolution from the nonmagnetic YbTi3Bi4 to short-range ordered PrTi3Bi4, with an anomaly around 8.2 K, and finally to FM NdTi3Bi4, with Tc = 8.5 K. Applying pressure slightly suppressed the FM order in NdTi3Bi4, with an increasing value of power, showing the tunable magnetism. Therefore, RETi3Bi4 (RE = Yb, Pr, and Nd) represents a promising family of kagome metals for in-depth investigation of the interplay among topologically nontrivial features, magnetism, and electron correlation.

Results and Discussion

Crystal structure

Unlike the hexagonal prototypes AM3X5 (A = K, Rb, and Cs; M = Ti, V; X = Sb, Bi)51,52,60, all RETi3Bi4 crystallize in the orthogonal space group Fmmm (No. 69) with a = 24.9(4) Å, b = 10.3(4) Å, c = 5.9(2) Å for YbTi3Bi4; a = 24.9668(114) Å, b = 10.3248(49) Å, c = 5.9125(26) Å for PrTi3Bi4; a = 24.9523(87) Å, b = 10.3327(27) Å, c = 5.9009(18) Å for NdTi3Bi4, and α = β = γ = 90° (Supplementary Table 1–5). As shown in Fig. 1a, the crystal structure consists of the alternating stacking of REBi, TiBi, and Bi layers along the a axis. Viewed along the a axis, a Ti kagome-like lattice and two Bi honeycomb-like lattices can be further resolved (Fig. 1b). There are two distinct differences between the crystal structure of AM3X5 and RETi3Bi4, i.e. (i) the increase of the a axis owing to the stacking of (ii) distorted TiBi layer with distorted Ti kagome lattice. Compared with ATi3Bi5, the Ti kagome lattice and Bi triangular lattice of RETi3Bi4 show inequivalent bonds and are not strictly in the bc plane, resulting in both in-plane and out-of-plane distortion of TiBi layer. The in-plane distortion can be simply evaluated by the orthorhombic lattice parameter ratio b/c, which should be the exact value of √3 = 1.732 for a perfect kagome lattice. For rare earth atoms shifting from Yb to Pr, and then to Nd, the orthorhombic lattice parameter ratio b/c changes from 1.7457 to 1.7462, and then to 1.7510, indicating a slight increase in the in-plane distortion. Similar to LnV3Sb4 (Ln = Yb, Eu)61, the bilayer of the REBi plane forms a quasi-one-dimensional zig-zag chain of RE atoms (Fig. 1c), on which the magnetic states could be tuned by rare-earth engineering.

Fig. 1: Crystal structure of RETi3Bi4 (RE = Yb, Pr, and Nd).
figure 1

a Crystal structure of RETi3Bi4 (RE = Yb, Pr, and Nd). b The Ti kagome-like lattice and Bi honeycomb-like lattices viewed along the a axis. c The REBi bilayer and zig-zag chain of RE atoms.

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The crystal structure is further confirmed by the X-ray diffraction patterns, which show a strong preferential orientation of (00 l) (l = even integer) reflections (Fig. 2a). Based on the position (~14.3°) of (004) diffraction peaks, the distance between corresponding structural units along the a axis is determined to be about 25 Å, close to the results of Single crystal X-ray diffraction (SCXRD). As shown in the insets of Fig. 2a, the as-grown single crystals of RETi3Bi4 are all plate-like flakes with shiny metal luster, indicating a clear quasi-two-dimensional feature. Fig. 2b shows the enlarged (0010) diffraction peaks for RETi3Bi4, where the peak position of PrTi3Bi4 shifts 0.08° to a lower angle and that of NdTi3Bi4 shifts 0.06° to a higher angle compared to YbTi3Bi4, indicating the largest distance between the structural units for PrTi3Bi4 and the smallest one for NdTi3Bi4. The different (0010) peak position corresponds well with the lattice parameter derived from SCXRD, where a(NdTi3Bi4) < a(YbTi3Bi4) < a(PrTi3Bi4). Considering the cationic radius r(Yb3+) = 0.0858 nm < r(Yb2+) = 0.093 nm < r(Nd3+) = 0.0995 nm < r(Pr3+) = 0.1013 nm, the abnormal enhancement of lattice parameter a in YbTi3Bi4 might be attributed to the weakened out-of-plane interaction between YbBi bilayer with Yb2+ ions rather than Yb3+ ions. As shown in the selected area electron diffraction (SAED) pattern and high-angle annular dark-field (HAADF) image of YbTi3Bi4 collected along the [0–26] zone axis (Fig. 2c, d), the construction layers can be clearly resolved along the a axis. In particular, the Ti atoms and Bi atoms are not on the same straight line, further confirming the out-of-plane distortion of TiBi layers. The chemical composition is determined to be RE: Ti: Bi ~1: 3: 4 with a homogeneous distribution according to the results of energy-dispersive spectroscopy (EDS) (Supplementary Fig. 1-2 and Supplementary Table 6–8).

Fig. 2: Single Crystals of RETi3Bi4 (RE = Yb, Pr, and Nd).
figure 2

a X-ray diffraction patterns of as-grown RETi3Bi4 (RE = Yb, Pr, and Nd) single crystals, showing (00 l) (l = even integer) reflections. The insets are the corresponding optical photographs of RETi3Bi4 (RE = Yb, Pr, and Nd) single crystals. b The enlarged (0010) peak of RETi3Bi4 (RE = Yb, Pr, and Nd) single crystals. c The SAED pattern of YbTi3Bi4 along the[0–26] zone axis. The inset is the thin specimen of YbTi3Bi4 etched by focused ion beam method. d The HAADF image collected along the[0–26] zone axis, where the cyan, blue, and purple balls represent Yb, Ti, and Bi atoms, respectively.

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Magnetic properties

Figure 3a–c shows the magnetic susceptibility of RETi3Bi4 under field parallel (H // bc) and normal (H ⊥ bc) to the bc plane. The in-plane (H // bc) magnetic susceptibilities are larger than the out-of-plane (H ⊥ bc) magnetic susceptibilities, showing the possible in-plane magnetic anisotropy in these three compounds. For YbTi3Bi4, the zero-field-cooling (ZFC) and field-cooling (FC) curves under a smaller magnetic field (0.5 T) exhibit no bifurcation or anomaly above 2 K, suggesting there is no magnetic transition above 2 K. Though without bifurcation in the ZFC and FC curves under the smaller magnetic field (0.5 T) above 2 K, a saturation tendency appears at low temperature in the magnetic susceptibility of PrTi3Bi4 for both H // bc and H ⊥ bc, possibly indicating a short-range ordering around Tanomaly ~ 8.2 K (Supplementary Fig. 3). By contrast, a bifurcation around 8.5 K (denoted as Tc) can be clearly resolved in the ZFC and FC curves for NdTi3Bi4.

Fig. 3: Various magnetic states of RETi3Bi4 (RE = Yb, Pr, and Nd).
figure 3

Temperature-dependent magnetic susceptibility of (a) YbTi3Bi4, (b) PrTi3Bi4, and (c) NdTi3Bi4 single crystal with magnetic field (1 T) parallel and perpendicular to the bc plane. The black lines are the Curie-Weiss fitting curves. The insets show the corresponding ZFC and FC curves under a smaller magnetic field. Field-dependent magnetization curves for (d) YbTi3Bi4, (e) PrTi3Bi4, and (f) NdTi3Bi4 single crystal with magnetic fields parallel and perpendicular to the bc plane.

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All the magnetic susceptibility curves decrease quickly around 20 K and follow the Curie-Weiss law at higher temperatures (black lines), given by χ = χ0 + C/(T - θCW), where χ0 is the temperature-independent contribution including the diamagnetic contribution of the orbital magnetic moment (negative) and the Pauli paramagnetic contribution of conduction electrons (positive), C the Curie constant, and θCW the Curie-Weiss temperature. The effective moment can be further calculated from the equation \({\mu }_{{{{{{\rm{eff}}}}}}}=\sqrt{\frac{8C}{n}}\), where n is the number of magnetic atoms. For YbTi3Bi4, an almost zero Curie-Weiss temperature (~0.5 K) and a small effective moment (<0.3 μB per Yb) were found for both H // bc and H ⊥ bc, indicating a possible non-magnetic ground state with zero spin (0 μB) Yb2+. For PrTi3Bi4, a positive but close-to-zero Curie-Weiss temperature (~2.5 K) was determined for H // bc, which may suggest weak magnetic exchange couplings between moments in the bc plane. The effective moment was calculated to be 3.67(3) μB per Pr for H // bc, close to the theoretical moment of Pr3+ (3.58 μB). Shifting the magnetic field configuration into H ⊥ bc, the large negative Curie-Weiss temperature (−100 K) indicates strong antiferromagnetic interactions between moments in different Pr triangular bilayers along the a axis. The overestimated effective moment (4.72 μB per Pr) could possibly be attributed to geometrical spin frustration on the Pr triangular lattice or crystal field effect when considering the coordination environment of Pr atoms (Supplementary Fig. 4). By substituting Pr with Nd, a small negative Curie-Weiss temperature (−3.74 K) for H // bc also suggests weak magnetic exchange couplings between moments in the bc plane. Compared with PrTi3Bi4, the reduced Curie-Weiss temperature (−36.7 K) for H ⊥ bc may correspond to a weakened antiferromagnetic interactions between different Nd triangular bilayers along the a axis, which might result in the emergence of FM order in NdTi3Bi4. The derived effective moments (~ 3.6 μB) of NdTi3Bi4 are close to the theoretical value of Nd3+ (3.62 μB). (For details of the Curie-Weiss fittings see Supplementary Table 9 and Supplementary Fig. 5-6.)

The magnetization curves of YbTi3Bi4 and PrTi3Bi4 show positive slopes and approach saturation around 7 T without any hysteresis (Fig. 3d, e), suggesting no FM order or spin-glass state at least above 2 K. The saturation moment for YbTi3Bi4 is 0.016 μB for H // bc and 0.006 μB for H ⊥ bc, further confirming the non-magnetic feature (4f14, μsat = 0 μB). The saturation moment for PrTi3Bi4 is 1.620 μB for H // bc and 0.855 μB for H ⊥ bc, with the former being close to the saturation moment of Pr3+ (4f 2, μsat = 2.0 μB). The significant difference between the in-plane and out-of-plane saturation moments should be attributed to the large anisotropy originating from the quasi-two-dimensional structure. For NdTi3Bi4, obvious hysteresis loops exist at 2 K and gradually vanish beyond Tc = 8.5 K (Fig. 3f and Supplementary Fig. 7). The smaller in-plane coercive magnetic field (Hc-// ~ 500 Oe < Hc-⊥ ~ 5000 Oe) and larger saturation moment (μsat-// ~ 1.426 μB > μsat-⊥ ~ 0.587 μB) suggest that the bc plane is the easy plane. For NdTi3Bi4, magnetization curves at various in-plane magnetic fields show the largest magnetization along the b axis (Supplementary Fig. 8-9), which should be the easy axis. Both the saturation moment and coercive magnetic field show a two-fold symmetry, corresponding to the quasi 1D arrangement of Nd atoms. Our results are consistent with those reported by a recently published work focusing on the evolution of highly anisotropic magnetism and complex electronic structure of the RETi3Bi4 family64.

Resistivity and heat capacity

Figure 4a shows the temperature-dependent in-plane resistivity of RETi3Bi4, which monotonically decreases with decreasing temperature, demonstrating a metallic-like behavior (For the electronic structure of PrTi3Bi4 and NdTi3Bi4 see Supplementary Fig. 10). The residual resistance ratios (RRR = ρ300 K/ρ10 K) are calculated to be 3.50 for YbTi3Bi4, 2.15 for PrTi3Bi4, and 3.70 for NdTi3Bi4, hinting at the good crystallinity of RETi3Bi4 single crystals. With a current (2 mA) applied in the bc plane, the resistivity of YbTi3Bi4 shows no obvious anomaly down to 2 K. Unlike YbTi3Bi4, the in-plane resistivity of PrTi3Bi4 at low temperature exhibits an anomaly with a broadened peak (5.2 K ~ 9.7 K) in its first derivative curve (Supplementary Fig. 11), which might be correlated with the possible short-range order. Due to the obvious magnetic transition in NdTi3Bi4, the resistivity shows a distinct drop around Tc = 8.5 K and then approaches a saturation at 2 K. Similar to AV3Sb5 or ATi3Bi5, the resistivity of RETi3Bi4 below 50 K can be fitted using the Power law: ρ = ρ0 + AT α, where the value of power α depends on the dominant scattering mechanism (Supplementary Table 10). Typically, α takes the value of 3/2 for diffusive electron motion caused by strong electron correlation65, 2 for moderate electron-electron scattering66,67, known as Fermi liquid behavior68, 3 for dominant s − d scattering or electron-magnon scattering69,70,71, and 5 for electron-phonon coupling72. As shown in Fig. 4b, the value of power (α) is fitted to be 2.00(3) for YbTi3Bi4, 1.64(3) for PrTi3Bi4, and 1.51(2) for NdTi3Bi4, indicating an evolution of dominant scattering mechanism by changing rare earth atoms. In particular, the resistivity of NdTi3Bi4 below Tc can also be fitted using the Power law with α = 5.35(6), showing strong electron-phonon coupling below Tc. By applying a magnetic field perpendicular to the bc plane, the resistivity of NdTi3Bi4 below Tc shows a slight enhancement up to 5 T with almost unchanged transition temperature (Fig. 4c), which is a typical characteristic of FM order.

Fig. 4: Electrical transport and specific heat capacity of RETi3Bi4 (RE = Yb, Pr, and Nd).
figure 4

a Temperature-dependent in-plane resistivity (ρbc) of RETi3Bi4 (RE = Yb, Pr, and Nd). b Power-law fittings of in-plane resistivity at low temperature. c In-plane resistivity of NdTi3Bi4 at low temperature under different magnetic field. d Temperature-dependent specific heat capacity of RETi3Bi4 (RE = Yb, Pr, and Nd). The inset shows zoomed specific heat capacity at low temperature. The black dashed line shows the Dulong-Petit limit of RETi3Bi4 compounds. e CP/T vs. T2 plot for RETi3Bi4 (RE = Yb, Pr, and Nd) and corresponding fittings (black lines) using the Debye model. f Zoomed specific heat capacity of NdTi3Bi4 at low temperature under different magnetic field.

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Figure 4d shows the temperature-dependent specific heat capacity of RETi3Bi4, where no anomaly in the entire measured temperature range, a broad anomaly around 8.2 K, and a sharp peak at Tc = 8.5 K is observed for YbTi3Bi4, PrTi3Bi4, and NdTi3Bi4, respectively. The specific heat capacity of all RETi3Bi4 single crystals exceed the Dulong–Petit limit (3NR ~ 200 J mol−1 K−1, black dashed line) at higher temperatures, which should be attributed to the more prominent phonon contribution at higher temperature of N-type grease used for protecting the samples73,74,75. For NdTi3Bi4, the peak at 8.5 K is reversible upon cooling (T↓) and warming (T↑), indicating no structural transition. The low-temperature (12 K–18 K) specific heat capacity of RETi3Bi4 is fitted by the Debye model C = γT + βT3, where γT and βT3 represent the contribution from the electron and lattice, respectively (Fig. 4e). The Sommerfeld coefficients γ are determined to be 33.5(2.6) mJ K−2 per formula for YbTi3Bi4 [20.7(7) mJ K−2 per formula fitted from 2 K to 5 K], 762.6(8.9) mJ K−2 per formula for PrTi3Bi4, and 809.6(7.5) mJ K−2 per formula for NdTi3Bi4. The large enhancement of Sommerfeld coefficient γ of PrTi3Bi4 and NdTi3Bi4 likely results from the contribution of magnons beyond the ordering temperatures. Taking the nonmagnetic YbTi3Bi4 as the reference of specific heat capacity contributed by electrons and phonons, the contribution of magnons and magnetic entropy of PrTi3Bi4 and NdTi3Bi4 are calculated (Supplementary Fig. 12), suggesting possible Pr3+ and Nd3+ valance states in PrTi3Bi4 and NdTi3Bi4, respectively. The λ-shaped peak of specific heat capacity for NdTi3Bi4 broadens and shifts toward higher temperature upon increasing the out-of-plane magnetic field (Fig. 4f), further confirming the FM order of NdTi3Bi4. Thus, various magnetic ground states have been realized in titanium-based kagome metals RETi3Bi4 through rare earth engineering, which so far includes nonmagnetic (YbTi3Bi4), possibly short-range ordered (PrTi3Bi4), and FM (NdTi3Bi4) states.

Resistance under high pressure for NdTi3Bi4

Upon applying hydrostatic pressure, multiple superconducting domes can be induced in AV3Sb5, illustrating the competition between charge density wave and superconductivity76,77,78. To explore potential superconductivity and the evolution of magnetism, in situ resistance measurements of NdTi3Bi4 in the pressure range of 1.5 GPa to 41.9 GPa were performed using a diamond-anvil cell (Fig. 5a, b). Up to 10.2 GPa, a small drop related to FM order can be observed in resistance, with a superconducting-like transition occurring beyond 3.8 GPa (inset of Fig. 5a), where both the FM ordering temperature and superconducting transition temperature are suppressed as the pressure increases (Supplementary Fig. 13). By increasing the pressure beyond 10.2 GPa, the drop related to FM order becomes unresolved because the superconducting transition temperature suddenly rises. Until the pressure reaches 28.1 GPa, the drop related to FM order reappears due to the quicker suppression of superconducting transition. However, zero resistance is not observed in any measured curves, which may hint a nonintrinsic superconducting transition. Upon carefully evaluating the upper critical field (Supplementary Fig. 14), the superconducting signals should be attributed to three pressure-induced Bi phases (Bi-II, Bi-III, and Bi-V)79, likely resulting from the remaining flux droplets or being induced by pressure in this Bi-rich compounds. Despite the superconducting side phase, the resistance of NdTi3Bi4 beyond FM ordering temperature (10 K–45 K) still follows the Power law, R = R0 + ATα (Supplementary Table 11). Fig. 5c illustrates the pressure dependence of fitted parameters and FM ordering temperature of NdTi3Bi4. The residual resistance (R0) increases monotonically with pressure, whereas the decreasing correlation coefficient (A), increasing value of power (α), and decreasing FM ordering temperature (Tc) all exhibit a saturation tendency as pressure exceeds ~20 GPa. The FM ordering temperature decrease from 8.5 K (0 GPa) to ~6 K ( > 20 GPa), demonstrating the tunability of ferromagnetism. Unlike directly changing the magnetic moments of RE atoms, hydrostatic pressure tunes the distance between RE atoms, affecting the magnetic exchange interaction and consequently the FM ordering temperature.

Fig. 5: Magnetism tuned by pressure.
figure 5

Temperature-dependent resistance of NdTi3Bi4 under pressure from (a) 1.5 GPa to 10.2 GPa, and (b) 12.4 GPa to 41.9 GPa. The insets show the resistance at low temperature ranging from 1.7 K to 12 K. The arrows show the suppression trend of FM ordering temperature of NdTi3Bi4 and superconducting transition temperature of Bi. c The evolution of fitted parameters of resistance at low temperature using Power law fitting R = R0 + ATα and FM ordering temperature of NdTi3Bi4 under pressure. The error bars of R0, A and are determined by the standard error of Power law fitting and the error bar of Tc is denoted by the half-height width of the peak in the first derivative curves of resistance (dR/dT).

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Conclusions

In summary, three titanium-based kagome metals, RETi3Bi4 (RE = Yb, Pr, and Nd) have been reported. Various magnetic states have been realized, including the nonmagnetic YbTi3Bi4, paramagnetic-like PrTi3Bi4 with an anomaly around Tanomaly ~ 8.2 K, and FM NdTi3Bi4 with Tc = 8.5 K, indicating rare-earth engineering as an effective strategy to explore materials and tune their properties. Particularly for NdTi3Bi4, the FM ordering temperature is suggested to be tunable under high pressure. According to the crystal structure and magnetic properties, the materials can be simplified as distorted Ti atomic kagome bilayers with zig-zag rare earth atomic chains intercalated. Specifically, magnetism can be further tuned by changing the rare earth elements or applying external pressure. This work extends the RETi3Bi4 family with diverse magnetic states a promising platform to investigate the interplay between topologically nontrivial features, magnetism, and electron correlation. Further calculations and experimental characterizations, such as anisotropic magnetism or magnetoresistance, angle-resolved photoemission spectroscopy, and scanning tunneling microscopy or spectroscopy, are all desired to unravel the potential exotic topological phases of titanium-based kagome metals RETi3Bi4.

Note added: During the submission process of this manuscript, several related works were posted on arXiv80,81,82,83,84 and published64 within a short period of time, showcasing the RETi3Bi4 family as an excellent platform for exploring kagome materials.

Methods

Single crystal growth

RETi3Bi4 (RE = Yb, Pr, and Nd) single crystals were grown by a high-temperature solution method using Bi as flux. The as-received Yb/Pr/Nd ingot (99.9%, Alfa Aesar) was cut into small pieces, then mixed with Ti powder (99.95%, Alfa Aesar) and Bi granules (99.999%, Sinopharm) with a molar ratio of Yb/Pr/Nd: Ti: Bi = 2: 4: 12 in a fritted alumina crucible set (Canfield crucible set)85 and sealed in a fused-silica ampoule under vacuum. The ampoule was heated to 1073 K over 15 h, held at the temperature for 24 h, and then slowly cooled down to 873 K at a rate of 2 K/h. At 873 K, hexagonal-shaped, shiny-silver single crystals with sizes up to 5 mm × 5 mm × 0.5 mm were separated from the remaining liquid by centrifuging the ampoule. Considering the potential air sensitivity of the surface, all manipulations and specimen preparation for structure characterization and property measurements were handled in an argon-filled glove box.

Structure characterization and composition analysis

X-ray diffraction data were obtained using a PANalytical X’Pert PRO diffractometer (Cu Kα radiation, λ = 1.54178 Å) operated at 40 kV voltage and 40 mA current, with a graphite monochromator in a reflection mode (2θ = 5°–100°, step size = 0.017°). Indexing and Rietveld refinement were performed using the DICVOL91 and FULLPROF programs86. SCXRD data were collected using a Bruker D8 VENTURE with Mo Kα radiation (λ = 0.71073 Å) at 280 K for PrTi3Bi4 and NdTi3Bi4. The structure was solved using a direct method and refined with the Olex287 and Jana202088 packages. Due to the air sensitivity and two-dimensional feature of YbTi3Bi4, its crystal structure cannot be determined solely by SCXRD. The focused ion beam method was used to prepare thin specimens of YbTi3Bi4 with a thickness of ~50 nm for scanning transmission electron microscopy analysis. The crystal structure of YbTi3Bi4 was characterized by high-angle annular dark-field (HAADF) images obtained using a JEOL ARM-200F transmission electron microscope with double Cs correctors for the condenser and objective lens. The available spatial resolution is better than 78 picometers at 200 kV. The morphology and elemental analyses were characterized using a scanning electron microscope (SEM-4800, Hitachi) equipped with an electron microprobe analyzer for semi-quantitative elemental analysis in EDS mode. Three spots in three different locations were measured on each crystal using EDS.

Physical property measurements

Temperature-dependent magnetic susceptibility was measured using a vibrating sample magnetometer system (Quantum Design) under a magnetic field of 0.5 T parallel (H // bc) and normal (H ⊥ bc) to the bc plane using both the ZFC and FC protocols. Only magnetic susceptibility in FC protocol was measured under a larger field (1 T), and the field-dependent magnetization curves were measured under the magnetic field up to 7 T parallel and perpendicular to the bc plane. The resistivity and heat capacity measurements were carried out using a physical property measurement system (Quantum Design, 9 T). Resistivity was measured using the standard four-probe configuration with the applied current (about 2 mA) parallel to the bc plane. Heat capacity measurement was carried out at a temperature ranging from 2.2 K to 200 K at high vacuum (0.01 μbar). To protect the sample from air and moisture, thin film of N-type grease (~0.05 mg) was spread to cover the sample in an argon-filled glove box. Subsequently, the sample was mounted on the square plate of specialized heat capacity pucks in air.

In-situ high-pressure resistance measurement

The standard four-probe resistance measurement under high pressure for the NdTi3Bi4 sample was carried out at high-pressure synergetic measurement station, synergetic extreme condition user facility. A Cu-Be alloy diamond-anvil cell with a 300 μm diamond culet in diameter was used. For the sample chamber, a 100 μm diameter hole was drilled in a rhenium gasket with a c-BN insulating layer, which was then filled with KBr as the pressure-transmitting medium. A long-stick-shaped NdTi3Bi4 single crystal sample was loaded into the sample chamber in an argon-filled glove box. Four Pt electrodes were contacted to the sample in the four-probe configuration. The pressure in the sample chamber could be calibrated by ruby fluorescence at room temperature.

First principles calculations

First principles calculations were carried out with the projector augmented wave method as implemented in the Vienna ab initio simulation package89,90,91. The generalized gradient approximation92 of the Perdew-Burke-Ernzerhof 90 type was adopted for the exchange-correlation function. The cutoff energy of the plane-wave basis was 500 eV and the energy convergence standard was set to 10−8 eV. The 3 × 11 × 4 Monkhorst-Pack K-point mesh was employed for the Brillouin zone sampling of the 1 × 1 × 1 unit cell. Since Bi is a quite heavy element, spin-orbit coupling was taken into account by treating core electrons in fully relativistic method and valance electrons in second-variation method.