Crystal growth and electronic properties of LaSbSe

The ZrSiS-type materials have gained intensive attentions. The magnetic version of the ZrSiS-type materials, LnSbTe (Ln = Lanthanide), offers great opportunities to explore new quantum states owing to the interplay between magnetism and electronic band topology. Here, we report the growth and characterization of the non-magnetic LaSbSe of this material family. We found the metallic transport, low magnetoresistance and non-compensated charge carriers with relatively low carrier density in LaSbSe. The specific heat measurement has revealed distinct Sommerfeld coefficient and Debye temperature in comparison to LaSbTe. Such addition of a new LnSbSe selenide compound could provide the alternative material choices in addition to LnSbTe telluride materials.

In topological materials, spin-orbit coupling (SOC) is a known parameter that affects electronic states, which is relatively easily tunable by elementary substitutions. In LnSbTe, replacing Te with other chalcogen elements is one possible route to vary SOC. Thus far, CeSb(Te 1-x Se x ) [40,53] has been reported to show a complex magnetic ordering that results in a possible devil's staircase in magnetization measurements. In addition, features suggesting a Kondo lattice with a small charge carrier density has been observed in CeSbSe [53]. Extending from tellurides to selenides, those LnSbSe compounds provide additional opportunities to investigate the topological materials and topological physics in WHM family. This motivated us to study the previously unexplored non-magnetic WHM compound LaSbSe in this work. We found that LaSbSe exhibits metallic behavior in electron transport, with small magnetoresistance and non-compensated charge carriers, which is distinct from the telluride compound LaSbTe.

Materials and Methods
The LaSbSe single crystals were synthesized by a two-step chemical vapor transport (CVT) method. First, a polycrystalline precursor was prepared by heating the stoichiometric mixture of La, Sb, and Se at 750°C for 2 days. The precursor was then used as the source material for the subsequent CVT growth with selenium tetrachloride as a transport agent. Millimeter-size rectangular crystals with metallic luster were obtained after two weeks' growth with a temperature gradient from 1000 to 850 °C, as shown in the inset of figure  1(b). The obtained single crystals for LaSbSe are found to be relatively softer and easy to cleave than LnSbTe compounds, which is in line with the lower Debye temperature in comparison to the LnSbTe compounds [39,41,44,46] as will be discussed below. The elemental composition was checked by using energy-dispersive X-ray spectroscopy (EDS). The crystal structure was determined by both powder and single crystal X-ray diffraction (XRD) performed at room temperature by using Rigaku XtaLAB Synergy-S diffractometers. The powder diffraction was performed using Cu Kα radiation, and the single crystal XRD spectrum was collected by using Mo Kα radiation. The refinements of powder and single crystal XRD data were performed by JANA2006 [75]. Electronic transport and heat capacity measurements were performed by using a physical properties measurement system (PPMS).

Results and Discussions
Stoichiometric LnSbTe compounds crystallize in the tetragonal lattice with nonsymmorphic space group P4/nmm, in which the Sb square nets are sandwiched between the Ln-Te layers [28,43,45,48,50]. This Sb plane can be substituted by Te, resulting in nonstoichiometric compositions LnSb 1−x Te 1+x which is accompanied by orthorhombic distortions [41,52]. In addition, vacancies in the Sb layer have also been observed in those nonstoichiometric compounds [43,45]. To resolve the crystal structure of LaSbSe, we performed both powder and single crystal XRD. The crystal structure was solved and refined from single crystal XRD, which was then used as the model structure for a Rietveld refinement with the powder diffraction pattern. The refined lattice atomic parameters are listed in Table 1 and  Table 2. Figure 1b shows the powder XRD spectrum and refinement., The refined crystal structure of LaSbSe is a distorted variant of the P4/nmm structure of LnSbTe. It is pseudotetragonal but the Sb square net is distorted, rendering from which a monoclinic structure with a space group of P21/c can be determined for our LaSbSe. The structure parameters are summarized in Table 1. Compared to a previous report on LaSbSe [76], our refined structure is consistent in space group and atomic positions but evidently different in lattice parameters. A stoichiometric composition, LaSbSe, was also obtained from the structure refinement, which is consistent with the composition analysis using EDS. To further confirm the structure of LaSbSe, we have also resolved the structure using single crystal XRD, from which a consistent crystal structure was obtained as shown in Table 2.
Many TSMs exhibit large positive magnetoresistance (MR) when magnetic field is applied perpendicular to the current direction [66], including the tetragonal non-rare earth WHM [21,[57][58][59]67] and the orthorhombic LaSbTe (space group Pmcn) [54] which is structurally related to the LaSbSe studied in this work. However, our LaSbSe show very small MR. Figure. 2(b) presents the normalized MR define as [ρ(H) − ρ(0)] ∕ ρ(0), where ρ(0) and ρ(H) are the resistivity at zero and μ 0 H applied field respectively [66]. LaSbSe shows weak positive MR only up to 3.3% at T = 2 K and μ 0 H = 9 T, with a nearly quadratic field dependence. The classical transport theory [68] predicts that in the small field limit, orbital MR due to Lorentz effect exhibits a parabolic field dependence and scales with the square of mobility, i.e., MR ∝ (μH) 2 where μ is mobility of charge carriers. The electron-hole compensation prevents MR from saturating, which is also an important factor for large MR. To extract carrier densities and mobilities, we have performed Hall effect experiments. As shown in Fig. 2(c), Hall resistivity ρ xy shows linear field dependence at 300 K, but deviations from linearity can be observed with decreasing temperature. Such non-linearity indicates that both electron-and hole-type carriers contribute to electronic transport in LaSbSe, which has also been observed in non-magnetic ZrSiS-type compounds [21,54,69] but is different from the linear ρ xy (H) seen for a few LnSbTe compounds [39,44,46]. For such a multiband system, carrier densities and mobilities can be obtained by simultaneously fitting both the longitudinal resistivity ρ xx (H) and Hall resistivity ρ xy (H) to a two-band model [66]: ρ xx = 1 e (n ℎ μ ℎ + n e μ e ) + μ ℎ μ e (n ℎ μ e + n e μ ℎ )B 2 (n ℎ μ ℎ + n e μ e ) 2 + μ ℎ 2 μ e 2 (n ℎ − n e ) 2 B 2 (1) ρ xy = B e (n ℎ μ ℎ 2 − n e μ e 2 ) + μ ℎ 2 μ e 2 (n ℎ − n e )B 2 (n ℎ μ ℎ + n e μ e ) 2 + μ ℎ 2 μ e 2 (n ℎ − n e ) 2 B 2 (2) where n e(ℎ) and μ e(ℎ) are carrier density and mobility for electrons (holes) respectively. As shown in Figs. 3(a-b), the two-band model fits ρ xx (H) and ρ xy (H) very well, from which the carrier densities and the mobilities of the electron and hole bands are obtained and shown in Figs. 3(c-d).
As shown in Fig. 3(c), n e and n ℎ are in the order of ~ 10 20 cm -3 . Such values are comparable to WHM-type topological nodal-line semimetals such as ZrSiM (M = S, Si, Te). In those materials, carrier densities are lower than conventional metals but much higher than many Dirac nodal-point semimetals, which has been attributed to the nodal-line band structures that possess band crossings along a line near the Fermi level [21,69]. Nevertheless, unlike ZrSiM which exhibit nearly perfect electron-hole carrier compensation [21,69], n e and n ℎ in LaSbSe differs a lot, by nearly an order of magnitude at T = 2 K (5.66×10 20 and 7.45×10 19 cm −3 for n e and n ℎ respectively). Similarly, the electron and hole mobilities are also quite different in the entire temperature range from 2 to 300 K. For example, 129 cm 2 /V s for electrons and 339 cm 2 /V s for holes at T = 2 K. Such values are significantly lower than LaSbTe [54] and ZrSiS [69], which is in line with the bad metallicity and small magnetoresistance for LaSbSe as stated above. As a comparison, in NdSbTe which show even lower mobility, the metallicity is fully suppressed and the material exhibits non-metallic transport behavior [46].
Magnetic LnSbTe compounds provide excellent platforms to investigate the new phenomena brought in by magnetic rare earth element Ln, such as engineering topological electronic states [28] and electron correlation enhancement [44]. For those telluride materials, nonmagnetic LaSbTe provides a good reference to evaluate the effects of magnetism in those magnetic LnSbTe. For example, specific heat measurement is a useful bulk measurement tool to extract information of magnetism and electronic correlations. Magnetic LnSbTe compounds [39,41,44,46,48,50] display clear specific-heat anomalies around the magnetic phase transition temperatures. A few LnSbTe compounds such as NdSbTe [46], SmSbTe [44] and HoSbTe [48] exhibit possible enhanced electronic correlations characterized by large Sommerfeld coefficient γ. In previous specific heat studies, LaSbTe has been used as a reference material to precisely evaluate the electronic specific heat for magnetic LnSbTe because of the absence of magnetic specific heat in non-magnetic LaSbTe [44][45][46]. Similarly, for magnetic selenide materials LnSbSe such as CeSbSe which displays interesting electronic properties such as magnetic Devil's staircase [40,53] and Kondo lattice behavior [53], the non-magnetic LaSbSe can also act as a good reference for specific heat study. In Fig. 4 we present the temperature dependence of specific heat divided by temperature C(T)/T for LaSbSe. Data for LaSbTe is also provided for comparison. No anomaly is seen in both compounds from 1.8K to 30K, consistent with their non-magnetic nature. Therefore, the total specific heat can be expressed by C tot = C el + C ph , where C el = γT is the electronic specific heat and C ph = βT 3 represents the phonon contribution in the low temperature limit. This is clearly reflected by the linear dependence when plotting the low temperature C/T data against T 2 , as shown in the inset of Fig. 4. The linear fits yield Sommerfeld coefficients γ of 2.19 and 0.51 mJ mol/K 2 for LaSbSe and LaSbTe, respectively. Such γ values are much lower than magnetic LnSbTe compounds [28,39,44,46], in which large γ above 100 mJ mol/K 2 has been observed and ascribed to the effective mass enhancement due to the presence of flat 4f bands near the Fermi level in the magnetically ordered state [44].

Discussion
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Conclusions
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Funding:
This work was mainly supported by the U.S. Department of Energy Office of Science under Award No. DE-SC0022006 (crystal growth and electronic, magnetic, and thermal property measurements). F. W acknowledges the support from NSF under award MRI 2117129 for single crystal XRD and structure refinements. J. S acknowledges the support from NIH under award P20GM103429 for powder XRD.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.   Temperature dependent specific heat divided by temperature C/T for LaSbSe and LaSbTe. Inset: linear fit for C/T vs. T 2 at low temperatures for LaSbSe and LaSbTe