Stabilization of Bi vibration along c-axis in BiS2-based layered compounds La(O,F)Bi(S,Se)2 by Se substitution

BiCh2-based layered compounds have been extensively studied as potential thermoelectric and unconventional superconducting materials. For both functionalities, in-plane chemical pressure effects improve their thermoelectric or superconducting properties. In this study, we investigate the effects of in-plane chemical pressure on atomic vibrations of Bi by analyzing lattice specific heat measured at T = 1.9–300 K with multiple Debye and Einstein models for thermoelectric LaOBi(S,Se)2 and superconducting LaO0.5F0.5Bi(S,Se)2. We reveal that in-plane chemical pressure enhances the oscillator number of the Einstein mode corresponding to large-amplitude Bi vibration along the c-axis in both the systems.

[8][9][10][11][12][13][14][15][16][17] The typical parent system is LaOBiS 2 where high thermoelectric performance or superconductivity can be induced by element substitutions. The cryal structure of LaOBiS 2 is composed of an alternate stacking of a LaO blocking layer and a BiS 2 conducting layer.1,9) Thoccted via S2 site (see Fig. 2), and van der Waals gap exists in between two BiS conducting planes.LaOBiS 2 is a semiconductor, 6,17,18) and F substitution for the O site generates electron carriers, and superconductivity is induced in F-substituted materials.1,9) However, the F-doped phases La(O,F)BiS 2 does not show bulk superconductivity and bulk nature can be achieved by application of external pressure effects 9,19,20) or chemical pressure effects by Se substitution for the S site.21,22) In La(O,F)BiS 2−y Se y , the substituted Se selectively occupies the in-plane S1 site.23) Hence, positive in-plane chemical pressure is generated by Se substitution in the system.22) Although the ionic radius of Se 2− (198 pm) 24) is larger than that of S 2− (184 pm), 24) due to the tough structure (bonding) in the LaO blocking layers, the in-pane expansion is smaller than that expected from the ionic radius difference, which is the reason positive in-plane chemical pressure effects are generated.22) The in-plane chemical pressure suppresses inplane local structural disorder at the S1 site, [25][26][27] and the essential metallic conductivity is induced by Se substitution, which results in the emergence of bulk superconductivity.Since unconventional superconductivity features are observed in BiS 2 -based compounds optimized by the in-plane chemical pressure effects, further understanding of the in-plane chemical pressure effects is important.In thermoelectric phases LaOBiS 2−x Se x , in which electron carriers are not doped, inplane chemical pressure by Se substitutions improves the carrier mobility and the thermoelectric power factor.28) Furthermore, thermal conductivity is suppressed by Se substitution, which results in a high thermoelectric figure-of-merit ZT, which is given by ZT = S 2 T/ρκ where S, ρ, and κ are Seebeck coefficient, electrical resistivity, and thermal conductivity, respectively. 5) S ions substituted in LaOBiS 2−x Se x occupy the in-plane S1 site, and in-plane local disorder is suppressed by Se substitution, which is the cause of the enhancement of mobility.29) The cause of the suppression of thermal conductivity is explained by large-amplitude atomic vibrations of heavy Bi ions and unique vibration mode along the c-axis.30,31) From analogy to one-dimensional-rattling thermoelectric materials, tetrahedrites, 32) we proposed that the c-axis Bi vibration is like a one-dimensional rattling mode on the basis of the analysis of phonon by inelastic neutron scattering and phonon calculations.31) Therefore, further investigation of the unique Bi vibration along the c-axis and its evolution by Se substitution at the S1 site is essential for deepening the understanding both thermoelectric and superconducting properties that are enhanced by in-plane chemical pressure effects.
In this study, we use specific heat (C), particularly lattice contribution of C (C lat ), to analyze phonons in LaOBiS 2−x Se x (x = 0, 1.0) and LaO 0.5 F 0.5 BiS 2−y Se y (y = 0, 1.0).C based on the Debye model and the Einstein model, C D and C E , are described as the following Eqs.( 1) and (2) using parameters of n (oscillator number), k B (Boltzmann constant), θ D (Debye temperature), x D ( T D / q ), and E q (Einstein temperature).
When the contributions of low-energy optical phonons are negligible, C D well reproduces experimental data of C lat .When low-energy optical phonons are not negligible, both C D and C E should be considered to explain the C lat .For example, the optical-phonon analysis was used to discuss the one-dimensional rattling in the tetrahedrites 33) and the origins of negative thermal expansion in ZrW 2 O 8 . 34)In the case of ZrW 2 O 8 , the combination of two Debye models and three Einstein models was used to explain the C lat data. 34)The use of double Debye models is required for the case of ZrW 2 O 8 because of the coexistence of the oxide units with a higher θ D and the framework with a lower θ D , which is connecting the oxide units.Therefore, the analysis of C lat for systems with low-energy optical phonons and complicated crystal structures with different bonding states requires the combination of multiple Deby and Einstein models.After testing several models, we conclude that the La(O,F)Bi(S,Se) 2 system is an example where the multimode analysis is needed.
Although we reported the presence of a peak structure related to optical phonons in C lat /T 3 in Ref. 35, data at a wide temperature range were necessary to conduct the analyses.We, therefore, measured the temperature dependences of C for the polycrystalline samples of LaOBiS 2−x Se x (x = 0, 1.0) and LaO 0.5 F 0.5 BiS 2−y Se y (y = 0, 1.0) at T = 1.9-300K.The polycrystalline samples were prepared in an evacuated quartz tube by heating at T = 973 K for x = 0 and y = 0 ant at T = 923 K for x = 1.0 and y = 1.0; the details of sample preparations are written in Refs. 4 and 21.The Se-substituted samples contain tiny impurities of La 2 O 2 S and Bi 2 Se 3 for x = 1.0 and LaF 3 for y = 1.0.The C-T data were taken by a relaxation method on a Physical Property Measurement System (PPMS Dynacool, Quantum Design).For LaOBiS 2−x Se x , data taken at H = 0 T were used for the analyses.The samples were attached to the sample stage using N grease, and the weight of samples used in this study is 16.80, 11.93, 15.55, and 21.18 mg for x = 0, x = 1.0, y = 0, and y = 1.0, respectively.For superconducting LaO 0.5 F 0.5 BiS 2−y Se y , to avoid the affection of superconducting transitions, the data at T < 5 K and H = 3 T and the data at T > 5 K and H = 0 T were merged and used for the analyses.
We start from LaOBiS 2 because the total C is contributed by C lat only because of no carrier doping.Figure 1 I.Although we used three Einstein modes for fitting, the Einstein model with the highest θ E1 has a large n, which implies the presence of major vibrations of Bi at the energy of θ E = 78 K.
To confirm the validity of the analysis with the combination of multiple models, we show the calculation results of C/T 3 in Fig. 2(a).The original data of the calculation of phonons have been published in Ref. 31 (see Ref. 31 for details of calculations).The calculation is based on the monoclinic (P2 1 /m) structure; LaOBiS 2−x Se x undergoes structural transition from tetragonal (P4/nmm) to monoclinic. 1,36)In contrast, F-doped LaO 0.5 F 0.5 BiS 2−y Se y does not undergo the structural transition, and the tetragonal structure remains at low temperatures. 37)However, the monoclinicity in this system is quite small, and the affections of the structural symmetry lowering to phonon characteristics are limited.Therefore, we use the result as a reference.The calculated C/T 3 −T exhibits a trend quite similar to the experimental result.The difference is the presence/absence of the low-T upturn in experimental and calculated results, which would be due to the presence of local structural disorders that cannot be incorporated into the calculations.Another difference is the absolute values of the peak amplitude.The calculated peak height is higher than that obtained by the experiment; this difference would also be caused by the in-plane disorder because the inconsistency is removed by Se substitution.Figure 2(b) shows the phonon DOS with the contributions from Bi.The phonon band structure is displayed in Fig. S1 (supplementary data).It is clear that the phonon DOS below 10 meV are dominated by Bi vibrations.Figures 2(c) and 2(d) show typical vibration modes at E = 3.4 and 7.4 meV, respectively, with arrows showing atomic displacements.Since Bi is very heavy, the size of the arrows becomes smaller than that of the others, but there are clear Bi vibrations seen in those figures.We consider that the two Einstein modes with θ E1 = 78 K and θ E2 = 35 K (Table I) are corresponding to those modes of Bi vibrations.
Next, we analyze the phonons of LaOBiSSe (x = 1.0)where the S1 site is completely substituted by Se.The analysis with double Debye and triple Einstein models similar to model 4 [Fig.1(f)] is applied, and the result is shown in Fig. 3.The used model parameters are listed in Table II.With Se substitution, θ D1 and θ D2 decrease, and θ E1 slightly decreases, which is consistent with the peak shift in C/T 3 −T between LaOBiS 2 and LaOBiSSe.The noticeable trend is the increase in n E1 and n E2 by the Se substitution.Instead of that, n D1 is reduced, implying the increase in the oscillator number of the optical-phonon modes and the stabilization of the modes by the in-plane chemical pressure effects.Because LaOBiS 2 possesses huge local structural disorders in the conducting plane, 27) we consider that the 013002-3 © 2023 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd suppression of the disorder is essential for the emergence of intrinsic Bi vibrations expected from the phonon calculations.
In other words, in the Se-free Bi-S1 planes with local disorders, the Bi vibrations along the c-axis are largely suppressed by the local disorder, which results in the smaller n E1 .As a fact, the experimental value of the peak of C/T 3 is almost the same as the calculated value.This scenario is consistent with previous works on X-ray absorption spectroscopy, which reported a large change in the bonding states of the Bi-S1plane from glassy to crystalline by Se substitution. 27,29)Furthermore, Bi vibration along the c-axis contributes to phonon scattering because of large-amplitude anharmonic vibration of a large atom according to our previous inelastic neutron scattering on LaOBiS 2−x Se x . 31)he stabilization of the large-amplitude Bi vibrations along the c-axis should be linked to the suppression of thermal conductivity, which is a key factor for the high ZT.A similar enhancement of one-dimensional huge atomic vibration by chemical pressure effects was observed in tetrahedrite materials. 38)Therefore, chemical pressure effects are useful for tuning properties of thermoelectric materials having onedimensional rattling-like vibrations.In Fig. 4, the results of the analyses of C lat /T 3 for superconducting LaO 0.5 F 0.5 BiS 2-y Se y (y = 0 and 1.0) are displayed.C lat was obtained by C lat = C−γT, where γ is an electronic specific heat coefficient and determined by low-T fitting of C/T−T 2 to C/T = γ + βT 2 .As mentioned above, we used data taken at H = 3 T for T < 5 K to avoid the contribution from superconducting states.The C−T data at the low temperature regime for LaO 0.5 F 0.5 BiS 2 are shown in Fig. S2 (supplementary data).We confirmed that the low-T (H = 3 T) data are smoothly connected to the higher-T data.In La(O,F)BiS 2 , a previous study showed that the phonon DOS are not largely affected by F substitution. 39)s shown in Fig. 4(a), the T-dependence of C lat /T 3 for superconducting LaO 0.5 F 0.5 BiS 2 is well-fitted with model 4.
Here, γ = 0.96(2) mJ/mol K 2 is used for LaO 0.5 F 0.5 BiS 2 .The results are quite similar to LaOBiS 2 , where the peak amplitude for the Einstein mode with θ E1 is relatively smaller than that in the calculation.Since the oscillator number n E1 is around 0.5 for LaOBiS 2 and LaO 0.5 F 0.5 BiS 2 , the difference between the experimental data and the calculation result is basically caused by the small n E1 .Figure 4(b) shows the analysis result for LaO 0.5 F 0.5 BiSSe with model 4. The γ is 2.71(4) mJ/mol K 2 for LaO 0.5 F 0.5 BiSSe.As compared to LaO 0.5 F 0.5 BiS 2 , the experimental values are close to the calculation result, particularly at the Einstein-mode peak.The trend of the affection by the Se substitution at the in-plane S1 site is quite similar to the case of LaOBiSSe.The n E1 increases from 0.52 (for LaO 0.5 F 0.5 BiS 2 ) to 0.60 (for LaO 0.5 F 0.5 BiSSe).Because of the almost same θ E1 in both analyses, the increase in n E1 should be an essential feature caused by the in-plane chemical pressure effects.On the superconductivity in LaO 0.5 F 0.5 BiS 2−y Se y , bulk nature of superconductivity is enhanced by Se substitution. 21,35,40,41)ble II.The parameters used for the C lat /T 3 analyses for LaOBiS 2 , LaOBiSSe, LaO 0.5 F 0.5 BiS 2 , and LaO 0.5 F 0.5 BiSSe.Although the Debye and Einstein temperatures decreases with Se substitution, γ increases with Se substitution.Therefore, we cannot simply discuss the cause of the enhanced superconducting properties by the Se substitution in LaO 0.5 F 0.5 BiS 2−y Se y in the framework of the conventional phonon-mediated mechanism. 42)However, the fact that the enhancement of bulk nature occurs when the Bi vibration along the c-axis with θ E1 is stabilized suggests positive relationship between the Bi vibration and superconductivity.

Model parameter
In conclusion, we investigated the optical-phonon modes, particularly for that related to the large-amplitude Bi vibration, for LaOBiS 2−x Se x and LaO 0.5 F 0.5 BiS 2−y Se y through the analyses of the temperature dependences of C lat /T 3 .By assuming double Debye and triple Einstein models, the experimental data are well explained.The in-plane chemical pressure effects, which are essential for the suppression of inplane local structural disorder and improve the thermoelectric or superconducting properties, commonly result in the stabilization of the Einstein mode corresponding to the large-amplitude Bi vibration along the c-axis in LaOBiSSe and LaO 0.5 F 0.5 BiSSe.The oscillator number n E1 clearly increases by Se substitution.Noticeably, the experimental data of C lat /T 3 for Se-substituted samples are consistent with the calculation results on LaOBiS 2 , while the experimental data (the peak amplitude for the Einstein mode with θ E1 ) for Se-free samples are smaller than the calculation result.We conclude that the Bi vibration along the c-axis is suppressed in Se-free Bi-S1 planes due to on-plane structural disorder, and the essential feature of the Bi vibration (Einstein mode with θ E1 ) is recovered by the in-plane chemical pressure effects.
(a) shows the C-T data for LaOBiS 2 , and Fig. 1(b) shows the fitting to C/T = βT 2 where β is the coefficient of lattice specific heat.From the obtained β, θ D is estimated as 222.6(4)K. First, analysis with a single Debye model was tested, and the result is shown in Fig. 1(c).Because of assumed atomic number of 5 per formula unit, the sum of n should be 5 in the analyses.It is clear that a single Deby model with θ D = 223 K does not explain the experimental data.We tested a single Debye model with different θ D , but no successful fitting was obtained.Therefore, we applied double Debye models, and the combination of θ D1 = 223 K (n D1 = 2) and θ D2 = 450 K (n D2 = 3) gave a good fitting at a high-temperature data as shown in Fig. 1(d), where n D1 and n D2 are corresponding oscillator numbers.From the results, we decided to fix θ D1 (lower θ D ) to be the value obtained by low-T fitting to the C/T−T 2 plot.In addition, n D2 is fixed to 3, which is reasonable when considering that La and O in blocking layers and S2 are contributing a higher θ D2 , and lower θ D1 is contributed by Bi and S1 in the conducting plane with anomalous bonding states with local disorder and Bi vibration along the c-axis.Basically, C with a lower θ D dominates low-T C lat , which is the reason why θ D1 estimated from the fitting in Fig. 1(b) could work as θ D1 .In Fig. 1(e), one Einstein mode with θ E1 is added to the model in Fig. 1(d).To create n E1 , n D1 was reduced accordingly, because the lowenergy phonons are mainly contributed by Bi as discussed later.Finally, as shown in Figs.1(f), 1(a) model with double Debye and triple Einstein modes was found to well explain the experimental result in all temperature ranges except very low temperatures.Although residual C/T 3 is present at lower temperatures, we did not include further Einstein modes because the expected peak positions are lower than the lowest data point, and the oscillator number of that mode is extremely low.The obtained model parameters for

Fig. 1 . 2 ©
Fig. 1.(a) Temperature dependence of specific heat (C) for LaOBiS 2 .(b) Low-T fitting results on the T 2 dependence of C/T, where data points between two cursors were used for fitting.(c)-(f) Analyses of C/T 3 with different four models: model 1 with single Debye model, model 2 with double Debye models, model 3 with double Debye and single Einstein models, and model 4 with double Debye and triple Einstein models.The horizontal axis is in log scale.

Fig. 2 .
Fig. 2. (a) Calculated temperature dependence of C/T 3 for LaOBiS 2 with a monoclinic P2 1 /m structure.The horizontal axis is in log scale.(b) Energy dependence of phonon DOS for LaOBiS 2 .The original data has been published in C. H. Lee et al., Appl.Phys.Lett.112, 023903 (2018). 31)(c), (d) Schematic images of crystal structure of LaOBiS 2 and atomic vibrations at E = 3.4 and 7.4 meV.The arrows indicate displacements of the atoms.

Fig. 3 .Fig. 4 . 4 ©
Fig. 3. Temperature dependence of C/T 3 for LaOBiSSe.The horizontal axis is in log scale.Double Debye and triple Einstein models are assumed.