Muon spin relaxation and electron/neutron diffraction studies of BaTi${}_2$(As${}_{1-x}$Sb${}_x$)${}_2$O: Absence of static magnetism and superlattice reflections

We present the results of muon spin relaxation/rotation, transmission electron microscopy, and neutron diffraction measurements performed on several specimens of BaTi${}_2$(As${}_{1-x}$Sb${}_x$)${}_2$O, which is known to have either charge density or spin density wave ordering at $T_{\mathrm{DW}}$ for all $x$, and superconductivity below $T_{\mathrm{c}}$ ≈ 1 K for $x$ $=$ 1. Zero-field muon spin relaxation measurements show no significant increase in relaxation rate at the density wave ordering temperature for any composition, indicating that the density wave is of the charge rather than spin type. The absence of any superstructure peaks in selected area electron and high-resolution neutron diffraction measurements below $T_{\mathrm{DW}}$ suggests that the charge density wave does not involve modulation of atomic arrangement. Transverse field muon spin rotation measurements reveal a robust superconducting state below $T_{\mathrm{c}}$ ≈ 1 K for $x$ $=$ 1.

Figure 1

Electronic phase diagram of BaTi${}_2$(As${}_{1-x}$Sb${}_x$)${}_2$O and BaTi${}_2$(Sb${}_{1-y}$Bi${}_y$)${}_2$O showing the S/CDW order for BaTi${}_2$(As${}_{1-x}$Sb${}_x$)${}_2$O and the two-dome structure of the superconducting state in BaTi${}_2$(Sb${}_{1-y}$Bi${}_y$)${}_2$O, adapted from Ref. 10. The arrows indicate the compositions studied for this paper. The inset displays the crystal structure of BaTi${}_2$$P{n}_2$O with the space group $P$4/mmm, where the Ti${}_2$$P{n}_2$O slabs stack in a uniform manner along the tetragonal $c$ axis.

Figure 2

Results of zero-field muon spin relaxation measurements on BaTi${}_2$(As${}_{1-x}$Sb${}_x$)${}_2$O. (a) Asymmetry versus time spectra for the two end members of BaTi${}_2$As${}_2$O and BaTi${}_2$Bi${}_2$O showing only a moderate increase in relaxation rate at low temperatures. Error bars represent 1σ and are smaller than the symbol size. (b) Refined relaxation rates for four specimens of BaTi${}_2$(As${}_{1-x}$Sb${}_x$)${}_2$O. The lack of a significant increase in relaxation rate at the density wave ordering temperature excludes the possibility of SDW ordering.

Figure 3

Neutron diffraction patterns at 60 K (left) and 2.5 K (right), showing observed (red circle), calculated (green line), and difference (blue line) profiles. Space group $P$4/mmm, with Ba on 1$d$, Ti on 2$f$, Sb on 2$g$ (0,0, $z$), and O on 1$c$, with 100$\%$ occupation. Refined parameters and goodness-of-fit factors for 60 K [2.5 K] are $a$ $=$ 4.1069(2) [4.10711(4)] Å, $c$ $=$ 8.0517(4) [8.0482(1)] Å, $z$ $=$ 0.7520(2) [0.7519(2)] Å,100$U_{\mathrm{iso}}$ $=$ 0.28(3) [0.16(3)] Å${}^2$ for Ba, 0.36(2) [0.35(2)] Å${}^2$ for Ti, 0.43(2) [0.41(2)] Å${}^2$ for Sb, 0.43(3) [0.40(3)] Å${}^2$ for O, $R_{\mathrm{wp}}$ $=$ 7.073 [7.530]$\%$, $R_{\mathrm{p}}$ $=$ 4.963 [4.994]$\%$. Values in parentheses represent one standard deviation of the fit parameter.

Figure 4

Selected area electron diffraction patterns from [001] for BaTi${}_2$Sb${}_2$O at (a) 300 K and (b) 14 K, showing the absence of superstructure below $T_{\mathrm{DW}}$. (c) A proposed √2 × √2 × 1 superstructure as a result of CDW transition,[23] where the blue, red, and brown spheres denote, respectively, Ti, O, and Sb. The unit cell of the original structure is shown by the broken lines.

Figure 5

Results of TF muon spin rotation measurements on BaTi${}_2$Sb${}_2$O. (a) Asymmetry versus time spectra at two different temperatures. The increased damping of the oscillating signal is due to the presence of the vortex lattice in the superconducting state. (b) Observed and calculated temperature evolution of the superconducting relaxation rate ${\sigma }_{\mathrm{sc}}$. The calculated best fit assumes an isotropic BCS superconductor in the weak coupling limit. (c) The temperature evolution of the precession frequency showing a decrease in frequency below $T_{\mathrm{c}}$.