Superconductivity and spin fluctuations in the actinoid–platinum metal borides $\left\{\mathrm{Th},\mathrm{U}\right\}{\mathrm{Pt}}_3\mathrm{B}$

Investigating the phase relations of the system $\left\{\mathrm{Th},\mathrm{U}\right\}$-Pt-B at $900{}^{\circ }\mathrm{C}$ the formation of two compounds has been observed: cubic ${\mathrm{ThPt}}_3\mathrm{B}$ with $Pm\overline{3}m$ structure as a representative of the perovskites, and tetragonal ${\mathrm{UPt}}_3\mathrm{B}$ with $P4mm$ structure being isotypic to the noncentrosymmetric structure of ${\mathrm{CePt}}_3\mathrm{B}$. The crystal structures of the two compounds are defined by combined x-ray diffraction and transmission electron microscopy. Characterization of physical properties for ${\mathrm{ThPt}}_3\mathrm{B}$ reveals a superconducting transition at 0.75 K and an upper critical field at $T=0$ exceeding 0.4 T. For nonsuperconducting ${\mathrm{UPt}}_3\mathrm{B}$ a metallic resistivity behavior was found in the entire temperature range; at very low temperatures spin fluctuations become evident and the resistivity $\rho \left(T\right)$ follows non-Fermi liquid characteristics, $\rho ={\rho }_0+A{T}^n$ with $n=1.6$. Density functional theory (DFT) calculations were performed for both compounds for both types of structures. They predict that the experimentally claimed cubic structure of ${\mathrm{ThPt}}_3\mathrm{B}$ is thermodynamically not stable in comparison to a tetragonal phase, with a very large enthalpy difference of 25 kJ/mol, which cannot be explained by the formation energy of B vacancies. However, the presence of random boron vacancies possibly stabilizes the cubic structure via a local strain compensation mechanism during the growth of the crystal. For ${\mathrm{UPt}}_3\mathrm{B}$ the DFT results agree well with the experimental findings.

Figure 1

View of the crystal structures of ${\mathrm{ThPt}}_3\mathrm{B}$ and ${\mathrm{UPt}}_3\mathrm{B}$.

Figure 2

TEM selected area diffraction patterns of low index zone axes [100], [110], [111], and [211] together with their simulations for unambiguously cubic ${\mathrm{ThPt}}_3\mathrm{B}$.

Figure 3

TEM selected area diffraction patterns of low index zone axes [100], [101], [110], and [001] together with their simulations for tetragonal ${\mathrm{UPt}}_3\mathrm{B}$.

Figure 4

(a) Temperature dependent electrical resistivity $\rho$ of ${\mathrm{ThPt}}_3\mathrm{B}$. The inset shows the field response of the superconducting transition measured at various externally applied magnetic fields [for clarity, the legend is collected in panel (b)]. (b) Normal state $\rho \left(T\right)$ data of ${\mathrm{ThPt}}_3\mathrm{B}$ at zero field. The solid line is a least squares fit as explained in the text.

Figure 5

(a) Low temperature specific heat $C_p$ of ${\mathrm{ThPt}}_3\mathrm{B}$ plotted as $C_p/T$ vs $T$ for various external magnetic fields. The dashed line sketches the idealized specific heat jump at $T=T_c$. (b) Temperature dependent upper critical field of ${\mathrm{ThPt}}_3\mathrm{B}$ as deduced from specific heat and resistivity measurements. The initial slope of the upper critical field, ${\mu }_0{H}_{c2}^{\prime }\left(T\right)$, is about $-0.83$ T/K (dashed line). The solid line corresponds to the WHH model, as explained in the text.

Figure 6

Temperature dependent specific heat $C_p$ of ${\mathrm{ThPt}}_3\mathrm{B}$, (a) plotted as $C_p/T$ vs $T$. The inset in (a) shows low temperature details; (b) plotted as $\left(C_p-\gamma T\right)/T^3$ vs $\text{ln}T$. The dashed line is a least squares fit of the experimental data using the model described in the text. The essential parameters of the model used to construct the spectral function $F\left(\omega \right)$ (solid lines, right axis) are ${\theta }_D^{☆}=199$ K, ${\omega }_{E1}=33.3$ K with a width of $\pm 6.4$ K, ${\omega }_{E2}=72.1$ K with a width $\pm 6.2$ K, and finally ${\omega }_{E3}=600$ K with a width $\pm 10$ K.

Figure 7

DFT calculated vibrational properties of ${\mathrm{ThPt}}_3\mathrm{B}$. (a) Phonon dispersion within the harmonic model along high symmetry directions for a cubic lattice. Imaginary frequencies are represented by negative values. (b) Phonon dispersion within the harmonic model along high symmetry directions for a tetragonal lattice. (c) Phonon density of states for the cubic harmonic (full black line), the anharmonic at 100 K model (red dashed line), and for the tetragonal structure (blue dashed-dotted line). The phonon densities of states are normalized to 1.

Figure 8

Temperature dependent specific heat $C_p$ of ${\mathrm{ThPt}}_3\mathrm{B}$. Filled circles: experimental data points. DFT results for $C_V$ of vibrations are shown by lines. Dark blue dashed: harmonic model for tetragonal structure; blue dash-dotted line: harmonic model for cubic compound (A); purple dashed line: anharmonic model at 100 K for cubic compound (B); red full line: linear interpolation according to $C_V\left(T\right)=[(100-T)C_V\left(A\right)+T{C}_V\left(B\right)]/100$. The measured heat capacity $C_p$ is derived at constant pressure, whereas from DFT the heat capacity at constant volume $C_V$ is derived. The difference between these two quantities is neglected.

Figure 9

Electronic band structure of cubic ${\mathrm{ThPt}}_3\mathrm{B}$ referring to the scalar-relativistic calculation omitting spin-orbit coupling (blue dashed lines) and to the fully relativistic calculation including spin-orbit coupling (red solid lines).

Figure 10

Fermi surface of cubic ${\mathrm{ThPt}}_3\mathrm{B}$ referring to the fully relativistic calculation. The corner points (in units of $2\pi /a$) are $\mathrm{\Gamma }$(0 0 0), $X$(1/2 0 0), $M$(1/2 1/2 0), and $X$(0 1/2 0).

Figure 11

Total and site-projected electronic density of states (DOS) of ${\mathrm{ThPt}}_3\mathrm{B}$ for the cubic (upper panel) and the tetragonal structure (lower panel) for the fully relativistic calculation.

Figure 12

Temperature dependent resistivity $\rho$ of ${\mathrm{UPt}}_3\mathrm{B}$. The inset shows low temperature details and the solid line is a least squares fit based on $\rho ={\rho }_0+A{T}^n$ with $n=1.6$.

Figure 13

Temperature dependent specific heat $C_p$ of ${\mathrm{UPt}}_3\mathrm{B}$ plotted as $C_p/T$ vs $T$. The inset shows low temperature details and the solid line is a least squares fit based on a spin fluctuation model.