Ab initio studies of magnetism and topology in solid Pd-rich [Formula: see text]-PdSi alloys

Abstract

In 1965 Duwez et al. reported having generated an amorphous, stable phase of palladium-silicon in the region 15 to 23 atomic percent, at.%, silicon. These pioneering efforts have led to the development of solid materials that are now known as Bulk Metallic Glasses, BMG. In 2019 Rodríguez et al. discovered, computationally, that bulk amorphous Pd becomes magnetic, and so does porous/amorphous Pd. Puzzled by these results, the study of several solid binary systems in the Pd-rich zone was undertaken; in particular, the study of the glassy metallic alloy a-Pd[Formula: see text]Si[Formula: see text], for [Formula: see text], (c in at.%) to see what their topology is, what their electronic properties are and to inquire about their magnetism. In this work it is shown that this metallic glass is in fact magnetic in the region [Formula: see text]. Collaterally [Formula: see text] and [Formula: see text] magnetization curves are shown where the net magnetic moment is presented. The topology and the position of the first few peaks of the pair distribution functions, which agrees well with experiment, are also discussed. The BMGs produced experimentally so far are limited in size, but despite this limitation, recent industrial efforts have developed some useful devices that may revolutionize technology.

Figure 1

Region of the Pd-Si phase diagram near the eutectic point. The atomic concentrations deployed are $0\le c\le 40$ at.%. This figure is a linear (black lines) and parabolic (red lines) fit to the experimental values contained in References^–.

Figure 2

Total pair distribution functions, tPDFs, for the 8 alloys studied in this work and for the pure bulk palladium sample. The bimodal character of the second peak, typical of amorphous Pd, gradually disappears as the silicon concentration increases. The tPDFs were calculated using Correlation, an open-source software developed by Rodríguez et al..

Figure 3

Comparison of the Pd-Pd pPDF for the Pd${}_{80}$Si${}_{20}$ sample with the partial experimental result of Masumoto (in Waseda’s book). The bimodal elephant-like nature of the second peak is depicted in the inset.

Figure 4

Comparison of the XRD pattern obtained from the experimental results of Ref. ($c=15$ at.%), green line, with our simulations, dark solid profile. See text.

Figure 5

Spin up ($\alpha$ spins) and spin down ($\beta$ spins) densities of states for the 9 supercells. (a) Total densities of states. (b) Palladium partial densities of states. (c) Silicon partial densities of states. The net magnetic moment tends to zero as the silicon concentration increases.

Figure 6

Average magnetic moment, AMM, per atom after the GO runs. The alloy a-Pd${}_{86.66}$Si${}_{13.34}$ was studied to investigate a possible linear fit to our magnetic results. The fit is not linear, green line, it is quadratic, red broken line. See text.

Figure 7

Qualitative comparison of our results for the AMM per atom of the solid a-PdSi alloys (vertical scale on the left) with the magnetic susceptibility measurements for the liquid counterpart (vertical scale on the right).