X-ray charge-density studies $-$ a suitable probe for superconductivity?

TL;DR

X-ray diffraction studies can detect subtle structural changes related to superconductivity, but their interpretation requires high resolution and appropriate models, as demonstrated in studies of MgB$_2$ and other superconductors.

Contribution

This work shows that temperature-dependent electron density changes in MgB$_2$ are mainly due to atomic displacement parameters, clarifies the role of vacancies, and emphasizes the importance of high-resolution XRD analysis.

Findings

Temperature-dependent density changes are due to atomic vibrations.

MgB$_2$ does not necessarily have magnesium vacancies.

High-resolution XRD clarifies structural features related to superconductivity.

Abstract

Case studies of $1T$-TiSe$_2$ and YBa$_2$Cu$_3$O$_{7-\delta}$ have demonstrated that x-ray diffraction (XRD) studies can be used to trace even subtle structural phase transitions which are inherently connected with the onset of superconductivity in these benchmark systems. Yet, the utility of XRD in the investigation of superconductors like MgB$_2$ lacking an additional symmetry-breaking structural phase transition is not immediately evident. Even though, high-resolution powder XRD experiments on MgB$_2$ in combination with maximum entropy method (MEM) analyses hinted at differences between the electron density distributions at room temperature and 15K, i.e. below the $T_c$ of approx. 39K. The high-resolution single-crystal XRD experiments in combination with multipolar refinements presented here can reproduce these results, but show that the observed temperature-dependent density changes are almost entirely due to a decrease of atomic displacement parameters as a natural consequence of reduced thermal vibration amplitude with decreasing temperature. Our investigations also shed new light on the presence or absence of magnesium vacancies in MgB$_2$ samples $-$ a defect type claimed to control the superconducting properties of the compound. We propose that previous reports on the tendency of MgB$_2$ to form non-stoichiometric Mg$_{1-x}$B$_2$ phases ($1 - x \sim$0.95) during high-temperature (HT) synthesis might result from the interpretation of XRD data of insufficient resolution and/or usage of inflexible refinement models.