Figure 1: The crystal structure of LnBa2Cu3O7, where Ln may be the element Y or a rare earth element.
Aim: Was to provide new experimental data that might help to clarify why PrBa2Cu3O6+x (abbreviated PrBCO) does not superconduct.
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The first high-temperature superconductor was discovered in 1986. CuO2 sheets are a feature found in the crystal structure of the majority of high-temperature superconductors including LnBa2Cu3O7, abbriviated LnBCO, as shown in Fig 1.
Many of the theoretical models that have been proposed for explaining the mechanisms behind high-temperature superconductors focus on these CuO2 sheets. The aim of this work was to shed light on which theoretical model fits best with additional experimental data. In particular, the compound PrBCO was studied at the neutron source at Institut Laue Langevin (ILL), Grenoble, France.
PrBCO is isostructural to YBCO, perhaps the most well studied high-temperature superconductor, and both have the structure shown in Fig. 1 (one with Ln=Pr and the other with Ln=Y). In contrast with YBCO, the PrBCO compound does not superconduct and one possible explanation is that the presence of Pr ions between the CuO2 sheets prohibits superconductivity in these layers.
A single crystal of PrBCO was grown by Th. Wolf. Growing inorganic single crystals of a size suitable for neutron diffraction experiments is rarely trivial. Th. Wolf managed to grow a crystal with mass 23mg. This crystal was then studied using the polarised neutron diffraction (PND) technique at ILL.
The suppression of superconductivity in PrBCO is thought to be caused by the 4f electrons of Praseodymium (Pr) interacting with states in the superconducting CuO2 sheets. If this is true, this should be detectable experimentally by measuring the shape of the electron density in the regions between the Pr ions and the CuO2 planes. The most common way of measuring an electron density is using X-ray diffraction. However, Pr contains many more electrons in addition to its 4f electrons and X-rays do not differentiate between these. X-ray diffraction from Pr would therefore be dominated by scattering from the large number of non 4f electrons.
Pr in PrBCO is paramagnetic above the Neil temperature, which is about 15K. Hence the magnetic moments of Pr, which means its 4f electrons, can be aligned by applying a magnetic field over the sample. A. Boothroyd came up with the idea of using the D3/D9 instruments at ILL to measure the magnetic structure factors of PrBCO, which signal would include information about the magnetisation density of Pr and its 4f electrons.
The data in table 5.5 in [1] represents magnetic structure factors, these are Fourier components of the magnetisation density of PrBCO. The more Fourier components that are measured the higher the resolution of the magnetisation density map constructed from such data. The data in table 5.5 can be expected to reveal features in the density map of about 0.75-1.25 Å (1Å = 10-10 m). Although, this is small, it may not be small enough to give a definite answer to whether the Pr 4f electrons are the cause of suppression of superconductivity in PrBCO. An effort was therefore put into trying to 'enhance' the data to 'higher' resolution using Bayesian statistics and the maximum entropy method (MaxEnt). For this I modified a software program provided by Buck/Macaulay [3] to work with polarised neutron diffraction data. Indeed, using the MaxEnt method the magnetisation density maps appear clearer. Isosurfaces at different contour levels (CL) of PrBCO are shown in Fig. 2. An 'isosurface' displays all points with equal density; in Fig. 2 all points with density equal to +/- CL are displayed in dark grey colours and light grey colours respectively.
Figure 2:
Shows isosurfaces of PrBCO at different contour levels (CL).
Comparing the isosurfaces in Fig 2 with the crystal structure in Fig. 1 the strongest feature (at highest CL) is a circular density located at the Pr site, i.e. originating from the 4f Pr electrons. Further, the following concluding points were reached:
For more details see Ref. [1,2].