T. Wirtz | Searcharxiv

arXiv2021

Patterning enhanced tetragonality in BiFeO3 thin films with effective negative pressure by helium implantation

Helium implantation in epitaxial thin films is a way to control the out-of-plane deformation independently from the in-plane strain controlled by epitaxy. In particular, implantation by means of a helium microscope allows for local implantation and patterning down to the nanometer resolution, which is of interest for device applications. We present here a study of bismuth ferrite (BiFeO3) films where strain was patterned locally by helium implantation. Our combined Raman, XRD and TEM study shows that the implantation causes an elongation of the BiFeO3 unit cell and ultimately a transition towards the so-called super-tetragonal polymorph via states with mixed phases. In addition, TEM reveals the onset of amorphization at a threshold dose that does not seem to impede the overall increase in tetragonality. The phase transition from the R-like to T-like BiFeO3 appears as first-order in character, with regions of phase coexistence and abrupt changes in lattice parameters.

cond-mat.mtrl-sci↗

arXiv2015

Completing the picture for the smallest eigenvalue of real Wishart matrices

Rectangular real $N \times (N + ν)$ matrices $W$ with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central question concerns the correlations encoded in the spectral statistics of $WW^T$. The extreme eigenvalues of $W W^T$ are of particular interest. We explicitly compute the distribution and the gap probability of the smallest non-zero eigenvalue in this ensemble, both for arbitrary fixed $N$ and $ν$, and in the universal large $N$ limit with $ν$ fixed. We uncover an integrable Pfaffian structure valid for all even values of $ν\geq 0$. This extends previous results for odd $ν$ at infinite $N$ and recursive results for finite $N$ and for all $ν$. Our mathematical results include the computation of expectation values of half integer powers of characteristic polynomials.

math-ph↗