Spin-Resolved Fermi Surface of the Localized Ferromagnetic Heusler Compound ${\mathrm{Cu}}_2\mathrm{MnAl}$ Measured with Spin-Polarized Positron Annihilation

We determined the bulk electronic structure of the prototypical Heusler compound ${\mathrm{Cu}}_2\mathrm{MnAl}$ by measuring the angular correlation of annihilation radiation using spin-polarized positrons. To this end, a new algorithm for reconstructing 3D densities from projections is introduced that allows us to corroborate the excellent agreement between our electronic structure calculations and the experimental data. The contribution of each individual Fermi surface sheet to the magnetization was identified, and summed to a total spin magnetic moment of $3.6\pm 0.5{\mu }_B/\mathrm{f}.\mathrm{u}.$.

Figure 1

2D projections along [100] of ${\mathrm{Cu}}_2\mathrm{MnAl}$ at room temperature. The measured anisotropy of (a) majority and the (b) minority density, respectively, is compared with the theoretical results. The theoretical spectra were convolved with the resolution function of the spectrometer. The column (c) depicts the difference between majority and minority density with the total number of counts in each spectrum normalized to one. The lower row shows cuts through the upper pictures as indicated by the arrows in (a) along [001] and [011] directions for theory (orange) and experiment (green).

Figure 2

Majority (left) and minority sheets (right) of the Fermi surface of ${\mathrm{Cu}}_2\mathrm{MnAl}$. Spin-resolved Fermi sheets are obtained (a) from fixed spin moment ($3.2{\mu }_B/\mathrm{f}.\mathrm{u}.$) calculations, (b) from isosurfaces of reconstructed simulated data convolved with the experimental resolution function including statistical noise, and (c) from the isosurfaces of experimental data. The occupied fraction of the BZ volume of the experimentally determined Fermi surface is given below each sheet.