Magnetic Response and Spin Polarization of Bulk Cr Tips for In-Field Spin-Polarized Scanning Tunneling Microscopy

Abstract

In non-abelian gauge theories without matter fields, expectation values of large Wilson loops and loop correlation functions are difficult to compute through numerical simulation, because the signal-to-noise ratio is very rapidly decaying for increasing loop sizes. Using a multilevel scheme that exploits the locality of the theory, we show that the statistical errors in such calculations can be exponentially reduced. We explicitly demonstrate this in the SU(3) theory, for the case of the Polyakov loop correlation function, where the efficiency of the simulation is improved by many orders of magnitude when the area bounded by the loops exceeds 1 fm 2 .

Electronic and magnetic properties of bulk Cr tips for scanning tunneling spectroscopy

“…Next, both experimental A(V ) show the presence of sign changes (zeros) which where ascribed to the energy dependence of the sample spin polarization. 9,46 Conversely, the differences in the position of zeros (which can be seen here around V = −0.1 and +0.45 V) can be attributed to different energy behaviors for P t (E) in the corresponding (reversed) energy windows, namely at about E = +0.1 and −0.45 eV.…”

“…We note that also definitions leading to the opposite sign of A are used. 9,46 In the framework of the WKB model already used to interpret our spin-integrated results, it is possible to show that at zero bias A is the product of the sample and the tip spin polarizations at the Fermi level, A(0) = P s (0)P t (0), 25 allowing for the determination of P t (0) when the other quantities are known. At finite bias, the relation between A, P s , and P t is in general not available, but one can approximate it as A(V ) ≈ P s (eV )P t (0) or A(V ) ≈ P t (−eV )P s (0) by neglecting the tip or sample dependence on energy of the DOS and spin polarization.…”

“…8,9 Schlenhoff et al 8 presented SP-STS measures on a 1.5 ML Fe film on W(110). The interpretation of their experimental data is however complicated by a bias-dependent tip-sample distance, 43,45 following the dI/dV acquisition, obtained in a constant current mode.…”

“…The interpretation of their experimental data is however complicated by a bias-dependent tip-sample distance, 43,45 following the dI/dV acquisition, obtained in a constant current mode. Hence we focus on the SP-STS results by Corbetta et al, 9 performed in a constant height mode on ferromagnetic Co islands on Cu(111). By applying an external magnetic field perpendicular to the surface plane, the authors obtained both an antiparallel and a parallel alignment between the sample and the tip magnetization axis.…”

“…Proposed since the invention of the SP-STM technique, 6 bulk Cr tips have been demonstrated to provide spin contrast in SP-STM 7 and SP-STS experiments 8,9 only in recent years. Such works pointed out the sensitivity of these probes, but the magnetic behavior of bulk Cr tips, i.e., the sign and the energy dependence of spin polarization, as well as the tip magnetic easy axis and response to magnetic field, seems to differ among the various experiments.…”