Effects of Substrate Eddy Current on Magnetic Anisotropy in Permalloy Underlayer for Perpendicular Media

Abstract

The local electronic structure of Nd 2 CuO 4 is determined from ab initio cluster calculations in the framework of density functional theory. Spin-polarized calculations with different multiplicities enable a detailed study of the charge and spin density distributions, using clusters that comprise up to 13 copper atoms in the CuO 2 plane. Electron doping is simulated by two different approaches and the resulting changes in the local charge distribution are studied in detail and compared to the corresponding changes in hole-doped La 2 CuO 4 . The electric field gradient (EFG) at the copper nucleus is investigated and good agreement is found with experimental values. In particular a careful study of the various contributions to the EFG exhibits that the drastic reduction of the main component of the EFG in the electron-doped material with respect to La 2 CuO 4 is due to a reduction of the occupancy of the 3d 3z 2 −r 2 atomic orbital. Furthermore, the chemical shieldings at the copper nucleus are determined and are compared to results obtained from nuclear magnetic resonance (NMR) measurements. The magnetic hyperfine coupling constants are derived from the spin density distribution calculated for different spin multiplicities.

Analytic theory of hydrostatic stress effect on switching dynamics in ferroelectrics

“…This change is observed prominently at electric fields slightly larger than the coercive electric field but is not noticeable at high electric field according to simulation carried out in this work. Furthermore the switching time is obtained in closed form as a complicated function of hydrostatic stress in addition to temperature and electric field that was determined previously [24,25,34]. Although trends concerning the effect of hydrostatic stress on the equilibrium polarization and the switching time have been reported earlier both in experimental work and shown in numerical computations [19,21,41], the findings in this paper are important in confirming the correctness of these trends theoretically through analytical arguments and simulation work.…”

“…The inclusion of hydrostatic stress modifies the factorized Landau-Khalatnikov equation [33,34] derived previously for the stress free case to become where τ is the scaled time defined by τ = γ aT t C 0 with γ as the kinetic coefficient, t 0 as time and = − − ( )…”

“…Furthermore, this choice of δ = 0.9999 is in accordance with the standard criteria used in the computation of the switching time. In comparison with the definition of switching time τ s used in this study, the switching time used in several previous studies reported in the literature [28,[34][35][36][37] was based on the time required to reverse the polarization of a ferroelectric material from −p e to p 0.9 e [34] or −p e to 0 [13] depending on the type of experimental methods used to carry out the measurement.…”

Analytical properties of switching current transients in ferroelectrics

“…In previous works [51,61], equation (18) has been solved numerically to model polarization decay and backswitching current in ferroelectric material. However in this work analytically exact formulae for polarization decay and back-switching current as explicit functions of time t are derived by solving equations (18)…”

“…In response to changes in polarity of bipolar square wave electric pulses this sequence of complete switching current transients alternating with back-switching currents is repeated periodically. The complete switching current transients flow alternately in polar and anti-polar directions interspersed in between by back-switching currents that adjust their direction of flow opposite to the preceding switching current transient [45,46,61,64,69]. In conjunction the temporal graph of switched polarization (black) in figure 11 is generated using the algorithm t…”