Hard axis

Fig. II. (a) Temperature dependence of the magnetization for 200-nm thick Ga, MnrAs with x =0.053. The magnetic field is applied perpendicular to the sample surface (hard axis). The inset shows the temperature dependence of the remanent magnetization (0 T) and the magnetization at 1 T in a field parallel to the film surface, (b) Temperature dependence of the saturation magnetization determined from the data shown in (a) by using ArTott plots (closed circles). Open circles show inverse magnetic susceptibility and the Curie-Weiss fit is depicted by the solid straight line (Ohno and Matsukura 2001).

Fig. 26. Computed minimum value of the magnetic field Hm necessary to align the saturation value of magnetization along the hard axis as a function of biaxial strain component for two values of the hole concentrations in Gao.95Mno.05As. The symbol (100) - 1001) means that the easy axis is along IOO], so that Hun is applied along [001] (Dietl et al. 2001c).

Fig. 25. Room temperature parallel magnetostriction for (Tb x Dyx XFeo.45C00.55 )2.1 measured along the hard axis after annealing at 250°C. After Due et al. (1996).

Fig. 43. Easy-axis and hard-axis hysteresis loops of an anisotropic, as-sputtered TbFe/Fe multilayer, deposited under a dc field (Hdep 0). After Le Gall et al. (2000).

An applied field in the xy-plane can tune the tunnel splittings Amm. via the Sx and Sy spin operators of the Zeeman terms that do not commute with the spin Hamiltonian. This effect can be demonstrated by using the Landau-Zener method (Section 3.1). Fig. 8 presents a detailed study of the tunnel splitting A 10 at the tunnel transition between m - +10, as a function of transverse fields applied at different angles (p, defined as the azimuth angle between the anisotropy hard axis and the transverse field (Fig. 4). 

The hysteresis loops of selected samples are shown in Fig. 22. For each of the thicknesses shown the loops are square with high coercivity when measured with the applied field perpendicular to the film plane. When magnetization curves are measured parallel to the plane of the film a straight line results which is characteristic of a hard axis loop. The SAD patterns in Fig. 21 showed a (001) texture which corresponds to the c axis of FePt along the direction perpendicular to the plane. Since the c axis is the easy axis of the FCT the loops in Fig. 22 confirm the perpendicular orientation seen in the electron diffraction pattern. 

Figure 14. Memory cell with one MTJ / one transistor. The arrows indicate the easy axis and hard axis fields created during the write mode operation. Notice that the bottom word line is separated from the MTJ/bottom electrode by a thin insulating layer.

Here Ku is the switching layer uniaxial anisotropy and Ny, Nx the demagnetizing factors along the hard axis (small axis of ellipsoid) and easy axis direction( long axis of ellipsoid). 

The switching field Hs is obtained from Hs — 2K IMS. Figure 16(b) clearly shows the advantage of the use of simultaneous easy axis and hard axis write fields the switching field is significantly reduced when compared with easy axis only or hard axis only fields. From Eq. 8 one can determine the energy barrier between switched (bit 1) and non-switched cells (bit 0). 

Figure 5.27 Measured variation of the tunnel splitting A between Ms = -10 and Ms = S- (in the pure quantum regime) with applied magnetic field along the hard axis (x). Reprinted with permission from Wernsdorfer and Sessoli, 1999 [32]. Copyright (1999) American Association for the Advancement of Science...

Fig. 10. Easy- and hard-axis magnetization curves of several high-anisotropy compounds on which...

In most cases HA was measured as the hard-axis saturation field and A", calculated from Ha = 2K,/Ms. 

Measured along the C-axis (magnetic hard axis). 

This issue was addressed in 1979 by McBride and Jacobs. Jacobs was from Fluor in Houston. The principle was to calculate stresses in two distinct areas, membrane and bending. Membrane stresses are based on pressure area times metal urea. Bending is based on AISC beam formulas. The neck-and-shell section (and sometimes the flange as well) is assumed as bent on the hard axis. This is not a beam-on-elastic-foundation calculation. It is more of a brute-force approach. 

This analysis combines the primary membrane stress due to pressure with the secondary bending stress resulting from the flexure of the nozzle about the hard axis. 

Fig. 24. Hysteresis loops for Tbo27Dyo,73Co2 thin film (1) as-deposited (2,3) annealed at 250"C along (2) induced easy axis and (3) hard axis. After Due et al. (2000a).

Point-dipolar interactions favor a perpendicular arrangement of the spins with respect to the ring plane and thus provide a hard-axis type contribution (D >0). " However, with few excep-the observed anisotropy largely exceeds the calculated dipolar term. For instance, in... 

The theory shows (Jensen et al., 1975) that for isotropic exchange [B(q) B(0)] should be zero (A(0), B(0) can be determined by subsidiary experiments in magnetic fields). Jensen et al. found [B(q) + B(0)] quite small when the field was applied along the hard axis, but quite large for the field applied along the easy axis. 

---