Magnetic Anisotropy at Nanoscale

Abstract

Nanoscale objects often behave differently than their "normal-sized" counterparts. Sometimes it is enough to be small in just one direction to exhibit unusual features. One example of such a phenomenon is a very specific in-plane magnetic anisotropy observed sometimes in very thin layers of various materials. Here we recall a peculiar form of the free energy functional nicely describing the experimental findings but completely irrelevant and thus never observed in larger objects. Intriguing Experimental ObservationsIn [1] we find the experimentally observed in-plane magnetic anisotropy energy (MAE) diagrams for multilayer structure Cr(4)/Fe(2)/Cr(d Cr )/Fe(4)/Cr(2), where numbers are thicknesses of components, expressed in nm. The thickness of the middle Cr layer, d Cr , was varied in few nm range, and the complete structures were deposited on Si(100) substrate, covered with natural SiO 2 layer 1.5-2.0 nm thick. The substrate was not perfectly flat-as a result of ion beam erosion it was covered with quite well-ordered ripples (see atomic force microscopy (AFM) images of the substrates, Figure 1 in [1]). The metallic layers were deposited using molecular beam epitaxy (MBE) technique. Their transmission electron microscopy (TEM) cross-sections revealed mostly amorphous structure with small inclusions of polycrystalline character. The values of MAE were derived from hysteresis loop area observed while exciting field was oriented along successive in-plane directions.In principle, samples of this kind should not exhibit any in-plane magnetic anisotropy. This is indeed the case when the substrate is flat (see Figure 4(a) in [1]). On the rippled substrate, however, this is no longer true and the sample exhibits peculiar twofold in-plane anisotropy (coercive field, Figure 4(b) in [1], MAE-in Figure 4(c)). It is peculiar since it is not the uniaxial anisotropy: four maxima are visible instead of just two. The Surface Magnetic Anisotropy of a CylinderConsider the static configuration of individual spins located on a surface of a long (ideally: infinitely long), hollow ferromagnetic cylinder. In absence of any external field, one may expect that individual spins may adopt one of the two stable configurations:(i) they all may be aligned with C ∞ symmetry axis of a cylinder. This is the lowest exchange energy configuration; (ii) they all may be oriented perpendicularly to the above symmetry axis. Now the exchange energy is no longer at its global minimum. Nevertheless, such a configuration is stable since it realizes a local minimum of exchange energy.In the second case we may again distinguish two cases: either individual spins are aligned with local C 2 symmetry axis (there are infinitely many of them, each perpendicular to C ∞ ) thus pointing inwards or outwards of a cylinder and being perpendicular to the cylinder's surface, or they can be perpendicular to the local C 2 axis (laying on the cylinder's circumference), making a ring-shaped configuration and producing no net magnetization. It is easy to see that both of thos...

Interval Identification of FMR Parameters for Spin Reorientation Transition in (Ga,Mn)As

“…If this was true, then the free energy expression should be appended with the surface term [11], proportional to | cos(φ − π/4)|. This, however, is beyond the scope of a current paper.…”