Analysis of checkerboard pattern in ultrathin magnetic films

We discuss the magnetostatic energy of checkerboard domain structures in ultrathin magnetic films (of a few monolayer thickness) and in an atomic monolayer using simple magnetostatic considerations where the easy direction of magnetization is perpendicular to the film. The checkerboard domain size, D, the domain-wall width, ω, the ratio f of the uniaxial surface anisotropy, K_s, to the dipolar energy and the binding energy, (BE), have been calculated numerically with the variational parameter δ and the number of atomic layers, n_l, as parameters.     

Simultaneous observation of atomic step and domain wall structure of ultrathin Co films by magnetic force microscopy in ultrahigh vacuum

We have applied magnetic force microscopy in ultrahigh vacuum to study the correlation between the atomic step and magnetic domain wall structure of ultrathin Co films prepared in situ on Au(111) substrates. For the first time we were able to achieve high-resolution images showing simultaneously a clear domain wall contrast and the underlying atomic step structure. Although for in-plane magnetized Co films the domain walls were found to run preferentially in a direction perpendicular to the steps, no such correlation could be observed for out-of-plane magnetized Co films. Received: 3 June 1999 / Accepted: 4 June 1999 / Published online: 29 July 1999     

Domain morphology in ultrathin ferromagnetic films with perpendicular magnetization

We determine the minimal domain structure for the equilibrium thickness of stripes as well as for the minimal energy of the domain configuration in ultrathin films of ferromagnetically coupled spins, where the easy direction of magnetization is perpendicular to the film. It is found that the equilibrium thickness of stripes and walls depend on the exchange energy. The normalized anisotropy, f, depends on interplay between the magnetic and anisotropy energies and is almost independent of the exchange energy inside the wall. The results are compared with the experimental data for thin Ag/Fe/Ag (0 0 1) films and a good coincidence is obtained between both results.     

Magnetic field dependence of asymmetry in the magnetization reversal of ultrathin Co films and Co/Pt multilayers with perpendicular anisotropy

We studied the magnetization reversal in ultrathin [Co/Pt]_n films (n=1, 2, and 4) using magneto-optical Kerr microscopy. These materials demonstrate unusual asymmetries in the activity of nucleation centers and domain wall motion. It was found that application of very high holding magnetic field prior to magnetization reversal, exceeding some critical value much larger than the apparent saturation field, suppresses the subsequent ‘asymmetric’ nucleation centers, activity. We revealed that the ‘asymmetric’ nucleation centers become active again after subsequent reversal cycles coming from a smaller holding field and studied how the asymmetry returns with the decrease of applied holding field. It was found that in low-coercivity ultrathin Co films, the asymmetry in domain wall velocity decreased sharply with the applied field increase and disappeared when the reversal field is greater than μ₀H=1.5 mT.     

Hysteresis of two interacting magnetic pairs with inequivalent perpendicular anisotropy

We consider a model for magnetic memory that consists of strongly coupled dipolar or antiferromagnetic (AF) pairs with inequivalent perpendicular anisotropy _K1$K_1$ and _K2$K_2$. For appropriate parameter values, determined in this work, they have two inequivalent storage states with zero net magnetic moment. Both analytical and numerical calculations are performed, in some cases yielding different results because of relaxation effects (i.e., a dependence on the damping parameter α$\alpha$). Hysteresis loops for a wide variety of parameter values are obtained, both for the AF case and the dipole case. An Appendix gives analytic results for slightly non-collinear spins in an applied field, which were used to test the numerical results.     

Spin-spiral and domain wall structures in monolayer Fe/W(1 1 0)

The stability of spin-spiral and domain wall structures in an Fe monolayer on a W(1 1 0) substrate is theoretically investigated. By analyzing the exchange parameters obtained from first principles total energy calculations, we find that a competition between the nearest-neighbor ferromagnetic and long-distant antiferromagnetic exchange interactions leads to a stabilization of the spin-spiral structures. When the strong magnetocrystalline anisotropy (MCA) arising from the Fe/W(1 1 0) interface is introduced, however, the formation of the spin-spiral structures is suppressed and the ground state appears to be the ferromagnetic state—as observed in experiments. In addition, the strong MCA is found to play a key role in determining the domain wall structures.     

Magnetic domain structure in Fe78.8−xCoxCu0.6Nb2.6Si9B9 nanocrystalline alloys studied by Lorentz microscopy

The magnetic domain structures of Fe_78.8−xCo_xCu_0.6Nb_2.6Si₉B₉ (x=0, 20, 40, 60) alloys are investigated by Lorentz microscopy coupled with the focused ion beam method. The specimen prepared using the FIB method is found to have a considerably more uniform thickness compared to that prepared using the ion-milling method. In Fe_38.8Co₄₀Cu_0.6Nb_2.6Si₉B₉ and Fe_18.8Co₆₀Cu_0.6Nb_2.6Si₉B₉ alloys, 180° domain walls extending in the direction of the induced magnetic anisotropy are observed. Analysis with Lorentz microscopy reveals that the width of the magnetic domains decreases with an increase in the cobalt content or the induced magnetic anisotropy K_u, that is, the domain width d is proportional to the induced magnetic anisotropy (K_u)^−1/4. On the other hand, in the in situ Lorentz microscopy observation as a function of temperature, magnetic ripple structures are found to appear in a localized area due to the fluctuation of magnetization vectors from 423 K. It is observed that the induced magnetic anisotropy caused by the applied magnetic field at 803 K is not suppressed by the magnetic ripple structures observed at 423–443 K.     

Saturation field direction dependence of domain structures in NiFe elements

The domain structures in NiFe elements were studied by magnetic force microscopy measurement and micromagnetic modeling. The remanent states in the elements were dependent on the direction of the saturation field. The “S” and “U” states were observed at remanence by applying the saturation field at different directions. The “S” and “U” states are metastable: magnetic force microscopy tip field-induced switching from the “S” and “U” states to the flux closure configuration was observed.     

Monte Carlo simulation of the reorientation transition in Heisenberg model with dipole interactions

The change of magnetic states in ultrathin films with temperature have been simulated by Monte Carlo method. A Heisenberg model with long-range dipole interactions was adopted in our calculations. The results were qualitatively in good agreement with the experimental phenomena. That is at low temperatures the magnetization is perpendicular to the plane, and at higher temperatures but below the Curie point, the magnetization is mostly within the plane. In between these two regions, the magnetization seems to be suppressed. The simulations show that the loss of magnetization is a consequence of the special magnetic states in which the local domains orientations are reverse with the neighbor ones.     

Magnetic properties of field-annealed FeCo thin films

Fe₅₀Co₅₀ thin films with thickness of 30 and 4 nm have been produced by rf sputtering on glass substrates, and their surface has been observed with atomic force microscopy (AFM) and magnetic force microscopy (MFM); MFM images reveal a non-null component of the magnetization perpendicular to the film plane. Selected samples have been annealed in vacuum at temperatures of 300 and 350 °C for times between 20 and 120 min, under a static magnetic field of 100 Oe. DC hysteresis loops have been measured with an alternating gradient force magnetometer (AGFM) along the direction of the field applied during annealing and orthogonally to it. Samples with a thickness of 4 nm display lower coercive fields with respect to the 30 nm thick ones. Longer annealing times affect the development of a harder magnetic phase more oriented off the film plane. The field applied during annealing induces a moderate magnetic anisotropy only on 30 nm thick films.     

Magnetic properties of FeSiB thin films displaying stripe domains

FeSiB amorphous thin films with thicknesses from 25 to 600 nm have been produced by rf sputtering on Si₃N₄ substrates. A spin reorientation transition has been observed on the as-prepared samples, as a function of thickness and temperature. Spin reorientation transition is shown to depend on the thermal treatments to which the as-prepared samples have been submitted. Static hysteresis loops obtained as a function of temperature, and magnetic force microscopy images taken at room temperature at the remanence and as a function of an applied magnetic field, have been employed to study the magnetic domain configuration of all the samples, and to see how it is affected by sample thickness, measurement temperature and annealing conditions.     

Exploring magnetic properties of ultrathin epitaxial magnetic structures using magneto-optical techniques

We describe magneto-optic Kerr effect studies of ultrathin Fe and Ni films on single crystal surfaces of Ag and Cu. Monolayer Fe films on Ag(100) exhibit the theoretically predicted spin-orbit anisotropy, but also yield some interesting discrepancies between behavior predicted by Kerr effect and by spin-polarized photoemission experiments. Layer-dependent studies of the magnetic moment of Ni on Ag(111) and Ag(100) suggest sp-d hybridization effects quench the first layer magnetic moment on Ag(111) but not on Ag(100). Temperature dependent studies of thin film magnetization obtained from Kerr effect measurements yield thickness dependent Curie temperatures, and critical exponents for several thin film systems.     

From bubble to Skyrmion: Dynamic transformation mediated by a strong magnetic tip

Skyrmions in thin metallic ferromagnetic films are stable due to competition between the RKKY interaction and uniaxial magnetic anisotropy. We study static nonlinear excitations in magnetic film in the presence of strong cylindrical magnetic tip of nanometer size. We mimic the RKKY interaction by the next-nearest-neighbors ferromagnetic and antiferromagnetic exchange interactions. We demonstrate analytically and numerically dissipative transformation of a bubble created by a strong magnetic tip into a stable Skyrmion.     

Magnetic domain structures and magnetotransport properties in Co-Ag granular thin films

The magnetic microstructures and magnetotransport properties in granular Co_xAg_1-x films with 17%≤x≤62% were studied. Magnetic force microscopy (MFM) observations showed the presence of magnetic stripe domains in as-deposited samples with x≥45% and the evolution of the magnetic domain patterns to in-plane domains with annealing. A perpendicular magnetic anisotropy as high as about 8×10⁵ ergs/cc for as-deposited Co₆₂Ag₃₈ and about 6×10⁵ ergs/cc for as-deposited Co₄₅Ag₅₅ was observed by magnetization and torque measurements. With increasing annealing temperature, the perpendicular magnetic anisotropy became negative. The origin of the perpendicular magnetic anisotropy may be attributed to a rhombohedral distortion of the cubic cell due to residual substrate-film stresses. The magnetic stripe domains are the consequence of the interplay of the indirect or direct exchange, perpendicular magnetic anisotropy and dipolar interactions. Finally, magnetoresistance (MR) curves displayed training behaviours and different shapes when measured with different configurations (parallel, transverse and perpendicular). It is proposed that the existence and the evolution of the magnetic domain structures strongly affect the magnetotransport properties due to the extra contribution of the electron scattering at the domain walls. Furthermore, an anisotropic MR also contributes to the overall MR curves. Received: 2 March 2000 / Accepted: 28 March 2000 / Published online: 23 May 2001     

Thickness-dependent magnetic domain structures of ultrathin Co/Au(111) films studied by means of magnetic force microscopy in ultrahigh vacuum

Received: 10 December 1997/Accepted: 11 December 1997     

Domain structures of ultrathin magnetic nanobelts

We use a simple magnetization model to determine domain structures of ultrathin magnetic nanobelts. A train of alternate domains are formed along the length direction. Optimal domain length decreases with belt width. Experimental domain length distributions of Fe bilayer nanobelts can be naturally explained. This approach should be applicable to similar nanomagnets.     

The influence of size on coercive field of ultra soft magnetic materials

We report here a size dependence of the coercive field in the millimeter–centimeter range length scale of ribbon like samples prepared from ultra soft amorphous and nanocrystalline alloys. A model is proposed where surface pinned domain walls are considered having an effective stiffness constant linearly increasing with the demagnetization factor.