Magnetic dipolar interaction in ultrathin films: Structural and size effects

Magnetic patterns in dipolar films with close packed structures

“…The system energy results from the intralayer and the interlayer contributions, due to the interaction between dipoles of the same and different layers, respectively. The intralayer contribution always favors the ip magnetization, but the interlayer contribution can assist either the ip or the op magnetization, as it was widely discussed in a previous work [22]. Two layers are conventionally said to be coupled only when their interlayer contribution is significant for the system energy.…”

“…Physical grounds and details of the approximation to calculate the dipolar energy can be found in previous works [17,22,23], where it is shown that the assumption of infinite lateral dimensions of a Q2D crystal allows to pay attention to the effects related to the 2D lattice symmetry and the layer stacking sequence, disregarding its lateral shape and size, in contrast with the case of 3D crystals, where the body shape is important even when its volume is infinitely augmented. This assumption works well when the ratio between the characteristic lateral dimension of the system to its thickness exceeds five or six hundreds [26,22], depending on the desired accurateness in the comparison with other calculations or experimental data.…”

“…This assumption works well when the ratio between the characteristic lateral dimension of the system to its thickness exceeds five or six hundreds [26,22], depending on the desired accurateness in the comparison with other calculations or experimental data. The system energy results from the intralayer and the interlayer contributions, due to the interaction between dipoles of the same and different layers, respectively.…”

“…Magnetization reversal in thin films have been extensively studied both theoretically [10][11][12][13] and experimentally [14][15][16]. It has been argued that the continuum approach fails in the nanometric scale, [17][18][19][20][21] the 3D approximation is no longer valid in ultrathin films, since no proper demagnetizing tensor can be defined along the direction where the nanoscale is realized [22,23].…”

“…Such study for the long-range dipolar interaction has been carried out in dipole layered structures with homogeneous magnetization [17,19,26,27,22,28]. If we relax somehow the condition of homogeneous magnetization and allow each layer in the film to have independent in-plane forward or out-of-plane upward magnetization, a wealth of magnetic patterns, understood as layer magnetization sequences, can rise as different state variables, such as number of layers, structural aspect ratio c/a and temperature, change.…”