The micromagnetic simulation has been carried out to analyze and analyze the magnetic characteristics of permalloy nanostructures. The Object Oriented MicroMagnetic Framework (OOMMF) software has been used to estimate the values to study magnetic characteristics. The critical size of nanoisland of square shape is estimated for transition from vortex state (four domains) to a single domain state. The dependence of the magnetizing curve parameter - coercive force for different thicknesses, areas and anisotropic constants of nanoisland has been studied. The results estimated can be useful in creating the topology of the elements of spintronics which is based on magnetic nanostructures.
Introduction
The storage density ofhard disc drivesis increasing along an exponential growth curve, since because spintronics based devices like GMR and TMR sensors have increased the sensitivity of the read head which even measures the magnetic state of very small magnetic domains on the spinning platter. Single and multiple film nanostructures have great belief for the development of memory matrixes and magnetic detectors with respect to magnetoresistance. So in order to develop a topology for magnetoresistive structures, estimating their magnetic properties is of much important. So it is essential to use a theoretical analysis of magnetic properties of nano structures using micromagnetic simulation. In this paper a simulation work has been made to study the magnetic characteristics of single layer, square shaped permalloy nanostructures.
Nowadays, the micromagnetic method of simulation has become a popular tool for theoretical analysis of nanosized magnetic systems. Several micromagnetic simulation methods were published and in this work, a oommf simulation method has been used.
The magnetic characteristics of magnetic materials mainly depend on their sizes and shapes and this is due to fact that a magnetic system is pointed in reducing stray field flows by producing peripheral domains and magnetic vortexes. Micromagnetic simulation gives us a chance for identification of qualitative and quantitative information of a change in the magnetic parameters based on the geometry values of the sample.
Model of study
As the first stage of study, the need of domain structure on lateral sizes of the nanoisland was determined when there is no external field. This corresponds completely under the demagnetized state of the sample. It has been forecasted that magnetic characteristics of ultra-thin magnetic films relied on the model of single domain nanostructure particle.
As the second and third stage of the work, it has been determined the role of the magnetizing curve parameters like coercive force and anisotropy constant on the nanoisland thickness and lateral side.
Estimation of a Critical Size for a Transition
to a Single-Domain State
The critical size of a square shaped nanoisland for transition from vortex state (four domains) to a single domain state has been estimated here. For demagnetized sample, the distribution of magnetization meets the minimum of functional at the zero external fields. A single-layer, square-shaped, film permalloy island is used as sample here.
Procedure of simulation
The anisotropy constant (K) was taken to be zero. The thickness of the film was taken as 10 nm. The length of the square varied from 100 nm to 30 nm. The calculations of the domain structure of a system at various sizes were carried out. The size of the cell also varied from 10 to 1 nm so as to get the calculation accuracy. Exchange interaction constant (A) was taken as 1.3 - 10^-11 J/m^3, anisotropy (K) as 0J/m3, saturation magnetization (Ms) as 800kA/m and damping coeffient as 0.5. A mmDisp function in oommf is used to display the magnetization distribution.
Analysis of critical Size for a Transition to a Single-Domain State
As a result of modelling, the simulated pictures of magnetization distributions for the square shaped permalloy with varying sizes were obtained. The cell size used here was 1 nm. As clearly shown from the above figures, it has been seen that with a decrease in the system size, the domain structure alters. In the samples where the length of square is more than 80 nm, there are four domains i.e. vortex state, whereas, in the sizes below 50nm there is a transition to the single-domain state. So for the samples where the side length is less than 50 nm, it is sure to conform that, the state transfers to the single-domain state. This single-domain state is called the "leaf state". Also it has been observed that the single domain state is characterized by a very low energy barrier to alternating magnetization indicating that thermal fluctuations are switching the system from one state into another state at even low temperatures. Thus the results obtained allow us to analyze the magnetic characteristics of ultra-thin magnetic films based on single-domain nanosized particle model.
Dependence of the Coercive Force on the sample thickness
As the second stage of study, the dependence of the magnetizing curve parameter - coercive force for different nanoisland thicknesses was determined. A static problem on micromagnetism is solved at a specified value of the external magnetic field.
Procedure of simulation
In problem editor of oommf, the material parameters were given as - exchange interaction constant (A) was taken to be equal to 1.3 - 10^-11 J/m^3. The single-axis anisotropy (K) varied on the limits from 0 to 20000 J/m3. The saturation magnetization (Ms) was taken to be 800kA/m and damping coeffient as 0.5. Then the constant magnitude was chosen in demagnetization menu. In part geometry the sample's geometric specifications were included. The thickness of the island is changed from 10-100 nm. The cell size used in this problem was 10 nm. The lateral size of the island is fixed with the specified square as 250 x 250 nm (width x height). A mask option was selected to import the square shaped sample. The initial magnetization is to be vortex. The field ranges has to be chosen correctly depending on the expected curve parameters. If the output curve is not clear to measure the parameters, the field ranges has to be varied accordingly until we get the clear output curve. The external magnetic field was applied in plane of the film, along the easy axis and it was varied from -200 to 200 Oe. Then this problem editor values were loaded in Solve2D option. Now mmGraph option is to be used to get the magnetization curve. In Solve2D, mmGraph is selected in scheduled outputs. Now the its time to run the program. For each value of the thickness, the corresponding magnetization curve (hysteresis loop) was obtained with same procedure and the value of the coercive force (Hc) is thus calculated for different sample thicknesses. The dependence of the coercive force for different thicknesses of the nanoisland was simulated and included in the table 1. This shows dependences obtained for three different values of the anisotropy constant (i.e. for K = 0,1000,20000 J/m^3).
The anisotropy parameter can be changed within wide limits based on the manufacturing technique of the sample under test. Fig. 2 shows graphical representation of the tabulated values. By analyzing this graph, we can see that the given dependences have both general and strongly different characteristics. An important factor to note down is, while increasing anisotropy constant K, the coercive force increases alternatively in the small thickness regions. So we can point out that the value of the coercive force is to be determined by the magnetic anisotropy and the shape anisotropy. The contribution of the anisotropy at small thicknesses seems to be dominating. Then in large thickness regions, there is a common tendency to decrease the coercive force irrespective of anisotropy value while growing the thicknesses.
The procedure to get the magnetization curve for different lateral sizes is same as explained before. Except that as before the lateral side is fixed and thickness was varies, but here thickness is fixed and lateral side was varied. The dependence of the coercive force for different lateral sides of the nanoisland is simulated and included in the table 2.
The dependence of the coercive force (or coercivity) depending on the size of lateral side (SX) is represented graphically in Fig. 3. By analyzing this graph, it is obvious to judge that the given dependences have a general feature, that is, a tendency on the coercive force reduction while increasing the lateral sizes of the nanoisland. It is seen that the coercive force is decreasing depending on the factor of the shape anisotropy on increasing the island size. So the anisotropy value plays an important role in deciding the lateral size of the island for specific applications.
A snapshot of typical hysteresis loop curve obtained from oommf simulation is shown in Fig. 4. Sometimes an unusual shape of the hysteresis loop will be obtained and this is due to increasing the vortex state in the relatively small fields.
Conclusion
Thus the performed calculations made us to estimate the important magnetic characteristics of a single layer, square shaped permalloy nanoisland based on its geometric specifications. This allows us to estimate the critical size of nanostructure for transition from multiple domain state to single domain state. Apart from that, the dependence in change of main magnetic parameters of magnetization reversal for given square shaped nanostructure has been calculated. These dependence characteristics of magnetic parameters can be helpful in developing the elements of spintronics, using magnetic nanostructures.
