Energy states in a frustrated magnetic system
Soh, Chin Sheng
Date of Issue2015
School of Physical and Mathematical Sciences
Frustrated magnetic systems, which consist of nano-sized ferromagnetic islands or geometrically arranged nanowires, have recently been used as a test bed to investigate the possibility of creating magnetic monopoles when the islands are aligned to a single point collectively. Here, it is shown that the total energy of such frustrated system is quantized into several energy levels due to the coupling between the islands. The energy levels are shown to be stable over a wide range of temperature, and it is possible to change the temperature range significantly by adjusting the strength of the coupling between the islands. In this work, a Y-shaped vertex is tessellated to create an octagonal square design with 50 and 100nm separation between the islands as shown by Figure 1 (a), which is similar to [Ln(O2NO)3(L3)1.5]∞. The energy value for the 8 possible magnetic configurations is calculated using Object Oriented MicroMagnetic Framework (OOMMF) software, as shown in Figure 1 (b). By running Monte Carlo simulation of this type of tessellation, the density of low/medium/high energy vertices at its relaxed state is recorded and plotted against temperature (T) from 1K to 250K at intervals of 3K. The system was first randomized, and then a random island is selected to be flipped. If the energy in the vertex after the flip becomes lower, the flip is accepted with a probability of 1; if the energy becomes higher, the probability (P) is calculated based on Maxwell-Boltzmann approximation P=e^((-ΔE)/kT). The process is repeated until the system has reached equilibrium. The distribution of the vertices afterwards are shown in Figure 2, which shows that as T increases, the probability of accepting higher energy flips increases. Consequently, it results in the decrease of the number of low energy (LE) vertices while the number of medium energy (ME) vertices increases. Although not as significant, the number of HE vertices is also found to increase as shown by figure 2. The simulation results also show that there is a quantization phenomenon on the distribution of energy vertices as T increases. Similar results were first observed by E. Mengotti et al. where there is degeneracy of energy states found in hexagonal spin ice structures due to the coupling between the islands. In the octagonal square design, the discrete energy levels are not observed at higher temperatures (i.e >250K) due to the minute change in the distribution value; however, the quantization can clearly be observed at T < 250 K. Moreover, the robustness of the quantization is shown to be increased significantly as the distance between each ferromagnetic island is reduced. For instance, the temperature range for the vertices to be fixed in the ME level is extended to ~190 K as the separation between the islands is reduced to 50 nm. Thus, this design can potentially be used as a framework to investigate the quantization phenomenon of frustrated magnetic system at elevated temperature.
Final Year Project (FYP)