Research Work
Maximum Entropy Analysis of Muon-Spin Rotation (MEμSR) At San Jose State University
In this research project, with Dr. Carolus Boekema as my research Advisor, I studied Muon-Spin Resonance (µSR) data using Maximum Entropy (ME). In µSR the muon is used as a magnetic probe. The muon is unique, as it probes interstitially its local magnetic environment. The positive muon (+µ) is embedded into a solid where the muon-spin precesses. The +µ decays into two neutrinos and a positron. The positrons are collected. Due to violation of conservation of parity in muon decay, the positron is preferentially released in the direction of muon-spin, precessing in transverse fields thus the Frequency is directly proportional to the magnetic field (B) at the muon-stop site.
The torque exerted on the muon by the magnetic field is given by the Larmor precession. The Larmor frequency is directly proportional to the magnetic Field.
Muon decay process. Positrons are preferentially released in direction of muon-spin.
The muon-spin polarization and time series S(t) can be transformed into a frequency domain. ME is an advantageous method that produces sharper signals in a frequency transform, while reducing noise and eliminating sinc wiggles, commonly seen in Fourier analysis. Also, for signals that are weak, Fourier and curve fitting are less effective.
ME-µSR has an experimental detection lower limit of approximately 0.2 MHz . The ME-Burg technique is an auto-regressive method that assumes a correlation between the muon-spin signal, S(i) at any time i, and previous times, S(i-k).
The optimal number of auto-regression coefficients (p) lies between N/3 and N/5, where N represents the number of data points. The ME transformation or spectral density is obtained by taking the square root of the power of the spectral density, P(f). This the frequency probability distribution.
ME-Burg Algorithm
Spectral Density
Fe3O4 Study
This study seeks to understand the internal magnetic environment and conduction of the spin-polarized electrons by looking at a transition at 250 K. This could lead to a better understanding of spin currents in magnetite helping advance the field of spintronics. We find two frequency signals at room temperature (RT). These two broad signals suggest two separate magnetizations at RT. At 205 K The sharp MEμSR signals also show two separate magnetizations. In both cases, these effects are plausibly caused by glassy, precursor effects above the Verwey transition (123 K) and induced by small magnetic fields below demagnetization field.This work was published in AIP Advances: Precursor effects and field-induced short-range order above the Verwey transition in single Fe3O4 crystals.
Precursor effects and field-induced short-range order above the Verwey transition in single Fe3O4 crystals.pdf