1


2

 Using MC relaxation to Study
 Motion of vortices.
 Sylvester Kofi Gyan
 Mentor: Dr. Gary Wysin
 Department of Physics, Kansas State University, Manhattan, KS 66506

3

 Vortices??
 Vortex excitations in nanodots have been studied a lot by
experimentalists and theoretical physicists
 These studies of magnetic nanodots usually had one hole/defect, usually
at the center of the system.
 I did my studies with two defects
in the magnetic nanodot, to study how the vortex motion, stability and
dynamics

4

 Nanomagnetics is a future
industry!
 Uderstanding of the stability and dynamics of vortices > helps with
the development of high density memory devices.

5

 In our model we consider a thin
circular cylindrical nanomagnetic dot.
 Diameter= 100nm, thickness =10nm.
 Our diskshaped nanodot has two vertical holes of equal radius, R_{h}
cut out of it, in a symmetric position.

6


7

 Spins interact in two main ways
 Exchange Interactions
 And Dipolar interactions
 Short range exchange interactions are between nearest neighbour spins.
 The Exchange Hamiltonian, H_{ex} = J Σ S_{i} ˇ S_{j,
where}
 J is the exchange coupling strength.
 S_{i} and S_{j } are
any nearby spins close to each other.

8

 Dipoledipole interactions, which are weaker and longrange forces.
 Dipolar interactions are given by
 >H_{dd =} (μ_{0}/4π) Σ[3(μˇr_{ij})(μˇr_{ij})
μ_{i}ˇμ_{j}]
 _{ } r_{ij}^{3}
 Where r_{ij }is the
displacement between any two spins S_{i and} S_{j.}

9

 And μ is the magnetic dipole moment of any atomic spin, given by μ
= g μ_{B}S
 Where
 g > Landé gfactor
 μ_{B}> is the Bohr Magneton
 S> is the Spin length
 Total Internal Energy =H_{dd }+H_{ex}

10


11

 Image
 There are blocks of cells, a model of one is displayed above.
 Each small square dot is an atom modelling hundreds /thousands of
magnetic dipoles.
 μ_{cell }averages out, approximately the dipole moment in each cell, μ_{cell
}=N_{spins }*μ
 Why the micromagnetics approach? Because MC simulation using the atomic
model is a challenge

12

 Using this approach, we consider the effective exchange coupling between
the cells to be
 J_{cell} ==(4lα/α₀)JS^{2}
 The cell dipoles have an effective dipolar coupling, D_{cell }= (μ₀/4π)*μ^{2}_{cell}/α^{3}
 δ_{cell }= ratio of the dipolar energy scale to the
exchange energy scale (D_{cell}/J_{cell})

13

 Changing spin configuration
 Calculate the ΔE of the system
 Accept the Δ with a probability of
 p = min[1,e^{}^{Δ}^{E/KT}]

14

 Size matters? > To experimentalists, and represents more realistic
simulations.
 We considered a thin circular cylindrical nanomagnet of cell
size(thickness), α=10nm, and diameter 100nm.
 δ_{cell }works out to be 0.0427.
 And a finite temperature of 300K

15

 Primarily interested in testing two scenarios
 Vortex attraction to a hole
 Sample test shown below
 Diameter of nanodot =100nm
 Cell size of 10nm
 Temperature of 300K
 δ_{cell }==0.0427;
 No magnetic field
 Holes placed a distance of 8 lattice units from the center on either
side
 Random seeding number == 87942013

16


17


18


19

 Second test
 Vortex switching b/n holes.
 Magnetic field applied antiparallel to vortex angle
 For the example below, a field of 0.05 was applied
 Diameter of nanodot ==100nm, thickness =10nm
 δ_{cell }==0.0427, temperature =300K
 Field applied 270 degrees to the horizontal axis
 Seeding number of 710.

20


21


22


23


24


25


26


27


28


29

 Dr. Wysin
 Dr. Larry Weaver
 Dr. Korwin
 REU 2008 group

30


31


32


33


34


35


36

