### Gary Wysin

**Professor**

309 Cardwell Hall

(785) 532-1628

wysin@phys.ksu.edu

Personal Webpage

Ph.D. Cornell University, 1985

M.S. University of Toledo, 1980

B.S. University of Toledo, 1978

#### Research Area

##### Theoretical Condensed Matter Physics

###### Studies of Magnetic Models with Pinned Magnetic Vortices

Vortex-in-nanodot potentials in thin circular magnetic dots. Vortex states in thin circular magnetic nanodots are studied using auxilary constraining fields as a way to map out the potential energy space of a vortex, while avoiding a rigid vortex approximation. In the model, isotropic Heisenberg exchange competes with the demagnetization field caused both by surface and volume magnetization charge density. The system energy is minimized while applying a constraint on the vortex core position, using Lagrange's method of undetermined multipliers. The undetermined multiplier is seen to be the external field needed to hold the vortex core in place at a desired radial distance r from the dot center. For a uniform nanodot, the potential energy is found to be very close to parabolic with r, as in the rigid vortex approximation, while the constraining field increases linearly with r. Effects of nonmagnetic holes and impurities in the medium can also be estimated and compared with other descriptions.

###### Influence of Impurity-Pinned Magnetic Vortices on Dynamic Correlations

In a real magnetic crystal, most lattice sites have magnetic ions, but some sites are occupied by impurity ions that are non-magnetic. Magnetic vortices (twists in the direction of the spins) will tend to form centered on the non-magnetic sites, because that will involve lower exchange energy. The magnetic vortices that get formed on top of non-magnetic ions or impurities in a 2D XY model can strongly influence the spin-spin dynamic correlations. By using a combined Monte Carlo / spin dynamics numerical simulation, the real-time dynamics of the system in thermal equilibrium can be studied. The spin-spin dynamic correlation function can be calculated, which gives an insight into how the impurities affect the center frequencies of the spin waves, and their lifetimes (or widths). By controlling the density of impurities, the response behaviors of the magnetic degrees of freedom can be affected.

###### Dipolar Effects on Pinned Magnetic Vortices

The long-range dipole interactions have different geometric effects on magnetic vortices, compared to the short-range exchange interactions. Through Monte Carlo simulations, the energetics of a vortex trapped either on an impurity, or even forced to form around a hole in the magnetic lattice, can be studied. A switching between different stable states of a vortex can be expected, which can be controlled by an externally applied magnetic field. Better control of this system could be a new design for nano-scaled memory devices.

###### Optical Cavities

Resonant modes in hexagonal cross-section optical cavities. Different methods might be applied to determine the optical resonances in micro-sized dielectrics, such as the hexagonal cross-section. One set of methods involves boundary value schemes, which need only information on the 2D boundary of the crosssection to calculate the optical field everywhere. By considering other related geometries, new optical devices might be designed, that could act as optical guides, switches, and memory elements. By related numerical methods, either scattering or resonance information can be determined.

###### Other General Topics

- Monte Carlo simulations of phase transitions in XY-symmetry magnets with vacancies.
- Theory for stability of singly-charged and doubly-charged vortices pinned on vacancies.
- Development of projection quantum Monte Carlo schemes to calculate dynamic modes at fixed momentum for magnetic models.

#### Recent Selected Publications

G.M. Wysin (2015). *Magnetic Excitations & Geometric Confinement: Theory and Simulations*. Bristol, UK:IOP Publishing.

G.M. Wysin, W.A. Moura-Melo, L.A.S. Mól and A.R. Pereira (2013). Dynamics and hysteresis in square lattice artificial spin ice. *New Journal of Physics,* 15, 045029.

R.C. Silva, R.J.C. Lopes, L.A.S. Mól, W.A. Moura-Melo, G.M. Wysin and A.R. Pereira (2013). Nambu monopoles interacting with lattice defects in two-dimensional artificial square spin ice. *Physical Review B,* 87, 014414.

L.C. Fai and G.M. Wysin (2012). *Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems*. Boca Raton, FL: CRC Press.

G.M. Wysin and W. Figueiredo (2012). 'Thermal vortex dynamics in thin circular ferromagnetic nanodisks. *Physical Review B* 86, 104421 (2012).