En este trabajo de fin de master se pretende adaptar la formulación de fermiones de Ginsparg-Wilson y sus consecuencias (por ejemplo el “teorema del índice”), desarrolladas en el área de la física de altas energías, al área reciente de los materiales topológicos. En el desarrollo se combinarán ideas matemáticas de topología y teoría de operadores con teoría cuántica de campos y conceptos de física de estado sólido.

CONCEPTOS QUE SERÁN ADQUIRIDOS:

• topología algebraica, teoría de operadores
• teoría cuántica de campos, grupo de renormalización, realización de simetrías, anomalías
• ecuaciones diferenciales, algebra numérica
• propiedades topológicas de los materiales

TAREAS

• Bibliografía y estudio de propiedades topológicas de la materia, fermiones de Dirac y de Weyl en potenciales periódicos, fermiones de Ginsparg-Wilson, anomalías y teorema del índice
• Estudio de la viabilidad de la implementación de fermiones de Ginsparg-Wilson para describir excitaciones fermiónicas en materiales
• calculos analiticos y numericos

More information please contact Victor Laliena and Javier Campo

The chiral solitons stabilized by the DMI are very interesting because they can present advantages over skyrmions, since their movement is not gyro-tropic and they will be easier to control. Moreover, it is interesting to elucidate the advantages that they can present with respect to the domain walls. On the other hand, the theoretical techniques used to study the dynamics of magnetic structures are of two types: i) the introduction of a few collective variables to describe the structure and ii) the numerical resolution of the LLG equation. In the first case, a generalization of the method of collective variables recently developed is used, and it will be necessary to deduce the equations that govern the dynamics of collective variables. For linear structures such as domain walls and chiral solitons in two dimensions (thin films) the center of the structure forms a line and its dynamics can be described by an elastic line model. The rest of the collective variables (for example, the width) could qualitatively change the dynamics of the elastic line.

Objectives

Main objective is the study of the response of solitons in monoaxial chiral magnets to applied magnetic fields and spin transfer torques induced by polarized electric currents, by means of effective models of collective variables and numerical simulations of the Landau-Lifshitz-Gilbert equation (LLG)

Task to be developped

Mainly numerical techniques will be used, although it will also be necessary to apply analytical techniques. In particular, numerical resolution techniques of initial value problems will be used in deterministic and stochastic differential equations (explicit or implicit methods) and border value problems (relaxation methods). The analytical techniques will be of a perturbative nature and will be applied to cases where external forces are weak.

More Information

Please contact Victor Laliena or Javier Campo.

Further information is also available on this website:

https://erasmusintern.org/traineeship/soliton-dynamics-monoaxial-chiral-magnets

The goal of the present TFM is double. On one side we are interested in the exploration of the magnetic phase diagram of F4BIPBNN by the determination the magnetic structure of below 0.4K. For this goal we will collect data of neutron diffraction in deuterated single crystals of F4BIPBNN and, as a first step, we will model the different magnetic structures allowed by the symmetry in the organic radical. On the other hand, we will determine with polarized neutrons diffraction the spin density in the radical. The real experimental spin density determination at F4BIPBNN will help us to validate the MO and Broken Symmetry calculations and to have another independent experimental estimation of the intra and inter molecular interactions. However, previously to the experiment, we will simulate the real experiments taken into account the theoretical spin density obtained by DFT calculations.

Concepts that will be acquired:

• Single crystal diffraction
• Group theory and magnetic crystallography
• Neutron scattering

Task to be developped:

• Bibliography on the subject.
• magnetic structure simulation
• spin density modelization

More information contact with Javier Campo

(1) Naoki Amaya, et al Journal of the Physical Society of Japan 86, 074706 (2017)