# Atomistic spin dynamics

**Atomistic spin dynamics** is a microscopic method of modelling magnetization dynamics in solid state combining first principle (*ab initio*) calculations with Landau-Lifshitz-Gilbert equation. By means of this method one assign a magnetic moment to each atom in the studied system. These magnetic moments interact via the exchange interactions, calculated using *ab initio* methods. Finally, the exchange interactions are included in the local effective magnetic fields, which govern the manetization dynamics

Atomistic spin dynamics can be used to examine magnetic properties of various materials as well as complex behaviour of magnetic moments influeced by spin transfer torque or temperature gradients studied in spintronics.

## Involved researchers

# CuMnAs

**Copper magmanese arsenide** is an antiferromagnetic material, which rystallizes in the orthorhombic phase. However, using molecular-beam epitaxy, it can be prepared in a tetragonal phase having interesting propertie for applications in spintronics.

CuMnAs is an room-temperature antiferromagnetic material with significant spin-orbit interaction. Due to the symmetry of the crystal lattice, the ordering parameter of CuMnAs can be efficiently manipulated due to so called staggered current-induced fields (Phys. Rev. Lett. 113, 157201).

# Domain wall dynamics

In magnetism, a **domain wall** is an interface separating magnetic domains, i.e. areas where magnetization is homogeneous. Domain wall is a transition area between different magnetic moments and usually undergoes an angular displacement of 90 or 180 degrees (Wikipedia).

Apart from magnetic field, domain walls can be moved by spin current. **Current-induced domain wall dynamics** is an important effect for spintronic applications. The best known concept of domain-wall-based magnetic memory is the **racetrack memory** (Wikipedia).

## Involved researchers

# Magnetism

**Magnetism** is a class of physical phenomena that are mediated by magnetic fields (Wikipedia).

A large part of the research in our group is focused on study of magnetic materials, especially ferromagnets and antiferromagnetis. Both types of materials are important for spintronics since some of them can be used for generation of spin currents and/or their magnetic moment can be manipulated by spin currents.

# Magnetization dynamics

**Magnetization dynamics** is extensively studied in physics due to its importance for magnetic memories, data processing, and field sensors. In solid state, magnetic degrees of freedom are influenced by various phenomena to some extent. Thus, apart from magnetic fields, magnetic moments can be manipulated by spin-polarized current, thermal fluctuations, temperature gradients, laser pulses and spin-orbit torques. Importantly, mutual interactions between magnetic moments via exchange coupling and magnetostatic fields becomes important in larger structures and diluted magnetic systems with disorder.

## Involved researchers

# Micromagnetic simulations

**Micromagnetics** is a field of physics dealing with the prediction of magnetic behaviors at sub-micrometer length scales. The length scales considered are large enough for the atomic structure of the material to be ignored (the continuum approximation), yet small enough to resolve magnetic structures such as domain walls or vortices (Wikipedia).

## Involved researchers

# Monte Carlo

**Monte Carlo methods** are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. Their essential idea is using **randomness** to solve problems that might be deterministic in principle. They are often used in physical problems and are most useful when it is difficult or impossible to use other approaches (Wikipedia).

In condensed matter physics, Monte Carlo methods are used to study **magnetic properties** of materials at elevated temperatures. In combination with atomistic spin models, one can study magnetic phase transitions in different systems.

## Involved researchers

# Multiferroics

**Multiferroics** are defined as materials that exhibit more than one of the primary ferroic order parameters, ferromagnetism, ferroelectricity, or ferroelasticity in the same phase (Wikipedia).

In our group we focus on **multilayer systems** consisted of ferroelectric and ferromagnetic layers. It has been shown, that the adjacent ferroelectric layer can modify magnetic anisotropy in the ferromagnetic layer. Thus the magnetic moments can be manipulated by spin current as well as by electric field applied to the ferroelectric part.

## Involved researchers

# Quantum Monte Carlo

**Quantum Monte Carlo** encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution of the quantum many-body problem. Quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem (Wikipedia).

## Involved researchers

# Spin currents

When electric current passes through a magnetic conductor, the electron flux becomes spin-polarized. We talk about **spin current** or **spin-polarized current**. Apart from electric charge, spin current transfer also momentum. This momentum transfer can be observed eg. in magnetic multilayers with noncollinear magnetizations, where **spin transfer torques**, trasfered by the spin current, act on the localized magnetic moments.

Today, number of different methods of spin current generations are known: spin filtering, spin Seebeck effect, spin Hall effect, spin pumping, or ultrafast laser-induced demagnetization.

## Involved researchers

# Spin transfer torque

**Spin-transfer torque** is an effect in which the orientation of a magnetic layer in a magnetic tunnel junction or spin valve can be modified using a spin-polarized current (Wikipedia).

The effect of spin transfer torque is extensively studied in spintronics due to its potential for magnetic random access memories and data processing. Apart from the magnetic multilayers, spin transfer torque appears also in magnetic thin films with nonhomogeneous magnetization textures and can be used to manipulate with magnetic domain walls, vortices, or skyrmions.

## Involved researchers

# Spin valves

A **spin valve** is a device, consisting of two or more conducting magnetic materials, whose electrical resistance can change between two values depending on the relative alignment of the magnetisations in the layers. The resistance change is a result of so called **giant magnetoresistive effect** (Wikipedia).

When current density flowing through a spin valve is large enought, it exerts **spin transfer torque** on the magnetizations, which can lead to **magnetization dynamics** and **magnetization switching**.

## Involved researchers

# Spin waves

**Spin waves** are propagating disturbances in the ordering of magnetic materials. These low-lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as magnons, which are boson modes of the spin lattice (Wikipedia).

In our group we study spin waves and their potential utilization in spintronics. Using analytical and numerical methods we study, how spin waves can be generated by means of spin current, laser pulses, and domain wall dynamics.

## Involved researchers

# Spin-orbit torques

**Spin–orbit interaction** (a.k.a. spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential. In solid state, spin-orbit interaction can be understood as a momentum-dependent magnetic field acting on the spin of the electron. As a result, when electric current flows through a single magnetic layer, spin-orbit interaction can generate torques, known as **spin-orbit torques** acting on the localized magnetic moments.

In many magnetic systems lacking bulk or structure inversion symmetry spin-orbit torques substantially influence **magnetization dynamics**. In some systems, spin-orbit torques can lead to magnetization switching.

## Involved researchers

# Spintronics

**Spintronics**, also known as spin electronics, is the scope of physics which study the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices. In the last decades, spintronics is one of the most developing area in solid state physics connecting physics with material science and engineering.

# Topological insulators

A topological insulator is a material with non-trivial topological order that behaves as an insulator in its interior but whose surface contains conducting states, meaning that electrons can only move along the surface of the material (Wikipedia).

In our group we continuously study bulk conductivity and magnetic properties of Bismuth chalcogenides (Bi_{2}Se_{3} and Bi_{2}Te_{3}) doped by magnetic atoms like Mn, Fe or Cr.

# Transition metals

**Transition metal** is an element whose atom has a partially filled d sub-shell, or which can give rise to cations with an incomplete d sub-shell (Wikipedia).

In spintronics, transition metals like Fe, Co, or Ni are widely used due to their ferromagnetic properties and conductivity. Due to exchange interactions between the condutive (s) electrons and localized (d) electrons, these materials can be used for generation of **spin current**. On the other hand, spin current flowing through these metals can exert **spin transfer torque** on the localized magnetic moments.

## Involved researchers

# Ultrafast demagnetization

In 1996 Beaurepaire *et al.* have shown that a laser pulse can induced a significant reduction of magnetization of a Nickel thin film, which occur in less than a picosecond (Phys. Rev. Lett. **76**, 4250). This observation demonstrated that one can manipulate with magnetization in ultrafast way, which is very promising for the future evolution of magnetic memories and data processing.

In our group we study this effect by *ab initio* calculations as well as by various phenomenological models. We focus mainly on ultrafast demagnetization due to superdiffusive spin transport of hot electrons excited by the laser pulse (Phys. Rev. Lett. **105**, 027203).

## Involved researchers

**Direct URL:**http://theory.kfkl.cz/staff/balaz

# Contact details

ORCID: 0000-0003-0016-9271

Scopus Author ID: 23033051900

Google Scholar ID: Oh7h8Z0AAAAJ

# Research interests

**Ultrafast demagnetization in metals**with focus on laser-induced electronic transport in metallic multilayers**Magnetization dynamics**including numerical simulations and analytical models of magnetization dynamics induced by magnetic fields, spin currents, spin-orbit torques or laser pulses; with special interest in the dynamics of magnetic domain walls and other magnetic topological defects**Magnetic properties of disordered alloys**ranging from ferro- and antiferromagnets up to noncollinear topological insulators doped by magnetic atoms; the main method of research is the atomistic spin dynamics based on ab initio calculations

# Recent publications

## Regular articles

- F. Máca, J. Kudrnovský, P. Baláž,
*et al.*

Tetragonal CuMnAs alloy: Role of defects

J. Magn. Magn. Mater.**474**, 467 (2019) - P. Baláž, S. J. Hämäläinen, and S. Van Dijken

Static properties and current-induced dynamics of pinned magnetic domain walls under applied fields: An analytic approach

Phys. Rev. B**98**, 064417 (2018) - P. Baláž, M. Žonda, K. Carva,
*et al.*

Transport theory for femtosecond laser-induced spin-transfer torques

J. Phys.: Cond. Matter**30**, 115801 (2018)

## Books and chapters

- K. Carva, P. Baláž, and I. Radu
**Handbook of Magnetic Materials:**Laser-Induced Ultrafast Magnetic Phenomena

Elsevier B.V. (2017),**ISBN:**978-0-444-63927-1

- See list of all publications by P. Baláž

# Available projects for students

## Bachelor theses

- Study of the dynamic properties of 90-degree magnetic domain walls

Studium dynamických vlastností 90-stupnových magnetických doménových stěn

## Projects for students of 1st and 2nd year

- Magnetic dynamics in spintronic nanostructures

Magnetická dynamika v spintronických nanostrukturách