# Theory of Condensed Matter

Theoretical physics of condensed matter is one of the **most progressive** parts of modern physics. The wealth of systems studied by condensed matter physics provides opportunities for **fascinating physical phenomena** and open new ways for **technological innovations**.

## Physics goes quantum [+]

The basic physics of many phenomena studied by condensed matter physics happens on the atomic scale, where **quantum properities** of atoms and charge carriers become important. Thus condensed matter can serve as a real **playground for quantum-mechanical effects**.
With advent of new materials and technologies the **quatum-relativistic physics** in condesed matter have become more important. An important manifestation of relativistic behaviour in condensed matter is coupling of spins and orbital momenta, called **spin-orbit interaction**.
This interactions appears to be important ingredient for novel materials with possible application in spintronics.

## Studying new materials [+]

In our group we focus on various aspects of quantum physics in the solid state of matter. In close collaboration with experiment we study basic physical properties of novel **functional materials for spintronics** featuring magnetic moments and/or spin-orbital interaction.
Apart from standard three-dimensional bulk materials with disorder (like diluted magnetic semiconductors) we study also effects on interfaces, two-dimensional materials (like graphene), one-dimensional structures (like quantum wires), and zero-dimensional systems (like quantum dots).
Especially, we focus on **quantum transport** in these structures, which is of great importance for engineering of novel technical applications.

## Proposing new devices [+]

For novel technological applications, more complex structures need to be proposed and studied. On one hand side we study magnetotransport through **multilayer structures** consisted of magnetic layers separated by nonmagnets. These structures are well know for a possibility of manipulating with their magnetizations by means of **spin transfer torque**.
The effect of spin transfer torque has a potential for magnetic **random access memories**.
Spin transfer torque acts on magnetic domain wall in single magnetic layers when electric current flows in the layer's plane. This effect gives rise to an alternative geometry of magnetic memory known as **magnetic racetrack memory**.

Studying various models of devices, we study their functionality and look for their **improvements** and **innovations**.

## Developing new methods [+]

To study the problems of condensed matter physics, we use both paper-and-pencil theory as well as numerical calculations.
For studying the basic physical features of materials we use **ab initio** calculations.
For examining more complex system **multiscale approaches** and **phenomenological models** are used.

In our group we do not only use accesible software for numerical calculations but also develope our **own numerical codes** in order to tackle with more advanced problems of condensed matter physics.

# Ab initio

A calculation is said to be *ab initio* (or "from first principles") if it relies on basic and established laws of nature without additional assumptions or special models
(Wikipedia).

In our group we use various *ab initio* approaches to study basic properties of different materials ranging from electron density of states up to magnetic and transport properties.

# 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).

# Density functional theory

**Density functional theory** is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases (Wikipedia).

# 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

# Dynamical mean field

**Dynamical mean-field theory** is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure calculations, breaks down (Wikipedia).

## Involved researchers

# GaMnAs

**Gallium manganese arsenide**, (Ga,Mn)As, is a dilute magnetic II-VI semiconductor, which is formed by doping a standard semiconductor (GaAs) with magnetic element (Mn) (Wikipedia).

## Involved researchers

# Gilbert damping

The term **Gilbert damping** represents the rate at which magnetization relaxes towards its equilibrium position. In magnetization dynamics it is usually modeled using a phenomenological term in the Landau-Lifschitz-Gilbert equation, with direction proportional to the vector product of the magnetization and its time derivative. Magnitude of the Gilbert damping torque is proportional to a dimensionless parameter known as Gilbert damping.

In our group we focus on the origin of the Gilbert damping, which can be studied using *ab initio* calculations.

## Involved researchers

# Graphene

**Graphene** is an form of carbon consisting of a single layer of carbon atoms arranged in an hexagonal lattice. Graphene is a transparent and flexible conductor that holds promise for various material/device applications, including solar cells, light-emitting diodes (LED), touch panels and smart windows or phones (Wikipedia).

## Involved researchers

# Josephson junctions

The Josephson effect is the phenomenon of supercurrent across a device known as a Josephson junction, which consists of two superconductors coupled by a weak link (Wikipedia).

## Involved researchers

# Kondo effect

The Kondo effect is an unusual scattering mechanism of conduction electrons in a metal due to magnetic impurities, which contributes a term to the electrical resistivity that increases logarithmically with temperature as the temperature T is lowered as log(T) (Scholarpedia).

# Magnetic tunnel junctions

Magnetic tunnel junction is a multilayer structure consisted of two ferromagnets separated by a thin insulator. If the insulating layer is thin enough (typically a few nanometers), electrons can tunnel from one ferromagnet into the other. The resistance of magnetic tunnel junction is generally dependent on the relative magnetic configuration of the ferromagnetic layers. This phenomena is known as **tunnel magnetoresistance** (TMR).

## 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

# Molecular magnets

**Single-molecule magnets** are a class of metalorganic compounds that show superparamagnetic behavior below a certain blocking temperature at the molecular scale. In this temperature range, single-molecule magnets exhibit magnetic hysteresis of purely molecular origin. Contrary to conventional bulk magnets and molecule-based magnets, collective long-range magnetic ordering of magnetic moments is not necessary (Wikipedia).

For more information visit CTCM.

## Involved researchers

# Molecular wires

**Molecular wires** are chains of molecules that can conduct electric current. They are the proposed building blocks for molecular electronic devices.

For more information visit CTCM.

## 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

# Numerical renormalization group

The **numerical renormalization group** is a technique devised by Kenneth Wilson to solve certain many-body problems where quantum impurity physics plays a key role. It is an inherently non-perturbative procedure, which was originally used to solve the Kondo model (Wikipedia).

## Involved researchers

# Open systems

**Real quantum systems** are never completely isolated. They interaction with environment leads to quantum dissipation and quantum decoherence. Both this effects present conceptual and technical challenges with implications for different areas of physics and technology including quantum computing and nano-science.

## Involved researchers

# Quantum dots

Quantum dots are very small objects, only several nanometres in size, so small that their optical and electronic properties differ from those of larger particles (Wikipedia).

## 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

# Quantum transport

The advent of new technologies made possible study of electronic transport through quantum objects like single molecules, molecular wires, and quantum dots. The research of **quantum transport** opens new ways of understanding quantum-mechanical behaviour of strongly correlated systems.

For more information visit CTCM.

# Semiconductors

A semiconductor material has an electrical conductivity value falling between that of a conductor and an insulator. Their resistance decreases as their temperature increases, which is behavior opposite to that of a metal. Their conducting properties may be altered in useful ways by the deliberate, **controlled introduction of impurities** ("doping") into the crystal structure (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 fluctuations

Nanowires, molecules and even single atoms are a realization of low-dimensional quantum junctions.
Naturally, the electric current can be thought to be a consequence of charge fluctuations.
**The fluctuations of electron’s spin** come into play, when there is a spot in the junction where the Coulomb repulsion between electrons becomes very strong.

For more information visit CTCM.

## 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.

# Stochastic dynamics

A **stochastic dynamical system** is a dynamical system subjected to the effects of noise (Scholarpedia).

In our group we study both **classical** and **quantum** dynamical systems. We focus on bistability and switching in stochastic dynamical system as well as on stochastic termodynamics.

## Involved researchers

# Superconducting quantum dot

**Superconducting quantum dot** consists of a quantum dot, a device that allows to store and manipulate single electrons, and superconducting leads, where superconductivity is a macroscopic quantum phenomena.

Superconducting quantum dots are rich physical playgrounds with tremendous potential for real world applications. Our primarily effort is focused on making the theoretical analyses of real superconducting quantum dots as easy as possible.

## Involved researchers

# Superconductivity

**Superconductivity** is a phenomenon of exactly zero electrical resistance and expulsion of magnetic flux fields occurring in certain materials, called superconductors, when cooled below a characteristic critical temperature (Wikipedia).

In our group we focus on superconductive electron transport through nanoscale objects like **Josephson junctions** or **superconductive quantum dots**.

## Involved researchers

# 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

# Tunnel magnetoresistance

**Tunnel magnetoresistance** (TMR) is a magnetoresistive effect that occurs in a **magnetic tunnel junction**, which is a component consisting of two ferromagnets separated by a thin insulator (). In such structures, the total electric resistance generally depends on the relative magnetic configuration of the magnetic layers.

## 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

# Uranium compounds

In our group we also study **uranium based materials** using *ab initio* methods. These materials are interesting since they can show both ferromagnetism and superconductivity at the same time. These compounds show existence of strong correlations between the magnetic moments of the uranium ions and the conduction electrons. These correlations lead to unusual magnetic properties at low temperatures.

## Involved researchers

# Research Wall

Clicking on the tags you can get basic information and researchers involved in the field.

- Ab initioAb initio
- Atomistic spin dynamicsAtomistic spin dynamics
- CuMnAsCuMnAs
- Density functional theoryDensity functional theory
- Domain wall dynamicsDomain wall dynamics
- Dynamical mean fieldDynamical mean field
- GaMnAsGaMnAs
- Gilbert dampingGilbert damping
- GrapheneGraphene
- Josephson junctionsJosephson junctions
- Kondo effectKondo effect
- Magnetic tunnel junctionsMagnetic tunnel junctions
- MagnetismMagnetism
- Magnetization dynamicsMagnetization dynamics
- Micromagnetic simulationsMicromagnetic simulations
- Molecular magnetsMolecular magnets
- Molecular wiresMolecular wires
- Monte CarloMonte Carlo
- MultiferroicsMultiferroics
- Numerical renormalization groupNumerical renormalization group
- Open systemsOpen systems
- Quantum dotsQuantum dots
- Quantum Monte CarloQuantum Monte Carlo
- Quantum transportQuantum transport
- SemiconductorsSemiconductors
- Spin currentsSpin currents
- Spin fluctuationsSpin fluctuations
- Spin transfer torqueSpin transfer torque
- Spin valvesSpin valves
- Spin wavesSpin waves
- Spin-orbit torquesSpin-orbit torques
- SpintronicsSpintronics
- Stochastic dynamicsStochastic dynamics
- Superconducting quantum dotSuperconducting quantum dot
- SuperconductivitySuperconductivity
- Topological insulatorsTopological insulators
- Transition metalsTransition metals
- Tunnel magnetoresistanceTunnel magnetoresistance
- Ultrafast demagnetizationUltrafast demagnetization
- Uranium compoundsUranium compounds

# Scientific contributions

In 2013 Prof. Bedřich Velický was awarded by prize Neuron for his contribution to the world science especially for his research in the area of **semiconductors, disordered systems and quantum transport**.

Find more information about his research in his lecture (in Czech language).