spin dynamics

Thomas Bose

Postdoctoral Research Fellow

Overview of research topics

Here is a summary of the research topics I am interested in which include:

In the following the ideas and some selected results are presented. For the full mathematical treatment and the detailed results the reader is referred to the corresponding publications. If you would like to discuss a particular topic please email me.

The complete list of my publications can be found here.

Collective Decision Making

The enhancement of our understanding of the decision making process is currently a vital research field. Studies of natural systems that are able to make a decision and which at first glance seem to be completely different pose interesting questions for the theory of decision making. For example, one may ask what are the similarities and differences between the functioning of the human brain and social insect colonies such as ants or honeybees in terms of the decision making process? Answering questions like this may reveal if decision making could be explained based on a unified theory. Although our konowledge of the underlying mechanisms have improved over the last decades, decision making mechanisms are far from being completely understood.

The current project I am involved in aims at advancing the current understanding of decentralized decision making within a group of individuals where not the detailed characteristics of the individuals but the interactions amongst them are thought to play the pivotal role.

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Arbitrary temperature gradients in spin-caloritronics

Temperature gradients in spin-caloritronics
Fig: Temperature gradients affect magnetization dynamics.

A new direction in magnetic nanostructure research has evolved by combining the control of heat currents and spin currents which is known as spin-caloritronics. Phenomena in spin-caloritronics are interesting from the point of view of fundamental as well as applied physics as they offer the opportunity to manipulate the spin degree of freedom with heat.

Occurring in the same system heat currents and spin currents can be expected to interact mutually. To introduce a coupling between both we propose an action functional including the coupling of the scalar temperature field and its derivatives with respect to the spatial coordinates to the magnetization and its variation in space. Applying variational principles enables to derive the relevant equation of motion for the temperature as well the magnetization which are now coupled. This allows to investigate how magnetic systems behave when the temperature distribution is varied. Regarding this, the choice of the boundary conditions and the shape of the initially distributed temperature are particularly important and influence the spin wave dispersion relation as well as spin wave damping.

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Ab-initio calculations of Fe/MgO-systems using SIESTA

Fe/MgO-interfaces in magnetic multilayer structures are of great importance in magnetic material science with regard to promising applications and devices. In our present investigation we are looking at basic properties of Fe/MgO-slab geometries.

Unit cells of Fe and MgO

Within a systematic study we are currently investigating the effect of altering the Fe-layer thickness on quantities like layer resolved magnetic moments, charge distributions and magnetocrystalline anisotropy. We make use of the SIESTA package which is based on density functional theory (DFT) and utilizes pseudo potentials and localized atomic orbitals as basis set. Our DFT-based calculations are performed within the generalized gradient approximation (GGA) for the exchange correlation potential. Typical calculations include the construction of the system under study and its relaxation to find the final atomic coordinates. Subsequent, information about energies, atomic magnetic moments and charges can be obtained directly from the SIESTA output. In particular, the magnetocrystalline anisotropy energy which is an important quantity regarding magnetic data storage devices can be calculated as well.

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Nonlinear magneto-optical response to light carrying orbital angular momentum

Ultrafast laser pulses as applied to observe the inverse Faraday effect induce electron motion
Fig: Laser pulse induced electron motion.

The design and fabrication of ever smaller and faster magnetic devices for data storage, sensorics and information processing entail the development of efficient tools to control the dynamic behavior of the magnetization. In particular, femtosecond laser-induced magnetic excitations, originating in thermal and nonthermal effects, offer the possibility to study magnetic systems on time scales down to 10-100 femtoseconds.

Nonthermal opto-magnetic effects bear high potential for promising magnetic devices and applications and pose interesting questions for theory. In the present study we worked out the role of nonlinear effects which are not negligible for intensities in the range of 1014 - 1016 W/cm2. Utilizing a classical treatment of the laser-driven carrier in a given symmetry environment, it is possible to separate the electron motion into a first-order displacement that is directly proportional to the electrical field of the optical pulse and a second-order displacement that depends on the square of the electrical field. Considering magnetic insulators with a certain symmetry configuration we found that both the first-order and the second-order electron displacement create current loops that generate the light-induced magnetic fields B(1) and B(2). As the direction of rotation of the first-order electron displacement always opposes that of the second-order displacement, the light-induced fields B(1) and B(2) also carry opposite signs. Applying Laguerre-Gaussian laser beams which carry orbital angular momentum characterized by the number L, the total optically-generated magnetic field B(1) + B(2) can be controlled by varying |L|.

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Nonlocal feedback in ferromagnetic resonance

Ferromagnetic resonance including retardation
Fig: Geometry of the system under study including retardation.

Ferromagnetic resonance enables the investigation of spin wave damping in thin or ultrathin ferromagnetic films. The relevant information is contained in the linewidth of the resonance signal. Whereas the intrinsic damping included in the Landau-Lifshitz-Gilbert equation, predicts a linear frequency dependence of the linewidth, the extrinsic contributions associated with two-magnon scattering processes show a nonlinear behavior. A superposition of both the Gilbert damping and the two-magnon contribution turned out to be in good agreement with experimental data displaying the dependence of the linewidth on the frequency. However, both contributions to the linewidth originate from different theoretical treatments. Therefore, it was our aim to propose an equation of motion for the magnetization from which it is possible to derive an expression for the ferromagnetic resonance linewidth including all contributions from intrinsic and extrinsic damping.

The geometry referring to the film, applied fields and magnetization is sketched in the figure. Correlations between the position-dependent magnetization are taken into account via the retardation length ξ. Our detailed study of spatiotemporal feedback effects and intrinsic damping terms offers that both mechanisms become relevant in ferromagnetic resonance. Due to the superposition of both effects it results a nonlinear dependence of the total linewidth on the frequency which is in accordance with experiments. In getting the results the conventional model including Landau-Lifshitz-Gilbert damping is extended by considering additional spatial and temporal retardation and non-conserved Bloch damping terms. Our analytical approach enables to derive explicit expressions for the resonance condition and the peak-to-peak linewidth. As expected the retardation gives rise to an additional damping process. Furthermore, the complete linewidth offers a nonlinear dependence on the frequency which is also triggered by the Gilbert damping. From here we conclude that for sufficient high frequencies the linewidth is dominated by retardation effects.

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Colored noise in the Landau-Lifshitz-Gilbert equation

Ferromagnet influenced by colored noise
Fig: Ferromagnet influenced by colored noise. J is a measure for the exchange integral and a is the lattice constant.

Magnetism can be characterized and analyzed on different length and time scales. The description of fluctuations of the magnetization, the occurrence of damped spin waves and the influence of additional stochastic forces are successfully performed on a mesoscopic scale where the spin variables are represented by continuous spatio-temporal quantities. In this case, a well established approach is based on the Landau-Lifshitz-Gilbert equation which describes the damped precessional motion of the magnetization in an effective magnetic field. This field consists of a superposition of an external field and internal fields, produced by interacting magnetic moments. The latter ones are strongly influenced by the isotropic exchange interaction and the magnetocrystalline anisotropy.

The modelling of fluctuations occurring in magnetic systems often relies on the introduction of white noise. Although this approach is valid in the limit when the timescale of fluctuations is several orders of magnitudes smaller than that of the dynamic behaviour of the magnetization it loses its validity if both timescales are similar. Given that nowadays experiments can be performed with magnetic fields as large as 20 Tesla and, therefore, presumably creating significant fluctuations which influence the magnetic system on comparable timescales, we had a look at the effect of colored noise in the Landau-Lifshitz-Gilbert equation in terms of a generic study.

Coupling the effective field to the spin orientation the stochastic process is a multiplicative one. Microscopically, such a random process might be originated by a fluctuating coupling strength for instance. The situation associated with our model is illustrated in the figure and can be understood as follows: The stochastic vector field η is able to change the orientation of the localized moment at different times. Therefore, phase relations between adjacent spins might be altered. Moreover, the stochastic fields at different times are interrelated due to the finite correlation time. The anisotropy axis defines the preferred orientation of the mean value of magnetization. Due to the inclusion of fluctuations the deterministic Landau-Lifshitz-Gilbert equation is transformed into its stochastic version.

After deriving an approximate Fokker-Planck equation the dynamic behaviour of the mean value of the magnetization can be studied. As the result, both the intrinsic damping controlled by the Gilbert damping parameter and the relaxation originating from correlated fluctuations are able to compete leading to a more complex behaviour. In particular, the introduction of colored noise leads to instabilities of spin waves.

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Stochastic tumor cells - immune cells interactions

Tumor growth has become an important issue in medicine, biology and physics. Thus, understanding of cancer growth mechanisms is necessary to develop relevant strategies against this disease. It is widely accepted that the immune system plays an important role during tumor evolution and therapy.

Tumor-immune cells interaction after introducing randomness
Fig: Tumor-immune cells interaction after introducing randomness.

Introduced in the early 1900's and again suggested in the middle of the 20th century there is the hypothesis that the immune system is able to detect and to eliminate nascent transformed cells. During the last decade the concept of the immune surveillance of the body was emphasized again, supported by experimental results verifying the immune surveillance hypothesis. Later on, the immune surveillance concept was modified and is now known as 'immunoediting' which reflects the dual role of the immune response during the early stages of cancer growth. The term immunoediting means both the ability of the immune system to destroy the tumor cells and a possible sculpting of the cancer cells. As the result all cells with a low immunogenicity will survive and begin to proliferate which is often referred to as escape of the tumor from the control of the immune system.

Here, we investigate tumor evolution in presence of an intact immune system taking further into account stochasticity to demonstrate that tumor-immune cell reactions can be induced by stochastic forces. To that purpose we consider three types of cells:

  • tumor cells the density of which is denoted by x(t),
  • effector cells with density y(t), and
  • tumor detecting cells with density z(t).
Whereas the last kind of cells is only able to recognize tumor cells but not to kill them, the effector cells have the ability to eliminate tumor cells.

After introducing a system of coupled differential equations describing the interaction between different cell species we find that tumor extinction is only observed in the presence of randomness and noise. The mutual interaction of the different kinds of cells is shown in the figure. The quantities in the brackets are mean values derived by a probabilistic treatment of the equations describing the stochastic dynamic system. The parameters of the noise correlation function have a great impact on the behavior of the coupled tumor-immune cell interaction, especially on the response of the immune system. In particular we show that the auto-correlation time and the cross-correlation strength are able to control the evolution of the tumor. More precise, these two quantities discriminate whether the system tends to tumor suppression, tumor progression or tumor dormancy. The assistance of inevitable noisy influences seems to play a crucial role during cancer genesis and growth in humans. The involved random forces may be originated in the tumor as well as inside the immune system and can even interact mutually which is manifested in the cross-correlation. Our model should be considered as an attempt toward a more detailed analysis of tumor-immune systems. It elucidates that noise plays an decisive role in such systems.

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