Michał Antkowiak

A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings

The term “frustration” in the context of magnetism was originally used by P. W. Anderson and quickly adopted for application to the description of spin glasses and later to very special lattice types, such as the kagomé. The original use of the term was to describe systems with competing antiferromagnetic interactions and is important in current condensed matter physics in areas such as the description of emergent magnetic monopoles in spin ice. Within molecular magnetism, at least two very different definitions of frustration are used. Here we report the synthesis and characterization of unusual nine-metal rings, using magnetic measurements and inelastic neutron scattering, supported by density functional theory calculations. These compounds show different electronic/magnetic structures caused by frustration, and the findings lead us to propose a classification for frustration within molecular magnets that encompasses and clarifies all previous definitions.

Single-Ion Anisotropy Estimates for the Rhenium(IV-Based) Molecular Magnets: Modeling and Simulations Studies

We prove that the tetranuclear oxalato-bridged complex Re3(IV)Ni(II) demonstrating the single molecule magnet behavior is a good anisotropic spin Heisenberg model. Our comprehensive analysis, based on an exact diagonalisation technique, genetic algorithm ideas, and EPR resonances, leads to a unique set of the single-ion anisotropy parameters (DRe/kB = −8.8 K, DNi/kB = 9.9 K, E = 0). The parameters determine the model that quantitatively describes the zero-field splitting as well as the temperature dependence of magnetic susceptibility and the field dependence of single-crystal magnetisation isotherms, they also reveal pronounced maxima in the field dependence of the differences between the transverse magnetisation components, which are directly related to the rhombicity factor E/D. They are noticeable enough to be detected experimentally and also occur for mononuclear complexes. Finally, we propose the rationale for the unusual reduction in the energy barrier with respect to the zero-field splitting.

Effective Parallelization of Quantum Simulations: Nanomagnetic Molecular Rings

The effective parallelization of processing exploiting the MPI library for the numerically exact quantum transfer matrix (QTM) and exact diagonalization (ED) deterministic simulations of chromium-based rings is proposed. In the QTM technique we have exploited parallelization of summation in the partition function. The efficiency of the QTM calculations is above \(80\,\%\) up to about \(1000\) processes. With our test programs we calculated low temperature torque, specific heat and entropy for the chromium ring Cr\(_8\) exploiting realistic Hamiltonian with single-ion anisotropy and the alternation of the nearest neighbor exchange couplings. Our parallelized ED technique makes use of the self-scheduling scheme and the longest processing time algorithm to distribute and diagonalize separate blocks of a Hamiltonian matrix by slave processes. Its parallel processing scales very well, with efficiency above \(90\,\%\) up to about 10 processes only. This scheme is improved by processing more input data sets in one job which leads to very good scalability up to arbitrary number of processes. The scaling is improved for both techniques when larger systems are considered.

Genetic Algorithm and Exact Diagonalization Approach for Molecular Nanomagnets Modelling

We combined the genetic algorithm search procedure and exact diagonalization method to obtain the fitting system with two-level parallelism and optimally balanced workload which was implemented in the HPC environment. Applying the system to the experimental magnetic susceptibility data of Cr\(_8\)Ni molecule we obtained the non-uniform exchange couplings parameters for more general models and we achieved not only better agreement with experiment but we also demonstrated that the values known in literature are systematically overestimated.

Non-perturbative Methods in Phenomenological Simulations of Ring-Shape Molecular Nanomagnets

Two non-perturbative numerically exact methods: exact diagonalization and quantum transfer matrix are applied to computationally complex Heisenberg-like spin models of ring shaped molecular nanomagnets and implemented in the high performance computing environment. These methods are applicable to the wide class of ring-shaped nanomagnets. For the hypothetical antiferromagnetic nanomagnet Ni\(_{12}\) the influence of single-ion anisotropy on the ground states is investigated. For Cr\(_8\) it is demonstrated that the alternation of the nearest-neighbor bilinear exchange couplings leads to small changes in the magnetic torque with respect to the uniformly coupled system. Specific heat and entropy for Cr\(_8\) are showed to be good indicators of crossing fields. The applicability of the Lande rule to both systems is checked.

Parallel Exact Diagonalization Approach to Large Molecular Nanomagnets Modelling.

The exact diagonalization method is used to calculate the energy levels of ring-shaped molecular nanomagnets of different sizes and spin numbers. Two-level hybrid parallelization is used to increase the efficiency and obtain the optimally balanced workload. The results of the successful runs of our application on two Tier-0 supercomputers are presented with emphasis on the satisfactory speedup obtained by threading the diagonalization process.