##### Date

2012-02-27##### Author

Mokkath, Junais Habeeb##### Subject

530 Physics DichtefunktionalformalismusElektronenstrukturMagnetismus75.75.+a, 36.40.Cg, 75.50.Bb, 73.22.-f##### Metadata

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Dissertation

## Theoretical study of magnetism, structure and chemical order in transition-metal alloy clusters

##### Abstract

Research on transition-metal nanoalloy clusters composed of a few atoms is fascinating by their unusual properties due to the interplay among the structure, chemical order and magnetism. Such nanoalloy clusters, can be used to construct nanometer devices for technological applications by manipulating their remarkable magnetic, chemical and optical properties. Determining the nanoscopic features exhibited by the magnetic alloy clusters signifies the need for a systematic global and local exploration of their potential-energy surface in order to identify all the relevant energetically low-lying magnetic isomers.

In this thesis the sampling of the potential-energy surface has been performed by employing the state-of-the-art spin-polarized density-functional theory in combination with graph theory and the basin-hopping global optimization techniques. This combination is vital for a quantitative analysis of the quantum mechanical energetics.

The first approach, i.e., spin-polarized density-functional theory together with the graph theory method, is applied to study the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. We carried out a thorough and systematic sampling of the potential-energy surface by taking into account all possible initial cluster topologies, all different distributions of the two kinds of atoms within the cluster, the entire concentration range between the pure limits, and different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling.

The remarkable magnetic properties shown by FeRh and CoPd nanoclusters are attributed to the extremely reduced coordination number together with the charge transfer from 3$d$ to 4$d$ elements.

The second approach, i.e., spin-polarized density-functional theory together with the basin-hopping method is applied to study the small Fe$_6$, Fe$_3$Rh$_3$ and Rh$_6$ and the larger Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$ clusters as illustrative benchmark systems. This method is able to identify the true ground-state structures of Fe$_6$ and Fe$_3$Rh$_3$ which were not obtained by using the first approach. However, both approaches predict a similar cluster for the ground-state of Rh$_6$. Moreover, the computational time taken by this approach is found to be significantly lower than the first approach. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. All the clusters display a remarkable variety of structural and magnetic behaviors.

It is observed that the isomers having similar shape with small distortion with respect to each other can exhibit quite different magnetic moments.

This has been interpreted as a probable artifact of spin-rotational symmetry breaking introduced by the spin-polarized GGA. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach having the advantage of avoiding efficiently the search over irrelevant regions of the potential energy surface.

In this thesis the sampling of the potential-energy surface has been performed by employing the state-of-the-art spin-polarized density-functional theory in combination with graph theory and the basin-hopping global optimization techniques. This combination is vital for a quantitative analysis of the quantum mechanical energetics.

The first approach, i.e., spin-polarized density-functional theory together with the graph theory method, is applied to study the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. We carried out a thorough and systematic sampling of the potential-energy surface by taking into account all possible initial cluster topologies, all different distributions of the two kinds of atoms within the cluster, the entire concentration range between the pure limits, and different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling.

The remarkable magnetic properties shown by FeRh and CoPd nanoclusters are attributed to the extremely reduced coordination number together with the charge transfer from 3$d$ to 4$d$ elements.

The second approach, i.e., spin-polarized density-functional theory together with the basin-hopping method is applied to study the small Fe$_6$, Fe$_3$Rh$_3$ and Rh$_6$ and the larger Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$ clusters as illustrative benchmark systems. This method is able to identify the true ground-state structures of Fe$_6$ and Fe$_3$Rh$_3$ which were not obtained by using the first approach. However, both approaches predict a similar cluster for the ground-state of Rh$_6$. Moreover, the computational time taken by this approach is found to be significantly lower than the first approach. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. All the clusters display a remarkable variety of structural and magnetic behaviors.

It is observed that the isomers having similar shape with small distortion with respect to each other can exhibit quite different magnetic moments.

This has been interpreted as a probable artifact of spin-rotational symmetry breaking introduced by the spin-polarized GGA. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach having the advantage of avoiding efficiently the search over irrelevant regions of the potential energy surface.

##### Sponsorship

University of Kassel##### Citation

@phdthesis{urn:nbn:de:hebis:34-2012022740836,

author={Mokkath, Junais Habeeb},

title={Theoretical study of magnetism, structure and chemical order in transition-metal alloy clusters},

school={Universität Kassel, Institut für Theoretische Physik},

month={02},

year={2012}

}

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2012-02-27T13:06:58Z 2012-02-27T13:06:58Z 2012-02-27 urn:nbn:de:hebis:34-2012022740836 http://hdl.handle.net/123456789/2012022740836 University of Kassel eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Magnetic nano alloy clusters Density functional theory Alloy magnetism Electronic structure theory 530 Theoretical study of magnetism, structure and chemical order in transition-metal alloy clusters Dissertation Research on transition-metal nanoalloy clusters composed of a few atoms is fascinating by their unusual properties due to the interplay among the structure, chemical order and magnetism. Such nanoalloy clusters, can be used to construct nanometer devices for technological applications by manipulating their remarkable magnetic, chemical and optical properties. Determining the nanoscopic features exhibited by the magnetic alloy clusters signifies the need for a systematic global and local exploration of their potential-energy surface in order to identify all the relevant energetically low-lying magnetic isomers. In this thesis the sampling of the potential-energy surface has been performed by employing the state-of-the-art spin-polarized density-functional theory in combination with graph theory and the basin-hopping global optimization techniques. This combination is vital for a quantitative analysis of the quantum mechanical energetics. The first approach, i.e., spin-polarized density-functional theory together with the graph theory method, is applied to study the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. We carried out a thorough and systematic sampling of the potential-energy surface by taking into account all possible initial cluster topologies, all different distributions of the two kinds of atoms within the cluster, the entire concentration range between the pure limits, and different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling. The remarkable magnetic properties shown by FeRh and CoPd nanoclusters are attributed to the extremely reduced coordination number together with the charge transfer from 3$d$ to 4$d$ elements. The second approach, i.e., spin-polarized density-functional theory together with the basin-hopping method is applied to study the small Fe$_6$, Fe$_3$Rh$_3$ and Rh$_6$ and the larger Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$ clusters as illustrative benchmark systems. This method is able to identify the true ground-state structures of Fe$_6$ and Fe$_3$Rh$_3$ which were not obtained by using the first approach. However, both approaches predict a similar cluster for the ground-state of Rh$_6$. Moreover, the computational time taken by this approach is found to be significantly lower than the first approach. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. All the clusters display a remarkable variety of structural and magnetic behaviors. It is observed that the isomers having similar shape with small distortion with respect to each other can exhibit quite different magnetic moments. This has been interpreted as a probable artifact of spin-rotational symmetry breaking introduced by the spin-polarized GGA. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach having the advantage of avoiding efficiently the search over irrelevant regions of the potential energy surface. open access Mokkath, Junais Habeeb Universität Kassel, Institut für Theoretische Physik Pastor, G. M. Garcia, M. E. Träger, F. Zijlstra, E. S. The principal motivation of this thesis was to enrich the fundamental understanding of the structural and magnetic properties exhibited by the TM nanoalloy clusters in view of applications in cluster-based magnetic nanometer devices. The results presented in this thesis open the way to several near future investigations and developments in this field. Specific conclusions concerning each chapter have already been mentioned at the end of the corresponding chapters. For this reason the present final chapter is quite compact. In the following, I briefly discuss how the thesis has been progressed. Chapter 1 through 3 are devoted to present the essential background material for the calculations performed in this thesis, while chapters 4 through 7 demonstrate the results. In the first part, i.e., in chapters 4 and 5, we combined the state-of-the-art Hohenberg-Kohn Sham's DFT with a global optimization technique based on a graph theory method. This method has been used to perform a thorough and systematic study on the interplay between cluster structure, magnetism and the chemical order in the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ nanoclusters having $N = m+n \leq 8$ atoms. For $N = m+n \leq 6$ a thorough sampling of all cluster topologies has been performed. We would like to emphasis that this kind of study is rather unique. For $N = 7$ and $8$ only a few representative topologies were considered including both open and compact structures. Choosing a small set of representative topologies for $N = 7$ and $8$ is justified by the fact that the number of isomers (number of local minima on the PES) increases exponentially with the cluster size $N$. Indeed, the computational complexity increases even more rapidly in the case of binary clusters, since one has to take into account all possible homotops. For all the clusters the entire concentration range is systematically investigated, and the different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling are considered. The results in the case of FeRh clusters are the following: an increase of the average magnetic moment ($\overline\mu_N$) and magnetic stabilization energy ($\Delta E_m$) with increasing Fe concentration, the presence of small differences in the average magnetic moment ($\overline\mu_N$) between low-lying isomers, the dominant role of the $d$-electron spin polarization within the PAW spheres, the enhancement of the Fe moments upon Rh doping, and a general tendency to maximize the number of mixed bonds. We have adopted a similar approach in the case of Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. The main results in this case are the following: The optimized cluster structures have a tendency to maximize the number of nearest-neighbor CoCo pairs. An increase of $\overline\mu_N$ and $\Delta E_m$ is observed with increasing Co concentration. The magnetic order is ferromagnetic-like (FM) for all ground-state structures. However, an antiferromagnetic-like (AF) order has been obtained in some of the first exited isomers. The maximal local spin polarization for Co and Pd atoms are found in the equiatomic compositions (Co$_2$Pd$_2$, Co$_3$Pd$_3$ and Co$_4$Pd$_4$). We found that taking into account spin-orbit (SO) interactions in FeRh and CoPd clusters does not alter the ground-state structures found by using the scalar relativistic (SR) calculations. FeRh and CoPd clusters are expected to develop a variety of further interesting behaviors, which still remain to be explored. For instance, larger FeRh cluster should show a more complex dependence of the magnetic order as a function of concentration. In particular for large Rh content one should observe a transition from FM-like to AF-like order with increasing cluster size, in agreement with the AF phase found in solids for more than 50\% Rh concentration. Moreover, the metamagnetic transition observed in bulk FeRh alloys also puts forward the possibility of similar interesting phenomena in nanoalloys as a function of temperature. In chapter 6 we have developed a DFT based spin-polarized basing-hopping algorithm. This methodological approach has been applied to study the structural and magnetic properties of pure and alloy TM nanoclusters. This method is found to be very impressive. For instance, in the case of pure clusters, we obtained several Jahn-Teller distorted magnetic isomers of the same basic structural motif which, being similar, would have been most likely missed by using the graph or topographical scheme employed in the first part of this thesis. A similar situation has also been encountered in the case of mixed clusters, where we identified several Jahn-Teller distorted magnetic isomers having the same composition and a similar distributions of the two kinds of atoms. We have discussed extensively the technicalities used for choosing the ideal move parameters for the optimizations. Moreover, we have implemented a \textit{window acceptance criterion}. Moreover, in the case of mixed clusters we swap or exchange the positions of the dissimilar atoms on the fly. We noticed that this method greatly enhances the performance of our calculations by significantly reducing the CPU time. For the small clusters (e.g. Fe$_6$, Rh$_6$ and Fe$_3$Rh$_3$) the main result is the presence of dominant (or frequently visited) isomers. We found that this is an intrinsic feature of the basin-hopping method. This is interpreted as a consequence of the reduced system size and the resulting small number of low-lying isomers. The dominant isomers govern the overall computational demand of the sampling and are therefore the relevant isomers for the performance analysis. In the case of larger clusters (e.g. Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$) we applied a similar computational procedure as the one used in the case of small clusters. In fact, both pure and mixed clusters display remarkable structural and magnetic diversity. We found that isomers having similar shape but with a small distortion among each other can exhibit often quite different magnetic moments. This has been interpreted as a probable artifact of the spin-rotational symmetry breaking introduced by the spin-polarized LDA or GGA. In the case of Fe$_6$Rh$_7$ cluster, an implementation consisting of small move distances of about 0.15$a$ (where $a$ is the length of the shortest bond) in combination with swapping of Fe and Rh atoms, could identify all the relevant isomers including the ground-state. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach by having the advantage of efficiently avoiding search over irrelevant regions of the potential energy surface. In chapter 7 we investigated the composition dependence of orbital magnetism and magnetic anisotropy energy in FeRh nanoclusters. A remarkable non-monotonous dependence of the MAE is observed as a function of Fe content, i.e., upon going from pure Fe to pure Rh. This leads to an important increase of the MAE, which reaches about 3 times the value for pure clusters at the optimal Fe concentration. This offers multiple possibilities of tailoring the magneto-anisotropic behavior in nanoalloys. In conclusion, it is our hope to see the experimental verification of the reported results in this thesis. 75.75.+a, 36.40.Cg, 75.50.Bb, 73.22.-f Dichtefunktionalformalismus Elektronenstruktur Magnetismus 2012-02-15

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