Session A16: Ab-initio Theory of Spin Dependent Properties

Electronic structure theory of wide gap dilute magnetic semiconductors

The recent exciting reports that wide gap semiconductors, most notably ZnO, TiO$_2$ and GaN, when doped with transition metal elements, may have Tc's that are higher than room temperature have attracted great interest. When interpreted with care, highly precise first principles FLAPW calculations such as used here\footnote{E.Wimmer,H.Krakauer,M.Weinert,A.J.Freeman, PRB {\bf 24}, 864(1981)}, are now providing insights into the nature of their strong ferromagnetism (FM). Here, we present an analysis to the electronic structures of several typical wide gap DMS's and illustrate how first principles calculations can lead to correct predictions of their magnetic properties for both Cr:TiO$_2$ and Mn:GaN. The results demonstrate the importance of defect compensation in the determination of the magnetism. A comparison between Mn:ZnO and Co:ZnO highlights the fundamental difference in their electronic structures which explains why their FM is dependent on carriers of different polarity. Correct predictions of their magnetism are found to be due to the correct treatment of the LDA band gap problem. Finally, we provide semi-quantitative discussions of Co doped TiO$_2$, and illustrate why it is highly non- trivial to fully explain its FM based on first principles calculations.   

Spin-driven transition metal clustering in the wide-gap ferromagnetic semiconductor Cu$_2$O:Co

Cu$_2$O is a prototype material for p-type transparent conductive oxides, and a host material for diluted magnetic semiconductors. Using local density-functional supercell calculations we study (1) the origin of p-type behavior of pure Cu$_2$O, and (2) the short and long range magnetic interactions of Co atoms substituting Cu. We find that (i) Cu vacancies produce holes, which O vacancies are not able to destroy thus explaining the natural p-typeness, (ii) a single Co induces a fully occupied and localized level near midgap. This would suggest Co--Co magnetic interactions to be weak because there is no energy gain in magnetic coupling. Nevertheless, (iii) we find that Co--Co pairs lead to a huge ferromagnetic stabilization energy and binding energy, both of around 0.5~eV/pair. This dimerization is accompanied by strong lattice relaxation and symmetry breaking together with level splitting. Both clustering and ferromagnetism are caused by the fact that the bonding states of the previously unoccupied levels become occupied and are lower in energy relative to the antibonding levels of previously occupied levels. Such binding is allowed only for Co atoms with the same spins, leading to ferromagnetism (albeit short ranged).   

Mechanism of ferromagnetism in wide band gap semiconductors

Several wide bandgap semiconductors/oxides doped with small concentrations of transition metal impurities have been found to exhibit ferromagnetism at temperatures higher than room temperature. As the typical dopant concentrations are far below the percolation threshold associated with nearest neighbor cation coupling, a picture of ferromagnetism has been proposed which attributes an important role played by the intrinsic defects which are present in these materials. We have considered several examples of the most common defects found in GaN and ZnO, and examined within ab-initio calculations how their presence modifies ferromagnetism. Some defects, such as Ga-vacancies in GaN favor strongly spin polarised configurations with exchange splittings as large as 1 eV. However, the exchange splittings are quenched if the defect induced levels are below the transition-metal induced levels. We consider various scenarios for the location of the defect induced levels and the transition metal levels and identify the regime of defect enhanced ferromagnetism and examine various features of this regime.   

First-principles Investigation of the Neutral and Charged Embedded Clustering in Mn doped GaN: Revisited

Based on extensive density functional theory calculations, the spatial distribution and magnetic coupling of Mn atoms in Mn:GaN has been re-investigated by doping up to 5 Mn atoms in large supercells, where both the neutral and selected charged valence states are studied. The Mn atoms are found to have a tendency to form substitutional embedded clusters with the long-range wurtzite structure maintained. While for neutral pair-doping, the coupling is ferromagnetic regardless of the distance and orientation of Mn atoms, for the experimentally observed oxidation charged state $\rm Mn^{2+} $($d\rm^{5}$), antiferromagnetic coupling becomes favorable. Furthermore, for both neutral and negatively charged states, for larger (than pair) cluster configurations, states containing antiferromagnetic coupling are always favored. The size of supercell and the atomic relaxation are found important. The electrical conductivity of Mn:GaN depends sensitively on the valence charged states, where the oxidation states $\rm Mn^{2+}$($d\rm^{5}$) exhibit highly insulating character as observed in experiments. Our results highlight the intrinsic complex nature in transition metal doped dilute magnetic semiconductors, and can rationalize some hitherto puzzling experimental observations.   

Heusler clusters

Heusler alloys are known for their bulk properties, for example the magnetic shape-memory Ni$_2$MnGa [1]. Using first principles simulations, based on the real space pseudopotential method implemented in PARSEC [2], we examine Heusler alloy clusters. Clusters with various Ni-Mn-Ga compositions are examined in the size from 15 up to 113 atoms. Clusters with compositions being the closest to the stoichiometric Ni$_2$MnGa are the most stable. The geometry of tetrahedral coordination in Heusler structures is energetically favorable. In order to retain this coordination, clusters have to be symmetrically shaped. This implies that even in very small clusters the structure is bulk-like. However, the electronic densities of states do not show Kohn-like anomalies at the Fermi level, that are characteristic for bulk Ni-Mn-Ga alloys. [1] P. Entel, V. D. Buchelnikov, V. V. Khovailo et al. J. Phys. D: Appl. Phys. 39, 865 (2006) [2] http://www.ices.utexas.edu/parsec/   

Control of Magnetic Order in Monolayer Films by Substrate Tuning

Surprisingly, antiferromagnetic order has recently been observed in a monolayer (ML) film of Fe on W(001) [1] and a novel, nanoscale magnetic structure has been discovered for a ML Fe on Ir(111) [2] showing the crucial influence of the substrate. Here, we therefore propose to tailor exchange interactions in magnetic monolayer films by tuning the adjacent non-magnetic substrate. Using first-principles calculations based on density functional theory, we demonstrate a ferromagnetic-antiferromagnetic phase transition for one ML Fe on a Ta$_{x}$~W$_{1-x}$(001) surface as a function of the Ta concentration. At the Ta concentration of the transition, the nearest-neighbor exchange interaction becomes negligible and exchange terms beyond nearest-neighbors and higher order spin interactions beyond the Heisenberg Hamiltonian become crucial. In this regime, the accessible magnetic phase space is dramatically enhanced, and we study complex magnetic order such as spin-spiral states, multiple-$q$ states, or even disordered local moment states. [1] A.\ Kubetzka, {\sl et al.}, Phys.\ Rev.\ Lett.{\bf 94}, 087204 (2005). [2] K.\ von Bergmann, {\sl et al.}, Phys.\ Rev.Lett.\ {\bf 96}, 167203 (2006).   

Linear scaling \textit{ab initio} approach to the electronic structure calculation for L1$_{0}$-FePt nanoparticles embedded in FePt random alloy

Magnetic nanostructures present substantial theoretical challenges due to the need to treat the electronic interactions quantum-mechanically whilst dealing with a large number of atoms. In this presentation, we show a direct quantum mechanical simulation of~magnetic nano-structures made of spherical L1$_{0}$-FePt nanoparticles, with diameter within 2.5 nm $\sim $ 5 nm, embedded in an fct-FePt random alloy. The calculation is performed using the locally self-consistent multiple scattering method, a linear scaling \textit{ab-initio} all-electron method capable of treating tens of thousands of atoms. We found that there exists a screening region below the surface of each nanoparticle which essentially screens out the effect of the external random alloy to keep the physical properties of the interior region unchanged from the bulk of L1$_{0}$-FePt. Interestingly, the depth of this screening region is independent of the size of the nanoparticles we have investigated. We will show a non-collinear electronic structure calculation for the nano-structure and discuss the exchange coupling between the nanoparticle and the surrounding random alloy.   

Surface magnetism of Fe/W(110): an ab-initio study of the substrate effects

The pseudomorphic monolayer of Fe grown on a W(110) surface is very interesting from the point of view of magnetism. In studies of the surface magneto-crystalline anisotropy, the Fe monolayer on top of a W substrate has become the system of choice, since (a) the growth of the first Fe monolayer is pseudomorphic, (b) the W substrate has a large spin-orbit coupling, and (c) the interface anisotropy is the strongest ever observed. This makes the Fe monolayer on a W substrate a good candidate for an {\em ab initio} benchmark investigation of how the properties of the magneto-crystalline anisotropy are influenced by the substrate. Our investigation is done as a function of the substrate thickness (up to 8 layers). Analyzing the magnetocrystalline anisotropy energies, we find stable (with respect to the number of substrate layers) in-plane easy and hard axes of magnetization along the [1$\bar{1}$0]- and [001]-directions, respectively, reaching a value in good agreement with experiment for thick substrates. Additionally, the magnetic spin- and orbital moments, and the density of the Fe $d$-states are analyzed at different numbers of substrate layers as well as with respect to the direction of magnetization, confirming recent observations that ``Hund's 3rd rule is broken'' for the W substrate.   

Giant magneto-crystalline anisotropies in transition-metal monowires

The magneto-crystalline anisotropy energy (MAE) proved to be crucial for stability of magnetism in low-dimensional structures against thermal fluctuations. Here, we report on magnetic properties of free standing $3d$, $4d$, and $5d$ transition-metal (TM) monowires, paying special attention to the influence of spin-orbit interaction, revealing its utter importance for magnetism in these structures. The calculations were performed with the one-dimensional (1D) version of the full-potential linearized augmented plane-wave (FLAPW) method. The new 1D-FLAPW scheme [1] is extremely fast and allows a natural treatment of structures with 1D geometry. We present equilibrium interatomic distances, spin- and orbital moments, and the values of MAE. Across the series the easy axis of magnetization oscillates between two possible directions: perpendicular and along the wire axis. The largest values of the MAE occur at the end of the series. Giant values of 30-100 meV/atom can be obtained upon stretching of $4d$- and $5d$-TM wires. Certain chains change the magnetization direction upon wire stretching, opening new perspectives in controlling the spin-dependent ballistic conductance in these structures [2]. [1] Y.Mokrousov {\sl et al.}, Phys.\ Rev.\ B\ {\bf 72}, 045402 (2005), [2] Y.Mokrousov {\sl et al.}, Phys.\ Rev.\ Lett.\ {\bf 96}, 147201 (2006)   

Qualitative aspects of magnetism formation in Gd and its compounds

Using highly precise full-potential electronic structure calculations, we study the formation of magnetism in gadolinium. By manipulating the 4f-shell magnetic moments in a large supercell, the interplay between on-site and off-site contributions to the spin polarization of valence electrons is analyzed. Qualitative features of exchange coupling are discussed, and the limitations of model RKKY-like approaches are demonstrated. We also analyze the magnetization density distribution in ferromagnetic hcp Gd which, unlike transition- metal ferromagnets, shows a strongly inhomogeneous, directional structure in the interstitial region. The qualitative features revealed in this study are very generic, and we discuss their relevance to other rare-earth elements and their compounds.   

First-principles Calculation of Atom-scale Magnetic Interaction

The advance of manipulating atoms on surfaces by STM has made it possible to study atomic magnetism. It has been shown that STM can build chains of magnetic atoms and measure magnetic excitation of such chains [1]. This new technique has potential application to explore the limits of magnetic data storage, by engineering the energy required to flip the collective orientation of a small number of magnetically coupled atoms. We have applied GGA+U to determine the atomic spin and calculate the exchange coupling J (several meV) for Mn chains on a CuN/Cu(100) surface. Our spin-density analysis shows that Mn atoms in such a surface preserve their atomic spins S=5/2. To demonstrate the potential to engineer the coupling between atomic spins, we calculate the J's for the Mn dimers atop Cu atoms and atop N in the CuN layer, and find the Cu-site dimer has its J twice as large as the N-site. The local structures of the Mn dimers on these two sites determined by relaxation account for this difference in J.The charge transfers between Mn and its neighboring atoms are also calculated. [1] C. F. Hirjibehedin, C. P. Lutz, A. J. Heinrich, Science \underline {312}, 1021 (2006).   

Ab-initio determination of magnetic properties of Fe-Co nanoclusters on Cu(100).

By making use of the fully-relativistic screened Korringa-Kohn-Rostoker method supplemented by the embedded cluster method the spin and orbital magnetic moments as well as the magnetocrystalline anisotropy energy (MAE) of Fe-Co nanoclusters of different sizes are explored as a function of the cluster composition. The MAE and magnetic moments are found to vary strongly in dependence on the concentration of Fe and Co atoms as well as on specific arrangements of atoms within the clusters. Consequently the easy magnetization axis can be tuned by controlling the cluster composition. In contrast to clusters of a pure material there exist additional contributions to the anisotropy in the surface plane due to the two different atomic species.   

Magnetism of small Co clusters as a probe of \textit{ab initio} theory

We report \textit{ab initio} calculations of the electronic and magnetic properties of small Co clusters. We performed pseudopotential-based and all-electron calculations. In view of the ``unwritten theorem'' that electron localization enhances the electronic correlations, we have also considered the LDA+U functional, which is tailored for the strong-correlation problem associated with, e.g., partially-filled $d$ shells. As a result of the weak dependence of the total energy on the calculated magnetic moment, the latter is very sensitive to the method employed. Thus, the magnetic moments obtained in the all-electron and pseudopotential calculations are quite different. Furthermore, the on-site Hubbard $U$ enhances the magnetic moment significantly. The available experimental data for the magnetic moment of small clusters [Billas et al., Science \textbf{265}, 1682 (1994)] are consistent with this enhancement.~ Additional Stern-Gerlach measurements for smaller clusters would, in combination with our \textit{ab initio} results, constitute a direct determination of the $U$ for these prototypes of correlated-electron behavior. (*) Supported by NSF Grant ITR DMR-0219332 (+) Managed by UT-Battelle for the U.S. DOE under contract DE- AC05-00OR22725   

Non-collinear magnetism in Permalloy ($\mathrm{Ni}_{0.8} \mathrm{Fe}_{0.2}$)

Permalloy is an important material in a wide variety of magnetic systems, most notably in GMR read-heads. However, despite this great interest its properties are not fully understood. For an in depth analysis of important physical properties as e.g. electric transport or magnetic anisotropy a detailed understanding of the distribution of magnetic moments on an atomic level is necessary. Using our first principles Locally Self-consistent Multiple Scattering (LSMS) method we calculate the magnetic ground state structure for a large super-cell model of Permalloy. Our code allows us to solve both the usual non-relativistic Schr\"odinger equation as well as the fully relativistic Dirac equation and to find the magnitude and direction of the magnetic moments at each atomic site. While the non-relativistic calculation yields a collinear ground state in accordance with previous calculations, we find the ground state for the fully relativistic calculation to be slightly non-collinear. We also investigate the influence of variations in the iron concentration on the distribution of magnetic moments. Research sponsored by DOE-OS and BES-DMSE under contract number DE-AC05-00OR22725 with UT-Battelle LLC. The calculations presented were performed at the Center for Computational Sciences (CCS) at ORNL and at the National Energy Research Scientific Computing Center (NERSC).