Research

The research activity of the Computational Spintronics group is centered over two main areas: the atomistic modeling of both materials properties and nano-scale devices, and the development of novel, efficient and practical algorithms needed for such a modeling. The main current research areas are described here.

• The Smeagol project
• The magnetism of diluted and defective wide-gap semiconductors
• Magnetic nano-structures for spintronics applications
• Organic Spintronics
• Time dependent spin-dynamics
• Development and implementation of DFT-based advanced numerical methods
• 1D semiconductor nanostructures

The Smeagol project

The Computational Spintronics group develops and maintains the Smeagol code . This is a state of the art quantum transport code combining the non-equilibrium Green's functions method for transport with density functional theory. The code is distributed freely to the Academic community and at present it counts over 100 users distributed over the 5 continents. The core of the code is an efficient algorithm for calculating the Green's function, G, of a scattering region in the presence of two current-voltage probe (see figure 1). Such a core algorithm is currently interfaced with the efficient density functional theory code Siesta , although other interfaces are under construction. The code allows the calculations of the I-V characteristics of nano-scale devices from first principles, i.e. without the need of adjustable parameters derived from experiments. Crucially, both the current and the potential drop in a junction are the output of the calculation, which therefore has full prediction power. In recent times Smeagol has been optimized to run over large-scale computational infrastructures. This has been achieved through collaborations with the Trinity Center for High Performance Computing (TCHPC) , the Irish Center for High End Computing (ICHEC) and IBM.

Schematic two-probe device simulated by the Smeagol code. The yellow two boxes represent the unit cell of the electrodes, while the colored area is the scattering region.

As flagship demonstration of the capability of Smeagol we wish to mention some recent work aimed at predicting and explaining the longitudinal transport properties of polymeric poly(G)-poly(C) DNA strands. Typical calculations are performed for unit cells containing over 2000 atoms and counting more then 10,000 atomic orbital basis functions (see figure 2). An I-V characteristic usually requires about 2 running days over 512 CPUs for each bias point. The main conclusion of our investigation is the demonstration that band conduction is not responsible for longitudinal DNA transport. For short strands direct tunneling between the electrodes across the DNA dominates the low voltage transport, but for longer strands such a mechanism is ineffective and it is replaced by incoherent hopping conductance.

Two terminal device in which the scattering region is a poly(G)-poly(C) DNA strand.

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The magnetism of diluted and defective wide-gap semiconductors

The goal of integrating memory and logic operations on the same device is the main engine driving the field of spintronics. This requires the synthesis of novel materials displaying both semiconducting properties and magnetism, possibly at room temperature. An important class of such materials is formed by conventional oxides doped with transition metal ions, for which the claims of room temperature ferromagnetism are numerous in literature. However, despite these claims, the understanding of such materials remains at best incomplete. To complicate the situation conventional first principles theoretical modeling, using DFT with local and semi-local approximations of the exchange and correlation functional, provides a wrong starting point. In fact the considerable underestimation of the native oxide band-gap often returns an incorrect occupation of the transition metal dopant d-shell and consequentially the ferromagnetism is erroneously predicted.

Our research in the area has as a starting point the band description obtained with an approximated atomic self-interaction corrected (ASIC) scheme to DFT. This returns band-gaps in excellent agreement with the experimental values and a qualitative and quantitative accurate description of both the local environment and the magnetic coupling between the transition metal dopants. In general we find that, once the ASIC method is employed, carrier mediated mechanisms are not justified and sustainable and the ferromagnetism becomes extremely fragile. In particular our recent interest has been focussed to ZnO:Co and to the so called d0 magnets.

We have recently demonstrate that the magnetism in ZnO:Co does not originate from Co2+ ions doped in the ZnO matrix but instead from Co2+ oxygen-vacancy pairs with a partially filled level close to the ZnO conduction band minimum. The magnetic interaction between these pairs is sufficiently long-ranged to cause percolation at moderate concentrations (>7%). However, magnetically correlated clusters large enough to show hysteresis at room temperature already form below the percolation threshold and may explain the current controversial experimental findings. Our work demonstrates that the magnetism in ZnO:Co is entirely governed by intrinsic defects and a phase diagram is proposed (see figure 1). This suggests a recipe for tailoring the magnetic properties of spintronics materials by controlling their intrinsic defects. Additional work has been devoted to investigate the uncompensated magnetism at the surface of CoO wurtzite polymorphs and to simulate by Monte Carlo methods hysteresis loops of nanoclusters.

Phase diagram ZnO:Co as a function of Co2+ and Co2+ oxygen (CoV) pairs concentration [taken from Phys. Rev. B 78, 054428, (2008)].

d0 magnets are materials, which display a magnetic response despite the fact they do not contain any ions with partially filled d or f shells. Usually the magnetism is attributed to 2p orbitals, but predicting magnetism originating from 2p orbitals is a delicate problem, which depends on the subtle interplay between covalency and Hund's coupling. Calculations based on density functional theory and the local density approximation fail in two remarkably different ways. On the one hand the excessive delocalization of spin-polarized holes leads to half-metallic ground states and the expectation of room temperature ferromagnetism. On the other hand, a magnetic ground state may not be predicted at all. Our recent research demonstrate that a simple self-interaction correction scheme modifies both these situations via an enhanced localization of the holes responsible for the magnetism and possibly Jahn-Teller distortion. In both cases the ground state becomes insulating and the magnetic coupling between the impurities weak.

Isosurface of the hole (the magnetization) associated to ZnGa in GaN as calculated with LSDA (left) and ASIC (right). In LDA the hole is unpolarized and distributed uniformly over all the four N ions surrounding the vacancy, while it spin-splits and localizes around the longer bond in ASIC.

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Magnetic nano-structures for spintronics applications

The discovery of the giant magnetoresistance (GMR) effect has revolutionarized the data storage industry since it has enabled the construction of ultra-sensitive magnetic field sensors. The workhorse device in the field is the spin-valve. This is formed by two magnetic layers sandwiching a non-magnetic spacer. In a spin-valve the mutual orientation of the magnetization vectors of the magnetic layers determines the resistance of the device itself. Currently the most popular choice for the spacer are wide gap oxides, so that the spin-valve is a tunnel junctions. In particular the Fe/MgO/Fe combination is to date the one showing the largest effect, due to the peculiar electronic structure of the constituting materials when the device is grown along the bcc [100] direction. Our research activity in the area is focussed onto two main aspects: 1) the investigation of the main materials factors affecting the GMR in Fe/MgO/Fe[100], 2) the exploration of different materials for the spacer, in particular of materials displaying an intrinsic order parameter (magnetism, ferroelectricity, piezoelectricity).

Our research on the Fe/MgO/Fe[100] system is concentrated in predicting I-V characteristics under different conditions. In particular we have recently demonstrated that for perfectly crystalline junctions and voltages smaller than 20 mVolt the I-V characteristics and the GMR are dominated by resonant transport through narrow interface states in the minority spin-band. In the parallel configuration this contribution is quenched by a voltage comparable to the energy width of the interface state, whereas it persists at all voltages in the anti-parallel configuration. At higher bias the transport is mainly determined by the relative positions of the Δ1 band-edge in the two Fe electrodes, which causes a decrease of the GMR. In addition we have explored the role of defects in the barrier and concluded that both Mg and O vacancies are scattering centers that strongly reduce the polarization of the junction and consequently the GMR. Similarly we have investigated the role of metallic non-magnetic interlayers intercalated between the magnetic electrodes and the barrier and demonstrated an oscillatory behaviour of both the conductivity and the GMR as a function of the interlayer thickness (in collaboration with the group of Meb Alouani at CNRS Strasbourg, France). Finally we have conducted pioneering calculations for double tunnel junctions and demonstrated the importance of quantum wells located in between the barriers over the transport properties.

Bound interfacial states of a Fe/MgO/Fe(100) magnetic tunnel junction.

Our seminal work on multifunctional magnetic tunnel junctions has initially considered SrRuO3/BaTiO3/SrRuO3 and Fe/BaTiO3/Fe junctions where the insulating BaTiO3 spacer undergoes a paraelectric to ferroelectric transtion when its thickness is increased over a few nm. We have first evaluated the structural properties of these two devices. This has proved a difficult theoretical task. Standard local exchange and correlation functional to DFT in fact return good structural properties but bad band alignment, in contrast our ASIC scheme returns good band alignment but the ferroelectricity of BaTiO3 is severely underestimated. Our working strategy is then to compute the structure with LDA/GGA and the transport with ASIC. Preliminary transport calculations for the SrRuO3/BaTiO3/SrRuO3 system in the paraelectric state reveal huge GMRs.

Transmission coefficient maps over the 2D Brillouin zone transverse to the transport direction for a SrRuO3/BaTiO3/SrRuO3 tunnel junction as a function of the energy. Yellow areas indicate large transmission while dark regions are for weak.

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Organic Spintronics

The spin properties of non-magnetic organic materials are unique to the materials world. In particular molecules present extremely long spin relaxation times, TS (the average time an electron spin takes to change it initial direction), but due to the typical low mobility, rather short spin relaxation lengths, lS (the average distance an electron spin travels before changing its direction). This fact is mostly due to the lack of substantial spin-orbit and hyperfine interaction in organics, which makes them an interesting playground for spintronics. The field has recently broadened up and includes the study of the spin-transport properties of magnetic molecules, the magnetoresistance in organic layers, and more generally the investigation of planar self-assembled layers of organometallic molecules on surfaces.

Diagram displaying the spin relaxation time, TS, and the spin relaxation length, lS, for a selection of materials both organic (blue dots) and inorganic (black, red and green dots). Data are plotted from [S. Sanvito, J. Mater. Chem. (Highlight), 17, 4455, (2007)].

In our group the research on organic spintronic develops along three main directions: 1) first principles calculations of exchange coupling and spin-transport in organic spin-valves, 2) construction of transport models based on parameterized Hamiltonian for diffusive spin-transport in large organic media and 3) STM simulations of organometallic molecules on metallic surfaces.

For first research line Smeagol is our main theoretical tool. At the moment we are exploring tunneling junctions made of magnetic electrodes sandwiching an organic molecule, or of non-magnetic electrodes sandwiching a magnetic molecule. In the first case the magnetoresistance is that of a typical spin-valves, while in the second it is the magnetic state of the molecule itself to determine the current flowing across the device. In most cases the calculations are rather numerical intensive since the typical unit cells are large and one need to take into account spin-polarization. As a flagship result, we have demonstrated that the magnetic state of a Mn12 molecule can be deduced from the detailed knowledge of the I-V characteristic of a two-terminal device sandwiching the molecule. Most importantly for the identification of the magnetic state of the molecule the electrodes do not need to be ferromagnetic.

In contrast organometallic molecules on surfaces are investigated with standard DFT calculations. STM simulations are conducted in the Tersoff-Hamann spirit, where one just needs the local density of states of the molecule and of the scanning tip to determine two-dimensional current maps. These images are then compared to experimental STM pictures obtained by our partners.

Simulated STM topographic image for a Cu-Salen molecule deposited on a Cu(111) surface.

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Time dependent spin-dynamics

In the mid nineties Slonczewski and Berger predicted the possibility of inducing spin-dynamics by means of spin-polarised current. This effectively was the prediction of the “inverse” GMR effect, i.e. the prediction that a spin-polarised current could change the magnetic state of a device. The essential idea is that a spin-polarised current can transfer angular momentum to the magnetisation of a magnetic system, thus generating a torque. In the right conditions this current-induced torque can balance or even surpass the magnetic Gilbert damping, thus creating new dynamical solutions to the equations of motions for the magnetisation. Magnetic switching, magnetic resonator and enhanced Gilbert damping can all be generated by a spin-polarised current. Importantly the current-induced torque does depend on the current density and not on the total current. This clearly opens new prospects for switching MRAM, and largely justifies the growing interest for this area of research.

In our group we have a large activity focused on developing both static and time-dependent methods at the atomic level for describing spin-dynamics in nano-scale magnets either in the presence or absence of an electrical current. In this area we work with both model Hamiltonians combining a quantum description of the current-carrying electrons and classical spins providing the magnetic moments, and with time-dependent density functional theory. Note that in general there are no fundamental obstacles to molecular dynamics involving spins. Ultra-fast spin-switching in the pico-second range has been demonstrated, indicating that the fastest time-scale of atomic spin-dynamics is indeed in (or below) the pico-second range. Since the typical time scale for electronic processes is in the fempto-second range, one needs between 103 to 105 time steps to evolve the electronic structure to times relevant for the spin-dynamics. This is well in reach of state of the art time integration techniques.

Examples of spin-wave dispersion obtained by Fourier-transforming the time-dependent spin-dynamics of a magnetic single-atom nanowire. Different panels represent wires of different lengths. The top panels are for no exchange coupling between conductive electrons and local spins, while in the lower panels the coupling is switched on.

Examples of how time-dependent spin-dynamics can be used are the calculation of spin-wave dispersion in magnetic nanowires, the study of current-induced domain wall motion and the study of the spin-dynamics of magnetic atoms immersed in a paramagnetic metal. With these techniques recently we have investigated the so called “spin motive force” in magnetic nanowires. This is the generation of a net electrical potential across a nanowires, due to the time-dependent dynamics of its magnetization, in our case the precession of a domain-wall. In particular, in contrast to previous explanations, we proved that this is an entirely classical effect, which originates from the adiabatic motion of magnetic dipoles in a magnetic media, whose magnetic “texture” changes in time.

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Development and implementation of DFT-based advanced numerical methods

Density functional theory is today the most versatile and still advanced theory for solid state and molecular modeling. However it suffers from a number of shortfalls that make the prediction of “critical” materials more problematic. One problem over all is the inability of the most common approximations to the exchange and correlation potential (local density approximation and generalized gradient approximation) to describe accurately localized states. This problem reflects into the erroneous prediction of Mott insulator as metallic, in the usually large overestimation of molecule polarizability and in a number of other problems. Some of these shortfalls can be traced back to the self-interaction error, i.e. to the spurious interaction of electrons with the electrostatic and exchange and correlation potential generated by themselves. In our group we investigate some of these problems. Our general research strategy in the area is twofold.

On the one hand we implement and develop orbital dependent functionals (self-interaction corrected LDA, exact exchange) in the spirit of the optimized effective potential method. These are self-interaction free either by construction or at least to a good level of approximation. On the other hand we work on approximated, but computational inexpensive, schemes to be employed in specific situations (LDA+U, ASIC method). Importantly it is the interplay between these two research activities that makes the progress faster and more effective. Also important it is the fact that our methods are implemented in the DFT platform, which is also used by the Smeagol code. This means that any new development in the DFT area is readily transferable to electron transport problems.

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1D semiconductor nanostructures

One-dimensional objects present physical properties completely different from those of their 2D and 3D counterparts. Most of the electronic ones originate from quantum confinement, however other effects such as the large surface to volume fraction can also drastically change the chemical reactivity and in general the ability of 1D objects to interact with their external environment.

Our current research interest is on semiconducting structures. In particular we are exploring the possibility of using the naturally occurring 1D wires at the surface of Si (100) layers.

Wave function isosurface plot for the first surface sub-bands of the Si (100) p(2x2) reconstructed surface.

Our research is sponsored by