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Spin-orbit coupling gives rise to a range of spin-charge interconversion phenomena in non-magnetic systems where certain spatial symmetries are reduced or absent. Chirality-induced spin selectivity (CISS), a term that generically refers to a spin-dependent electron transfer in non-magnetic chiral systems, is one such case, appearing in a variety of seemingly unrelated situations ranging from inorganic materials to molecular devices. In particular, the origin of CISS in molecular junctions is a matter of an intense current debate. Here we derive a set of geometrical conditions for this effect to appear, hinting at the fundamental role of symmetries beyond otherwise relevant quantitative issues. Our approach, which draws on the use of point-group symmetries within the scattering formalism for transport, shows that electrode symmetries are as important as those of the molecule when it comes to the emergence of a spin-polarization and, by extension, to the possible appearance of CISS. It turns out that standalone metallic nanocontacts can exhibit spin-polarization when relative rotations which reduce the symmetry are introduced. As a corollary, molecular junctions with $\textbf{achiral}$ molecules can also exhibit spin-polarization along the direction of transport, provided that the whole junction is chiral in a specific way. This formalism also allows the prediction of qualitative changes of the spin-polarization upon substitution of a chiral molecule in the junction with its enantiomeric partner. Quantum transport calculations based on density functional theory corroborate all of our predictions and provide further quantitative insight within the single-particle framework., 34 pages, 4 figures, 1 table

Low-temperature scanning tunneling microscopy is used here to study the dynamic bonding of gold atoms on surfaces under low coordination conditions. In the experiments, using an atomically sharp gold tip, a gold adatom is deposited onto a gold surface with atomic precision either on the first hollow site near a step edge or far away from it. Classical molecular dynamics simulations at 4.2 K and density-functional theory calculations serve to elucidate the difference in the bonding behavior between these two different placements, while also providing information on the crystalline classification of the STM tips based on their experimental performance. This work was supported by the Generalitat Valenciana through Grants No. CDEIGENT/2018/028, No. PROMETEO/2017/139, and No. PROMETEO/2021/017. The authors also acknowledge financial support from Spanish MICIN through Grant No. PID2019-109539 GB-C43, the María de Maeztu Program for Units of Excellence in R&D (Grant No. CEX2018-000805-M), the Comunidad Autónoma de Madrid through the Nanomag COST-CM Program (Grant No. S2018/NMT-4321). The theoretical modeling was performed on the high-performance computing facilities of the University of South Africa and the University of Alicante. Netherlands Organization for Scientific Research (NWO/OCW) supported the experiments.

We report a first-principles investigation of the structural, electronic and magnetic properties of cobalt–vacancy defect complexes in graphene, within the framework of density-functional theory (DFT), incorporating DFT+U. Specifically, we consider the interactions of cobalt and vacancies in graphene, at varying separations and sub-lattices. We show that it is energetically favorable for substitutional Co in graphene to trap an additional vacancy in graphene, forming a Co–vacancy complex. In all the configurations considered, the most stable configuration is when the Co atom is embedded in a divacancy. The magnetic moment induced on the cobalt atom varies as the vacancy–cobalt separation changes, depending not only on the separation, but also on the sub-lattice of the vacancy relative to cobalt. Furthermore, for each separation and sub-lattice considered, the linear density of states of graphene is modified such that Dirac point is either not discernible or has shifted above the Fermi energy. Since individual vacancies or transition metal (TM) atoms, such as cobalt in graphene, have mostly been studied in isolation up to now, ignoring possible transition metal–vacancy interactions, these results have important implications to the fundamental understanding of TM–vacancy defect interactions in graphene.

Our analysis of the contact formation processes undergone by Au, Ag and Cu nanojunctions, reveals that the distance at which the two closest atoms on a pair of opposing electrodes jump into contact is, on average, two times longer for Au than either Ag or Cu. This suggests the existence of a longer range interaction between those two atoms in the case of Au, a result of the significant relativistic energy contributions to the electronic structure of this metal, as confirmed by ab initio calculations. Once in the contact regime, the differences between Au, Ag and Cu are subtle, and the conductance of single-atom contacts for metals of similar chemical valence is mostly determined by geometry and coordination., 4 pages, 4 figures

We present a first principles study of Cu in diamond using DFT+U electronic structure methods, by carefully considering the impact of co-doping, charge state, and Fermi level position on its stability, lattice location, spin states, and electronic properties. We show that the energetic stability and spin states of Cu are strongly dependent on the Fermi level position and the type of diamond co-doping, with Cu being energetically more favorable in n-type or p-type co-doped diamond compared to intrinsic diamond. Since Cu has been predicted to order magnetically in a number of other wide band-gap semiconductors, we have also evaluated this possibility for Cu doped diamond. We show that while Cu exhibits strong spin interactions at specific interatomic separations in diamond, a detailed consideration of the impact of Fermi level position and Cu aggregation precludes magnetic ordering, with Cu forming non-magnetic, antiferromagnetic, or paramagnetic clusters. These results have important implications in the un...

The shallow n-type doping of boron doped diamond with an excess of deuterium has attracted considerable attention. However, despite numerous studies, the nature of this donor is the subject of continued debate. We show that BH 2 possesses a substantial number of metastable states, which are likely to play a role in the properties of the BH 2 defect, and that it is possible in principle for these higher energy metastable structures to be reached. The levels induced by these metastable BH 2 defects are shown to be shallower than the original deep BH 2 levels, but still deeper than the experimentally observed donor levels. We also report spin density distributions of BH 2 centres, which may be compared with experiment, towards establishing the nature of the new donor.

Diamond is a promising candidate material for high power, high temperature and high frequency electronics. Boron is well known as a shallow acceptor in diamond. Recently diamond has been successfully shallow n-type doped by introducing an excess of deuterium in high quality B doped diamond, enabling a reversible p-type to n-type conversion of B doped diamond. However, the nature of this new shallow donor has been the subject of debate. We calculate the properties of boron and its complexes with hydrogen in diamond, using accurate ab initio plane wave Density Functional Theory (DFT) methods, and show that BH2 centres are stable with small binding energies of 0.23 to 0.71 eV, consistent with experimentally observed dissociation of the new donor at relatively low temperatures of 200 °C, and explain the two-step deuteration process in high quality boron doped diamond. Our ab initio Plane Wave periodic supercell DFT theory calculations confirm the existence of a BH induced level at Ec – 0.96 eV. We further show that the BH2 centre possesses a very deep donor level, excluding the possibility of BH2 doping the BH impurity band previously suggested. To facilitate experimental determination of the nature of the new shallow donor, we determine the Local Vibrational Modes of BH and BH2 centres in different charge states, together with isotope shifts, which may be compared with experiment, towards establishing the nature of the new donor.

Although diamond has been successfully n-type doped with phosphorus, the search for shallower n-type dopants in diamond has continued. Interstitial Li and Na have been predicted to be shallow donors, however, experimental results have been contradictory. Aluminum, if incorporated, may be expected to form an acceptor in the same way as boron, and it too was modeled here. We report ab initio Density Functional Theory modeling of Li, Na and Al in diamond and show that although interstitial lithium and sodium are shallow donors, interstitial Li will readily diffuse and that it is favorable for migrating Li to be trapped at vacancies. The resulting substitutional Li is not only passivated but also compensates remaining interstitial donors, explaining the high resistivity or electrical inactivity observed in Li doped diamond. Na is shown to be most stable as a substitutional acceptor, in agreement with Na diffusing as a negative ion in diamond. Substitutional aluminum is found to induce a deep acceptor level in the band gap, much deeper than the boron acceptor level, inducing greater distortion of the host lattice.

Interstitial Li and Na have been suggested as alternatives for achieving shallow n-type doping of diamond. Experimental results have however been contradictory. We report ab initio density functional theory modeling of Li and Na in diamond and compare results using periodic pseudopotential plane wave, and all-electron APW + lo methods together with finite clusters using Gaussian basis sets. We show that although interstitial Li and Na are likely to behave as shallow donors, interstitial Li readily diffuses and it is energetically favorable for interstitial Li and Na to be trapped at existing vacancies in diamond. The resulting substitutional centers are not only passivated but also compensate other interstitial Li and Na donors. Na is shown to be incorporated in diamond as a substitutional acceptor, consistent with experimental observations.

Ferromagnetic ordering of transition metal dopants in semiconductors holds the prospect of combining the capabilities of semiconductors and magnetic systems in single hybrid devices for spintronic applications. Various semiconductors have so far been considered for spintronic applications, but low Curie temperatures have hindered room temperature applications. We report ab initio DFT calculations on the stability and magnetic properties of Fe and Cr impurities in diamond, and show that their ground state magnetic ordering and stabilization energies depend strongly on the charge state and type of co-doping. We predict that divacancy Cr+2 and substitutional Fe+1 order ferromagnetically in p-type diamond, with magnetic stabilization energies (and magnetic moment per impurity ion) of 16.9 meV (2.5 μB) and 33.3 meV (1.0 μB), respectively. These magnetic stabilization energies are much larger than what has been achieved in other semiconductors at comparable impurity concentrations, including the archetypal dilu...

We report ab initio pseudopotential DFT calculations on the energetic stability and magnetic ordering of Cr in diamond at various lattice sites and charge states and show that Cr is most stable at the divacancy site in diamond, with the lowest formation energy occurring in $n$- or $p$-type diamond, compared to intrinsic diamond. The incorporation of Cr introduces strongly spin polarized impurity bands into the diamond band gap, with both the spin polarization and magnetic stabilization energies critically dependent on the charge state of Cr and the position of the Fermi level in diamond. In $p$-type diamond, we predict Cr${}^{+2}$ at the divacancy site possesses a ferromagnetic stabilization energy of 17 meV and magnetic moment of 2.5 ${\ensuremath{\mu}}_{\mathrm{B}}$, with Cr in diamond likely to form a diluted ferromagnetic semiconductor, which may successfully be considered for room temperature spintronic applications.

Interstitial lithium and sodium have been suggested as alternatives to phosphorus to achieve shallow $n$-type doping of diamond. Experimental results have, however, been contradictory. We report ab initio density functional theory modeling of lithium and sodium in diamond and show that although interstitial Li and Na are likely to behave as shallow donors, interstitial Li will readily diffuse with a low activation energy and that it is energetically favorable for both species to be trapped at existing vacancies in diamond. The resulting substitutional centers are themselves not only passivated but also induce deep levels in the band gap of diamond, compensating the remaining donors. This explains the high resistivity observed in lithium and sodium doped diamond. This demonstrates that samples should not be exposed to elevated temperatures in order to prevent Li diffusion, while concentrations of vacancies and other defects should be minimized to restrict the formation of compensating substitutional Li acceptors, if $n$-type doping of diamond is to be achieved with Li. For sodium, we show that it is energetically favorable for Na to be incorporated in diamond as a substitutional acceptor rather than as an interstitial donor. This is consistent with experimental observations of Na diffusing as a negative ion under electric bias in diamond. It is therefore unlikely that diamond will be successfully $n$-type doped with Na.

We use ab initio methods to study the binding, diffusion, and magnetic properties of cobalt atom embedded in graphene vacancies. We investigate the diffusion of Co-monovacancy (Co-MV) and Co-divacancy (Co-DV) defect complexes, and determine the minimum energy path (MEP), as well as the activation energy barrier of migration. We obtained similar activation energy barriers, of ∼5.8 eV, for Co-MV and Co-DV diffusion, respectively. Our calculations also suggest that, at electron–irradiation energy of 200 keV as used in a related experiment, the maximum energy transfer to the Co atom, of approximately 9.0 eV is sufficiently high to break metal-carbon bonding. The incident electron energy is also high enough to displace graphene's carbon atoms from their lattice positions. The breaking of metal-carbon bonding and the displacement of graphene atoms may act to facilitate the migration of Co. We conclude therefore that the detrapping and diffusion of cobalt as observed experimentally is likely to be radiation-induced, similar to what has been observed for Au and Fe in electron-irradiated graphene. Furthermore, we show that Co migration in graphene is such that its magnetic moment varies along the diffusion path. The magnetic moment of Co is consistently higher in Co-DV diffusion when compared to that of Co-MV diffusion.

We present ab initio full-potential density functional calculations of the electronic structure of ${\mathrm{Ti}}_{0.0625}{\mathrm{Zn}}_{0.9375}\mathrm{O}$. We show that it is likely for Ti to order ferromagnetically in $\mathrm{ZnO}$, forming a dilute magnetic semiconductor, in agreement with experiment. The ferromagnetic ordering occurs despite Ti being nonmagnetic in its natural phase. ${\mathrm{Ti}}_{0.0625}{\mathrm{Zn}}_{0.9375}\mathrm{O}$ is shown to possess a magnetic moment of $0.63{\ensuremath{\mu}}_{B}$ per supercell, with a spin-polarized impurity band at the bottom of the $\mathrm{ZnO}$ conduction band and the Fermi level lying within the former band. The impurity band is found to primarily arise from the hybridization of the Ti $3d$ level with O $2p$ states.

It is shown that a $4d$ metal (palladium) orders ferromagnetically in GaN, forming a dilute magnetic semiconductor. The ferromagnetic ordering occurs despite Pd being nonmagnetic in its natural phase. ${\mathrm{Pd}}_{0.0625}{\mathrm{Ga}}_{0.9375}\mathrm{N}$ is shown to possess a magnetic moment of $1.3\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}$ per supercell, with a spin-polarized impurity band in the GaN band gap and the Fermi level lying within this band. The impurity band is shown to arise from the hybridization of the Pd $4d$ level with N $2p$ states. Though the largest experimental and theoretical focus up to now has been on $3d$ metals such as Mn in III--V and II--VI semiconductors, the results presented here show that $4d$ metals such as palladium, may also be considered as candidates for ferromagnetic dopants in semiconductors. This broadens the range of dopants which may be taken into account in attempts to overcome technological and other barriers related to the dopants used presently to obtain magnetically ordered semiconductors for potential spintronic applications.

The production of $n$-type doped diamond has proved very difficult. Phosphorus, and possibly sulfur, when in substitutional sites in the lattice, forms a donor which could be used in electronic devices. Boron, which is a relatively shallow acceptor, can be passivated by hydrogen, and it is possible that some of the difficulties in producing electrically active donors could be due to their passivation by the hydrogen which is present during the chemical vapor deposition growth of diamond. We report ab initio modeling of these dopants and their complexes with hydrogen in diamond and show that it is energetically favorable for hydrogen to be trapped and to passivate boron and phosphorus. We predict that sulfur with one hydrogen atom produces shallow donor levels in the band gap of diamond with a previously unconsidered configuration being the most stable and producing the shallowest level. We show that the S-H pair is stable under conditions of limited H availability. Further, we show that it is energetically favorable for both P-H and $\mathrm{P}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ to dissociate forming $\mathrm{H}_{2}{}^{*}$. H diffusion in $n$-type P-doped diamond is inhibited by this formation of immobile $\mathrm{H}_{2}{}^{*}$. This is in contrast to B-doped diamond, where we predict that $\mathrm{H}_{2}{}^{*}$ will dissociate in the presence of substitutional B atoms, forming B-H complexes. We demonstrate that the recently observed shallow $n$-type conductivity is unlikely to arise from $\mathrm{B}\text{\ensuremath{-}}{\mathrm{D}}_{2}$ complexes, because these complexes would dissociate into B-D plus a distant deuterium interstitial. We also predict that they would induce deep levels in the band gap.

Half-metallic ferromagnetic ordering in semiconductors, essential in the emerging field of spintronics for injection and transport of highly spin polarised currents, has up to now been considered mainly in III–V and II–VI materials. However, low Curie temperatures have limited implementation in room temperature device applications. We report ab initio Density Functional Theory calculations on the properties of Fe in diamond, considering the effects of lattice site, charge state, and Fermi level position. We show that the lattice sites and induced magnetic moments of Fe in diamond depend strongly on the Fermi level position and type of diamond co-doping, with Fe being energetically most favorable at the substitutional site in p-type and intrinsic diamond, while it is most stable at a divacancy site in n-type diamond. Fe induces spin polarized bands in the band gap, with strong hybridization between Fe-3d and C-2s,2p bands. We further consider Fe-Fe spin interactions in diamond and show that substitutional ...