Derivation of the spin Hamiltonians for Fe in MgO

A method to calculate the effective spin Hamiltonian for a transition metal impurity in a non- magnetic insulating host is presented and applied to the paradigmatic case of Fe in MgO. In a first step we calculate the electronic structure employing standard density functional theory (DFT), based on generalized-gradient approximation (GGA), using plane waves as a basis set. The corresponding basis of atomic-like maximally localized Wannier functions is derived and used to represent the DFT Hamiltonian, resulting in a tight-binding model for the atomic orbitals of the magnetic impurity. The third step is to solve, by exact numerical diagonalization, the N electron problem in the open shell of the magnetic atom, including both effect of spin-orbit and Coulomb repulsion. Finally, the low energy sector of this multi-electron Hamiltonian is mapped into effective spin models that, in addition to the spin matrices S, can also include the orbital angular momentum L when appropriate. We successfully apply the method to Fe in MgO, considering both, the undistorted and Jahn-Teller (JT) distorted cases. Implications for the influence of Fe impurities on the performance of magnetic tunnel junctions based on MgO are discussed.Comment: 10 pages, 7 Figure

Electronic properties of transition metal atoms on Cu2_2N/Cu(100)

We study the nature of spin excitations of individual transition metal atoms (Ti, V, Cr, Mn, Fe, Co and Ni) deposited on a Cu$_2$N/Cu(100) surface using both spin-polarized density functional theory (DFT) and exact diagonalization of an Anderson model derived from DFT. We use DFT to compare the structural, electronic and magnetic properties of different transition metal adatoms on the surface. We find that the average occupation of the transition metal d shell, main contributor to the magnetic moment, is not quantized, in contrast with the quantized spin in the model Hamiltonians that successfully describe spin excitations in this system. In order to reconcile these two pictures, we build a multi-orbital Anderson Hamiltonian for the d shell of the transition metal hybridized with the p orbitals of the adjacent Nitrogen atoms, by means of maximally localized Wannier function representation of the DFT Hamiltonian. The exact solutions of this model have quantized total spin, without quantized charge at the d shell. We propose that the quantized spin of the models actually belongs to many-body states with two different charge configurations in the d shell, hybridized with the p orbital of the adjacent Nitrogen atoms. This scenario implies that the measured spin excitations are not fully localized at the transition metal.Comment: 12 pages, 14 figures, regular articl

Electronic properties of transition metal atoms on Cu2_2N/Cu(100)

We study the nature of spin excitations of individual transition metal atoms (Ti, V, Cr, Mn, Fe, Co and Ni) deposited on a Cu$_2$N/Cu(100) surface using both spin-polarized density functional theory (DFT) and exact diagonalization of an Anderson model derived from DFT. We use DFT to compare the structural, electronic and magnetic properties of different transition metal adatoms on the surface. We find that the average occupation of the transition metal d shell, main contributor to the magnetic moment, is not quantized, in contrast with the quantized spin in the model Hamiltonians that successfully describe spin excitations in this system. In order to reconcile these two pictures, we build a multi-orbital Anderson Hamiltonian for the d shell of the transition metal hybridized with the p orbitals of the adjacent Nitrogen atoms, by means of maximally localized Wannier function representation of the DFT Hamiltonian. The exact solutions of this model have quantized total spin, without quantized charge at the d shell. We propose that the quantized spin of the models actually belongs to many-body states with two different charge configurations in the d shell, hybridized with the p orbital of the adjacent Nitrogen atoms. This scenario implies that the measured spin excitations are not fully localized at the transition metal.Comment: 12 pages, 14 figures, regular articl

One-to-one correspondence between thermal structure factors and coupling constants of general bilinear Hamiltonians

A theorem that establishes a one-to-one relation between zero-temperature static spin-spin correlators and coupling constants for a general class of quantum spin Hamiltonians bilinear in the spin operators has been recently established by Quintanilla, using an argument in the spirit of the Hohenberg-Kohn theorem in density functional theory. Quintanilla's theorem gives a firm theoretical foundation to quantum spin Hamiltonian learning using spin structure factors as input data. Here we extend the validity of the theorem in two directions. First, following the same approach as Mermin, the proof is extended to the case of finite-temperature spin structure factors, thus ensuring that the application of this theorem to experimental data is sound. Second, we note that this theorem applies to all types of Hamiltonians expressed as sums of bilinear operators, so that it can also relate the density-density correlators to the Coulomb matrix elements for interacting electrons in the lowest Landau level.J.F.R. acknowledges financial support from FCT (Grant No. PTDC/FIS-MAC/2045/2021), FEDER / Junta de Andalucía — Consejería de Transformación Económica, Industria, Conocimiento y Universidades, (Grant No. P18-FR-4834), and Generalitat Valenciana funding Prometeo20XXX, MICIIN-Spain (Grant No. PID2019-109539GB-C41). B.M. acknowledges support from the FCT PhD Scholarship No. SFRH/BD/08444/2020

Colossal anisotropy in diluted magnetic topological insulators

We consider dilute magnetic doping in the surface of a three dimensional topological insulator where a two dimensional Dirac electron gas resides. We find that exchange coupling between magnetic atoms and the Dirac electrons has a strong and peculiar effect on both. First, the exchange-induced single ion magnetic anisotropy is very large and favors off-plane orientation. In the case of a ferromagnetically ordered phase, we find a colossal magnetic anisotropy energy, of the order of the critical temperature. Second, a persistent electronic current circulates around the magnetic atom and, in the case of a ferromagnetic phase, around the edges of the surface.This work has been financially supported by MEC-Spain (Grant Nos MAT07-67845, FIS2010-21883-C02-01 and CONSOLIDER CSD2007-0010), by Proyecto de Iniciación en Investigación Fondecyt 11070008 and by Núcleo Científico Milenio “Magnetismo Básico y/o Aplicado” P06022-F. ASN acknowledges funding from Universidad de Alicante

From Heisenberg to Hubbard: An initial state for the shallow quantum simulation of correlated electrons

The widespread use of the noninteracting ground state as the initial state for the digital quantum simulation of the Fermi-Hubbard model is largely due to the scarcity of alternative easy-to-prepare approximations to the exact ground state in the literature. Exploiting the fact that the spin- 1/2 Heisenberg model is the effective low-energy theory of the Fermi-Hubbard model at half-filling in the strongly interacting limit, here we propose a three-step deterministic quantum routine to prepare an educated guess of the ground state of the Fermi-Hubbard model through a shallow circuit suitable for near-term quantum hardware. First, the ground state of the Heisenberg model is initialized via a hybrid variational method using an ansatz that explores only the correct symmetry subspace. Second, a general method is devised to convert a multi-spin- 1/2 wave function into its fermionic version. Third, taking inspiration from the Baeriswyl ansatz, a constant-depth single-parameter layer that adds doubloon-holon pairs is applied to this fermionic state. Numerical simulations on chains and ladders with up to 12 sites confirm the improvement over the noninteracting ground state of the overlap with the exact ground state for the intermediate values of the interaction strength at which quantum simulation is found to be most relevant. More broadly, the general scheme to convert a multi-spin- 1/2 state into a half-filled fermionic state may bridge the gap between quantum spin models and lattice models of correlated fermions in the realm of digital quantum simulation.B.M. acknowledges financial support from Fundação para a Ciência e a Tecnologia (FCT)–Portugal through Ph.D. Scholarship No. SFRH/BD/08444/2020. J.F.R. acknowledges financial support from FCT (Grant No. PTDC/FISMAC/2045/2021), the Generalitat Valenciana funding No. Prometeo2021/017 and No. MFA/2022/045, and funding from MICIIN-Spain (Grants No. PID2019-109539GB-C41 and No. PID2022-141712NB-C22)

From Heisenberg to Hubbard: An initial state for the shallow quantum simulation of correlated electrons

The widespread use of the noninteracting ground state as the initial state for the digital quantum simulation of the Fermi-Hubbard model is largely due to the scarcity of alternative easy-to-prepare approximations to the exact ground state in the literature. Exploiting the fact that the spin-$\frac{1}{2}$ Heisenberg model is the effective low-energy theory of the Fermi-Hubbard model at half-filling in the strongly interacting limit, here we propose a three-step deterministic quantum routine to prepare an educated guess of the ground state of the Fermi-Hubbard model through a shallow circuit suitable for near-term quantum hardware. First, the ground state of the Heisenberg model is initialized via a hybrid variational method using an ansatz that explores only the correct symmetry subspace. Second, a general method is devised to convert a multi-spin-$\frac{1}{2}$ wave function into its fermionic version. Third, taking inspiration from the Baeriswyl ansatz, a constant-depth single-parameter layer that adds doublon-holon pairs is applied to this fermionic state. Numerical simulations on chains and ladders with up to 12 sites confirm the improvement over the noninteracting ground state of the overlap with the exact ground state for the intermediate values of the interaction strength at which quantum simulation is bound to be most relevant.Comment: Main text: 4 pages, 3 figures. Supp. Mat.: 10 pages, 9 figure

Magnetic Edge Anisotropy in Graphenelike Honeycomb Crystals

The independent predictions of edge ferromagnetism and the quantum spin Hall phase in graphene have inspired the quest of other two-dimensional honeycomb systems, such as silicene, germanene, stanene, iridates, and organometallic lattices, as well as artificial superlattices, all of them with electronic properties analogous to those of graphene, but a larger spin-orbit coupling. Here, we study the interplay of ferromagnetic order and spin-orbit interactions at the zigzag edges of these graphenelike systems. We find an in-plane magnetic anisotropy that opens a gap in the otherwise conducting edge channels that should result in large changes of electronic properties upon rotation of the magnetization.J. F. R. acknowledges financial support by MEC-Spain (FIS2010-21883-C02-01) and Generalitat Valenciana (ACOMP/2010/070), Prometeo. This work has been financially supported in part by FEDER funds. We acknowledge financial support by Marie-Curie-ITN 607904-SPINOGRAPH

Single-electron transport in electrically tunable nanomagnets

We study a single-electron transistor (SET) based upon a II–VI semiconductor quantum dot doped with a single-Mn ion. We present evidence that this system behaves like a quantum nanomagnet whose total spin and magnetic anisotropy depend dramatically both on the number of carriers and their orbital nature. Thereby, the magnetic properties of the nanomagnet can be controlled electrically. Conversely, the electrical properties of this SET depend on the quantum state of the Mn spin, giving rise to spin-dependent charging energies and hysteresis in the Coulomb blockade oscillations of the linear conductance.This work has been financially supported by MEC-Spain (Grants No. FIS200402356, No. MAT2005-07369-C03-03, and the Ramon y Cajal Program) and by CAV (No. GV05-152)

Spin decoherence of magnetic atoms on surfaces

We review the problem of spin decoherence of magnetic atoms deposited on a surface. Recent breakthroughs in scanning tunnelling microscopy (STM) make it possible to probe the spin dynamics of individual atoms, either isolated or integrated in nanoengineered spin structures. Transport pump and probe techniques with spin polarized tips permit measuring the spin relaxation time T1T1, while novel demonstration of electrically driven STM single spin resonance has provided a direct measurement of the spin coherence time T2T2 of an individual magnetic adatom. Here we address the problem of spin decoherence from the theoretical point of view. First we provide a short general overview of decoherence in open quantum systems and we discuss with some detail ambiguities that arise in the case of degenerate spectra, relevant for magnetic atoms. Second, we address the physical mechanisms that allows probing the spin coherence of magnetic atoms on surfaces. Third, we discuss the main spin decoherence mechanisms at work on a surface, most notably, Kondo interaction, but also spin–phonon coupling and dephasing by Johnson noise. Finally, we briefly discuss the implications in the broader context of quantum technologies.JFR acknowledges financial supported by MEC-Spain (FIS2013-47328-C2-2-P) and Generalitat Valenciana (ACOMP/2010/070), Prometeo. This work is funded by ERDF funds through the Portuguese Operational Program for Competitiveness and Internationalization COMPETE 2020, and National Funds through FCT – The Portuguese Foundation for Science and Technology, under the project ‘‘PTDC/FIS-N AN/4662/2014” (016656). FD acknowledges funding by the Ministerio de Economía y Competitividad (MINECO, Spain), with grant MAT2015-66888-C3-2-R., and Gobierno Vasco by grant IT986-16