Spin transport on magnetic skyrmions. — Magnetic skyrmions are real-space non-collinear spin structures with intriguing properties and they are promising building blocks for high-density information storage and low-power information carrier applications in spintronics due to their small size and topological properties. They are formed of closed magnetic domain walls of diverse complexity in real space, and are characterized by topological invariants. The winding number or topological charge of the three-dimensional spin vectors is the most commonly used quantity. There are several challenges to overcome to be able to use these objects in real device applications: room temperature stability, controlled writing, reading and deleting, moving them by electric currents or other ways, all-electrical detection and manipulation, switching their topological properties, etc. First-principles calculations provide deep insight into the role of antisymmetric Dzyaloshinsky-Moriya, isotropic Heisenberg and symmetric anisotropic magnetic exchange interactions, exchange frustration, higher-order magnetic interactions, and magnetocrystalline anisotropy in the formation of skyrmions in thin magnetic films. Tailoring their dynamical properties requires an advanced understanding of their spin transport, spin dynamics and spin switching properties. Due to their small size a viable route to controllably manipulate their spins is through locally focused perturbations, like laser beams, or scanning probe methods.
Spin-polarized scanning tunneling microscopy (SP-STM) has been extensively used to image (with atomic resolution) and manipulate magnetic skyrmions and other complex magnetic objects at surfaces thanks to atomically sharp scanning tips. The controlled creation and annihilation of skyrmions have been demonstrated by using local current pulses of the tip of an STM with opposite voltage polarities. These effects have been explained by the electric fields in the STM junction, but the roles of the tunneling spin transfer torque (STT) and other spin transport processes in an SP-STM, where the spin-polarized current exerts a torque on the spin moments of the sample, are less understood. This motivated our very recent work , where the tunneling electron spin transport properties of six topologically distinct magnetic skyrmions in an ultrathin film were investigated based on theoretical calculations. An electron tunneling theory for the combined calculation of scalar charge and vector spin transport in SP-STM within the three-dimensional Wentzel-Kramers-Brillouin framework was utilized. The topologies of the maps of the calculated tunneling vector spin transport quantities, the longitudinal spin current (LSC) and the STT, were compared with those of the underlying spin structures, depending on the magnetization orientation of the SP-STM tip. The magnitudes of the spin transport LSC and STT vector quantities exhibit close relations to charge current SP-STM images irrespectively of the skyrmionic topologies. An important quantity, the STT efficiency, measures the exerted torque on the spins of the skyrmionic structures per unit charge current. Such STT efficiency maps were calculated in high spatial resolution for the first time above topologically different skyrmionic spin textures. A great variation of the STT efficiency depending on the lateral position of the SP-STM tip was found, and regions for large values up to ~25 meV/μA (~0.97 h/e) above the rim of the magnetic objects were identified. An illustration of the calculated tunneling electron quantities is given for a selected skyrmionic object in Fig. 1.
Figure 1. Summary of the investigated spin transport properties of magnetic skyrmions  taking an example of an antiskyrmion with topological charge of 2: The spin structure and the topological charge density distribution are shown together with high-resolution tunneling electron charge and spin transport maps calculated with two types (out-of-plane (1st row) and in-plane (2nd row) magnetized) SP-STM tips: charge current (dark: lower, bright: higher apparent height in constant-current mode), longitudinal spin current (LSC) magnitudes and vectors, spin transfer torque (STT) magnitudes and vectors, and STT efficiency. For the magnitudes of the spin transport quantities blue means lower, and red means higher values. For the vector maps the coloring of the vector components corresponds to red: outward, blue: inward, gray: in-plane.
Theoretical contributions to various surface science topics. — Van der Waals-corrected density functional theory (DFT) calculations were performed in collaboration with a Korean group to examine the initial stages of CuI (p-type transparent semiconductor at room temperature) ultrathin film formation on Cu(111) within the framework of ab initio atomistic thermodynamics. Simulated STM images are in good agreement with experimental results. Moreover, it was found that the surface work function is modulated by a competition between charge transfer and polarization effects, which is determined by the local surface structure.
In collaboration with another Korean group, DFT and STM calculations were employed to investigate the strain-induced structural instabilities between triangular and stripe phases in a pristine single layer NbSe2, and to analyze the energy hierarchy of the structural and charge modulations. The observed wavelength of the charge modulation is reproduced with a good accuracy in comparison to experiments.
Azobenzene molecular switch has been studied on h-BN/Rh(111) in collaboration with the University of Szeged. Experimental STM indicated a clear preference for trans-azobenzene adsorption in the pores, manifesting a templating effect, but in some cases one-dimensional molecular stripes also form, implying attractive molecule-molecule interaction. DFT calculations provided further details regarding the adsorption energetics and bonding and confirmed the experimental findings. Based on the results, a mechanism of initial azobenzene molecular growth on the h-BN/Rh(111) nanomesh structure was proposed. Furthermore, DFT calculations were employed to study ethanol adsorption and the decomposition product of atomic hydrogen on pristine h-BN/Rh(111), and also on a Au atomic cluster on h-BN/Rh(111). Strong B-H bonds were found in the absence of gold, and larger negative charges on low-coordinated Au atoms were identified responsible for their enhanced catalytic activity.
In collaboration with a Chinese group, we contributed to the extensive DFT study of finding a favorable transition metal center and pathway of electrocatalytic reduction of nitrogen (N2) for producing ammonia (NH3) at relatively low overpotential and high selectivity with respect to hydrogen evolution in single-atom catalytic systems on a 2D phthalocyanine molecular layer. Mo was found the best performing transition metal atom for this purpose. Moreover, the dipole of the N≡N triple bond in the adsorbed N2 molecule was proposed as a better theoretical indicator for predicting the catalytic performance of active sites in the nitrogen reduction reaction.
Degenerate manifolds in the classical antiferromagnet on the fcc lattice — Even though the earliest works on magnetism on face-centered-cubic lattices have been around for almost a century, quite surprisingly systematic study of the classical phase diagram for exchanges going beyond the second nearest neighbour seems to be missing from the literature. Inspired to fill this gap, we performed a detailed study of the ground-state phase diagram of the classical frustrated Heisenberg model on the fcc lattice. We found quite many exciting results on the way. Most remarkably, we identified points in the phase diagram where the ordering momenta form lines and surfaces in reciprocal space, leading to sub-extensive degeneracy in the ground state manifolds. Writing the Hamiltonian as complete squares of spin motifs, we established a link between the real-space and reciprocal-space structures. Large classical ground-state degeneracies may lead to spin-liquid and spin-nematic phases when quantum effects are turned on. We believe that our results will prompt the community to study the more detailed physics of the Heisenberg model in close to these degenerate manifolds.
Negative thermal expansion in Cr spinel. — Most materials expand when heated and contract when cooled — this is the usual “thermal expansion”. The higher the temperature, the more the atoms move and the more they stretch the bonds between them, making the material expand. Only in a few exceptional cases does a material display “negative thermal expansion” (NTE), expanding as it is cooled. The water shows such a behavior close to freezing, and this made life on Earth possible.
In a paper published in Physical Review Letters , the international team including a researcher from Wigner RCP explains how the magnetic spinel material CdCr2O4 expands upon cooling. Experiments on the Chromium spinel CdCr2O4, carried out by scientists at the High Field Magnetic Laboratory in the Netherlands, reveal that this material also exhibits NTE under specific conditions, namely at low temperatures (below 4K) and high magnetic field (at 30T). This particular property of the CdCr2O4 is explained by the highly frustrated lattice the magnetic chromium ions form. Besides, there is a strong coupling between the lattice and the magnetic ions, called magnetostriction, which helps the spin to satisfy their magnetic energy at the price of deforming the material. Theoretical calculations show that the frustration and the magnetostriction are the key factors that can translate the heat stored in fluctuations of the spin into contraction of the sample, leading to negative thermal expansion.
Figure 1. The magnetization m (left panel) and its temperature derivative (right panel) as a function of magnetic field and temperature. The magnetization is calculated by Monte-Carlo calculations for an effective theoretical model with classical spins and 3456 pyrochlore lattice sites, and is given as a fraction of the saturation magnetization. The negative δm/δT leads to negative thermal expansion ΔL/L in the in the lower part of the half magnetization plateau, and above saturation (L is the linear size of the sample).
Theoretical contributions to various surface science topics. — The coordination-restricted ortho-site C-H bond activation of 1,3-BPyB and 1,4-BPyB molecules on different metal surfaces (Cu, Au) were studied by a combination of scanning tunneling microscopy (STM), non-contact atomic force microscopy (AFM), and density functional theory (DFT) calculations in collaboration with Chinese and German groups . Ultrathin Mo-oxide films on a Au(111) surface were theoretically studied in collaboration with Korean and Australian groups . The synthesis of N-doped single-layer graphene, doping properties, and doping-induced variation of the local work function of graphene have been investigated on the atomic scale by combining STM/STS, X-ray photoelectron spectroscopy (XPS), and DFT calculations in collaboration with USA, Chinese and Korean groups . The Cu2O(111) surface has been studied in collaboration with Korean groups using STM and DFT . The magnetic ground states of linear Fe chains with variable lengths on the Re(0001) superconductor surface and the emergence of chiral multispin interactions were reported in collaboration with the Budapest University of Technology and Economics . Adsorbing individual 3d transition metal atoms (Mn, Fe, Co) on the Re(0001) surface, the Kondo coupling, the magnetic anisotropy, and the Yu-Shiba-Rusinov states were investigated depending on the d-band filling of the adatoms in collaboration with German groups .
Figure 2. STM image of Mn atoms on the surface of Re(0001) .
Mixed phase High Entropy Alloys (HEA). — A new formula was worked out, which made possible for the first time to plan the BCC/FCC phase ratio engeneering in the double-phase region of the High Entropy Alloys (HEA). XRD, magnetization and Mössbauer spectra measurements were carried out to study the FCC to BCC phase transformations for 16 new HEA materials based on Mn-Co-Fe-Ni alloys doped with light and heavy sp elements. This phase transformation can be produced in the non-equilibrium, double-phase range of the composition marked by its Valence Electron Concentration between 7,4 and 7,82. It is our conjecture that new materials for magnetocaloric effect can be found between the metastable BCC phases.
Results in 2018
Multiferroic materials. — During the last few decades, the great potential of multiferroic materials in realizing magnetoelectric memory devices has led to the revival of the magnetoelectric effect and the search for multiferroic compounds. In multiferroics-based memory devices, the writing and reading of magnetic bits by electric field may be realized via the magnetoelectric coupling between the ferromagnetic and ferroelectric orders. However, ferro-ordered phases are extremely sensitive to externals fields. As an alternative approach, information could be stored in antiferromagnetic domains, a concept proposed for metallic compounds in the realm of antiferromagnetic spintronics. We searched whether similar phenomena happen in insulators with coupled antiferromagnetic and antiferroelectric orders. In LiCoPO4 we experimentally demonstrated that the magnetoelectric effect can be exploited not only for the control but also for the identification of antiferromagnetic domains via the strong directional dichroism detected in the THz frequency range -- the absorption coefficients in LiCoPO4 were different for light propagating along and opposite to a given direction in the crystal. Furthermore, we developed a microscopic theory identifying the main microscopic mechanism behind the magnetoeletric effect, which implies that the same effect arises in other antiferromagnets as well. We expect our study will motivate search for multiantiferroic materials. Moreover, the same principle can also be used for the imaging of antiferromagnetic domains with micrometer resolution in these materials via conventional optical absorption measurements.
Superconductivity: We have developed a relativistic spin-polarized microscopic theory for realistic superconducting materials which can treat relativistic effects and superconductivity together with spin and orbital magnetism on the same footing.
As an application, we have studied Nb/Au/Fe heterostructures where long-period oscillations were found in the critical temperature as a function of the gold thickness and no theoretical explanation existed. We placed different number of Au layers between the Nb and Fe layers, where a face-centered cubic (fcc) growth is assumed for the Au overlayers. While the results show that the Au layers remained non-magnetic, spin-polarized bands around the Fermi level can be observed as shown in the Fig. 1. This is the consequence of the different confinement for the spin-up and spin-down electrons: the spin-up electrons are confined in the Au layers only, while the spin-down electrons experience a confinement in both the Au and Fe layers. Therefore, due to the different confinement lengths between the spin channels, more bands are observed for the spin-up states than for the spin-down states. Since the order parameter is influenced mostly by the states in the close vicinity of the Fermi level, we can conclude that a pairing state (in the Au) can occur between two electrons on the induced split parts of the Fermi surface caused by the quantum well states. Hence, the Cooper pair can acquire a finite momentum leading to the oscillation of the order parameter (analogously to the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state). In fact, we found an oscillating behavior of the order parameter as shown in Fig. 2. The period of these oscillations depends on the number of Au overlayers since the band structure and the number of quantum well states depends on the thickness of the Au. For thicker Au overlayers as the number of the quantum well states are increasing, the bands in the spin-up and spin-down channel are separated by smaller and smaller q vectors, which leads to an increase of the period of oscillation as a function of the Au thickness. Our theoretical finding explains the oscillating behaviour of the order parameter and suggests that these Tc oscillations observed in that experiment may also be a consequence of the interplay between the quantum-well states and ferromagnetism.
Figure 1. Quantum well states in Fe/Au/Nb(100). Left column is for ↑ and right column is for ↓ states. First row is for top Nb layer, middle row is for a typical Au and bottom row is for a typical Fe layer.
Figure 2. Oscillation of the order parameter in Fe/Au/Nb(100)
High-Entropy Alloys. — The investigated multi-component high-entropy alloys (HEAs) represent a solution for an age-old problem: combination of high strength and high ductility of metallic alloys. In this respect, at present two competing materials are in the frontier of materials research:
- Nanoscale particle strengthened steels like the old oxide dispersion strengthened (ODS) alloys and the newly developed co-precipitation strengthened steels and
- Multicomponent high entropy alloys based on solid solution strengthening.
We have followed an integrated computational prediction and experimental validation approach. The computer-aided alloy design was based on first-principles calculations. First, we addressed the forming ability of single-phase HEAs predicting its maximum strength and confirmed the validity of the conjecture about strength (hardness) versus e/a correlation. The theoretical prediction of the elastic properties of various HEAs was contrasted with the available experimental values. Furthermore, we studied the twinning as the fundamental mechanism behind the increased strength and ductility in medium- and high-entropy alloys. Second, we dealt with dual-phase HEAs starting from single-phase NiCoFeCr and adding sp elements like Al, Ga, Ge and Sn. By combining the measured and theoretically predicted temperature-dependent lattice parameters, we revealed the structural and magnetic origin of the observed anomalous thermal expansion behavior. The nanoindentation test revealed a ‘fingerprint” of the two-phase structure. The Young’s and shear moduli of the investigated HEAs were also determined using ultrasound methods. The correlation between these two moduli suggests a general relationship for metallic alloys.
Results in 2017
Superconductivity in layered heterostructures. — During the previous years, a novel and unique computer code was developed which allows us to study the nature of the Andreev bound states related to the proximity effect in normal metal–superconductor heterostructures based on the first-principles Bogoliubov–deGennes (BdG) equations. For the first time, we succeeded in applying the SKKR method for solving the Kohn–Sham–Bogoliubov–deGennes (KSBdG) equation which allowed us to investigate the quasiparticle spectrum of superconducting heterostructures. This year, a fully relativistic generalization of the BdG equations within Multiple Scattering Theory has been derived. The method allows the solution of the first-principles Dirac–Bogoliubov–de Gennes equations combined with a semi-phenomenological parametrization of the exchange-correlation functional. The major difficulty during the development was to derive simple conditions for the case when the right-hand-side and left-hand-side solutions must be treated separately while setting up the corresponding Green function. As an application of the theory, we calculated the superconducting order parameter in Nb/Fe and Nb/Au/Fe systems. We found Fulde–Ferrell–Larkin–Ovchinnikov like oscillations in the iron layers, but more interestingly an oscillatory behaviour is observed in the gold layers as well.
Thin Film Magnetism. — Non-collinear magnetic structures have been investigated in ultrathin films by combining ab initio electronic structure calculations with numerical spin model simulations. The experimentally observed significant increase in the spin spiral period as a function of temperature of three-atomic-layer thick Fe films on Ir(111) has been explained. Ab initio calculations revealed how the addition of hydrogen to a two-atomic-layer thick Fe film on Ir(111) leads to the formation of magnetic skyrmions in place of the spin spiral ground state of the pristine system, in agreement with scanning tunneling microscopy measurements. Theoretical predictions have been made on the characterization of skyrmionic structures with various topological charges.
High Entropy Alloys. — Looking for high-strength and high-temperature-resistant high-entropy alloys (HEAs) new refractory HEA compositions have been predicted theoretically bycombining a refractory CrMoW alloy with late transition metals (LTM = Ni, Co, Fe, and Mn). Ab initio calculations revealed that the LTM additions increase the ductility, but reduce the strength of these CrMoW based alloys with single-phase BCC structure.
The magnetization components of permeability spectra for annealed nanocrystalline (Finemet) core have been studied and four contributions have been revealed for the first time in the literature: i) eddy current; ii) Debye relaxation of magnetization rotation, iii) Debye relaxation of damped domain wall motion and iv) resonant type DW motion. Although the relative weight of these contributions changes with the frequency and exciting field amplitude, the role of eddy current cannot be neglected even for the smallest applied field. These components can be found in the powder cores of soft magnetic composites as well.
Observation of spin-quadrupolar excitations in Sr2CoGe2O7 by high-field electron spin resonance. — When we think of a spin, usually we imagine an arrow pointing somewhere (representing the expectation values of the components of the spin operator), and with the arrow we associate a magnetic moment. Upon time reversal, the arrow reverses its direction. This is a reasonable picture for the spin 1/2 of the electron, but for larger spins this does not exhaust all the possibilities. For example, the dimension of the Hilbert space is 3 for the spin 1, and we can construct spin states for which the expectation values of all the three spin operators vanish — the state does not point anywhere, it cannot be represented by an arrow. The simplest example is the 0 eigenstate of the S2 operator. In fact, there are three linearly independent such states (the zero eigenstate of the Sx, Sy and Sz operators), spanning the Hilbert space. Though they cannot be represented by an arrow, they still break the rotational symmetry, since quadratic forms of spin operators differentiate among them. Instead of arrows, we can use directors (like in the case of liquid crystals), as the rotation by π around an axis perpendicular to the director returns the same state (up to a phase factor). These states are called spin-quadrupoles. Furthermore, these states do not break the time-reversal symmetry.
Similarly, the long-range-ordered states of interacting spins are usually time-reversal-breaking states, with a configuration of “arrows” that repeats itself on the lattice. However, under favorable conditions, interacting spins can produce ordered states where the order parameter is of spin-quadrupolar character which does not break the time reversal symmetry. Theoretically, such phases have been established in spin-one Heisenberg models extended with higher-order spin interactions. Even more interestingly, time-reversal invariant ordered states can also be realized in spin-1/2 systems, where the quadrupole-like order parameter is distributed between two spins on a bond, leading to a so-called nematic ordering.
These theoretical developments have inspired the quest to nematic and quadrupole phases in real materials. However, when relying on standard experimental methods, such phases usually remain hidden. Most of the experimental probes detect spin-dipolar (ΔS=1) transitions, and they do not interact with the spin-quadrupoles, as their detection requires ΔS=2 transitions.
In a collaboration with experimental researchers from Osaka University, we found an unambiguous experimental observation of spin-quadrupolar excitations in the layered Sr2CoGe2O7 multiferroic compound. In this compound, the Co ions are in the centers of tetrahedra formed by the four surrounding O ions (Fig. 1). Since the inversion symmetry is absent, the relativistic spin-orbit coupling allows the coupling of the electric polarizations to the spin-quadrupolar operators. Due to this magnetoelectric coupling present in the Sr2CoGe2O7, the non-magnetic, purely spin-quadrupolar excitation becomes electrically active and detectable by electromagnetic waves, like the electron spin resonance spectroscopy.
Figure 1. The schematic crystal structure of the Sr2CoGe2O7 multiferroic compound projected onto the ab plane. The green spheres represent the magnetic Co2+ ions with S = 3/2 surrounded by four O2− ions (red) in an alternating tetrahedral environment.
In the electron spin resonance spectra of Sr2CoGe2O7 above the saturation field of 20T, a mode with twice the g-factor of the usual modes is observed (Fig. 2). This indicates the absorption of two magnons, just what is needed for the creation of a quadrupole wave. Indeed, we could explaine the features of the experimental spectra taken in different geometries by a simple theoretical model of the spin-quadrupolar wave providing not only a qualitative description, but also a quantitative agreement.
Figure 2. Frequency-field diagrams of the ESR resonance fields of Sr2CoGe2O7 for magnetic fields parallel to the  direction of the external magnetic field. The solid lines represent the dipolar resonance modes from the multiboson spin-wave theory. The red dashed line indicates a resonance mode with a slope twice larger than the others, corresponding to a two-magnon excitation — the quadrupolar mode.
The most significant point of our finding is the first observation of non-magnetic spin-quadrupolar excitation in an antiferromagnetic material (Fig. 3). Such quadrupolar degrees of freedom become inherent in systems with larger than S=1/2 magnetic moments, regardless of the presence of magneto-electric coupling. Upon condensing such multipolar excitations, magnetically disordered exotic quantum phases may arise. The experimental identification of quadrupole excitations with vanishing gap gives us a possibility to identify long-sought nematic phases, which stand without any usual magnetic fingerprint and are almost impossible to tell apart from other non-magnetic phases. Furthermore, our work will stimulate the application of the magnetoelectric effect as a spectroscopy tool.
Figure 3. Schematic plot of (a) the Q1 quadrupolar mode for H∥ and (b) the dipolar modes for H∥, as seen from the direction of the magnetic field. In both cases the oscillating component of the uniform electric polarization P (shown by orange ellipse) is perpendicular to the external magnetic field H, therefore they are active in the Faraday configuration. The green ellipse represents the rotating quadrupolar moments, while the green arrows the precessing dipolar spins on the two sublattices. The red arrows show the electric polarization vectors which are excited by the oscillating electric field.