arXiv subjects

Stefan Heinze

Publications and source records attributed to Stefan Heinze.

At least 55 records · Page 3Linked to original sources

arXiv2020

Anisotropic vortices on superconducting Nb(110)

We investigate the electronic properties of type-II superconducting Nb(110) in an external magnetic field. Scanning tunneling spectroscopy reveals a complex vortex shape which develops from circular via coffee bean-shaped to elliptical when decreasing the energy from the edge of the superconducting gap to the Fermi level. This anisotropy is traced back to the local density of states of Caroli-de-Gennes-Matricon states which exhibits a direction-dependent splitting. Oxidizing the Nb(110) surface triggers the transition from the clean to the dirty limit, quenches the vortex bound states, and leads to an isotropic appearance of the vortices. Density functional theory shows that the Nb(110) Fermi surface is stadium-shaped near the Γpoint. Calculations within the Bogoliubov-de-Gennes theory using these Fermi contours consistently reproduce the experimental results.

cond-mat.supr-con↗

arXiv2020

Mechanisms of skyrmion collapse revealed by sub-nm maps of the transition rate

Magnetic skyrmions are key candidates for novel memory, logic, and neuromorphic computing. An essential property is their topological protection caused by the whirling spin texture as described by a robust integer winding number. However, the realization on an atomic lattice leaves a loophole for switching the winding number via concerted rotation of individual spins. Hence, understanding the unwinding microscopically is key to enhance skyrmion stability. Here, we use spin polarized scanning tunneling microscopy to probe skyrmion annihilation by individual hot electrons and obtain maps of the transition rate on the nanometer scale. By applying an in-plane magnetic field, we tune the collapse rate by up to four orders of magnitude. In comparison with first-principles based atomistic spin simulations, the experiments demonstrate a radial symmetric collapse at zero in-plane magnetic field and a transition to the recently predicted chimera collapse at finite in-plane field. Our work opens the route to design criteria for skyrmion switches and improved skyrmion stability.

cond-mat.mes-hall↗

arXiv2020

Electronic and magnetic properties of 3$d$ transition-metal adatoms on Mn/W(110)

Using density functional theory, we investigate the electronic and magnetic properties of $3d$ transition-metal adatoms adsorbed on a monolayer of Mn on W(110). Mn/W(110) has a noncollinear cycloidal spin-spiral ground state with an angle of 173$^\circ$ between magnetic moments of adjacent Mn rows. It allows to rotate the spin orientation of an adsorbed magnetic adatom quasi-continuously. Therefore, this surface is ideally suited for manipulating the spin direction of individual atoms and exploring their magnetic properties using scanning tunneling microscopy (STM). The adsorbed V and Cr transition-metal adatoms couple antiferromagnetically to the nearest neighbor Mn atom of Mn monolayer while Mn, Fe, Co, and Ni couple ferromagnetically. The magnetic moments of the $3d$ adatoms are large and show a Hund's rule type of trend with a peak in the middle of the series. We find large spin splitting of the $3d$ transition-metal adatoms, large spin polarization of the local vacuum density of states up to 73\% at the Fermi energy, and significant tunneling anisotropic magnetoresistance enhancement up to 27\%. We conclude that such large values stem from the strong hybridization between the adatoms and the Mn atoms of the monolayer. Furthermore, identification of spin orientations of the adatom using spin-polarized STM is only possible for Co and V adatoms.

cond-mat.mtrl-sci↗

arXiv2020

Quantifying Exchange Forces of a Non-Collinear Magnetic Structure on the Atomic Scale

The large interest in chiral magnetic structures for realization of nanoscale magnetic storage or logic devices has necessitated methods which can quantify magnetic interactions at the atomic scale. To overcome the limitations of the typically used current-based sensing of atomic-scale exchange interactions, a force-based detection scheme is highly advantageous. Here, we quantify the atomic-scale exchange force field between a ferromagnetic tip and a cycloidal spin spiral using our developed combination of current and exchange force detection. Compared to the surprisingly weak spin polarization, the exchange force field is more sensitive to atomic-scale variations in the magnetization. First-principles calculations reveal that the measured atomic-scale variations in the exchange force originate from different contributions of direct and indirect (Zener) type exchange mechanisms, depending on the chemical tip termination. Our work opens the perspective of quantifying different exchange mechanisms of chiral magnetic structures with atomic-scale precision using 3D magnetic exchange force field measurements.

cond-mat.mes-hall↗

arXiv2020

Discovery of magnetic single- and triple-Q states in Mn/Re(0001)

We experimentally verify the existence of two model-type magnetic ground states which were previously predicted but so far unobserved. We find them in Mn monolayers on the Re(0001) surface using spin-polarized scanning tunneling microscopy. For fcc stacking of Mn the collinear row-wise antiferromagnetic state occurs, whereas for hcp Mn a three-dimensional spin structure appears, which is a superposition of three row-wise antiferromagnetic states and is known as triple-Q state. Density functional theory calculations elucidate the subtle interplay of different magnetic interactions to form these spin structures and provide insight into the role played by relativistic effects.

cond-mat.mes-hall↗

arXiv2020

Role of higher-order exchange interactions for skyrmion stability

Transition-metal interfaces and multilayers are a very promising class of systems to realize nanometer-sized, stable magnetic skyrmions for future spintronic devices. For room temperature applications it is crucial to understand the interactions which control the stability of isolated skyrmions. Typically, skyrmion properties are explained by the interplay of pair-wise exchange interactions, the Dzyaloshinskii-Moriya interaction and the magnetocrystalline anisotropy energy. Here, we demonstrate that higher-order exchange interactions -- which have so far been neglected -- can play a key role for the stability of skyrmions. We use an atomistic spin model parametrized from first-principles and compare three different ultrathin film systems. We consider all fourth order exchange interactions and show that in particular the four-site four spin interaction has a giant effect on the energy barrier preventing skyrmion and antiskyrmion collapse into the ferromagnetic state. Our work opens new perspectives to enhance the stability of topological spin structures.

cond-mat.mes-hall↗

arXiv2019

Tailoring magnetic interactions in atomic bilayers of Rh and Fe on Re(0001)

Using density functional theory, we investigate the interplay between the stacking order and sequence of bilayers composed of an Fe and a Rh layer on the Re(0001) and their magnetic properties. We find that fcc/ffc stacked bilayers are energetically very unfavorable, while all other combinations of hcp and fcc stacking are energetically close. The magnetic interactions are evaluated by mapping the DFT total energies onto a spin model, which contains Heisenberg exchange, Dzyaloshinskii-Moriya interaction, the magnetocrystalline anisotropy energy, and higher-order exchange interactions. We find that the stacking sequence of the bilayer significantly modifies the magnetic interactions. As a result, we find a DMI driven cycloidal spin spiral ground state with a period of 11~nm for hcp-Fe/hcp-Rh. For fcc-Fe/hcp-Rh and hcp-Fe/fcc-Rh, we obtain a ferromagnetic ground state. The spin spiral energy dispersion of hcp-Fe/hcp-Rh including spin-orbit coupling suggests that isolated skyrmions can be stabilized in the field-polarized ferromagnetic background at external magnetic fields. If the Fe layer is sandwiched between the Rh overlayer and the Re(0001) substrate, there is a competition between the ferromagnetic coupling preferred by the Rh-Fe hybridization and the antiferromagnetic coupling induced by the Fe-Re hybridization. Due to the Fe/Re interface the DMI can become very large. For fcc-Rh/hcp-Fe, we obtain a cycloidal spin spiral with a period of 1.7~nm which is induced by frustration of exchange interactions and further stabilized by the DMI. For hcp-Rh/hcp-Fe, we find a DMI driven cycloidal spin spiral with a period of 4~nm and locally nearly antiparallel magnetic moments due to antiferromagnetic nearest-neighbor exchange. The higher-order exchange constants can be significant in the considered films, however, they do not stabilize multi-$Q$ states.

cond-mat.mes-hall↗

arXiv2019

Tunneling anisotropic magnetoresistance of Pb and Bi adatoms and dimers on Mn/W(110): A first-principles study

We show that Pb and Bi adatoms and dimers have a large tunneling anisotropic magnetoresistance (TAMR) of up to 60% when adsorbed on a magnetic transition-metal surface due to strong spin-orbit coupling and the hybridization of 6p orbitals with 3d states of the magnetic layer. Using density functional theory, we have explored the TAMR effect of Pb and Bi adatoms and dimers adsorbed on a Mn monolayer on W(110). This surface exhibits a noncollinear cycloidal spin spiral ground state with an angle of 173$^\circ$ between neighboring spins which allows to rotate the spin quantization axis of an adatom or dimer quasi-continuously and is ideally suited to explore the angular dependence of TAMR using scanning tunneling microscopy (STM). We find that the induced magnetic moments of Pb and Bi adatoms and dimers are small, however, the spin-polarization of the local density of states (LDOS) is still very large. The TAMR obtained from the anisotropy of the vacuum LDOS is up to 50-60 % for adatoms. For dimers the TAMR depends sensitively on the dimer orientation with respect to the crystallographic directions of the surface due to the formation of bonds between the adatoms with the Mn surface atoms and the symmetry of the spin-orbit coupling induced mixing. Dimers oriented along the spin spiral direction of the Mn monolayer display the largest TAMR of 60 % which is due to hybrid 6p-3d states of the dimers and the Mn layer

cond-mat.mtrl-sci↗

arXiv2019

On the preparation and electronic properties of clean superconducting Nb(110) surfaces

We have studied cleaning procedures of Nb(110) by verifying the surface quality with low-energy electron diffraction, Auger electron spectroscopy, and scanning tunneling microscopy and spectroscopy. Our results show that the formation of a surface-near impurity depletion zone is inhibited by the very high diffusivity of oxygen in the Nb host crystal which kicks in at annealing temperatures as low as a few hundred degree Celsius. Oxygen can be removed from the surface by heating the crystal up to $T = 2400^\circ$C. Tunneling spectra measured on the clean Nb(110) surface exhibit a sharp conductance peak in the occupied states at an energy of about $-450$\,meV. Density functional theory calculations show that this peak is caused by a $d_{z^2}$ surface resonance band at the $\barΓ$ point of the Brillouin zonewhich provides a large density of states above the sample surface. The clean Nb(110) surface is superconducting with a gap width and a critical magnetic field strength in good agreement to the bulk value. In an external magnetic field we observe the Abrikosov lattice of flux quanta (vortices). Spatially resolved spectra show a zero-bias anomaly in the vortex core.

cond-mat.supr-con↗

arXiv2019

Comparison of first-principles methods to extract magnetic parameters in ultra-thin films: Co/Pt(111)

We compare three distinct computational approaches based on first-principles calculations within density functional theory to explore the magnetic exchange and the Dzyaloshinskii-Moriya interactions (DMI) of a Co monolayer on Pt(111), namely (i) the method of infinitesimal rotations of magnetic moments based on the Korringa-Kohn-Rostoker (KKR) Green function method, (ii) the generalized Bloch theorem applied to spiraling magnetic structures and (iii) supercell calculations with non-collinear magnetic moments, the latter two being based on the full-potential linearized augmented plane wave (FLAPW) method. In particular, we show that the magnetic interaction parameters entering micromagnetic models describing the long-wavelength deviations from the ferromagnetic state might be different from those calculated for fast rotating magnetic structures, as they are obtained by using (necessarily rather small) supercell or large spin-spiral wave-vectors. In the micromagnetic limit, which we motivate to use by an analysis of the Fourier components of the domain-wall profile, we obtain consistent results for the spin stiffness and DMI spiralization using methods (i) and (ii). The calculated spin stiffness and Curie temperature determined by subsequent Monte Carlo simulations are considerably higher than estimated from the bulk properties of Co, a consequence of a significantly increased nearest-neighbor exchange interaction in the Co-monolayer (+50%). The calculated results are carefully compared with the literature.

cond-mat.mtrl-sci↗

arXiv2019

Isolated zero field sub-10 nm skyrmions in ultrathin Co films

Due to their exceptional topological and dynamical properties magnetic skyrmions - localized stable spin structures on the nanometre scale - show great promise for future spintronic applications. To become technologically competitive, isolated skyrmions with diameters below 10 nm that are stable at zero magnetic field and room temperature are desired. Despite finding skyrmions in a wide spectrum of materials, the quest for a material with these envisioned properties is still ongoing. Here we report zero field isolated skyrmions with diameters smaller than 5 nm coexisting with 1 nm thin domain walls in Rh/Co atomic bilayers on the Ir(111) surface. These spin structures are characterized by spin-polarized scanning tunnelling microscopy and can also be detected using non-spin-polarized tips due to a large non-collinear magnetoresistance. We demonstrate that sub-10 nm skyrmions are stabilised in these ferromagnetic Co films at zero field due to strong frustration of exchange interaction, together with Dzyaloshinskii-Moriya interaction and a large magnetocrystalline anisotropy.

cond-mat.mes-hall↗

arXiv2018

Skyrmion lifetimes in ultrathin films

We show that thermal stability of magnetic skyrmions can be strongly affected by entropic effects. The lifetimes of isolated skyrmions in atomic Pd/Fe bilayers on Ir(111) and on Rh(111) are calculated in the framework of harmonic transition state theory based on an atomistic spin model parametrized from density functional theory. Depending on the system the attempt frequency for skyrmion collapse can change by up to nine orders of magnitude with the strength of the applied magnetic field. We demonstrate that this effect is due to a drastic change of entropy with skyrmion radius which opens a novel route towards stabilizing sub-10 nm skyrmions at room temperature.

cond-mat.mes-hall↗

arXiv2018

Noncollinear spin density of an adatom on a magnetic surface

We show that an individual adatom on a magnetic surface can exhibit a noncollinear spin density. Using density functional theory we study Co and Ir adatoms on a Mn monolayer on the W(110) surface which possesses a noncollinear canted spin structure. Due to hybridization with the nearest and next-nearest Mn atoms of the monolayer the spin direction of the underlying substrate is encoded into the orbitals of the adatom. This explains recent scanning tunneling microscopy experiments showing a spin sensitive shape asymmetry of adatoms [Serrate \emph{et al.}, Phys. Rev. B \textbf{93}, 125424 (2016)] which confirms the intra-atomic noncollinear magnetism of the adatoms.

cond-mat.mtrl-sci↗

arXiv2018

Stability and magnetic properties of Fe double-layers on Ir (111)

We investigate the interplay between the structural reconstruction and the magnetic properties of Fe doublelayers on Ir (111)-substrate using first-principles calculations based on density functional theory and mapping of the total energies on an atomistic spin model. We show that, if a second Fe monolayer is deposited on Fe/Ir (111), the stacking may change from hexagonal close-packed to bcc (110)-like accompanied by a reduction of symmetry from trigonal to centered rectangular. Although the bcc-like surface has a lower coordination, we find that this is the structural ground state. This reconstruction has a major impact on the magnetic structure. We investigate in detail the changes in the magnetic exchange interaction, the magnetocrystalline anisotropy, and the Dzyaloshinskii Moriya interaction depending on the stacking sequence of the Fe double-layer. Based on our findings, we suggest a new technique to engineer Dzyaloshinskii Moriya interactions in multilayer systems employing symmetry considerations. The resulting anisotropic Dzyaloshinskii-Moriya interactions may stabilize higher-order skyrmions or antiskyrmions.

cond-mat.mtrl-sci↗

arXiv2018

First-principles prediction of sub-10 nm skyrmions in Pd/Fe bilayers on Rh(111)

We show that stable skyrmions with diameters of a few nanometers can emerge in atomic Pd/Fe bilayers on the Rh(111) surface. Based on density functional theory we calculate the exchange and the Dzyaloshinskii-Moriya interaction as well as the magnetocrystalline anisotropy energy. The later two terms are driven by spin-orbit coupling and significantly reduced compared to Pd/Fe bilayers on Ir(111) as expected since Rh and Ir are isoelectronic $4d$ and $5d$ transition-metals. However, there is still a spin spiral ground state at zero magnetic field. Atomistic spin dynamics simulations show that a skyrmion phase occurs at small magnetic fields of $\sim$ 1 T. Skyrmion diameters amount to 2 to 8 nm and skyrmion lifetimes are up to 1 hour at temperatures of 25 to 45 K.

cond-mat.mtrl-sci↗

arXiv2018

B-T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo

We use an atomistic spin model derived from density functional theory calculations for the ultra-thin film Pd/Fe/Ir(111) to show that temperature induces coexisting non-zero skyrmion and antiskyrmion densities. We apply the parallel tempering Monte Carlo method in order to reliably compute thermodynamical quantities and the B-T phase diagram in the presence of frustrated exchange interactions. We evaluate the critical temperatures using the topological susceptibility. We show that the critical temperatures depend on the magnetic field in contrast to previous work. In total, we identify five phases: spin spiral, skyrmion lattice, ferromagnetic phase, intermediate region with finite topological charge and paramagnetic phase. To explore the effect of frustrated exchange interactions, we calculate the B-T phase diagram, when only effective exchange parameters are taken into account.

cond-mat.mtrl-sci↗

arXiv2018

Trochoidal motion and pair generation in skyrmion and antiskyrmion dynamics under spin-orbit torques

Skyrmions and antiskyrmions in magnetic ultrathin films are characterised by a topological charge describing how the spins wind around their core. This topology governs their response to forces in the rigid core limit. However, when internal core excitations are relevant, the dynamics become far richer. We show that current-induced spin-orbit torques can lead to phenomena such as trochoidal motion and skyrmion-antiskyrmion pair generation that only occurs for either the skyrmion or antiskyrmion, depending on the symmetry of the underlying Dzyaloshinskii-Moriya interaction. Such dynamics are induced by core deformations, leading to a time-dependent helicity that governs the motion of the skyrmion and antiskyrmion core. We compute the dynamical phase diagram through a combination of atomistic spin simulations, reduced-variable modelling, and machine learning algorithms. It predicts how spin-orbit torques can control the type of motion and the possibility to generate skyrmion lattices by antiskyrmion seeding.

cond-mat.mes-hall↗

arXiv2018

Competition of Dzyaloshinskii-Moriya and higher-order exchange interactions in Rh/Fe atomic bilayers on Ir(111)

Using spin-polarized scanning tunneling microscopy and density functional theory we demonstrate the occurrence of a novel type of noncollinear spin structure in Rh/Fe atomic bilayers on Ir(111). We find that higher-order exchange interactions depend sensitively on the stacking sequence. For fcc-Rh/Fe/Ir(111) frustrated exchange interactions are dominant and lead to the formation of a spin spiral ground state with a period of about 1.5 nm. For hcp-Rh/Fe/Ir(111) higher-order exchange interactions favor a double-row wise antiferromagnetic or "uudd" state. However, the Dzyaloshinskii- Moriya interaction at the Fe/Ir interface leads to a small angle of about 4° between adjacent magnetic moments resulting in a canted "uudd" ground state.

cond-mat.mes-hall↗