arXiv subjects

Stefan Heinze

Publications and source records attributed to Stefan Heinze.

At least 37 records · Page 2Linked to original sources

arXiv2024

Prediction of stable nanoscale skyrmions in monolayer Fe$_5$GeTe$_2$

Using first-principles calculations and atomistic spin simulations, we predict stable isolated skyrmions with a diameter below 10 nm in a monolayer of the two-dimensional van der Waals ferromagnet Fe$_5$GeTe$_2$, a material of significant experimental interest. A very large Dzyaloshinskii-Moriya interaction (DMI) is observed due to the intrinsic broken inversion symmetry and strong spin-orbit coupling for monolayer Fe$_5$GeTe$_2$. We show that the nearest-neighbor approximation, often used in literature, fails to describe the DMI. The strong DMI together with moderate in-plane magnetocrystalline anisotropy energy allows to stabilize nanoscale skyrmions in out-of-plane magnetic fields above $\approx 2$~T. The energy barriers of skyrmions in monolayer Fe$_5$GeTe$_2$ are comparable to those of state-of-the-art transition-metal ultra-thin films. We further predict that these nanoscale skyrmions can be stable for hours at temperatures up to 20 K.

cond-mat.mtrl-sci↗

arXiv2024

Kicking Co and Rh atoms on a row-wise antiferromagnet

Diffusion on surfaces is a fundamental process in surface science, governing nanostructure and film growth, molecular self-assembly, and chemical reactions. Atom motion on non-magnetic surfaces has been studied extensively both theoretically and by real-space imaging techniques. For magnetic surfaces density functional theory (DFT) calculations have predicted strong effects of the magnetic state onto adatom diffusion, but to date no corresponding experimental data exists. Here, we investigate Co and Rh atoms on a hexagonal magnetic layer, using scanning tunneling microscopy (STM) and DFT calculations. Experimentally, we "kick" atoms by local voltage pulses and thereby initiate strictly one-dimensional motion which is dictated by the row-wise antiferromagnetic (AFM) state. Our calculations show that the one-dimensional motion of Co and Rh atoms results from conserving the Co spin direction during movement and avoiding high induced Rh spin moments, respectively. These findings demonstrate that magnetism can be a means to control adatom mobility.

cond-mat.mtrl-sci↗

arXiv2024

Antiferromagnetic order of topological orbital moments in atomic-scale skyrmion lattices

Topological orbital moments can arise in non-coplanar spin structures even in the absence of spin-orbit coupling and a net topological orbital magnetization occurs for the triple-Q state and for isolated skyrmions. For atomic-scale skyrmion lattices, a significant effect can also be expected, however, no studies have been reported yet. Here, we observe via spin-polarized scanning tunneling microscopy a non-coplanar atomic-scale spin structure with a nearly square magnetic unit cell for a pseudomorphic Fe monolayer on three atomic Ir layers on the Re(0001) surface. Employing density functional theory (DFT) calculations we consider different skyrmionic lattices to find the magnetic ground state. By mapping the DFT total energies to an atomistic spin model we demonstrate that these spin textures are stabilized by the interplay of the Dzyaloshinskii-Moriya and four-spin interactions. We evaluate the emerging phenomena of the different non-coplanar magnetic states and find significant local topological orbital moments oriented perpendicular to the surface, which order in an antiferromagnetic fashion.

cond-mat.mtrl-sci↗

arXiv2024

Proposal for all-electrical skyrmion detection in van der Waals tunnel junctions

A major challenge for magnetic skyrmions in atomically thin van der Waals (vdW) materials is reliable skyrmion detection. Here, based on rigorous first-principles calculations, we show that all-electrical skyrmion detection is feasible in 2D vdW magnets via scanning tunneling microscopy (STM) and in planar tunnel junctions. We use the nonequilibrium Green's function method for quantum transport in planar junctions, including self-energy due to electrodes and working conditions, going beyond the standard Tersoff-Hamann approximation. We obtain a very large tunneling anisotropic magnetoresistance (TAMR) around the Fermi energy for a vdW tunnel junction based on graphite/Fe$_3$GeTe$_2$/germanene/graphite. For atomic-scale skyrmions the noncollinear magnetoresistance (NCMR) reaches giant values. We trace the origin of the NCMR to spin-mixing between spin-up and -down states of $p_z$ and $d_{z^2}$ character at the surface atoms. Both TAMR and NCMR are drastically enhanced in tunnel junctions with respect to STM geometry due to orbital symmetry matching at the interface.

cond-mat.mtrl-sci↗

arXiv2023

Tuning magnetic interactions of Co and 4$d$ transition-metal atomic bilayers on Re(0001) via interface engineering

Employing $\textit{ab-initio}$ density functional theory (DFT), we performed a systematic investigation of the electronic structures and the magnetic properties of atomic bilayers composed of a 4$d$ transition-metal layer (Rh, Pd and Ru) and a Co layer on the Re(0001) surface. Our DFT calculations reveal the influence of the bilayer composition and their stacking sequence on the magnetic ground state and magnetic interactions. We obtain the magnetic interactions by mapping the total energies onto an effective spin Hamiltonian which contains the exchange interaction and the Dzyaloshinskii-Moriya interaction (DMI) as well as the magnetocrystalline anisotropy energy (MAE). We observe noticeable changes in bilayer hybridization due to variation in bilayer composition and overlayer symmetry, leading to significant variation in magnetic interactions. In all considered systems, the nearest-neighbor exchange interaction is ferromagnetic, however, the value varies by up to a factor of 5. The effective, nearest-neighbor DMI constant exhibits variation in sign over the films considered, favoring either right- (clockwise) or left-handed (anticlockwise) cycloidal spin spirals. The value of the DMI changes by up to a factor of 27 among the films. For most of the systems, the MAE favors an out-of-plane easy magnetization axis, however, for hcp-Co/Rh and hcp-Co/Ru bilayers on Re(0001), it prefers an in-plane magnetization axis. The magnitude of the MAE varies from a small value of about 0.1 meV/Co atom up to about 2 meV/Co atom for Co/Pd bilayers. The spin spiral energy dispersion curve rises quite quickly close to the ferromagnetic state for films in which the Co layer is adjacent to the vacuum indicating a large effective exchange constant which stabilizes a ferromagnetic ground state in Co/$4d$ bilayers on Re(0001).

cond-mat.mtrl-sci↗

arXiv2023

Coupling of the triple-Q state to the atomic lattice by anisotropic symmetric exchange

We identify the triple-Q (3Q) state as magnetic ground state in Pd/Mn and Rh/Mn bilayers on Re(0001) using spin-polarized scanning tunneling microscopy and density functional theory. An atomistic model reveals that in general the 3Q state with tetrahedral magnetic order and zero net spin moment is coupled to a hexagonal atomic lattice in a highly symmetric orientation via the anisotropic symmetric exchange interaction, whereas other spin-orbit coupling terms cancel due to symmetry. Our experiments are in agreement with the predicted orientation of the 3Q state. A distortion from the ideal tetrahedral angles leads to other orientations of the 3Q state which, however, results in a reduced topological orbital magnetization compared to the ideal 3Q state.

cond-mat.mtrl-sci↗

arXiv2023

Evidence for a conical spin spiral state in the Mn triple-layer on W(001): spin-polarized scanning tunneling microscopy and first-principles calculations

The spin structure of a Mn triple layer grown pseudomorphically on surfaces is studied using spin-polarized scanning tunneling microscopy (SP-STM) and density functional theory (DFT). In SP-STM images a c$(4 \times 2)$ super structure is found. The magnetic origin of this contrast is verified by contrast reversal and using the c$(2 \times 2)$ AFM state of the Mn double layer as a reference. SP-STM simulations show that this contrast can be explained by a spin spiral propagating along the [110] direction with an angle close to $90^\circ$ between magnetic moments of adjacent Mn rows. To understand the origin of this spin structure, DFT calculations have been performed for a large number of competing collinear and non-collinear magnetic states including the effect of spin-orbit oupling (SOC). Surprisingly, a collinear state in which the magnetic moments of top and central Mn layer are aligned antiparallel and those of the bottom Mn layer are aligned parallel to the central layer is the energetically lowest state. We show that in this so-called "up-down-down" ($\uparrow \downarrow \downarrow$) state the magnetic moments in the Mn bottom layer are only induced by those of the central Mn layer. Flat spin spirals propagating either in one, two, or all Mn layers are shown to be energetically unfavorable to the collinear $\uparrow \downarrow \downarrow$ state even upon including the Dzyaloshinskii-Moriya interaction (DMI). However, conical spin spirals with a small opening angle of about $10^\circ$ are only slightly energetically unfavorable within DFT and could explain the experimental observations. Surprisingly, the DFT energy dispersion of conical spin spirals including SOC cannot be explained if only the DMI is taken into account. Therefore, higher-order interactions such as chiral biquadratic terms need to be considered which could explain the stabilization of a conical spin spiral state.

cond-mat.mtrl-sci↗

arXiv2023

Spontaneous square vs. hexagonal nanoscale skyrmion lattices in Fe/Ir(111)

We study the emergence of spontaneous skyrmion lattices in an Fe monolayer in fcc and hcp stacking on the Ir(111) surface using density functional theory (DFT). For fcc-Fe/Ir(111) we find the well-known square nanoskyrmion lattice. However, for hcp-Fe/Ir(111) the hexagonal skyrmion lattice previously proposed based on experiments is energetically unfavorable with respect to a hexagonal multi-Q state with nearly collinear magnetic moments. By mapping our DFT calculations to an atomistic spin model we demonstrate that the interplay of pair-wise exchange, higher-order exchange, and Dzyaloshinskii-Moriya interaction is decisive for the symmetry and collinearity of the obtained spin lattice.

cond-mat.mtrl-sci↗

arXiv2023

Lifetime of coexisting sub-10 nm zero-field skyrmions and antiskyrmions

Magnetic skyrmions have raised high hopes for future spintronic devices. For many applications it would be of great advantage to have more than one metastable particle-like texture available. The coexistence of skyrmions and antiskyrmions has been proposed in inversion symmetric magnets with exchange frustration. However, so far only model systems have been studied and the lifetime of coexisting metastable topological spin structures has not been obtained. Here, we predict that skyrmions and antiskyrmions with diameters below 10 nm can coexist at zero magnetic field in a Rh/Co bilayer on the Ir(111) surface -- an experimentally feasible system. We show that the lifetimes of metastable skyrmions and antiskyrmions in the ferromagnetic ground state are above one hour for temperatures up to 75 K and 48 K, respectively. The entropic contribution to the nucleation and annihilation rates differs for skyrmions and antiskyrmions. This opens the route to thermally activated creation of coexisting skyrmions and antiskyrmions in frustrated magnets with Dzyaloshinskii-Moriya interaction.

cond-mat.mtrl-sci↗

arXiv2023

Tuning the magnetic interactions in van der Waals Fe$_3$GeTe$_2$ heterostructures: A comparative study of \textit{ab initio} methods

We investigate the impact of mechanical strain, stacking order, and external electric fields on the magnetic interactions of a two-dimensional (2D) van der Waals (vdW) heterostructure in which a 2D ferromagnetic metallic Fe$_3$GeTe$_2$ monolayer is deposited on germanene. Three distinct computational approaches based on \textit{ab initio} methods are used, and a careful comparison is given: (i) The Green's function method, (ii) the generalized Bloch theorem, and (iii) the supercell approach. First, the shell-resolved exchange constants are calculated for the three Fe atoms within the unit cell of the freestanding Fe$_3$GeTe$_2$ monolayer. We find that the results between methods (i) and (ii) are in good qualitative agreement and also with previously reported values. An electric field of ${\cal E}= \pm 0.5$~V/Å applied perpendicular to the Fe$_3$GeTe$_2$/germanene heterostructure leads to significant changes of the exchange constants. We show that the Dzyaloshinskii-Moriya interaction (DMI) in Fe$_3$GeTe$_2$/germanene is mainly dominated by the nearest neighbors, resulting in a good quantitative agreement between methods (i) and (ii). Furthermore, we demonstrate that the DMI is highly tunable by strain, stacking, and electric field, leading to a large DMI comparable to that of ferromagnetic/heavy metal (FM/HM) interfaces. The geometrical change and hybridization effect explain the origin of the high tunability of the DMI at the interface. The electric-field driven DMI obtained by method (iii) is in qualitative agreement with the more accurate \textit{ab initio} method used in approach (ii). However, the field-effect on the DMI is overestimated by method (iii) by about 50\%. The magnetocrystalline anisotropy energy can also be drastically changed by the application of compressive or tensile strain in the Fe$_3$GeTe$_2$/germanene heterostructure.

cond-mat.mtrl-sci↗

arXiv2022

Strain-Driven Zero-Field Near-10 nm Skyrmions in Two-Dimensional van der Waals Heterostructures

Magnetic skyrmions $-$ localized chiral spin structures $-$ show great promise for spintronic applications. The recent discovery of two-dimensional (2D) magnetic materials opened new opportunities for exploring such topological spin structures in atomically thin van der Waals (vdW) materials. Despite recent progress in stabilizing metastable skyrmions in 2D magnets, their diameters are still beyond 100~nm and their lifetime, which is essential for applications, has not been explored yet. Here, using first-principles calculations and atomistic spin simulations, we predict that compressive mechanical strain leads to stabilizing zero-field skyrmions with diameters close to 10 nm in a Fe$_3$GeTe$_2$/germanene vdW heterostructure. The origin of these unique skyrmions is attributed to the high tunability of Dzyaloshinskii-Moriya interaction and magnetocrystalline anisotropy energy by strain, an effect which is shown to be general for Fe$_3$GeTe$_2$ heterostructures with buckled substrates. Based on our first-principles parameters for the magnetic interactions, we calculate the energy barriers protecting skyrmions against annihilation and their lifetimes using transition-state theory. We show that nanoscale skyrmions in strained Fe$_3$GeTe$_2$/germanene can be stable for hours at temperatures up to 20 K.

cond-mat.mtrl-sci↗

arXiv2022

Nano-scale collinear multi-Q states driven by higher-order interactions

Complex magnetic order arises due to the competition of different interactions between the magnetic moments. Recently, there has been an increased interest in such states not only to unravel the fundamental physics involved, but also with regards to applications exploiting their unique interplay with moving electrons. Whereas it is the Dzyaloshinskii-Moriya interaction (DMI) that has attracted much attention because of its nature to induce non-collinear magnetic order including magnetic-field stabilized skyrmions, it is the frustration of exchange interactions that can drive magnetic order down to the nano-scale. On top of that, interactions between multiple spins can stabilize two-dimensional magnetic textures as zero-field ground states, known as multi-Q states. Here, we introduce a two-dimensional itinerant magnet with various competing atomic-scale magnetic phases. Using spin-polarized scanning tunneling microscopy we observe several zero-field uniaxial or hexagonal nano-scale magnetic states. First-principles calculations together with an atomistic spin model reveal that these states are stabilized by the interplay of frustrated exchange and higher-order interactions while the DMI is weak. Unexpectedly, it is found that not only non-collinear magnetic states arise, but that higher-order interactions can also lead to collinear nano-scale multi-Q states.

cond-mat.mtrl-sci↗

arXiv2021

Electric-field driven stability control of skyrmions in an ultrathin transition-metal film

To realize future spintronic applications with magnetic skyrmions -- topologically nontrivial swirling spin structures -- it is essential to achieve efficient writing and deleting capabilities of these quasi-particles. Electric-field assisted nucleation and annihilation is a promising route, however, the understanding of the underlying microscopic mechanisms is still limited. Here, we show how the stability of individual magnetic skyrmions in an ultrathin transition-metal film can be controlled via external electric fields. We demonstrate based on density functional theory that it is important to consider the changes of all interactions with electric field, i.e., the pair-wise exchange, the Dzyaloshinskii-Moriya interaction, the magnetocrystalline anisotropy energy, and the higher-order exchange interactions. The energy barriers for electric-field assisted skyrmion writing and deleting obtained via atomistic spin simulations vary by up to a factor of three more than the variations of the interactions calculated from first-principles. This surprising effect originates from the electric-field dependent size of metastable skyrmions at a fixed magnetic field. The large changes of lifetimes allow the possibility of electric-field assisted thermally activated writing and deleting of skyrmions.

cond-mat.mtrl-sci↗

arXiv2021

Effects of interlayer exchange on collapse mechanisms and stability of magnetic skyrmions

Theoretical calculations of thermally activated decay of skyrmions in systems comprising several magnetic monolayers are presented, with a special focus on bilayer systems. Mechanisms of skyrmion collapse are identified and corresponding energy barriers and thermal collapse rates are evaluated as functions of the interlayer exchange coupling and mutual stacking of the monolayers using transition state theory and an atomistic spin Hamiltonian. In order to contrast the results to monolayer systems, the magnetic interactions within each layer are chosen so as to mimic the well-established Pd/Fe/Ir(111) system. Even bilayer systems demonstrate a rich diversity of skyrmion collapse mechanisms that sometimes co-exist. For very weakly coupled layers, the skyrmions in each layer decay successively via radially-symmetric shrinking. Slightly larger coupling leads to an asymmetric chimera collapse stabilized by interlayer exchange. When the interlayer exchange coupling reaches a certain critical value, the skyrmions collapse simultaneously. Interestingly, the overall energy barrier for the skyrmion collapse does not always converge to a multiple of that for a monolayer system in the strongly coupled regime. For a certain stacking of the magnetic layers, the energy barrier as a function of the interlayer exchange coupling features a maximum and then decreases with the coupling strength in the strong coupling regime. Calculated mechanisms of skyrmion collapse are used to ultimately predict the skyrmion lifetime. Our results reveal a comprehensive picture of thermal stability of skyrmions in magnetic multilayers and provide a perspective for realizing skyrmions with controlled properties.

physics.comp-ph↗

arXiv2021

Tuning exchange interactions in antiferromagnetic Fe/W(001) by 4d transition-metal overlayers

We use first-principles calculations based on density functional theory to study how the magnetic properties of an Fe monolayer on a W(001) surface -- exhibiting a $c(2 \times 2)$ antiferromagnetic ground state -- can be modified by an additional 4d transition-metal overlayer. To obtain an overview of how the 4d-band filling influences the exchange interactions in the Fe layer we have calculated the energy dispersion of spin spirals for 4d/Fe/2W unsupported quadlayers, in which the W(001)substrate is represented by only two atomic layers. Hybridization with the overlayer leads to a reduced ferromagnetic nearest-neighbor exchange interaction and the next-nearest neighbor exchange gains in strength. Surprisingly, we find that the $c(2 \times 2)$ antiferromagnetic state is unfavorable for all systems with a 4d overlayer. For 4d overlayers from the beginning (Nb) or end (Pd) of the series we find a ferromagnetic ground state. As one moves to the center of the series there is a transition via a spin spiral (Mo, Rh) to a $p (2 \times 1)$ antiferromagnetic ground state (Tc, Ru). We have studied the Mo, Ru, and Pd overlayer on Fe/W(001) representing the surface by a sufficiently large number of W layers to obtain bulk like properties in its center. The energy dispersion of spin spirals show qualitatively the same results as those from the 4\textit{d}/Fe/2W quadlayers. The Dzyaloshinskii-Moriya interaction calculated upon including spin-orbit coupling shows significant strength and considerable frustration effects. The calculated magnetocrystalline anisotropy energy is large as well. All 4d/Fe/W(001) films are potential candidates for complex non-collinear spin structures.

cond-mat.mtrl-sci↗

arXiv2021

Topological-chiral magnetic interactions in ultrathin films at surfaces

We demonstrate that topological-chiral magnetic interactions can play a key role for magnetic ground states in ultrathin films at surfaces. Based on density functional theory we show that significant chiral-chiral interactions occur in hexagonal Mn monolayers due to large topological orbital moments which interact with the emergent magnetic field. Due to the competition with higher-order exchange interactions superposition states of spin spirals such as the 2Q state or a distorted 3Q state arise. Simulations of spin-polarized scanning tunneling microscopy images suggest that the distorted 3Q state could be the magnetic ground state of a Mn monolayer on Re(0001).

cond-mat.mtrl-sci↗

arXiv2021

Trends of higher-order exchange interactions in transition-metal trilayers

We present a systematic study of higher-order exchange interactions beyond the pair-wise Heisenberg exchange in transition-metal trilayers based on density functional theory calculations. We show that these terms can play an important role in magnetic trilayers composed of a single hexagonal Fe or Co atomic layer sandwiched between $4d$ and $5d$ transition-metal layers. We study the dependence of the biquadratic and the three-site and four-site four spin interaction on the band filling of the $4d$ and $5d$ layers as well as the stacking sequence, i.e. fcc vs. hcp stacking. Our calculations reveal relatively small higher-order interactions for Co based trilayers. For Fe based trilayers with a Rh or Ir layer the higher-order terms can be on the same order of magnitude as pair-wise Heisenberg exchange. The trends obtained for freestanding trilayers are used to understand the higher-order interactions in ultrathin film systems on surfaces that are experimentally accessible. It is shown that hcp Rh/Fe/Ir(111) and hcp-Rh/Fe/Rh(111) exhibit the largest values for the biquadratic and the three-site four spin interaction of all systems under study. We further demonstrate that the three-site four spin interaction is responsible for the experimentally observed change of the magnetic ground state of Rh/Fe/Ir(111) from a spin spiral (single-Q) for fcc-Rh to a 2Q state for hcp-Rh. We find similar trends for Rh/Fe/Rh(111), i.e. replacing the Ir surface by the isoelectronic Rh surface. For Rh/Co/Ir(111), we obtain a negative value for the four-site four spin interaction which will lead to a reduced stability of magnetic skyrmions which are metastable in this film at zero magnetic field. In contrast, for Pd/Fe/Ir(111), the four-site four spin interaction is positive which leads to an enhanced stability of skyrmions.

cond-mat.mtrl-sci↗

arXiv2020

Toward room-temperature nanoscale skyrmions in ultrathin films

Breaking the dilemma between small size and room temperature stability is a necessary prerequisite for skyrmion-based information technology. Here we demonstrate by means of rate theory and an atomistic spin Hamiltonian that the stability of isolated skyrmions in ultrathin ferromagnetic films can be enhanced by the concerted variation of magnetic interactions while keeping the skyrmion size unchanged. We predict film systems where the lifetime of sub-10 nm skyrmions can reach years at ambient conditions. The long lifetime of such small skyrmions is due to exceptionally large Arrhenius pre-exponential and the stabilizing effect of the energy barrier is insignificant at room temperature. A dramatic increase in the pre-exponential is achieved thanks to softening of magnon modes of the skyrmion, thereby increasing the entropy of the skyrmion with respect to the transition state for collapse. Increasing the number of skyrmion deformation modes should be a guiding principle for the realization of nanoscale, room-temperature stable skyrmions.

cond-mat.mes-hall↗