arXiv subjects

Stefan Heinze

Publications and source records attributed to Stefan Heinze.

At least 19 recordsLinked to original sources

arXiv2026

Topological and spin-orbit effects on orbital moments in ultra-thin magnetic films

Topological orbital moments (TOMs) are a direct hallmark of a magnetic texture with a non-trivial spin topology. In addition to giving insight into the topology of the magnetic texture, TOMs could also be used to manipulate magnetic structures with a compensated total spin moment. Experimental evidence of TOMs has been provided via transport measurements of the Hall effect in intercalated van-der-Waals materials. However, a direct observation of TOMs is still missing. Another complication arises for the unambiguous proof of the topological origin since orbital moments can also occur due to spin-orbit coupling. Here, we use first-principles electronic structure theory to investigate the origin of orbital moments in different compensated spin structures with a non-trivial topology. We focus on ultrathin magnetic films at surfaces such as Pd/Mn bilayers on Re(0001) which represent ideal model systems for the detection of TOMs since it is possible to apply experimental techniques with local resolution of magnetic properties such as spin-polarized scanning tunneling microscopy. Due to its trivial topology we use the row-wise antiferromagnetic (RW-AFM) state in a hexagonal monolayer to analyze the spin-orbit induced contributions. The triple-Q (3Q) state is a superposition state of three RW-AFM (1Q) states and thus electronically similar, however, due to its non-trivial spin topology it exhibits TOMs. The comparison between these two spin states allows us to disentangle the topological and spin-orbit contributions to the orbital moments. We find that TOMs have an important contribution in spin-compensated systems, since the spin-orbit coupling induced orbital moments are nearly compensated. First-principles calculations for atomic-scale skyrmion lattices in Fe monolayers on different surfaces exhibit the same general trend found for the 3Q state.

cond-mat.mtrl-sci↗

arXiv2026

Electric-field induced trends of exchange interactions in transition-metal trilayers

Using density functional theory, we have performed a systematic study of the Heisenberg pairwise exchange interaction and the beyond Heisenberg multi-spin higher-order exchange interactions in unsupported transition-metal trilayers in the presence of external electric fields. The systems consist of a hexagonal atomic Fe layer sandwiched between 4$d$ (Ru, Rh, and Pd) and 5$d$ (Ir) transition-metal layers. Both fcc and hcp stackings of the 4$d$ overlayer have been taken into account. To scan a large part of the magnetic phase space, we have calculated the energy dispersion of spin spirals without and with applied electric fields up to $\pm 1.0$ V/Å. We find that the energy dispersion remains qualitatively the same upon applying the electric fields and the magnetic ground state remains unchanged. The exchange constants obtained by fitting the energy dispersions exhibit a linear dependence on the electric field up to values of about $\pm 0.5$ V/Å. The sign of the calculated pairwise and higher-order exchange constants remain unchanged with electric field, however, their values and field induced variation are sensitive to the 4$d$ overlayer. The changes are on the order of a few percent for the nearest-neighbor exchange constant and up to a few ten percent for beyond nearest-neighbor constants. The higher-order exchange constants are calculated based on the total energies of multi-$Q$ states, such as the $uudd$ and the 3$Q$ state. Similar to the pairwise exchange constants, we find a nearly linear field dependence of the higher order constants at small electric fields and variations of up to ten percent. We study the spin-dependent screening of the electric field for the three trilayers based on the spin- and orbital-decomposed electronic states.

cond-mat.mtrl-sci↗

arXiv2026

Lifetime of bimerons and antibimerons in two-dimensional magnets

Soliton-based computing architectures have recently emerged as a promising avenue to overcome fundamental limitations of conventional information technologies, the von Neumann bottleneck. In this context, magnetic skyrmions have been widely considered for in-situ processing devices due to their mobility and enhanced lifetime in materials with broken inversion symmetry. However, modern applications in non-volatile reservoir or neuromorphic computing raise the additional demand for non-linear inter-soliton interactions. Here, we report that solitons in easy-plane magnets, such as bimerons and antibimerons, show greater versatility and potential for non-linear interactions than skyrmions and antiskyrmions, making them superior candidates for this class of applications. Using first-principles and transition state theory, we predict the coexistence of degenerate bimerons and antibimerons at zero field in a van der Waals heterostructure Fe$_3$GeTe$_2$/Cr$_2$Ge$_2$Te$_6$ -- an experimentally feasible system. We demonstrate that, owing to their distinct structural symmetry, bimerons exhibit fundamentally different behavior from skyrmions and cannot be regarded as their in-plane counterparts, as is often assumed. This distinction leads to unique properties of bimerons and antibimerons, which arise from the unbroken rotational symmetry in easy-plane magnets. These range from anisotropic soliton-soliton interactions to strong entropic effects on their lifetime, driven by the non-local nature of thermal excitations. Our findings reveal a broader richness of solitons in easy-plane magnets and underline their unique potential for spintronic devices.

cond-mat.mes-hall↗

arXiv2026

Strongly enhanced lifetime of higher-order bimerons and antibimerons

Magnetic bimerons, similar to skyrmions, are topologically nontrivial spin textures characterized by topological charge $Q$. Most studies so far have focused on low-$Q$ solitons ($|Q| \leq 1$), such as skyrmions, bimerons, and vortices. Here, we present the first calculations of the lifetimes of {ring-like} high-$Q$ bimerons and demonstrate that they are fundamentally more stable than high-$Q$ skyrmions over a wide range of temperature. To obtain realistic results, our chosen system is an experimentally feasible van der Waals interface, Fe$_3$GeTe$_2$/Cr$_2$Ge$_2$Te$_6$. We show that the lifetimes of high-$Q$ (anti)bimerons can exceed the lifetime of those with $|Q|=1$ by 3 orders of magnitude. Remarkably, this trend remains valid even when extrapolated to room temperature (RT), as the lifetimes are dominated by entropy rather than energy barriers. This contrasts with high-$Q$ skyrmions, whose lifetimes fall with $|Q|$ near RT. We attribute this fundamental difference between skyrmions and bimerons to their distinct magnetic texture symmetries, which lead to different entropy-dominated lifetimes.

cond-mat.mes-hall↗

arXiv2026

Extended saddle points govern long-lived antiskyrmions

Achieving long-lived nanoscale magnetic solitons remains a central challenge, as their lifetimes typically decrease rapidly with temperature. Here, we demonstrate that anisotropic Dzyaloshinskii-Moriya interaction (aDMI) enables spatially extended saddle points (SPs) that fundamentally alter thermally activated decay. In contrast to conventional localized SPs, these extended configurations completely suppress the entropic contribution to the activation rate, rendering the lifetimes effectively temperature independent. To establish this mechanism, we develop a first-principles method based on spin spirals to compute DMI beyond the isotropic approximation, resolving its full directional dependence for arbitrary nearest neighbors. We apply this method to oxidized Fe$_3$GeTe$_2$ (FGT-O), an experimentally accessible van der Waals magnet. Oxygen adsorption simultaneously breaks inversion symmetry and lowers the in-plane crystalline symmetry, thereby generating a sizable aDMI. We demonstrate that aDMI stabilizes nanoscale antiskyrmions with energy barriers exceeding 120 meV at low external magnetic fields. Crucially, extended SPs enhance the lifetime in FGT-O by more than five orders of magnitude at room temperature compared to conventional ultrathin-film skyrmion systems. We further show that aDMI is not the only route to such extended SPs and identify the general conditions under which they emerge, establishing a general route to soliton decay pathways with temperature-independent prefactors. Our results uncover a new paradigm for enhancing soliton stability through transition-state geometry rather than energy-barrier height.

cond-mat.mes-hall↗

arXiv2026

Emergence of multiple topological spin textures in an all-magnetic van der Waals heterostructure

Magnetic solitons such as skyrmions and bimerons show great promise for both fundamental research and spintronic applications. Stabilizing and controlling topological spin textures in atomically thin van der Waals (vdW) materials has gained tremendous attention due to high tunability, enhanced functionality, and miniaturization. Here, we present an efficient spin-spiral approach based on first-principles, a method for mapping magnetic interactions from collective models onto arbitrary lattice symmetries, such as hexagonal and honeycomb lattices. Using atomistic spin models parametrized from first-principles, we predict the emergence of multiple topological spin textures in an all-magnetic vdW heterostructure Fe$_3$GeTe$_2$/Cr$_2$Ge$_2$Te$_6$ (FGT/CGT) -- an experimentally feasible system. Interestingly, the FGT layer favors out-of-plane magnetization, whereas the CGT layer prefers in-plane magnetocrystalline anisotropy. Néel-type nanoscale skyrmions are formed at zero field in the FGT layer due to interfacial Dzyaloshinskii-Moriya interaction (DMI), while nanoscale bimerons and antibimerons can co-exist in the CGT layer by the interplay between exchange frustration and DMI. Using the collective approach we apply, we reveal significant discretization effects in hexagonal and honeycomb geometries. In particular, we demonstrate that the lifting of geometric exchange frustration on the honeycomb significantly affects soliton barriers and pinning energetics. These fundamental results not only highlight the importance of spin simulations in discrete models for topological magnetism, especially in 2D materials, but may also help to pave the way for solitonic devices based on atomically thin vdW heterostructures.

cond-mat.mtrl-sci↗

arXiv2026

Skyrmions in 2D chiral magnets with noncollinear ground states stabilized by higher-order interactions

Magnetic skyrmions are intriguing topological spin textures that have attracted great attention due to their potential for future spintronic devices. Skyrmions have so far been explored in different magnetic materials, such as ferromagnets, antiferromagnets, and ferrimagnets. Here, we propose a new type of unconventional skyrmions stabilized in noncollinear magnets. Using first-principles calculations and atomistic spin simulations, we demonstrate that a noncollinear ground state can be stabilized in Rh/Co and Pd/Co atomic bilayers on the Re(0001) surface by four spin exchange interactions, although Co -- a material often used in applications -- is a prototypical ferromagnet with strong pairwise exchange interaction. We further show that unconventional skyrmion lattices and isolated skyrmions can emerge on this noncollinear magnetic background. Transition-state theory calculations reveal that these metastable skyrmions are protected by large energy barriers, suggesting that they could be observed in experiments. These unconventional types of skyrmions in noncollinear magnets might open new possibilities for topological spin transport or magnet-superconductor hybrid systems.

cond-mat.mtrl-sci↗

arXiv2026

Platform for zero-field isolated skyrmions: 4$d$/Co atomic bilayers on Re(0001)

Using first-principles density functional theory (DFT) combined with atomistic spin simulations, we explore the possibility of realizing zero-field isolated skyrmions in three 4$d$/Co atomic bilayers -- Rh/Co, Pd/Co, and Ru/Co -- grown on the Re(0001) surface. Our investigation employs an extended atomistic spin model, which goes beyond the standard model by including the multi-spin higher-order exchange interactions (HOI) in addition to the Heisenberg pairwise exchange interaction, Dzyaloshinskii-Moriya interaction (DMI), and magnetocrystalline anisotropy energy (MAE). All magnetic interactions of the extended spin model are calculated using DFT. The phase diagram obtained from atomistic spin simulations based on this spin model for Rh/Co and Pd/Co on Re(0001) reveals that isolated skyrmions emerge spontaneously on the ferromagnetic background even in the absence of an external magnetic field. The radius of zero-field isolated skyrmions in Rh/Co/Re(0001) is around 6 nm, whereas the radius of those skyrmions in Pd/Co/Re(0001) is about 12 nm. Transition-state theory calculations show that the skyrmions are protected by substantial energy barriers, approximately 150 meV, which predominantly arise from DMI, with a small contribution from the HOI interactions. The height of the barriers suggests that skyrmions could be observed in low-temperature experiments. Based on this work, we propose 4$d$/Co bilayers on Re(0001) as a new platform to realize nanoscale zero-field isolated skyrmions.

cond-mat.mtrl-sci↗

arXiv2025

Topological spin textures in an antiferromagnetic monolayer

Topological spin structures such as magnetic skyrmions are of fundamental interest and promising for various types of applications in spintronics. Skyrmions have been predicted to emerge also in antiferromagnetic materials where they exhibit superior transport properties. They were experimentally revealed in synthetic antiferromagnets, however, still remain elusive in intrinsic antiferromagnets. Here, we demonstrate the stabilization of topological spin structures in an antiferromagnetic monolayer. Using spin-polarized scanning tunneling microscopy, we observe an antiferromagnetic spin spiral in the Mn monolayer and a collinear antiferromagnetic state in the Mn double-layer on Ta(110). Near the boundary to the double-layer half-skyrmions form in the monolayer as revealed in combination with first-principles calculations and micromagnetic simulations. Our work shows how the topological state in antiferromagnetic material systems can be controlled by the configuration within a lateral heterostructure, resulting in trivial non-coplanar states or antiferromagnetic skyrmions.

cond-mat.mtrl-sci↗

arXiv2025

Impact of higher-order exchange on the lifetime of skyrmions and antiskyrmions

Reliable control of skyrmion lifetime is essential for realizing spintronic devices, yet the role of higher-order exchange - which can lead to skyrmion stabilization - remains largely unexplored. Here we calculate lifetimes of isolated skyrmions and antiskyrmions at transition-metal interfaces based on an atomistic spin model that includes all fourth-order exchange terms. Within harmonic transition-state theory, we evaluate both energetic and entropic contributions and find substantially enhanced lifetimes when higher-order exchange is included. The four-spin four-site interaction raises the energy barrier and lowers the curvature of the energy landscape at the collapse saddle point, increasing the pre-exponential factor. We show that skyrmions and antiskyrmions can remain thermally stable even without Dzyaloshinskii-Moriya interaction (DMI), and that tuning the four-spin term by a small amount modulates the prefactor over orders of magnitude. Our results identify higher-order exchange as a promising route to stabilize topological magnetic textures - in particular in systems lacking DMI - and to engineer their thermally activated decay.

physics.comp-ph↗

arXiv2025

A new skyrmion topological transition driven by higher-order exchange interactions in Janus MnSeTe

Two-dimensional (2D) van der Waals magnets offer a promising platform for pushing skyrmion technology to the single-layer limit with high tunability. While Dzyaloshinskii-Moriya interaction (DMI) is often recognized as central to skyrmion formation, their stability, collapse, and topological transition in 2D materials remain largely unexplored. In particular, the effect of higher-order exchange interactions (HOI) on these phenomena is unknown. Here, using first-principles calculations and atomistic spin simulations, we report a new topological transition generated by HOI, which we term 'ferric transition', in single-layer MnSeTe. Surprisingly, skyrmion stability and collapse remain largely unaffected by HOI due to the dominant role of DMI near the saddle point, whereas the Bloch point is strongly modified, giving rise to this novel transition. This mechanism is fundamentally distinct from the well-known radial and chimera transitions. Moreover, we predict that Janus MnSeTe exhibits remarkably high skyrmion energy barriers due to its strong DMI, among the highest reported for intrinsic 2D magnets. Our findings unveil an unexpected role of HOI in skyrmion topological transitions and establish Janus MnSeTe as a robust platform for 2D skyrmionics.

cond-mat.mes-hall↗

arXiv2025

Long lifetimes of nanoscale skyrmions in lithium-decorated van der Waals ferromagnet Fe$_3$GeTe$_2$

The Dzyaloshinskii-Moriya interaction (DMI), which originates from spin-orbit coupling and relies on broken inversion symmetry, is recognized as a key ingredient in forming magnetic skyrmions. However, most 2D magnets exhibit inversion symmetry; therefore, the DMI is suppressed. Here, we propose a strategy to induce large DMI via lithium absorption on the surface of 2D magnets -- an experimentally feasible approach. Using first-principles and atomistic spin simulations, we predict the formation of nanoscale skyrmions in lithium-decorated monolayer Fe$_3$GeTe$_2$ by imposing small out-of-plane magnetic fields ($B_z$). Notably, we find very large skyrmion energy barriers of more than 300 meV at $B_z = 0.4$ T, comparable to those observed in ferromagnet/heavy-metal interfaces. The origin of these unique skyrmions is attributed to the competition between strong DMI, exchange frustration, and small magnetocrystalline anisotropy energy. We further show that the lifetimes of metastable skyrmions exceed one hour for temperatures up to 75 K.

cond-mat.mtrl-sci↗

arXiv2025

Entropy-driven phase transition in a non-collinear antiferromagnet due to higher-order exchange interactions

The triple-Q state arises due to the superposition of three symmetry equivalent spin spirals stabilized by higher-order exchange interactions. It has been predicted more than 20 years ago but was only recently discovered in a Mn monolayer on the Re(0001) surface. To date little is known about the thermodynamic properties of this intriguing non-coplanar spin state. Here, we reveal a low-temperature phase transition between the triple-Q and the row-wise antiferromagnetic state in this system via Monte Carlo simulations based on an atomistic spin model parametrized by density functional theory. By modeling the free energy landscape in terms of thermal excitations we derive an analytical expression of the partition function, which allows us to prove that the phase transition is driven by entropy. The predicted phase transition is not unique to Mn/Re(0001) but appears for a wide range of magnetic interaction parameters and is expected to occur also for other multi-Q states.

cond-mat.mtrl-sci↗

arXiv2025

Spin-polarized edge modes between different magnet-superconductor-hybrids

The interplay of magnetism and superconductivity can lead to intriguing emergent phenomena. Here we combine two different two-dimensional antiferromagnetic magnet-superconductor hybrids (MSH) and study their properties using spin-polarized scanning tunneling microscopy. Both MSHs show the characteristics of a topological nodal point superconducting phase with edge modes to the trivial substrate superconductor. At the boundary between the two MSHs we find low-energy modes which are spin-polarized. Based on a tight-binding model we can explain the experimental observations by considering two different topological nodal point superconductors. This gives rise to spin-polarized chiral edge modes that connect topological nodal points of the two different MSH. We demonstrate via the complex band structure that due to an asymmetric lateral decay these edge modes are spin-polarized, regardless of the details of the spin structure at the boundary. The presence of spin-polarized edge states between different topological superconductors enables advanced functional design for the exploitation of MSHs as a platform for topology-based applications.

cond-mat.supr-con↗

arXiv2025

Bilayer triple-Q state driven by interlayer higher-order exchange interactions

Using first-principles calculations and an atomistic spin model we predict the stabilization of a bilayer triple-Q state in an atomic Mn bilayer on Ir(111) due to interlayer higher-order exchange interactions. Based on density functional theory (DFT) we study the magnetic interactions and ground state in a Mn monolayer and bilayer on the Ir(111) surface. We calculate the energy dispersion of spin spirals (single-Q states) to scan a large part of the magnetic phase space and to obtain constants of pair-wise exchange interactions. By including spin-orbit coupling we determine the strength of the Dzyaloshinskii-Moriya interaction. To reveal the role of higher-order exchange interactions in these films, we consider multi-Q states obtained by a superposition of spin spirals. For the Mn monolayer in fcc stacking on Ir(111), the triple-Q state exhibits the lowest total energy in DFT, while the Néel state is most favorable for hcp stacking. For the Mn bilayer on Ir(111), two types of the triple-Q state are possible. In both magnetic configurations, a triple-Q state occurs within each of the Mn layers. However, only in one of them the spin alignment between the layers is such that nearest-neighbor spins of different layers also exhibit the tetrahedron angles which characterize the triple-Q state. We denote this state -- which has the lowest total energy in our DFT calculations -- as the ideal bilayer triple-Q state. This state exhibits significant topological orbital moments within each of the two Mn layers which are aligned in parallel resulting in a large topological orbital magnetization. We interpret the DFT results within an atomistic spin model which includes pair-wise Heisenberg exchange, the Dzyaloshinskii-Moriya interaction, as well as higher-order exchange interactions....

cond-mat.mtrl-sci↗

arXiv2025

Eigenmode following for direct entropy calculation and characterization of magnetic systems

We present an eigenmode following method (EMF) that has been developed for the numerical scanning of the potential energy surface and the direct calculation of entropy and pre-exponential factors of Arrhenius-like transition rates in the framework of transition state theory. In contrast to other methods, we do not use EMF to move "uphill" or "downhill" in energy to find stationary points, but to obtain energy curves. By numerical integration of the Boltzmann factor along these curves, the partition functions of the followed eigenmodes can be calculated without making assumptions of the form of the energy curves. The EMF method is computationally more elaborate than traditional approaches as it requires iterative updates of the respective eigenpair spectrum. In order to mitigate this increase in computational cost, the EMF method can be combined with other approaches like the harmonic approximation for all eigenmodes but the softest which typically require the most accurate mod elling. In this work we first introduce the general theoretical background and algorithm of the EMF method before providing test calculations and relevant use-cases in the framework of atomistic spin simulations with a focus on magnetic skyrmions collapse.

cond-mat.mtrl-sci↗

arXiv2024

Strain-driven domain wall network with chiral junctions in an antiferromagnet

Materials with antiferromagnetic order have recently emerged as promising candidates in spintronics based on their beneficial characteristics such as vanishing stray fields and ultra-fast dynamics. At the same time more complex localized non-coplanar magnetic states as for instance skyrmions are in the focus of applications due to their intriguing properties such as the topological Hall effect. Recently a conceptual shift has occurred to envision the use of such magnetic defects not only in one-dimensional race track devices but to exploit their unique properties in two-dimensional networks. Here we use local strain in a collinear antiferromagnet to induce non-coplanar domain wall junctions, which connect in a very specific way to form extended networks. We combine spin-polarized scanning tunneling microscopy with density functional theory to characterize the different building blocks of the network, and unravel the origin of the handedness of triple-junctions and the size of the arising topological orbital moments.

cond-mat.mes-hall↗

arXiv2024

First-principles investigation of magnetic exchange force microscopy on adatoms adsorbed on an antiferromagnetic surface

Using density functional theory (DFT), we calculate the magnetic short-ranged exchange forces between a magnetic tip and an adatom adsorbed on the antiferromagnetic Mn monolayer on the W(110) surface [Mn/W(110)]. These exchange forces can be measured in magnetic exchange force microscopy allowing atomic-scale imaging of spin structures on insulating and conducting surfaces. We consider two types of $3d$ transition-metal atoms with intrinsic magnetic moments: Co and Mn and Ir as an example of a $5d$ transition-metal atom exhibiting an induced magnetic moment on Mn/W(110). The tips are modeled by Fe pyramids and terminated either with an Fe or a Mn apex atom. From our total energy DFT calculations for a parallel and antiparallel alignment between tip and adatom magnetic moments we obtain the exchange energy $E_{\rm ex}(d)$ as a function of tip-adatom distance $d$. The exchange forces, $F_{\rm ex}(d)$, are calculated based on the Hellmann-Feynman theorem. We show that structural relaxations of tip and sample due to their interaction need to be taken into account. Due to the exchange interaction the relaxations depend on the alignment between tip and adatom magnetization -- an effect which will affect the tunneling magnetoresistance that can be measured by a scanning tunneling microscope. A maximum in the exchange energy and force curves is obtained for magnetic adatoms at tip-adatom separations of about 3 to 4~Å. The exchange forces with an Fe terminated tip reach a maximum value of up to 0.2~nN and 0.6~nN for Co and Mn adatoms, respectively, and prefer an antiferromagnetic coupling. Surprisingly, we also find an exchange force of up to 0.2~nN for Ir adatoms. We analyze the exchange interaction between tip and adatom based on the spin-polarized electronic structure of the coupled system......

cond-mat.mtrl-sci↗