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Eigenmode following for direct entropy calculation and characterisation of magnetic systems
(Springer Nature, 2026-07-13) von Malottki, S.; Goerzen, Moritz A.; Schrautzer, Hendrik; Bessarab, Pavel F.; Heinze, Stefan; Faculty of Physical Sciences (UI); Raunvísindadeild (HÍ); School of Engineering and Natural Sciences (UI); Verkfræði- og náttúruvísindasvið (HÍ)
The effect of entropy can be crucial for magnetic skyrmions, and in some cases, its accurate prediction has been prevented by the limitations of the harmonic approximation. 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 transition rates. While the concepts of following eigenmodes and numerical direct entropy calculation have been known individually, their combination yields a new and general way of effective sampling of the energy surface for high-accuracy treatment of non-harmonic eigenmodes. For this, the EMF method requires iterative updates of the eigenpairs of the softest eigenmodes that need the most accurate modelling. In contrast to other methods, EMF does not 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 following eigenmodes can be calculated without making assumptions of their form. We 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 skyrmion collapse.
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Impact of higher-order exchange on the lifetime of skyrmions and antiskyrmions
(Springer Nature, 2026-03-23) Schrautzer, Hendrik; Goerzen, Moritz A.; Beyer, Bjarne; Haldar, Soumyajyoti; Bessarab, Pavel F.; Heinze, Stefan; Faculty of Physical Sciences (UI); Raunvísindadeild (HÍ); School of Engineering and Natural Sciences (UI); Verkfræði- og náttúruvísindasvið (HÍ)
Reliable control of skyrmion lifetime is essential for realizing spintronic devices, yet the role of higherorder 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.
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Chemical warfare in a degraded land: The allelopathic capacity and allelochemical diversity of Empetrum nigrum in Icelandic tundra ecosystems
(University of Iceland, School of Engineering and Natural Sciences, Faculty of Life and Environmental Sciences, 2026-11-11) Ryde, Ingvild; Prof. Emerita Ingibjörg Svala Jónsdóttir; Faculty of Life and Environmental Sciences (UI); Líf- og umhverfisvísindadeild (HÍ); School of Engineering and Natural Sciences (UI); Verkfræði- og náttúruvísindasvið (HÍ)
Iceland has major issues with land degradation due to centuries of unsustainable land use. Degraded Icelandic tundra ecosystems do not easily recover after removing one of the main drivers of degradation – livestock overgrazing – and they appear to be “trapped” in degraded states. It is important to identify the “trapping mechanisms” potentially interfering with restoration efforts to avoid further loss of plant and soil resources. One such mechanism may be “chemical warfare” through the release of allelochemicals by unpalatable plants that inhibit seed germination and seedling growth in neighbouring species and modify ecosystem processes. The aim of this thesis was to investigate the role of the unpalatable and allelopathic evergreen dwarf shrub Empetrum nigrum in keeping degraded Icelandic tundra ecosystems trapped in degraded states, by assessing the allelopathic capacity and allelochemical diversity of Icelandic Empetrum. This thesis comprises three research papers based on bioassays and chemical analyses following targeted and untargeted liquid chromatography-mass spectrometry metabolomics approaches. The results show that volcanic soils alleviate the allelopathic capacity of Empetrum considerably when compared with non-volcanic soils, reducing negative soil legacy effects of Empetrum-associated soils. Nevertheless, the allelopathic capacity of Empetrum is likely high enough to retard seedling establishment in Icelandic tundra ecosystems, considering the high amount of Empetrum leaf biomass in the system. The synoecious Empetrum group hermaphroditum was found to have a stronger allelopathic capacity than the monoecious nigrum group, partly explained by higher foliar concentrations of the previously designated key allelochemical Batatasin-III. Furthermore, male nigrum plants were found to have a stronger allelopathic capacity than female nigrum plants. That means that the magnitude of Empetrum allelopathic capacities likely vary with the relative abundance of intra-specific groups and sexes. These allelopathically distinct groups and sexes were used as a biological system to identify more potential Empetrum allelochemicals. The untargeted chemical analysis revealed an Empetrum chemical profile characterized by putative phenolics and terpenoids as expected, but also naphthalene- and alkaloid-derivatives which have not been recorded in Empetrum before. Chemical profiles were clearly distinct between the Empetrum groups, whereas there were no clear differences between the nigrum sexes. The allelopathic capacity of Empetrum may be driven by terpenoids, naphthalenes, alkaloids, and various phenolics besides Batatasin-III. Thereby, this thesis broadens our understanding of how Empetrum may chemically interact with its environment and is the first step towards expanding our mechanistic understanding of Empetrum allelopathic effects. In conclusion, Icelandic Empetrum has a high allelopathic capacity and produces a wide range of potential allelochemicals by which it may contribute to keeping Icelandic tundra ecosystems trapped in degraded states. Future studies should aim to assess Empetrum allelopathic capacities in natural Icelandic tundra ecosystems and how they may change with climate warming.
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Emergence of multiple topological spin textures in an all-magnetic van der Waals heterostructure
(American Physical Society, 2026-03-11) Goerzen, Moritz A.; Drevelow, Tim; Schrautzer, Hendrik; Haldar, Soumyajyoti; Heinze, Stefan; Li, Dongzhe; Faculty of Physical Sciences (UI); Raunvísindadeild (HÍ); School of Engineering and Natural Sciences (UI); Verkfræði- og náttúruvísindasvið (HÍ)
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 Fe3GeTe2/Cr2Ge2Te6 (FGT/CGT) – an experimentally feasible system. Interestingly, the FGT layer favors out-of-plane magnetization, whereas the CGT layer prefers in-plane magnetocrystalline anisotropy. Neel-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.
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Identification of mechanisms of magnetic transitions using an efficient method for converging on first-order saddle points
(American Physical Society, 2025-09-24) Schrautzer, Hendrik; Sallermann, Moritz; Bessarab, Pavel F.; Jónsson, Hannes; Faculty of Physical Sciences (UI); Raunvísindadeild (HÍ); School of Engineering and Natural Sciences (UI); Verkfræði- og náttúruvísindasvið (HÍ)
An efficient and scalable implementation of a method for locating first-order saddle points on the energy surface of a magnetic system is presented, along with several applications in which the mechanisms of various magnetic transitions are identified. The starting point for the iterative search algorithm can be anywhere, even close to a local energy minimum representing an initial state of the system, and the final state need not be specified. Convergence on a saddle point is obtained by inverting the component of the gradient along the minimum mode, thereby effectively transforming the neighborhood of the saddle point to that of a local minimum. The method requires only the lowest two eigenvalues and corresponding eigenvectors of the Hessian of the system’s energy and they are found using a quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno solver for the minimization of the Rayleigh quotient without explicit evaluation of the Hessian. The method is applicable to large systems, as it does not introduce additional scaling overhead to the computational complexity determined by the interactions present in the system. Applications are presented to transitions in systems that reveal significant complexity of coexisting magnetic states, such as skyrmions, skyrmion bags, skyrmion tubes, chiral bobbers, and globules. The identification of new metastable three-dimensional (3D) textures, such as magnetic bobbers with extended equilibrium distance between the base and the terminating Bloch point, and magnetic globules appearing as isolated states in 3D due to magnetostatic interactions, demonstrates the usefulness of the method for the characterization of complex energy surfaces of magnetic systems. When combined with rate theory within the harmonic approximation, the method can be used for simulations of the long timescale dynamics of complex magnetic systems characterized by multiple metastable states.