Spin-wave theory of two-dimensional ferromagnets in the presence of dipolar interactions and magnetocrystalline anisotropy

The antiferromagnetic phase of a wurtzite nickel sulfide monolayer

Two-dimensional intrinsic long-range magnetic monolayers with high transition temperatures have attracted great interest in both fundamental studies and practical applications. In this study, we use a combination of first-principles calculations based on density functional theory (DFT), and unitary transformation of the effective Heisenberg model to investigate the electronic structure and magnetic properties of a [NiS]2 monolayer. The phonon calculations reveal that the [NiS]2 monolayer is dynamically stable in the wurtzite phase. This material is an out-of-plane easy-axis antiferromagnetically ordered monolayer with the Néel temperature close to room temperature. The intrinsic AFM ground state arises from the presence of top and bottom FM sublattices coupled together via AFM coupling, in which the net magnetic moment of each Ni atom is evaluated as 0.5μB. The spectrum of the spin-wave of [NiS]2 is investigated within the spin-wave theory of antiferromagnets in terms of the first-order Holstein-Primakoff approximation of the anisotropic Heisenberg model combined with the Bogoliubov diagonalization transformation. For the long wavelength limit, the magnon dispersion shows linear behavior with the wave vector, which is expected for conventional antiferromagnetism. The magnon velocity of approximately ∼600 m s-1 is predicted for the [NiS]2 monolayer by calculating the slope of the magnon spectrum. Due to strong spin-orbit coupling, the [NiS]2 monolayer has relatively large magnetic anisotropy energy, causing the existence of the 12 meV gap at the Γ point in the magnon spectrum. The magnon energy gap limits the number of thermally excited states, which is essential for maintaining intrinsic long-range antiferromagnetic order in two dimensions.

Boosting the Curie temperature of GaN monolayer through van der Waals heterostructures

The pursuit of van der Waals (vdW) heterostructures with high Curie temperature and strong perpendicular magnetic anisotropy (PMA) is vital to the advancement of next generation spintronic devices. First-principles calculations are used to study the electronic structures and magnetic characteristics of GaN/VS2vdW heterostructure under biaxial strain and electrostatic doping. Our findings show that a ferromagnetic ground state with a remarkable Curie temperature (477 K), much above room temperature, exists in GaN/VS2vdW heterostructure and 100% spin polarization efficiency. Additionally, GaN/VS2vdW heterostructure still maintains PMA under biaxial strain, which is indispensable for high-density information storage. We further explore the electron, magnetic, and transport properties of VS2/GaN/VS2vdW sandwich heterostructure, where the magnetoresistivity can reach as high as 40%. Our research indicates that the heterostructure constructed by combining the ferromagnet VS2and the non-magnetic semiconductor GaN is a promising material for vdW spin valve devices at room temperature.

Mapping the phase-separated state in a 2D magnet

Intrinsic 2D magnets have recently been established as a playground for studies on fundamentals of magnetism, quantum phases, and spintronic applications. The inherent instability at low dimensionality often results in coexistence and/or competition of different magnetic orders. Such instability of magnetic ordering may manifest itself as phase-separated states. In 4f 2D materials, magnetic phase separation is expressed in various experiments; however, the experimental evidence is circumstantial. Here, we employ a high-sensitivity MFM technique to probe the spatial distribution of magnetic states in the paradigmatic 4f 2D ferromagnet EuGe2. Below the ferromagnetic transition temperature, we discover the phase-separated state and follow its evolution with temperature and magnetic field. The characteristic length-scale of magnetic domains amounts to hundreds of nanometers. These observations strongly shape our understanding of the magnetic states in 2D materials at the monolayer limit and contribute to engineering of ultra-compact spintronics.

Sliding Phase Transition in Ferroelectric van der Waals Bilayers

We address the sliding thermodynamics of van der Waals-bonded bilayers by continuum electromechanics. We attribute the robustness of the ferroelectricity recently observed in h-BN and WTe_{2} bilayers to large in-plane stiffness of the monolayers. We compute the electric susceptibility and specific heat in a mean-field self-consistent phonon approximation. We compare critical temperatures and electric switching fields with the observed values.

Proximity Coupling of Graphene to a Submonolayer 2D Magnet

Imprinting magnetism into graphene may lead to unconventional electron states and enable the design of spin logic devices with low power consumption. The ongoing active development of 2D magnets suggests their coupling with graphene to induce spin-dependent properties via proximity effects. In particular, the recent discovery of submonolayer 2D magnets on surfaces of industrial semiconductors provides an opportunity to magnetize graphene coupled with silicon. Here, synthesis and characterization of large-area graphene/Eu/Si(001) heterostructures combining graphene with a submonolayer magnetic superstructure of Eu on silicon are reported. Eu intercalation at the interface of the graphene/Si(001) system results in a Eu superstructure different from those formed on pristine Si in terms of symmetry. The resulting system graphene/Eu/Si(001) exhibits 2D magnetism with the transition temperature controlled by low magnetic fields. Negative magnetoresistance and the anomalous Hall effect in the graphene layer provide evidence for spin polarization of the carriers. Most importantly, the graphene/Eu/Si system seeds a class of graphene heterostructures based on submonolayer magnets aiming at applications in graphene spintronics.

Exchange Bias State at the Crossover to 2D Ferromagnetism

The inherent malleability of 2D magnetism provides access to unconventional quantum phases, in particular those with coexisting magnetic orders. Incidentally, in a number of materials, the magnetic state in the bulk undergoes a fundamental change when the system is pushed to the monolayer limit. Therefore, a competition of magnetic states can be expected in the crossover region. Here, an exchange bias state is observed at the crossover from 3D antiferromagnetism to 2D ferromagnetism driven by the number of monolayers in the metalloxene GdSi₂. The material constitutes a stack of alternating monolayers of Gd and silicene, the Si analogue of graphene. The exchange bias manifests itself as a shift of the hysteresis loop signifying coupling of magnetic systems, as evidenced by magnetization studies. Two features distinguish the phenomenon: (i) it is intrinsic, i.e. it is detected in an individual compound; (ii) the exchange bias field, 1.5 kOe, is unusually high, which is conducive to applications. The results suggest magnetic derivatives of 2D-Xenes to be prospective materials for ultracompact spintronics.

2D magnetic phases of Eu on Ge(110)

2D magnetic materials are at the forefront of research on fundamentals of magnetism; they exhibit unconventional phases and properties controlled by external stimuli. 2D magnets offer a solution to the problem of miniaturization of spintronic devices. A technological target of materials science is to find suitable magnetic materials and scale their thickness down as much as possible, a single monolayer being a natural limit. However, magnetism does not halt at one monolayer - it may persist beyond this boundary, to sparse but regular lattices of magnetic atoms. Here, we report 2D magnetic phases of Eu on the Ge(110) surface. We synthesized two submonolayer structures Eu/Ge(110) employing molecular beam epitaxy. The phases, identified by electron diffraction, differ in the surface density of Eu atoms. At low temperature, they exhibit magnetic ordering with magnetic moments lying in-plane. Strong dependence of the effective magnetic transition temperature on weak magnetic fields points at the 2D nature of the observed magnetism. The results are set against those on the Eu/Si system. The study of Eu/Ge(110) magnets demonstrates that a variety of substrates of different structure and symmetry can host submonolayer 2D magnetic phases, suggesting the phenomenon to be rather general.

Analysis of Ionicity-Magnetism Competition in 2D-MX3 Halides towards a Low-Dimensional Materials Study Based on GPU-Enabled Computational Systems

The acceleration of parallel high-throughput first-principle calculations in the context of 3D (three dimensional) periodic boundary conditions for low-dimensional systems, and particularly 2D materials, is an important issue for new material design. Where the scalability rapidly deflated due to the use of large void unit cells along with a significant number of atoms, which should mimic layered structures in the vacuum space. In this report, we explored the scalability and performance of the Quantum ESPRESSO package in the hybrid central processing unit - graphics processing unit (CPU-GPU) environment. The study carried out in the comparison to CPU-based systems for simulations of 2D magnets where significant improvement of computational speed was achieved based on the IBM ESSL SMP CUDA library. As an example of physics-related results, we have computed and discussed the ionicity-covalency and related ferro- (FM) and antiferro-magnetic (AFM) exchange competitions computed for some CrX3 compounds. Further, it has been demonstrated how this exchange interplay leads to high-order effects for the magnetism of the 1L-RuCl3 compound.

Two-Dimensional Magnets beyond the Monolayer Limit

Intrinsic two-dimensional (2D) magnetism has been demonstrated in various materials scaled down to a single monolayer. However, the question is whether 2D magnetism extends beyond the monolayer limit, to chemical species formed by sparse but regular 2D arrays of magnetic atoms. Here we show that sub-monolayer superstructures of Eu atoms self-assembled on the silicon surface exhibit strong magnetic signals. Robust easy-plane magnetism is discovered in both one- and two-dimensionally ordered structures with Eu coverage of half monolayer and above. The emergence of 2D magnetism manifests itself by a strong dependence of the effective transition temperature on weak magnetic fields. The results constitute a versatile platform for miniaturization of 2D magnetic systems and seed an expandable class of atomically thin magnets for applications in information technologies.

Meron-like topological spin defects in monolayer CrCl3

Noncollinear spin textures in low-dimensional magnetic systems have been studied for decades because of their extraordinary properties and promising applications derived from the chirality and topological nature. However, material realizations of topological spin states are still limited. Employing first-principles and Monte Carlo simulations, we propose that monolayer chromium trichloride (CrCl3) can be a promising candidate for observing the vortex/antivortex type of topological defects, so-called merons. The numbers of vortices and antivortices are found to be the same, maintaining an overall integer topological unit. By perturbing with external magnetic fields, we show the robustness of these meron pairs and reveal a rich phase space to tune the hybridization between the ferromagnetic order and meron-like defects. The signatures of topological excitations under external magnetic field also provide crucial information for experimental justifications. Our study predicts that two-dimensional magnets with weak spin-orbit coupling can be a promising family for realizing meron-like spin textures.

Accessing new magnetic regimes by tuning the ligand spin-orbit coupling in van der Waals magnets

Van der Waals (VdW) materials have opened new directions in the study of low dimensional magnetism. A largely unexplored arena is the intrinsic tuning of VdW magnets toward new ground states. Chromium trihalides provided the first such example with a change of interlayer magnetic coupling emerging upon exfoliation. Here, we take a different approach to engineer previously unknown ground states, not by exfoliation, but by tuning the spin-orbit coupling (SOC) of the nonmagnetic ligand atoms (Cl, Br, I). We synthesize a three-halide series, CrCl3 - x - y Br x I y , and map their magnetic properties as a function of Cl, Br, and I content. The resulting triangular phase diagrams unveil a frustrated regime near CrCl3. First-principles calculations confirm that the frustration is driven by a competition between the chromium and halide SOCs. Furthermore, we reveal a field-induced change of interlayer coupling in the bulk of CrCl3 - x - y Br x I y crystals at the same field as in the exfoliation experiments.

Anisotropic bulk and planar Heisenberg ferromagnets in uniform, arbitrarily oriented magnetic fields

Today, further downscaling of mobile electronic devices poses serious problems, such as energy consumption and local heat dissipation. In this context, spin wave majority gates made of very thin ferromagnetic films may offer a viable alternative. However, similar downscaling of magnetic thin films eventually enforces the latter to operate as quasi-2D magnets, the magnetic properties of which are not yet fully understood, especially those related to anisotropies and external magnetic fields in arbitrary directions. To this end, we have investigated the behaviour of an easy-plane and easy-axis anisotropic ferromagnet-both in two and three dimensions-subjected to a uniform magnetic field, applied along an arbitrary direction. In this paper, a spin-[Formula: see text] Heisenberg Hamiltonian with anisotropic exchange interactions is solved using double-time temperature-dependent Green's functions and the Tyablikov decoupling approximation. We determine various magnetic properties such as the Curie temperature and the magnetization as a function of temperature and the applied magnetic field, discussing the impact of the system's dimensionality and the type of anisotropy. The magnetic reorientation transition taking place in anisotropic Heisenberg ferromagnets is studied in detail. Importantly, spontaneous magnetization is found to be absent for easy-plane 2D spin systems with short range interactions.

Emerging two-dimensional ferromagnetism in silicene materials

The appeal of ultra-compact spintronics drives intense research on magnetism in low-dimensional materials. Recent years have witnessed remarkable progress in engineering two-dimensional (2D) magnetism via defects, edges, adatoms, and magnetic proximity. However, intrinsic 2D ferromagnetism remained elusive until recent discovery of out-of-plane magneto-optical response in Cr-based layers, stimulating the search for 2D magnets with tunable and diverse properties. Here we employ a bottom-up approach to produce layered structures of silicene (a Si counterpart of graphene) functionalized by rare-earth atoms, ranging from the bulk down to one monolayer. We track the evolution from the antiferromagnetism of the bulk to intrinsic 2D in-plane ferromagnetism of ultrathin layers, with its characteristic dependence of the transition temperature on low magnetic fields. The emerging ferromagnetism manifests itself in the electron transport. The discovery of a class of robust 2D magnets, compatible with the mature Si technology, is instrumental for engineering new devices and understanding spin phenomena.

Co thin films deposited directly on ZnO polar surfaces

A ferromagnetic (FM)-metal/oxide stack is the key structure determining the performance of spintronic devices. However, the effect of the electronic polarity of the oxide on the magnetic properties of the adjacent FM-metal has not been investigated previously. Here, we report the magnetic and structural properties of Co ultra-thin films sputter deposited directly on the Zn- and O-polar surfaces of ZnO substrates. The magnetic anisotropy and Curie temperature exhibit dramatic polarity-dependent differences for films on these surfaces. Structural analyses reveal that the heterointerface of the Co/O-polar surface is rather diffusive, whereas that of the Co/Zn-polar surface is atomically flat. These results suggest that the surface polarity plays a key role in determining the properties of the film. This novel FM-metal/polar-oxide system is expected to add new functionality to spintronic devices and provide an ideal basis for investigating the effect of a built-in electric field on the magnetism in a metallic monolayer.

Electric-field-induced modification of the magnon energy, exchange interaction, and curie temperature of transition-metal thin films

The electric-field-induced modification in the Curie temperature of prototypical transition-metal thin films with the perpendicular magnetic easy axis, a freestanding Fe(001) monolayer and a Co monolayer on Pt(111), is investigated by first-principles calculations of spin-spiral structures in an external electric field (E field). An applied E field is found to modify the magnon (spin-spiral formation) energy; the change arises from the E-field-induced screening charge density in the spin-spiral states due to p-d hybridizations. The Heisenberg exchange parameters obtained from the magnon energy suggest an E-field-induced modification of the Curie temperature, which is demonstrated via Monte Carlo simulations that take the magnetocrystalline anisotropy into account.

Structural relationships among LiNaMg[PO4]F and Na2M[PO4]F (M = Mn–Ni, and Mg), and the magnetic structure of LiNaNi[PO4]F

Both structures of LiNaMg[PO₄]F and LiNaNi[PO₄]F are isostructural and the magnetic structure of LiNaNi[PO₄]F can be described as AFM coupling of FM quasi-layers of zigzag edge sharing octahedral chains.

Magnetic transitions and spin-glass reentrance in two-dimensional [MnII(TCNE)(NCMe)2]X (X = PF6,AsF6,SbF6) molecular magnets

The structural, spectroscopic and magnetic properties of the two-dimensional (2D) molecule-based magnets of [Mn(II)(TCNE)(NCMe)2]X (X = PF6, AsF6, SbF6; TCNE = tetracyanoethylene, NCMe = acetonitrile) composition are reported. It is shown that the alteration of the interlayer distance by increasing the anion size has little effect on the critical magnetic ordering temperature, Tc, suggesting that it depends predominantly on the intra-plane magnetic exchange. The observed field-induced irreversibility in static magnetization, a slow decay of isothermal remanence below Tc, and the dynamic susceptibility data are in accord with a re-entrant spin-glass nature of the ground state of all materials. In contrast to the isostructural Fe-based magnets, in which strong magnetocrystalline anisotropy facilitates the finite temperature magnetic ordering with the magnetization easy axis perpendicular to the μ4-TCNE(•-) plane, in the studied Mn-based magnets the easy axis is canted away from the normal direction, due to a small magnetocrystalline anisotropy. The two magnetic transitions observed on cooling are assigned to the ferrimagnetic long-range ordering of the normal magnetization component followed by the re-entrant spin-glass type transition resulting from a random freezing of the in-plane magnetization component.

Electrical control of the ferromagnetic phase transition in cobalt at room temperature

Electrical control of magnetic properties is crucial for device applications in the field of spintronics. Although the magnetic coercivity or anisotropy has been successfully controlled electrically in metals as well as in semiconductors, the electrical control of Curie temperature has been realized only in semiconductors at low temperature. Here, we demonstrate the room-temperature electrical control of the ferromagnetic phase transition in cobalt, one of the most representative transition-metal ferromagnets. Solid-state field effect devices consisting of a ultrathin cobalt film covered by a dielectric layer and a gate electrode were fabricated. We prove that the Curie temperature of cobalt can be changed by up to 12 K by applying a gate electric field of about ±2 MV cm(-1). The two-dimensionality of the cobalt film may be relevant to our observations. The demonstrated electric field effect in the ferromagnetic metal at room temperature is a significant step towards realizing future low-power magnetic applications.

Magnetization and Curie Temperature of Ferromagnetic Ultrathin Films: The Influence of Magnetic Anisotropy and Dipolar Interactions (invited)

Theoretical investigations of the magnetization and Curie temperature of ferromagnetic ultrathin films in the presence of magnetic anisotropy and long-range dipolar interactions are presented. The Curie temperature of fcc (001) cobalt ultrathin films is calculated and compared with experimental results on Co/Cu (001) films. The influence of an external magnetic field, and the surface gradient of the magnetization are also discussed.

Asymmetric spin-wave dispersion on Fe(110): direct evidence of the Dzyaloshinskii-Moriya interaction

The influence of the Dzyaloshinskii-Moriya interaction on the spin-wave dispersion in an Fe double layer grown on W(110) is measured for the first time. It is demonstrated that the Dzyaloshinskii-Moriya interaction breaks the degeneracy of spin waves and leads to an asymmetric spin-wave dispersion relation. An extended Heisenberg spin Hamiltonian is employed to obtain the longitudinal component of the Dzyaloshinskii-Moriya vectors from the experimentally measured energy asymmetry.

Magnons in a ferromagnetic monolayer

We report the first observation of high wave vector magnon excitations in a ferromagnetic monolayer. Using spin-polarized electron energy loss spectroscopy, we observed the magnon dispersion in one atomic layer (ML) of Fe on W(110) at 120 K. The magnon energies are small in comparison to the bulk and surface Fe(110) excitations. We find an exchange parameter and magnetic anisotropy similar to that from static measurements. Our results are in sharp contrast to theoretical calculations, indicating that the present understanding of magnetism of the ML Fe requires considerable revision.

TWO-DIMENSIONAL FERROMAGNETIC ORDERING IN A METAL–ORGANIC MULTILAYER STRUCTURE

We demonstrate, using spin polarized neutron reflectivity measurements, that one can form a large stack of magnetically decoupled spin-membranes of Gadolinium ions and reduce the effect of the substrate substantially to study short-range two-dimensional (2D) ferromagnetic ordering. No spontaneous magnetization was observed in these membranes as the magnetic field was applied along an in-plane direction. The results are consistent with theoretical predictions of 2D in-plane spin systems having strong interplay of exchange, magneto-crystalline anisotropy and dipolar interactions. These metal–organic multilayer films will enable us to verify various theoretical predictions regarding spin-fluctuations in 2D systems using conventional magnetic measurements and neutron scattering studies.

Magnetic stripe domains in coupled magnetic sandwiches

Magnetic stripe domains in the spin reorientation transition region are investigated in (Fe/Ni)/Cu(001) and Co/Cu/(Fe/Ni)/Cu(001) using photoemission electron microscopy. For (Fe/Ni)/Cu(001), the stripe domain width decreases exponentially as the Fe/Ni film approaches the spin reorientation transition point. For Co/Cu/(Fe/Ni)/Cu(001), the Fe/Ni stripe orientation is aligned with the Co in-plane magnetization, and the stripe domain width decreases exponentially with increasing the interlayer coupling between the Fe/Ni and Co films. By considering magnetic stripes within an in-plane magnetic field, we reveal a universal dependence of the stripe domain width on the magnetic anisotropy and on the interlayer coupling.