Critical behavior of the uniaxial ferromagnetic monolayer Fe(110) on W(110)

Emergent Multifunctional Magnetic Proximity in van der Waals Layered Heterostructures

Proximity effect, which is the coupling between distinct order parameters across interfaces of heterostructures, has attracted immense interest owing to the customizable multifunctionalities of diverse 3D materials. This facilitates various physical phenomena, such as spin order, charge transfer, spin torque, spin density wave, spin current, skyrmions, and Majorana fermions. These exotic physics play important roles for future spintronic applications. Nevertheless, several fundamental challenges remain for effective applications: unavoidable disorder and lattice mismatch limits in the growth process, short characteristic length of proximity, magnetic fluctuation in ultrathin films, and relatively weak spin-orbit coupling (SOC). Meanwhile, the extensive library of atomically thin, 2D van der Waals (vdW) layered materials, with unique characteristics such as strong SOC, magnetic anisotropy, and ultraclean surfaces, offers many opportunities to tailor versatile and more effective functionalities through proximity effects. Here, this paper focuses on magnetic proximity, i.e., proximitized magnetism and reviews the engineering of magnetism-related functionalities in 2D vdW layered heterostructures for next-generation electronic and spintronic devices. The essential factors of magnetism and interfacial engineering induced by magnetic layers are studied. The current limitations and future challenges associated with magnetic proximity-related physics phenomena in 2D heterostructures are further discussed.

Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer

[Figure: see text].

Spin-Gapless States in Two-Dimensional Molecular Ferromagnet Fe2(TCNQ)2

Two-dimensional van der Waals magnetic atomic crystals have provided unprecedented access to magnetic ground states due to a quantum confinement effect. Here, using first-principles calculations, we demonstrate a spin-gapless molecular ferromagnet, namely, Fe₂(TCNQ)₂, with superior mechanical stability and a remarkable linear Dirac cone, which can be exfoliated from its already-synthesized van der Waals crystal. Especially, Young's modulus has values of 175.28 GPa·nm along the x- and y-directions with a Poisson's ratio of 0.29, while the Curie temperature within the Ising model is considerably higher than room temperature. Furthermore, spin-orbit coupling can open a band gap at the Dirac point, leading to topologically nontrivial electronic states characterized by an integer value of the Chern number and the edge states of its nanoribbon. Our results offer versatile platforms for achieving plastic spin filtering or a quantum anomalous Hall effect with promising applications in spintronics devices.

Substrate induced electronic phase transitions of CrI[Formula: see text] based van der Waals heterostructures

We perform first principle density functional theory calculations to predict the substrate induced electronic phase transitions of CrI[Formula: see text] based 2-D heterostructures. We adsorb graphene and MoS[Formula: see text] on novel 2-D ferromagnetic semiconductor-CrI[Formula: see text] and investigate the electronic and magnetic properties of these heterostructures with and without spin orbit coupling (SOC). We find that when strained MoS[Formula: see text] is adsorbed on CrI[Formula: see text], the spin dependent band gap which is a characteristic of CrI[Formula: see text], ceases to remain. The bandgap of the heterostructure reduces drastically ([Formula: see text] 70%) and the heterostructure shows an indirect, spin-independent bandgap of [Formula: see text] 0.5 eV. The heterostructure remains magnetic (with and without SOC) with the magnetic moment localized primarily on CrI[Formula: see text]. Adsorption of graphene on CrI[Formula: see text] induces an electronic phase transition of the subsequent heterostructure to a ferromagnetic metal in both the spin configurations with magnetic moment localized on CrI[Formula: see text]. The SOC induced interaction opens a bandgap of [Formula: see text] 30 meV in the Dirac cone of graphene, which allows us to visualize Chern insulating states without reducing van der Waals gap.

Curie temperature engineering in a novel 2D analog of iron ore (hematene) via strain

As a newly exfoliated magnetic 2D material from hematite, hematene is the most far-reaching ultrathin magnetic indirect bandgap semiconductor. We have carried out a detailed structural analysis of hematene via prefacing strain by means of first-principles calculations based on density functional theory (DFT). Hematene in the pristine form emerges out to be a magnetic semiconductor with a bandgap of 1.0/2.0 eV for the majority/minority spin channel. The dependence of magnetic anisotropy energy (MAE), T _C, and the bandgap on compressive and tensile strains has been scanned exclusively. It is examined that T _C depends firmly on the compressive strain and increases up to 21.1% at a compressive strain of 6% whereas it decreases significantly for tensile strain. The MAE is negatively correlated with the tensile and compressive strain. The value of MAE for all compressive strain cases is more than that of the pristine hematene. These results summarize that the studied 2D hematene has broad application prospects in spintronics, memory-based devices, and valleytronics.

A Symmetry-Breaking Phase in Two-Dimensional FeTe2 with Ferromagnetism above Room Temperature

Recently, ferromagnetism observed in monolayer two-dimensional (2D) materials has attracted attention due to the promise of its application in next-generation spintronics. Here, we predict a symmetry-breaking phase in 2D FeTe₂ that differs from conventional transition metal ditellurides shows superior stability and room-temperature ferromagnetism. Through density functional theory calculations, we find the exchange interactions in FeTe₂ consist of short-range superexchange and long-range oscillatory exchanges mediated by itinerant electrons. For six nearest neighbors, the exchange constants are calculated to be 50.95, 33.41, 2.70, 11.02, 14.46, and -4.12 meV. Furthermore, the strong relativistic effects on Te²⁺ induce giant out-of-plane exchange anisotropy and open up a significantly large spin wave gap (Δ^SW) of 1.22 meV. All of this leads to robust ferromagnetism with the T_c surpassing 423 K, which is predicted by the renormalization group Monte Carlo method, sufficiently higher than room temperature. Our findings shed light on the promising future of FeTe₂ in 2D magnetic research and spintronic applications.

Step-Edge-Induced Anisotropic Chiral Spin Coupling in Ultrathin Magnetic Films

Step edges represent a local break of lateral symmetry in ultrathin magnetic films. In our experiments, we investigate the spin coupling across atomic step edges on Fe/W(110) by means of spin-polarized scanning tunneling microscopy and spectroscopy. Local modifications of the spin texture toward step edges separating double from single layer areas are observed, and selection rules indicate a chiral spin coupling that significantly changes with the propagation along the [11[over ¯]0] or the [001] crystallographic direction. The findings are explained via anisotropic Dzyaloshinskii-Moriya interactions arising from the broken lateral symmetry at atomic step edges.

Intrinsic Van Der Waals Magnetic Materials from Bulk to the 2D Limit: New Frontiers of Spintronics

2D van der Waals (vdW) magnets, which present intrinsic ferromagnetic/antiferromagnetic ground states at finite temperatures down to atomic-layer thicknesses, open a new horizon in materials science and enable the potential development of new spin-related applications. The layered structure of vdW magnets facilitates their atomic-layer cleavability and magnetic anisotropy, which counteracts spin fluctuations, thereby providing an ideal platform for theoretically and experimentally exploring magnetic phase transitions in the 2D limit. With reduced dimensions, the susceptibility of 2D magnets to a large variety of external stimuli also makes them more promising than their bulk counterpart in various device applications. Here, the current status of characterization and tuning of the magnetic properties of 2D vdW magnets, particularly the atomic-layer thickness, is presented. Various state-of-the-art optical and electrical techniques have been applied to reveal the magnetic states of 2D vdW magnets. Other emerging 2D vdW magnets and future perspectives on the stacking strategy are also given; it is believed that they will excite more intensive research and provide unprecedented opportunities in the field of spintronics.

Raman fingerprint of two terahertz spin wave branches in a two-dimensional honeycomb Ising ferromagnet

Two-dimensional (2D) magnetism has been long sought-after and only very recently realized in atomic crystals of magnetic van der Waals materials. So far, a comprehensive understanding of the magnetic excitations in such 2D magnets remains missing. Here we report polarized micro-Raman spectroscopy studies on a 2D honeycomb ferromagnet CrI₃. We show the definitive evidence of two sets of zero-momentum spin waves at frequencies of 2.28 terahertz (THz) and 3.75 THz, respectively, that are three orders of magnitude higher than those of conventional ferromagnets. By tracking the thickness dependence of both spin waves, we reveal that both are surface spin waves with lifetimes an order of magnitude longer than their temporal periods. Our results of two branches of high-frequency, long-lived surface spin waves in 2D CrI₃ demonstrate intriguing spin dynamics and intricate interplay with fluctuations in the 2D limit, thus opening up opportunities for ultrafast spintronics incorporating 2D magnets.

Characteristics of spin waves in recently discovered two-dimensional (2D) Ising ferromagnets are still lacking. Here, Jin and Kim et al. report Raman resonance evidence of two sets of surface spin waves in the 2D honeycomb ferromagnet CrI₃.

Room Temperature Intrinsic Ferromagnetism in Epitaxial Manganese Selenide Films in the Monolayer Limit

Monolayer van der Waals (vdW) magnets provide an exciting opportunity for exploring two-dimensional (2D) magnetism for scientific and technological advances, but the intrinsic ferromagnetism has only been observed at low temperatures. Here, we report the observation of room temperature ferromagnetism in manganese selenide (MnSe _x) films grown by molecular beam epitaxy (MBE). Magnetic and structural characterization provides strong evidence that, in the monolayer limit, the ferromagnetism originates from a vdW manganese diselenide (MnSe₂) monolayer, while for thicker films it could originate from a combination of vdW MnSe₂ and/or interfacial magnetism of α-MnSe(111). Magnetization measurements of monolayer MnSe _x films on GaSe and SnSe₂ epilayers show ferromagnetic ordering with a large saturation magnetization of ∼4 Bohr magnetons per Mn, which is consistent with the density functional theory calculations predicting ferromagnetism in monolayer 1T-MnSe₂. Growing MnSe _x films on GaSe up to a high thickness (∼40 nm) produces α-MnSe(111) and an enhanced magnetic moment (∼2×) compared to the monolayer MnSe _x samples. Detailed structural characterization by scanning transmission electron microscopy (STEM), scanning tunneling microscopy (STM), and reflection high energy electron diffraction (RHEED) reveals an abrupt and clean interface between GaSe(0001) and α-MnSe(111). In particular, the structure measured by STEM is consistent with the presence of a MnSe₂ monolayer at the interface. These results hold promise for potential applications in energy efficient information storage and processing.

Probing of the interfacial Heisenberg and Dzyaloshinskii-Moriya exchange interaction by magnon spectroscopy

This Topical Review presents an overview of the recent experimental results on the quantitative determination of the magnetic exchange parameters in ultrathin magnetic films and multilayers grown on different substrates. The experimental approaches for probing both the symmetric Heisenberg and the antisymmetric Dzyaloshinskii-Moriya exchange interaction in ultrathin magnetic films and at interfaces are discussed in detail. It is explained how the experimental spectrum of magnetic excitations can be used to quantify the strength of these interactions.

Switching of Dirac-Fermion Mass at the Interface of Ultrathin Ferromagnet and Rashba Metal

We have performed spin- and angle-resolved photoemission spectroscopy on tungsten (110) interfaced with an ultrathin iron (Fe) layer to study an influence of ferromagnetism on the Dirac-cone-like surface-interface states. We found an unexpectedly large energy gap of 340 meV at the Dirac point, and have succeeded in switching the Dirac-fermion mass by controlling the direction of Fe spins (in plane or out of plane) through tuning the thickness of the Fe overlayer or adsorbing oxygen on it. Such a manipulation of Dirac-fermion mass via the magnetic proximity effect opens a promising platform for realizing new spintronic devices utilizing a combination of exchange and Rashba-spin-orbit interactions.

Atomistic spin dynamics and surface magnons

Atomistic spin dynamics simulations have evolved to become a powerful and versatile tool for simulating dynamic properties of magnetic materials. It has a wide range of applications, for instance switching of magnetic states in bulk and nano-magnets, dynamics of topological magnets, such as skyrmions and vortices and domain wall motion. In this review, after a brief summary of the existing investigation tools for the study of magnons, we focus on calculations of spin-wave excitations in low-dimensional magnets and the effect of relativistic and temperature effects in such structures. In general, we find a good agreement between our results and the experimental values. For material specific studies, the atomistic spin dynamics is combined with electronic structure calculations within the density functional theory from which the required parameters are calculated, such as magnetic exchange interactions, magnetocrystalline anisotropy, and Dzyaloshinskii-Moriya vectors.

Chiral asymmetry of the spin-wave spectra in ultrathin magnetic films

We raise the possibility that the chiral degeneracy of the magnons in ultrathin films can be lifted due to the presence of Dzyaloshinskii-Moriya interactions. By using simple symmetry arguments, we discuss under which conditions such a chiral asymmetry occurs. We then perform relativistic first principles calculations for an Fe monolayer on W(110) and explicitly reveal the asymmetry of the spin-wave spectrum in the case of wave vectors parallel to the (001) direction. Furthermore, we quantitatively interpret our results in terms of a simplified spin model by using calculated Dzyaloshinskii-Moriya vectors. Our theoretical prediction should inspire experiments to explore the asymmetry of spin waves, with a particular emphasis on the possibility to measure the Dzyaloshinskii-Moriya interactions in ultrathin films.

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.

Universal window for two-dimensional critical exponents

Two-dimensional condensed matter is realized in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic physics and chemical detail. To unify their physical description is therefore a complex and important challenge. Here we investigate the distribution of experimentally estimated critical exponents, β, that characterize the evolution of the order parameter through the ordering transition. The distribution is found to be bimodal and bounded within a window ∼0.1≤β≤0.25, facts that are only in partial agreement with the established theory of critical phenomena. In particular, the bounded nature of the distribution is impossible to reconcile with the existing theory for one of the major universality classes of two-dimensional behaviour-the XY model with four-fold crystal field-which predicts a spectrum of non-universal exponents bounded only from below. Through a combination of numerical and renormalization group arguments we resolve the contradiction between theory and experiment and demonstrate how the 'universal window' for critical exponents observed in experiment arises from a competition between marginal operators.

A Model System for Dimensional Competition in Nanostructures: A Quantum Wire on a Surface

The retarded Green’s function (E−H + iε)⁻¹is given for a dimensionally hybrid Hamiltonian which interpolates between one and two dimensions. This is used as a model for dimensional competition in propagation effects in the presence of one-dimensional subsystems on a surface. The presence of a quantum wire generates additional exponential terms in the Green’s function. The result shows how the location of the one-dimensional subsystem affects propagation of particles.

Dimensionality crossover in the induced magnetization of Pd layers

The magnetic ordering of a series of samples consisting of ultrathin Fe layers embedded in Pd was investigated using the magneto-optical Kerr effect. The samples consisted of a single Fe layer with nominal thickness 0.2≤d(Fe)≤1.6 monolayers sandwiched between two 20 monolayer Pd layers. A dimensionality crossover from two dimensions to three dimensions occurs as d(Fe) is increased from 0.4 to 1.0 monolayers. First-principles calculations were performed in order to determine the magnetic profile, and we used a spin-wave quantum well model for obtaining a qualitative description of the dimensionality crossover. The results clearly prove the existence of a dimensionality crossover in the induced magnetization, opening new routes for addressing the influence of extension on order.

Atomic-scale magnetic domain walls in quasi-one-dimensional Fe nanostripes

Fe nanostripes on W(110) are investigated by Kerr magnetometry and spin-polarized scanning tunneling microscopy (SP-STM). An Arrhenius law is observed for the temperature dependent magnetic susceptibility indicating a one-dimensional magnetic behavior. The activation energy for creating antiparallel spin blocks indicates extremely narrow domain walls with a width on a length scale of the lattice constant. This is confirmed by imaging the domain wall by SP-STM. This information allows the quantification of the exchange stiffness and the anisotropy constant.

Perpendicular spin orientation in ultrasmall Fe islands on W(110)

We have studied the magnetism of Ag-coated Fe islands on W(110) by nuclear resonant scattering of synchrotron radiation at the 14.4 keV resonance of (57)Fe. Separated islands with an average diameter of 2.0 nm and monolayer thickness are formed at a Fe coverage of theta = 0.57 bulk monolayers. Time spectra of the nuclear decay were measured in the temperature range from 4.5 to 300 K. We find strong evidence for perpendicular spin orientation, which most likely results from the interplay of shape anisotropy and elastic strain in the islands.