Monolayer Limit Research Articles

Electric field enhancement effect on Raman spectra in two-dimensional MoSi[formula omitted]N[formula omitted], TiSi[formula omitted]N[formula omitted] and MoGe[formula omitted]As[formula omitted] monolayers

Characterizing two-dimensional (2D) layered materials in the monolayer limit is key to discovering their new phenomena and unusual properties. We theoretically predict the electric field modulated Raman spectra of 2D MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, with two kinds of laser lines (532 and 633 nm). Based on the Raman tensor, we have calculated the angle-dependent Raman intensities of the major Raman peak (A1′1) in MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, locating at 1029 cm−1, 993 cm−1 and 317 cm−1, respectively. Applying the external electric field to MoSi2N4 monolayer, the symmetry of D3h reduces to C3v, which results in more peaks of Raman-active modes found in the Raman spectra. As a result, besides E′ and A1′ modes, three other major Raman peaks (A1′1, A1′2 and A1′3) are found in MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, which can help us to distinguish the 2D MA2Z4 materials. We find that the enhancement factor by external electric field can be up to 10 times. Moreover, the non-resonant Raman spectra peaks of doubly degenerate mode (E′) and one-dimensional modes A1′ and A2″ in MoSi2N4, TiSi2N4 and MoGe2As4 monolayer are calculated. These theoretical results of Raman spectra of MoSi2N4 monolayer may provide theoretical guidelines for its utilization in crystal structure characterizations and optoelectric devices.

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.

Spontaneous spin-valley polarization in NbSe2 at a van der Waals interface

A proximity effect at a van der Waals (vdW) interface enables creation of an emergent quantum electronic ground state. Here we demonstrate that an originally superconducting two-dimensional (2D) NbSe2 forms a ferromagnetic ground state with spontaneous spin polarization at a vdW interface with a 2D ferromagnet V5Se8. We investigated the anomalous Hall effect (AHE) of the NbSe2/V5Se8 magnetic vdW heterostructures, and found that the sign of the AHE was reversed as the number of the V5Se8 layer was thinned down to the monolayer limit. Interestingly, the AHE signal of those samples was enhanced with the in-plane magnetic fields, suggesting an additional contribution to the AHE signal other than magnetization. This unusual behavior is well reproduced by band structure calculations, where the emergence of the Berry curvature along the spin-degenerate nodal lines in 2D NbSe2 by the in-plane magnetization plays a key role, unveiling a unique interplay between magnetism and Zeeman-type spin-orbit interaction in a non-centrosymmetric 2D quantum material.

Structural, electronic, and magnetic properties of CrTe2

Two-dimensional chromium ditelluride (${\mathrm{CrTe}}_{2}$) is a promising ferromagnetic layered material that exhibits long-range ferromagnetic ordering in the monolayer limit. The formation energies of the different possible structural phases (1T, 1H, 2H) calculated from density functional theory (DFT) show that the 1T phase is the ground state, and the energetic transition barriers between the phases, calculated by the nudged elastic band method, are large, on the order of 0.5 eV. The self-consistent Hubbard $U$ correction parameters are calculated for all the phases of ${\mathrm{CrTe}}_{2}$. The calculated magnetic moment of 1T-${\mathrm{CrTe}}_{2}$ with $\ensuremath{\ge}2$ layers lies in the plane, whereas the magnetic moment of a monolayer is out-of-plane. Band filling and tensile biaxial strain cause the magnetic moment of a monolayer to switch from out-of-plane to in-plane, and compressive biaxial strain in a bilayer causes the magnetic moment to switch from in-plane to out-of-plane. The magnetic anisotropy is shown to originate from the large spin-orbit coupling (SOC) of the Te atoms and the anisotropy of the exchange coupling constants ${J}_{xy}$ and ${J}_{z}$ in an XXZ type Hamiltonian. Renormalized spin wave theory using experimental values for the magnetic anisotropy energy and Curie temperatures provides a range of values for the nearest neighbor exchange coupling.

Chemical Exfoliation toward Magnetic 2D VOCl Monolayers.

The diversification of magnetic two-dimensional (2D) materials holds the key to the further development of advanced technologies, such as spintronic devices and efficient data storage. However, the search for intrinsic magnetism down to the 2D limit is severely limited by the ability to reliably exfoliate large, air-stable nanosheets. Chemical exfoliation, a relatively underutilized method for delamination, offers many advantages, including a high degree of adaptability and higher yields of uniformly exfoliated materials. van der Waals (vdW) materials, in particular the family of transition-metal oxyhalides, are ideal candidates for chemical exfoliation due to their large interlayer spacing and the wide variety of interesting magnetic properties they exhibit. In this study, we employ a chemical exfoliation method to delaminate the layered antiferromagnet vanadium oxychloride (VOCl) down to the monolayer limit. The resulting nansoheets have lateral sizes of up to 20 μm, are air-stable, and can be easily isolated. Magnetic characterization was performed throughout the exfoliation process, tracking the changes in magnetic behavior among bulk VOCl, its lithiated intercalate, and the restacked nanosheet pellet. The results from this work demonstrate the potential of chemical exfoliation, along with illustrating the effects of low dimensionality on magnetic properties.

Momentum-Dependent Oscillator Strength Crossover of Excitons and Plasmons in Two-Dimensional PtSe2

The 1T-phase layered PtX2 chalcogenide has attracted widespread interest due to its thickness dependent metal-semiconductor transition driven by strong interlayer coupling. While the ground state properties of this paradigmatic material system have been widely explored, its fundamental excitation spectrum remains poorly understood. Here we combine first-principles calculations with momentum (q) resolved electron energy loss spectroscopy (q-EELS) to study the collective excitations in 1T-PtSe2 from the monolayer limit to the bulk. At finite momentum transfer, all the spectra are dominated by two distinct interband plasmons that disperse to higher energy with increasing q. Interestingly, the absence of long-range screening in the two-dimensional (2D) limit inhibits the formation of long wavelength plasmons. Consequently, in the small-q limit, excitations in monolayer PtSe2 are exclusively of excitonic nature, and the loss spectrum coincides with the optical spectrum. The qualitatively different momentum dependence of excitons and plasmons enables us to unambiguously disentangle their spectral fingerprints in the excited state spectrum of layered 1T-PtSe2. This will help to discern the charge carrier plasmon and locally map the optical conductivity and trace the layer-dependent semiconductor to metal transition in 1T-PtSe2 and other 2D materials.

Thickness and defect dependent electronic, optical and thermoelectric features of hbox {WTe}_2

Transition metal dichalcogenides (TMDs) receive significant attention due to their outstanding electronic and optical properties. In this study, we investigate the electronic, optical, and thermoelectric properties of single and few layer hbox {WTe}_2 in detail utilizing first-principles methods based on the density functional theory (DFT). Within the scope of both PBE and HSE06 including spin orbit coupling (SOC), the simulations predict the electronic band gap values to decrease as the number of layers increases. Moreover, spin-polarized DFT calculations combined with the semi-classical Boltzmann transport theory are applied to estimate the anisotropic thermoelectric power factor (Seebeck coefficient, S) for hbox {WTe}_2 in both the monolayer and multilayer limit, and S is obtained below the optimal value for practical applications. The optical absorbance of hbox {WTe}_2 monolayer is obtained to be slightly less than the values reported in literature for 2H TMD monolayers of hbox {MoS}_2, hbox {MoSe}_2, and hbox {WS}_2. Furthermore, we simulate the impact of defects, such as vacancy, antisite and substitution defects, on the electronic, optical and thermoelectric properties of monolayer hbox {WTe}_2. Particularly, the Te-hbox {O}_2 substitution defect in parallel orientation yields negative formation energy, indicating that the relevant defect may form spontaneously under relevant experimental conditions. We reveal that the electronic band structure of hbox {WTe}_2 monolayer is significantly influenced by the presence of the considered defects. According to the calculated band gap values, a lowering of the conduction band minimum gives rise to metallic characteristics to the structure for the single Te(1) vacancy, a diagonal Te line defect, and the Te(1)-hbox {O}_2 substitution, while the other investigated defects cause an opening of a small positive band gap at the Fermi level. Consequently, the real (varepsilon _1(omega )) and imaginary (varepsilon _2(omega )) parts of the dielectric constant at low frequencies are very sensitive to the applied defects, whereas we find that the absorbance (A) at optical frequencies is less significantly affected. We also predict that certain point defects can enhance the otherwise moderate value of S in pristine hbox {WTe}_2 to values relevant for thermoelectric applications. The described hbox {WTe}_2 monolayers, as functionalized with the considered defects, offer the possibility to be applied in optical, electronic, and thermoelectric devices.

Magnetic and electronic transitions in monolayer electride Gd2C induced by hydrogenation: A first-principles study

The recently synthesized two-dimensional electride ${\mathrm{Gd}}_{2}\mathrm{C}$ was proposed to be a ferromagnetic metal that possesses multiple pairs of Weyl points and may display a large anomalous Hall conductivity [Liu et al., Phys. Rev. Lett. 125, 187203 (2020)]. In view of its layered structure, here we carry out first-principles studies on the magnetic and electronic properties of ${\mathrm{Gd}}_{2}\mathrm{C}$ in the ultrathin monolayer limit. We find that monolayer ${\mathrm{Gd}}_{2}\mathrm{C}$ remains ferromagnetic like the bulk form and the hydrogenation can effectively tune its magnetism and electronic structure. With one-sided full coverage of hydrogen atoms, monolayer ${\mathrm{Gd}}_{2}\mathrm{C}$ becomes a half-metal with one spin channel around the Fermi level. For two-sided full hydrogenation, monolayer ${\mathrm{Gd}}_{2}\mathrm{C}$ transforms to an antiferromagnetic insulator with a band gap of 0.8 eV. Our studies show that monolayer electride ${\mathrm{Gd}}_{2}\mathrm{C}$ can perform multiple magnetic and electronic transitions with different levels of hydrogenation and may be also adopted to construct a planar heterojunction with selective area adsorption of hydrogen atoms, which has promising applications in future electronic and spintronic devices.

Nanopore-Patterned CuSe Drives the Realization of the PbSe-CuSe Lateral Heterostructure.

Monolayer PbSe has been predicted to be a two-dimensional (2D) topological crystalline insulator (TCI) with crystalline symmetry-protected Dirac-cone-like edge states. Recently, few-layered epitaxial PbSe has been grown on the SrTiO3 substrate successfully, but the corresponding signature of the TCI was only observed for films not thinner than seven monolayers, largely due to interfacial strain. Here, we demonstrate a two-step method based on molecular beam epitaxy for the growth of the PbSe-CuSe lateral heterostructure on the Cu(111) substrate, in which we observe a nanopore-patterned CuSe layer that acts as the template for lateral epitaxial growth of PbSe. This further results in a PbSe-CuSe lateral heterostructure with an atomically sharp interface. Scanning tunneling microscopy and spectroscopy measurements reveal a fourfold symmetric square lattice of such PbSe with a quasi-particle band gap of 1.8 eV, a value highly comparable with the theoretical value of freestanding PbSe. The weak monolayer-substrate interaction is further supported by both density functional theory (DFT) and projected crystal orbital Hamilton population, with the former predicting the monolayer's anti-bond state to reside below the Fermi level. Our work demonstrates a practical strategy to fabricate a high-quality in-plane heterostructure, involving a monolayer TCI, which is viable for further exploration of the topology-derived quantum physics and phenomena in the monolayer limit.

X-ray spectroscopy for the magnetic study of the van der Waals ferromagnet CrSiTe3 in the few- and monolayer limit

The study of magnetic order in few- and monolayer van der Waals materials poses a challenge to the most commonly employed magnetic characterization techniques as they normally lack magnetic sensitivity and/or lateral resolution enabling their thickness-dependent probing. Here we demonstrate the usefulness of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) measurements, carried out at the Cr and Te M 5 edges, for the study of the ferromagnetic semiconductor CrSiTe3 (CST) in the form of single- and few-layer flakes. By scanning the sample under the incident x-ray beam, a map of the exfoliated system was obtained, which reproduced the optical micrographs showing the detailed distribution and thicknesses of the flakes. In this way, XAS/XMCD was performed at selected sample areas, revealing the thickness-resolved spectroscopic and magnetic properties of the flakes, such as the spin and orbital magnetic moments. The spin moment, in line with the saturation field, is decreasing with film thickness, revealing a single-domain and out-of-plane magnetization for the thinnest films. For CST, the electronic properties are governed by the strong covalent bond between the Cr 3d(e g ) and Te 5p states, giving rise to a superexchange scenario. We observed a gradually increasing ratio of orbital to spin moment for thinner flakes, which could be due to a further increase of the covalent mixing. Hysteresis loops were recorded at the Cr L 3 edge, showing an open loop for 10 down to ∼3 layers, while the bulk shows a wasp-waist shaped loop. With the transition temperature from the soft to the hard ferromagnetic state decreasing with thickness, the monolayer shows a narrowed, closed loop at 10 K, suggesting its transition temperature 10 K. Our study demonstrates the unique capabilities of XAS/XMCD for the study of few-layer van der Waals magnets, highlighting the interplay between electron correlation and ferromagnetism in CST.

Determining the interlayer shearing in twisted bilayer MoS2 by nanoindentation

The rise of twistronics has increased the attention of the community to the twist-angle-dependent properties of two-dimensional van der Waals integrated architectures. Clarification of the relationship between twist angles and interlayer mechanical interactions is important in benefiting the design of two-dimensional twisted structures. However, current mechanical methods have critical limitations in quantitatively probing the twist-angle dependence of two-dimensional interlayer interactions in monolayer limits. Here we report a nanoindentation-based technique and a shearing-boundary model to determine the interlayer mechanical interactions of twisted bilayer MoS2. Both in-plane elastic moduli and interlayer shear stress are found to be independent of the twist angle, which is attributed to the long-range interaction of intermolecular van der Waals forces that homogenously spread over the interfaces of MoS2. Our work provides a universal approach to determining the interlayer shear stress and deepens the understanding of twist-angle-dependent behaviours of two-dimensional layered materials.

Stabilities, electronic and piezoelectric properties of blue-phosphorene-phase MXs (M = Ge, Sn; X = S, Se, Te) nanotubes

By means of first-principles calculations, the stabilities, electronic and piezoelectric properties of blue-phosphorene-like MXs (M = Ge, Sn; X = S, Se, Te) nanotubes (NT) were systematically investigated. Our results show that the strain energy decreases monotonically and even becomes slightly negative with increasing the tube diameter, indicative of a highly thermodynamic stability. The band gap increases gradually with increasing the tube diameter, and slowly converges to the monolayer limit. The predicted elastic constants are strongly dependent on the tube diameter and the chirality. Compared with the corresponding monolayer counterparts, the greatly increased elastic constants of NTs indicate that a reduction in dimensionality can effectively improve the rigidity. Due to the presence of centrosymmetry, the armchair-shaped NTs do not exhibit any piezoelectric behavior. In contrast, the magnitudes of piezoelectric coefficients of the zigzag-shaped NTs exhibit an interesting odd-even effect with the diameter of tube. The predicted largest piezoelectric coefficient of (27, 0) GeS NT reaches 3.20 C/m2, which is higher than most of the reported inorganic NTs. Our results suggest that these novel MXs NTs can be served as good piezoelectric materials due to high stability, suitable band gap, robust mechanical property, and adjustable piezoelectric coefficient.

Fast Intercalation of Lithium in Semi-Metallic γ-GeSe Nanosheet: A New Group-IV Monochalcogenide for Lithium-Ion Battery Application.

Existence of van der Waals gaps renders two-dimensional (2D) materials ideal passages of lithium for being used as anode materials. However, the requirement of good conductivity significantly limits the choice of 2D candidates. So far, only graphite is satisfying due to its relatively high conductivity. Recently, a new polymorph of layered germanium selenide (γ-GeSe) was proven to be semimetal in its bulk phase with a higher conductivity than graphite while its monolayer behaves semiconducting. In this work, by using first-principles calculations, the possibility was investigated of using this new group-IV monochalcogenide, γ-GeSe, as anode in Li-ion batteries (LIBs). The studies revealed that the Li atom would form an ionic adsorption with adjacent selenium atoms at the hollow site and exist in cationic state (lost 0.89 e to γ-GeSe). Results of climbing image-nudged elastic band showed the diffusion barrier of Li was 0.21 eV in the monolayer limit, which could activate a relatively fast diffusion even at room temperature on the γ-GeSe surface. The calculated theoretical average voltages ranged from 0.071 to 0.015 V at different stoichiometry of Lix GeSe with minor volume variation, suggesting its potential application as anode of LIBs. The predicted moderate binding energy, a low open-circuit voltage (comparable to graphite), and a fast motion of Li suggested that γ-GeSe nanosheet could be chemically exfoliated via Li intercalation and is a promising candidate as the anode material for LIBs.

Size effect on optical and vibrational properties of van der Waals layered In4/3P2S6

Metal thiophosphates have recently received increasing research interest, thanks to their diversity in regard to metal cation occupation within the P–S scaffold, which produces a broad array of functional properties. Among them, In4/3P2S6 belongs to a special case as regards the ordering of metal cations and vacancy sites, whose physical properties remain largely unexplored, especially in the atomically thin limit. In this work, we undertake a comprehensive investigation on the thickness-dependent optical and vibrational properties of In4/3P2S6 from the bulk scale down to a few-layer flakes. Both optical birefringence and anisotropic photoelectric response are observed, which are closely linked to the monoclinic symmetry of the crystal lattice. The vanishing of Raman, absorption, and photoluminescence intensities at about three to four layers signifies the enhanced structural disorder and lattice incoherence when approaching the monolayer limit. Before reaching this critical thickness, phonon softening due to weakened interlayer coupling and bandgap widening due to quantum confinement are accompanied by thickness reduction. These findings shed light on a general understanding of the finite size effect on the physical properties of metal thiophosphates and deliver possible device applications by exploiting the property of optical anisotropy.

Unusual Magnetic Features in Two-Dimensional Fe5GeTe2 Induced by Structural Reconstructions.

Recent experiments on Fe5GeTe2 suggested the presence of a symmetry breaking of its conventional crystal structure. Here, using density functional theory calculations, we elucidate that the stabilization of the (√3 × √3)R30° supercell structure is caused by the swapping of Fe atoms occurring in the monolayer limit. The swapping to the vicinity of Te atoms is facilitated by the spontaneous occurrence of Fe vacancy and its low diffusion barrier. Our calculated magnetic exchange parameters show the simultaneous presence of ferromagnetic and antiferromagnetic exchange among a particular type of Fe atom. The Fe sublattice projected magnetization obtained from Monte Carlo simulations clearly demonstrates an exotic temperature-dependent behavior of this Fe type along with a large canting angle at T = 0 K, indicating the presence of a complex noncollinear magnetic order. We propose that the low-temperature crystal structure results from the swapping between two sublattices of Fe, giving rise to peculiar magnetization obtained in experiments.

Monolithic In2Se3–In2O3 heterojunction for multibit non-volatile memory and logic operations using optoelectronic inputs

Stable ferroelectricity at room-temperature down to the monolayer limit, harnessed with strong sensitivity towards visible-to-near-infrared illumination in α-In2Se3, facilitates its potential as versatile building block for developing ultrathin multifunctional photonic integrated networks. Herein, we demonstrated a planar ferroelectric-semiconductor heterojunction (FeS-HJ) field-effect transistor (FET) fabricated out of α-In2Se3 and In2O3, where the ferroelectric-polarization state in α-In2Se3 is utilized to control the device characteristics. The robust in-plane (IP) polarization flipping triggered by out-of-plane (OOP) electrostatic field along with clear anticlockwise hysteresis loop were readily revealed by scanning Kelvin-probe force microscopy (KPFM) and electrical probing. The orthogonally tangled ferroelectric switching was used to manipulate the HJ channel conductance and thereby to realize non-volatile memory (NVM) states. Moreover, gate-tuneable diode-like characteristics and superior photoresponse in HJ compared to its individual constitutes were observed. Utilizing the concurrent ferro-photonic coupling, high bandwidth optical inputs further tailored the outputs into four distinguished current states induced by different polarization directions. Our results pave the way for developing advanced (opto) electronic devices with diverse signal modulation capability to realize next generation low-power neurocomputing, brain-inspired visionary systems, and on-chip optical communications.

Few-Layered MnAl2S4 Dielectrics for High-Performance van der Waals Stacked Transistors.

The gate dielectric layer is an important component in building a field-effect transistor. Here, we report the synthesis of a layered rhombohedral-structured MnAl2S4 crystal, which can be mechanically exfoliated down to the monolayer limit. The dielectric properties of few-layered MnAl2S4 flakes are systematically investigated, whereby they exhibit a relative dielectric constant of over 6 and an electric breakdown field of around 3.9 MV/cm. The atomically smooth thin MnAl2S4 flakes are then applied as a dielectric top gate layer to realize a two-dimensional van der Waals stacked field-effect transistor, which uses MoS2 as a channel material. The fabricated transistor can be operated at a small drain-source voltage of 0.1 V and gate voltages within ranges of ±2 V, which exhibit a large on-off ratio over 107 at 0.5 V and a low subthreshold swing value of 80 mV/dec. Our work demonstrates that the few-layered MnAl2S4 can work as a dielectric layer to realize high-performance two-dimensional transistors, and thus broadens the research on high-κ 2D materials and may provide new opportunities in developing low-dimensional electronic devices with a low power consumption in the future.

Dielectric-dependent hybrid functional calculations on the electronic band gap of 3d transition metal doped SnS2 and their optical properties

This paper is a computational investigation of the electronic band gap and optical properties of ${\mathrm{SnS}}_{2}$ and $3d$-series transition metal doped ${\mathrm{SnS}}_{2}$ systems. The ${\mathrm{SnS}}_{2}$ crystal is a nonmagnetic indirect band gap semiconductor both in bulk and in the monolayer limit. The transition metal substitution at Sn site induces magnetism inside the crystal. Therefore studying its doping by $3d$-series transition metals is essential from an application perspective. We use the dielectric-dependent hybrid functionals of ab initio calculations for computing the electronic band gap. The dielectric-dependent hybrid computations rely on the electronic static dielectric constant. In these calculations, we iteratively update the dielectric constant and exchange parameter from one another until the convergence. As a result, we present a range of possible band gap values. Specifically, we determine the lower and upper bounds of possible experimental band gap values for all these doped systems. Further, we explore the optical properties of each doped system in the monolayer and bulk forms. We discuss the absorption spectra, optical constants, and exciton binding energy of all the doped systems. We conclude that the transition metal doped ${\mathrm{SnS}}_{2}$ is a good candidate for optoelectronic device applications.

Ultrafast optical excitation of magnetic dynamics in van der Waals magnets: Coherent magnons and BKT dynamics in NiPS3

Optical pump-probe experiments carried out in the time domain reveal both the intrinsic low-energy dynamics and its connections to higher-energy excitations in correlated electron systems. In this work, we propose two microscopic mechanisms for the optical generation of coherent magnetic modes in van der Waals magnets, and derive the corresponding effective light-spin interactions: either through pumping atomic orbital excitations resonantly or via a light-induced Floquet spin Hamiltonian, the ground state of the system is driven out of equilibrium. The subsequent long-time relaxational dynamics can then be probed using, e.g., the magneto-optical Kerr effect or transient grating spectroscopy. As an example, we apply our framework to ${\mathrm{NiPS}}_{3}$, which is magnetically ordered in the bulk, and is conjectured to realize the XY model in the monolayer limit. Our theory makes explicit how the material's low-energy response depends sensitively on the microscopic details of the light-spin coupling as well as pump fluence, frequency, and polarization. For the case of bulk ${\mathrm{NiPS}}_{3}$, we find quantitative agreement with recent experiments [D. Afanasiev et al., Sci. Adv. 7, eabf3096 (2021)]. We further propose pump-probe experiments for monolayer ${\mathrm{NiPS}}_{3}$ and detail how anomalous relaxational behavior may reveal excitations of a (proximate) Berezinskii-Kosterlitz-Thouless phase in a proposed effective XY model.

Spin-Phonon Coupling in Ferromagnetic Monolayer Chromium Tribromide.

Novel 2D magnets exhibit intrinsic electrically tunable magnetism down to the monolayer limit, which has significant value for nonvolatile memory and emerging computing device applications. In these compounds, spin-phonon coupling (SPC) typically plays a crucial role in magnetic fluctuations, magnon dissipation, and ultimately establishing long-range ferromagnetic order. However, a systematic understanding of SPC in 2D magnets that combines theory and experiment is still lacking. In this work, monolayer chromium tribromide is studied to investigate SPC in 2D magnets via Raman spectroscopy and first principle calculations. The experimental Curie temperature and phonon shifts are found to be in good agreement with the numerical simulations. Specifically, it is demonstrated how magnetic exchange interactions affect phonon vibrations, which helps establish design fundamentals for 2D magnetic materials and other related devices.