How a certain ground state of complex physical systems emerges, especially in two-dimensional materials, is a fundamental question in condensed-matter physics. A particularly interesting case is systems belonging to the class of XY Hamiltonian where the magnetic order parameter of conventional nature is unstable in two-dimensional materials leading to a Berezinskii−Kosterlitz−Thouless transition. Here, we report how the XXZ-type antiferromagnetic order of a magnetic van der Waals material, NiPS3, behaves upon reducing the thickness and ultimately becomes unstable in the monolayer limit. Our experimental data are consistent with the findings based on renormalization-group theory that at low temperatures a two-dimensional XXZ system behaves like a two-dimensional XY one, which cannot have a long-range order at finite temperatures. This work provides the experimental examination of the XY magnetism in the atomically thin limit and opens opportunities of exploiting these fundamental theorems of magnetism using magnetic van der Waals materials.

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Raman spectra of few-layer MoSe2 were measured with 8 excitation energies. New peaks that appear only near resonance with various exciton states are analyzed, and the modes are assigned.The resonance profiles of the Raman peaks reflect the joint density of states for optical transitions, but the symmetry of the exciton wave functions leads to selective enhancement of the A1g mode at the A exciton energy and the shear mode at the C exciton energy. We also find Davydov splitting of intra-layer A1g, E1g, and A2u modes due to inter-layer interaction for some excitation energies near resonances. Furthermore, by fitting the spectral positions of inter-layer shear and breathing modes and Davydov splitting of intra-layer modes to a linear chain model, we extract the strength of the inter-layer interaction. We find that the second-nearest-neighbor inter-layer interaction amounts to about 30% of the nearest-neighbor interaction for both in-plane and out-of-plane vibrations. 2 KEYWORDSMoSe2, Molybdenum diselenide, Raman spectroscopy, Davydov splitting, excitonic resonance 3 Few-layer semiconducting transition metal dichalcogenides (TMD's) are studied intensively owing to bandgap energies in the range of near infrared to visible wavelengths which make them suitable for various electronic and optoelectronic applications. 1,2 Monolayer MoSe2 shows a luminescence peak at ~1.6 eV which is suitable for applications in deep red or near infrared regions of the spectrum. MoSe2 is also used in TMD heterostructures such as WSe2/MoSe2 3,4 or MoS2/MoSe2 5,6 which exhibit interesting physical properties due to unique band alignment between these atomically thin semiconductors. Raman spectroscopy is a powerful tool to characterize 2-dimensional materials such as graphene or TMD's. For TMD materials, Raman spectroscopy is used to characterize the number of layers, 7-9 the stacking order, 10-12 strain, 13,14 or doping density. 15 However, it has been reported that the Raman spectrum of a TMD material varies greatly depending on the excitation laser used, which is attributed to excitonic resonance effects. [16][17][18][19] Because of reduced dielectric screening in 2-dimensional materials, the excitons in TMD's are known to have very large binding energies, [20][21][22][23][24] and so tightly localized wave functions. Resonance with such exciton states greatly modifies the Raman scattering process to result in extraordinary resonance Raman effects. In the Raman spectra of MoTe2 and WS2, Davydov splitting of some of the main Raman peaks have been reported. [25][26][27] Davydov splitting, also known as factor-group splitting, is the splitting of bands in the electronic or vibrational spectra of crystals due to the presence of more than one equivalent entity in the unit cell. 28,29 Since this is due to breaking of degeneracy by interactions of each entity, it is an important probe to investigate interactions between each system. In TMD's, the weak inter-layer interaction causes splitting of the intra-layer vibration modes. Since this s...

Magnetic ordering in the two-dimensional limit has been one of the most important issues in condensed matter physics for the past several decades. The recent discovery of new magnetic van der Waals materials heralds a much-needed easy route for the studies of two-dimensional magnetism: the thickness dependence of the magnetic ordering has been examined by using Isingand XXZ-type magnetic van der Waals materials. Here, we investigated the magnetic ordering of MnPS3, a two-dimensional antiferromagnetic material of Heisenberg-type, by Raman spectroscopy from bulk all the way down to bilayer. The phonon modes that involve the vibrations of Mn ions exhibit characteristic changes as temperature gets lowered through the Néel temperature. In bulk MnPS3, the Raman peak at ~155 cm -1 becomes considerably broadened near the Néel temperature and upon further cooling is subsequently red-shifted. The measured peak positions and polarization dependences of the Raman spectra are in excellent agreement with our first-principles calculations. In few-layer MnPS3, the peak at ~155 cm -1 exhibits the characteristic red-shift at low temperatures down to the bilayer, indicating that the magnetic ordering is surprisingly stable at such a thin limit. Our work sheds light on the hitherto unexplored magnetic ordering in the Heisenberg-type antiferromagnetic systems in the atomic-layer limit. ∑ ∑where XY J and I J are spin-exchange energies on the basal plane and along the c-axis, respectively; j S α is the α (α = x, y, or z) component of total spin; and j and δ run through all lattice sites and all nearest-neighbors, respectively. All three fundamental models can be realized with the generic Hamiltonian: 0 XY J = for the Ising model, 0 I J = for the XY model, and XY I J J = for the Heisenberg model. According to the Mermin-Wagner theorem [4], no magnetic ordering is possible at any nonzero temperature in one-or two-dimensional isotropic Heisenberg models. On the other hand, 2D Ising systems can have magnetic ordering at finite temperatures according to Onsager [5].Transition metal phosphorus trisulfides (TMPS3) belong to a class of 2D van der Waals magnetic materials that can be exfoliated to atomically thin layers [6,7]. For transition metal elements like Fe, Ni, and Mn, the materials share the same crystal structures but the magnetic phase at low temperatures vary depending on the magnetic elements: Ising (Fe), XXZ (Ni), and

Since the stacking order sensitively affects various physical properties of layered materials, accurate determination of the stacking order is important for studying the basic properties of these materials as well as for device applications. Because 2H-molybdenum disulfide (MoS2) is most common in nature, most studies so far have focused on 2H-MoS2. However, we found that the 2H, 3R, and mixed stacking sequences exist in few-layer MoS2 exfoliated from natural molybdenite crystals. The crystal structures are confirmed by HR-TEM measurements. The Raman signatures of different polytypes are investigated by using 3 different excitation energies 2 which are non-resonant and resonant with A and C excitons, respectively. The low-frequency breathing and shear modes show distinct differences for each polytype whereas the highfrequency intra-layer modes show little difference. For resonant excitations at 1.96 and 2.81 eV, distinct features are observed which enable determination of the stacking order.3 Polytypism, a special type of polymorphism in layered materials, refers to different stacking sequences of monolayers with the same structure. 1-3 Since stacking sequence is one of the key attributes of layered materials, the effects of different stacking sequences on the electronic and other properties of 2-dimensional (2D) materials are of great interest. Although the crystal structure of each layer is identical, the properties of few-layer crystals are sensitively dependent on the stacking sequence due to different inter-layer interactions. For example, in the case of graphene, two stable stacking orders, ABA (Bernal) and ABC (rhombohedral) stacking orders, predominantly exist in nature. 4,5 Several studies have revealed the influence of the stacking order on transport 6,7 and optical properties. [8][9][10][11][12] Hence, identifying the stacking sequences has become an important issue, and Raman spectroscopy has proven to be a reliable and easy characterization tool to identify stacking orders in few-layer graphene. [9][10][11]13 Since the Raman spectrum reflects the phonon dispersion and the electronic band structure, it is an ideal tool for fingerprinting the polytypes of graphene without complicated sample preparations.In layered transition metal dichalcogenides (TMDs), polymorphism and polytypism are more important than in graphene because of more complex crystal structures. Among TMD materials, molybdenum disulfide (MoS2) is the most extensively studied. Thanks to a finite bandgap, electronic applications such as field effect transistors 14,15 or photodetectors 16,17 are explored.Single-layer MoS2 comprises a monolayer of Mo atoms sandwiched between two sulfur layers, forming a 'trilayer' (TL). 18,19 Each TL is connected via weak van der Waals interactions. Like other 2D materials, MoS2 has several polymorphs. For single-layer MoS2, there are two types of polymorphs: trigonal prism (1H-MoS2) and octahedral coordination (1T-MoS2). Since 1T-MoS2 is metastable, only the trigonal phase is found in natural bulk ...