Atomically thin films of layered chromium triiodide (CrI$_3$) have recently been regarded as suitable candidates to a wide spectrum of technologically relevant applications, mainly owing to the opportunity they offer to achieve a reversible transition between coexisting in-plane ferro- and out-of-plane antiferro-magnetic orders. However, no routes for inducing such a transition have been designed down to the single-layer limit. Here, we address the magnetic response of monolayer CrI$_3$ to in-plane lattice deformations through a combination of isotropic Heisenberg spin Hamiltonians and first-principles calculations. Depending on the magnitude and orientation of the lattice strain exerted, we unveil a series of direction-dependent parallel-to-antiparallel spins crossovers, which yield the emergence of ferromagnetic, Néel antiferromagnetic, zigzag and stripy antiferromagnetic ground states. Additionally, we identify a critical point in the magnetic phase diagram whereby the exchange couplings vanish and the magnetism is quenched. Our work establishes guidelines for extensively tailoring the spin interactions in monolayer CrI$_3$ via strain engineering, and further expands the magnetically ordered phases which can be hosted in a two-dimensional crystal.
We have employed one of the well-known many-body techniques, density functional theory plus dynamical mean-field theory (DFT + DMFT), to investigate the electronic structure of ferromagnetic monolayer CrI3 as a function of temperature and hole-doping concentration. The computed magnetic susceptibility follows the Curie's law, indicating that the ferromagnetism of monolayer CrI3 originates from localized magnetic moments of Cr atoms rather than Stoner-type itinerant ones. The DFT + DMFT calculations show a different coherent temperature for each spin component, demonstrating apparent strong spi…
Using {\it ab initio} density functional theory and single-orbital Hubbard model calculations via the density matrix renormalization group method, we systematically studied the monolayer VOI$_2$ with a $3d^1$ electronic configuration. Our phonon calculations indicate that the orthorhombic $Pmm2$ FE-II phase is the most likely ground state, involving a ferroelectric distortion along the $a$-axis and V-V dimerization along the $b$-axis. Specifically, the "pseudo Jahn-Teller" effect caused by the coupling between empty V ($d_{xz/yz}$ and $d_{3z^2-r^2}$) and O $2p$ states is proposed as the mechan…
Magnetic anisotropy is crucially important for the stabilization of two-dimensional (2D) magnetism, which is rare in nature but highly desirable in spintronics and for advancing fundamental knowledge. Recent works on CrI$_3$ and CrGeTe$_3$ monolayers not only led to observations of the long-time-sought 2D ferromagnetism, but also revealed distinct magnetic anisotropy in the two systems, namely Ising behavior for CrI$_3$ versus Heisenberg behavior for CrGeTe$_3$. Such magnetic difference strongly contrasts with structural and electronic similarities of these two materials, and understanding it …
The first magnetic 2D material discovered, monolayer (ML) CrI$_3$, is particularly fascinating due to its ground state ferromagnetism. Yet, because monolayer materials are difficult to probe experimentally, much remains unresolved about ML CrI$_{3}$'s structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin-phonon and spin-lattice coupling of ML CrI$_{3}$. We exploit a recently developed surrogate Hessian DMC line search technique to dete…
Ultrathin films of the itinerant ferromagnet SrRuO$_3$ were studied using transport and magnto-optic polar Kerr effect. We find that below 4 monolayers the films become insulating and their magnetic character changes as they loose their simple ferromagnetic behavior. We observe a strong reduction in the magnetic moment which for 3 monolayers and below lies in the plane of the film. Exchange-bias behavior is observed below the critical thickness, and may point to induced antiferromagnetism in contact with ferromagnetic regions.
Temperature and field dependence of collective spin excitations or magnon in monolayer honeycomb spin lattices is investigated using an anisotropic exchange XZ-Heisenberg model in an external field. Magnetic phase transition in the presence of the transverse field is the spin reorientation (SR) transition with magnon intensity existing above the SR temperature. The transverse field either decreases or sustains the spin-wave intensity in the temperature region below or above the SR temperature, respectively. The gap of the zero-momentum low-energy magnon branch closes at the SR transverse field…
The $ν=0$ quantum Hall state in a defect-free graphene sample is studied within the framework of quantum Hall ferromagnetism. We perform a systematic analysis of the pseudospin anisotropies, which arise from the valley and sublattice asymmetric short-range electron-electron (e-e) and electron-phonon (e-ph) interactions. The phase diagram, obtained in the presence of generic pseudospin anisotropy and the Zeeman effect, consists of four phases characterized by the following orders: spin-polarized ferromagnetic, canted antiferromagnetic, charge density wave, and Kekulé distortion. We take into ac…
Few-layer CrI$_3$ is the most known example among two-dimensional (2D) ferromagnets, which have attracted growing interest in recent years. Despite considerable efforts and progress in understanding the properties of 2D magnets both from theory and experiment, the mechanism behind the formation of in-plane magnetic ordering in chromium halides is still under debate. Here, we propose a microscopic orbitally-resolved description of ferromagnetism in monolayer CrI$_3$. Starting from first-principles calculations, we construct a low-energy model for the isotropic Heisenberg exchange interactions. …
A 2+1 dimensional fermion field theory is proposed as a model for the low-energy electronic excitations in monolayer graphene. The model consists of N=2 four-component Dirac fermions moving in the plane and interacting via a contact interaction between charge densities. For strong couplings there is a continuous transition to a Mott insulting phase. We present results of an extensive numerical study of the model's critical region, including the order parameter, its associated susceptibility, and for the first time the quasiparticle propagator. The data enables an extraction of the critical exp…
We present a detailed study on the microscopic origin of magnetism in suspended and dielectrically embedded CrI$_3$ monolayer. To this end, we down-fold two distinct minimal generalized Hubbard models with different orbital basis sets from \emph{ab initio} calculations using the constrained random phase approximation. Within mean-field approximation, we show that these models are capable of describing the formation of localized magnetic moments in CrI$_3$ and of reproducing electronic properties of full \emph{ab initio} calculations. We utilize the magnetic force theorem to study microscopic m…
The marked interplay between the crystalline, electronic, and magnetic structure of atomically thin magnets has been regarded as the key feature for designing next-generation magneto-optoelectronic devices. In this respect, a detailed understanding of the microscopic interactions underlying the magnetic responses of these crystals is of primary importance. Here, we combine model Hamiltonians with multi-reference configuration interaction wavefunctions to accurately determine the strength of the spin couplings in the prototypical single-layer magnet CrI$_3$. Our calculations identify the (ferro…
We analyze the phase diagram of the exact ground state (GS) of spin-$s$ chains with ferromagnetic $XXZ$ couplings under $n$-alternating field configurations, i.e, sparse alternating fields having nodes at $n-1$ contiguous sites. It is shown that such systems can exhibit a non-trivial magnetic behavior, which can differ significantly from that of the standard ($n=1$) alternating case and enable mechanisms for controlling their magnetic and entanglement properties. The boundary in field space of the fully aligned phase can be determined analytically $\forall\,n$, and shows that it becomes reacha…
We have studied the doping dependence of the in-plane and out-of-plane superfluid density, ρ^s(0), of two monolayer high-Tc superconductors, HgBa_2CuO_{4+δ} and La_{2-x}Sr_xCuO_4, using the low frequency ac-susceptibility and the muon spin relaxation techniques. For both superconductors, ρ^s(0) increases rapidly with doping in the under- and optimally doped regime and becomes nearly doping independent above a critical doping, p_c = 0.20.
We report clear experimental signatures of the theoretically unexpected gas-liquid transition in the first three monolayers of $^3$He adsorbed on graphite. The transition is inferred from the linear density dependence of the $γ$-coefficient of the heat capacity measured in the degenerate region (2 $\le T \le$80 mK) below a critical liquid density ($ρ_{c0}$). Surprisingly, the measured $ρ_{c0}$ values (0.6$\sim$0.9 nm$^{-2}$) are nearly the same for all these monolayers in spite of their quite different environments. We conclude that the ground-state of $^3$He in strict two dimensions is not a …
We present results from lattice simulations of a monolayer graphene model at non-zero temperature. At low temperatures for sufficiently strong coupling the model develops an excitonic condensate of particle-hole pairs corresponding to an insulating phase. The Berezinskii-Kosterlitz-Thouless phase transition temperature is associated with the value of the coupling where the critical exponent delta governing the response of the order parameter at criticality to an external source has a value close to 15. The critical coupling on a lattice with temporal extent N_t=32 (T=1/(N_t a_t) where a_t is t…
