Session H38: Monolayer Magnets I

First-principles approach to novel 2D ferromagnets

There is currently an increasing enthusiasm towards long-range magnetic order in two-dimensional materials (such as CrI3 and Cr2Ge2Te6), from the fundamental and from the applicative point of view, from theory and from experiments. In this work, we carry out an extensive investigation based on density functional theory on an extended class of such materials, starting from the database of exfoliable materials reported in N. Mounet et al., Nature Nano. 13, 26 (2018). In the aim of optimizing the properties of 2D-ferromagnets, in particular focusing on an increase of the Curie temperature, our analysis ranges from semiconducting chalcohalides (with formula M-VI-VI, where M is a transition metal, VI and VII are chalcogen and halogen elements) to di-halides (with formula M-(VII)2). In addition to structural and electronic properties, we analyse magnetic properties, in terms of magnetic moments, Heisenberg exchange coupling constants and magnetic anisotropy energy. Some of the considered materials (such as CrSBr or NiBr2) show exchange coupling constants significantly larger than the prototypical CrI3, so they might be promising candidates for larger transition temperatures.   

Anisotropic magnetic interactions in CrI3

CrI₃ is famous among van-der-Waals materials because it displays ferromagnetism in the bulk form, and also in the monolayer form, with an only slightly reduced Curie temperature. Since Heisenberg and XY models do not allow long-range ordering in 2D, it was initially assumed that the magnetic Hamiltonian in CrI₃ is of the Ising symmetry. However, it was later shown that it is not the single-site anisotropy, but exchange interaction anisotropy (driven by the spin-orbit coupling on I) that ensures the high Curie temperature. It was assumed, however, without any theoretical justification, that this interaction is of the simplest, pseudo-Ising, form, namely S^z S^z, z being the global hexagonal axis. In this talk, we will present first principle calculations showing that not only this pseudo-Ising interaction is present in the system, but all three nearest-neighbor anisotropic terms allowed by symmetry (S^xS^x-S^yS^y and S^xS^z-S^zS^x), plus proper rotations for two other bonds)are of similar order.   

Tuning Magnetism in Atomically Thin CrI3 by Hydrostatic Pressure

Atomically thin CrI₃ has recently been discovered as a two-dimensional magnetic semiconductor. Remarkably, while monolayer CrI₃ is ferromagnetic, antiferromagnetic inter-layer coupling is favored in few-layer CrI₃. Because the interlayer exchange coupling is relatively weak, it is expected to be sensitive to external perturbations. Indeed, control of the interlayer magnetic order in atomically thin CrI₃ by an electric field and electrostatic doping has recently been demonstrated. Here we report an experimental study of the magnetic order in few-layer CrI₃ under hydrostatic pressure. We utilized the giant tunneling magnetoresistance observed in CrI₃ spin-filter devices to probe the interlayer magnetic order. We found that the magnetic properties of atomically thin CrI₃ can be tuned by applying a moderate pressure.

  

Criticality, anisotropy and dimensionality in the van der Waals ferromagnet CrI3

Magnetic order is prohibited in the 2D Heisenberg isotropic model at finite temperatures by the long-established theorem put forward by Mermin and Wagner. Indeed, the recent studies on true 2D magnets have nothing but confirmed that magnetic anisotropy is pivotal for eliminating this restriction and allowing, for example, the onset of 2D ferromagnetism in a bilayer of chromium germanium telluride, or in a single layer of chromium triiodide (CrI3). These materials happen to be two identical uniaxial systems from the point of view of their magnetic anisotropy. However, the critical behavior of these 2D magnets is still a matter of debate amidst contradictory reports of the critical exponents. By modelling magnetometry experiments on bulk crystals and magneto-optic data of the monolayer we will shed new light on the universality class of these van der Waals magnets.   

Distinct spin-lattice and spin-phonon interactions in monolayer magnetic CrI3

We apply the density-functional theory to study various phases (including non-magnetic (NM), anti-ferromagnetic (AFM), and ferromagnetic (FM)) in monolayer magnetic chromium triiodide (CrI₃). We found that (1) the introduction of magnetism in monolayer CrI₃ gives rise to metal-to-semiconductor transition; (2) the electronic band topologies as well as the nature of direct and indirect band gaps in either AFM or FM phases exhibit delicate dependence on the magnetic ordering and spin-orbit coupling; and (3) the phonon modes involving Cr atoms are particularly sensitive to the magnetic ordering, highlighting distinct spin-lattice and spin-phonon coupling in this magnet. First-principles simulations of the Raman spectra demonstrate that both frequencies and intensities of the Raman peaks strongly depend on the magnetic ordering. The polarization dependent A_1g modes at 77 cm^-1 and 130 cm^-1 along with the E_g mode at about 50 cm^-1 in the FM phase may offer a useful fingerprint to characterize this material. Our results not only provide a detailed guiding map for experimental characterization of CrI₃, but also reveal how the evolution of magnetism can be tracked by its lattice dynamics and Raman response.   

Nature of the Magnetic Anisotropy in the Two-Dimensional Honeycomb Ferromagnet CrI3

The recent discovery of intrinsic ferromagnetism in two-dimensional (2D) van der Waals crystals, such as CrI₃, has drawn much interest due to its potential for future 2D spintronic applications; however, the nature of the anisotropic magnetic interactions that allow 2D ferromagnetism and determine T_C in these materials remains poorly understood. In this work, we provide a detailed description of the anisotropic spin interactions in monolayer CrI₃ using a microscopic spin Hamiltonian constructed from the symmetries of the system. We present the results of our mean field theory and linear spin-wave theory calculations for this model and explain which interaction is responsible for stabilizing 2D ferromagnetic order in this system. Finally, we provide estimates for the strength of each interaction by comparing these results to our experimental data from angle-dependent ferromagnetic resonance on bulk CrI₃ single crystals.   

Origin of magneto-crystalline anisotropy underlying 2D ferromagnetism in CrI3 single crystals from ferromagnetic resonance

We provide the detailed magnetic anisotropy structure of a CrI₃ single crystal obtained through the measurement of the angle dependence of ferromagnetic resonance. We present a microscopic spin model describing the anisotropic interactions in a monolayer in terms of the experimentally measured Heisenberg, Kitaev, symmetric-anisotropic and quadrupole interactions that incorporate the material’s crystal symmetries. Comparison of T_c calculated using spin wave theory with the experimentally known values reveals that CrI₃ is dominantly a Kitaev ferromagnet rather than Heisenberg. We also find that symmetric-anisotropic interaction stabilizes 2D ferromagnetic order by opening the magnon gap ~ 0.4 meV at the center of the Brillouin zone and we predict a Kitaev-interaction-induced ~ 5 meV magnon gap opening at the Dirac point. This work clarifies the complex anisotropic behaviour of spins in CrI₃, opening a route to develop 2D ferromagnets with higher T_c and explore novel 2D spin orders arising from Kitaev physics in van der Waals materials.
  

Stacking-dependent magnetism in bilayer CrI3

We report the connection between the stacking order and magnetic properties of bilayer CrI3 using first-principles calculations. We show that the stacking order defines the magnetic ground state. By changing the interlayer stacking order one can tune the interlayer magnetism between antiferromagnetism and ferromagnetism. To measure the predicted stacking-dependent magnetism, we propose using a linear magnetoelectric effect. Our results not only gives a possible explanation for the observed antiferromagnetism in bilayer CrI3 but also have direct implications in heterostructures made of two-dimensional magnets.   

Spectroscopic studies of magnetic ordering in two-dimensional trihalides and chromium-based compounds

Since the discovery of layer-dependent ferromagnetism in chromium triiodide(CrI₃), the two-dimensional(2-D) crystals with intrinsic magnetism persisting even into monolayer attract widespread concern. This kind of 2-D magnets provide us a totally new platform for further development of spintronics, magnetoelectronics etc. Even though the details of the magnetic coupling between layers have not been fully understood, such ferromagnetism in CrI₃ give us hint that other 2-D trihalides and chromium-based compounds may also show remarkable magnetic properties down to thin layers. Here we will present our work on looking for new 2-D magnets and the understanding of the magnetic ordering in these materials.   

High Curie-temperature intrinsic ferromagnetism and hole doping-induced half-metallicity in two-dimensional scandium chlorine monolayers

High Curie-temperature ferromagnetic two-dimensional (2D) materials with large spin polarization have been a long-sought goal due to their potential in spintronics applications. Here we report a promising 2D scandium chlorine (ScCl) monolayer with intrinsic ferromagnetism and high Curie temperature up to 185 K, which is much higher than that of the reported CrI3 monolayer (45 K) and the boiling point of liquid nitrogen (77 K). Moreover, a small amount of hole doping can turn the ScCl monolayer into a half-metal and further improves the magnetic moment and Curie temperature. The novel ferromagnetism can also be extended to ScCl bilayers. In addition, the ScCl monolayer possesses excellent thermal and dynamical stabilities and great feasibility of experimental exfoliation from its layered bulk. These intriguing electronic and magnetic properties make the ScCl monolayer a promising candidate for spintronic applications.   

Probing magnetism of a 2D magnet with Pt through magnetoresistance

2D magnetic materials have lately attracted tremendous research interest in condensed matter physics. Very interestingly, chromium triiodide (CrI₃), an insulating member of the 2D magnet family, has been discovered to possess antiferromagnetic coupling between layers, as demonstrated by magneto-optic Kerr effect and tunneling measurements in ultra-thin samples. In our work, we place a CrI₃ flake in direct contact with a pre-patterned Pt Hall bar which serves as a sensing layer. We observe a sharp increase in magnetoresistance (MR) at H(along c-axis) ~ 2T. This feature coincides with a major magnetization switching previously reported in CrI₃ flakes with thickness above 3 layers. Temperature and field direction dependent MR measurements have also been conducted and the results reveal further information about the nature of the magnetic interactions. Our approach offers a unique platform to study magnetic ordering in CrI₃ and other highly resistive 2D magnetic materials through electrical transport measurements. It also provides an interesting perspective for studying the intriguing physics of exchange proximity coupling and spin current effect at 2D van der Waals interfaces.   

Dipolar interaction and exchange anisotropy in two-dimensional ferromagnetic quantum Heisenberg spin lattices.

Spin wave majority gates are considered as a viable beyond CMOS technology [1], if sufficiently scaled down. Although quantum effects are important when considering such scaled-down devices with thin ferromagnets, these are not sufficiently taken into account in today’s device simulations. Similarly, the effect of magnetic dipolar interaction on both the direction and magnitude of magnetization is poorly understood.

We present results [2] on the magnetization in two-dimensional ferromagnets with exchange anisotropy in an external magnetic field applied in an arbitrary direction. Using double-time temperature-dependent Green’s functions, we take into account quantum and thermal effects and we show the existence of a magnetic reorientation transition in anisotropic Heisenberg ferromagnets. Additionally, the framework can be extended to fully take into account magnetic dipole-dipole interaction, including its effect on the magnetization direction.

[1] I.P. Radu et al., Spintronic majority gates, IEEE IEDM (2015)
[2] J.Vanherck et al., Anisotropic bulk and planar Heisenberg ferromagnets in uniform, arbitrarily oriented magnetic fields, J. Phys. Condens. Matter (2018)   

Checkerboard Antiferromagnetic Order in FeSe Monolayer

Although the paramagnetic state has been confirmed in FeSe bulk via inelastic neutron-scattering (INS), the magnetic states in FeSe monolayer and thin films remain mysterious due to the difficulties in both experimental and theoretical approaches. Experimentally, current magnetic measurement techniques are extremely difficult to be applied to thin film structures. Theoretically, first principle calculation can not deal with paramagnetic system with strong spin fluctuations. Here we report a systematic approach based on surface defects and in-plane strain, and utilizing scanning tunneling measurements (STM) combining with first-principles calculations, to identify the magnetic states in FeSe monolayer and thin films. We provide a strong evidence of the existence of checkerboard antiferromagnetic order in FeSe monolayer by measuring and computing scanning tunneling microscopy images of two typical surface defects. The checkerboard antiferromagnetic order in FeSe monolayer is further verified by estimating the magnetic property of surface defect experimentally and theoretically. Moreover, we confirm the checkerboard antiferromagnetic order exists also in FeSe thin films by studying the electronic band structure evolution with in-plane strain.