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Flat-band physics has attracted much attention in recently years because of its interesting properties and important applications. Some typical lattices have been proposed to generate flat bands, such as Kagome and Lieb lattices. The flat bands in these lattices contact with other bands rather than isolated. However, an ideal flat band should be isolated, because isolation is a prerequisite for a number of important applications. Here, we propose a new lattice that can produce isolated flat bands. The lattice is named as interlocking-circles lattice because its pattern seems like interlocking circles. Moreover, the new lattice is realized in graphene by hydrogenation. In the hydrogenated graphene, there are two nontrivial isolated flat bands appearing around the Fermi level. Upon hole or electron doping, the flat bands split into spin-polarized bands and then result in a ferromagnetic graphene. Our work not only proposes a new type of lattice but also opens a way to find systems with isolated flat bands.

We used a combination of polarized Raman spectroscopy and spin wave calculations to study magnetic excitations in the strong spin-orbit-coupled (SOC) bilayer perovskite antiferromagnet $Sr_3Ir_2O_7$. We observed two broad Raman features at ~ 800 $cm^{-1}$ and ~ 1400 $cm^{-1}$ arising from magnetic excitations. Unconventionally, the ~ 800 $cm^{-1}$ feature is fully symmetric ($A_{1g}$) with respect to the underlying tetragonal ($D_{4h}$) crystal lattice which, together with its broad line shape, definitively rules out the possibility of a single magnon excitation as its origin. In contrast, the ~ 1400 $cm^{-1}$ feature shows up in both the $A_{1g}$ and $B_{2g}$ channels. From spin wave and two-magnon scattering cross-section calculations of a tetragonal bilayer antiferromagnet, we identified the ~ 800 $cm^{-1}$ (~ 1400 $cm^{-1}$) feature as two-magnon excitations with pairs of magnons from the zone-center $\Gamma$ point (zone-boundary van Hove singularity X point). We further found that this zone-center two-magnon scattering is unique to bilayer perovskite magnets which host an optical branch in addition to the acoustic branch, as compared to their single layer counterparts. This zone-center two-magnon mode is distinct in symmetry from the time-reversal symmetry broken spin wave gap and phase mode proposed to explain the ~ 92 meV (742 $cm^{-1}$) gap in RIXS magnetic excitation spectra of $Sr_3Ir_2O_7$.

Exploring new parameter regimes to realize and control novel phases of matter has been a main theme in modern condensed matter physics research. The recent discovery of 2D magnetism in nearly freestanding monolayer atomic crystals has already led to observations of a number of novel magnetic phenomena absent in bulk counterparts. Such intricate interplays between magnetism and crystalline structures provide ample opportunities for exploring quantum phase transitions in this new 2D parameter regime. Here, using magnetic field and temperature dependent circularly polarized Raman spectroscopy of phonons and magnons, we map out the phase diagram of CrI3 that has been known to be a layered AFM in its 2D films and a FM in its 3D bulk. We, however, reveal a novel mixed state of layered AFM and FM in 3D CrI3 bulk crystals where the layered AFM survives in the surface layers and the FM appears in deeper bulk layers. We then show that the surface layered AFM transits into the FM at a critical magnetic field of 2 T, similar to what was found in the few layer case. Interestingly, concurrent with this magnetic phase transition, we discover a first-order structural phase transition that alters the crystallographic point group from C3i to C2h and thus, from a symmetry perspective, this monoclinic structural phase belongs to the 3D nematic order universality class. Our result not only unveils the complex single magnon behavior in 3D CrI3, but also settles down the puzzle of how CrI3 transits from a bulk FM to a thin layered AFM semiconductor, despite recent efforts in understanding the origin of layered AFM in CrI3 thin layer, and reveals the intimate relationship between the layered AFM-to-FM and the crystalline rhombohedral-to-monoclinic phase transitions. These findings further open up opportunities for future 2D magnet-based magneto-mechanical devices.

The ferro-rotational order, whose order parameter (OP) is an axial vector invariant under both time reversal (TR) and spatial inversion (SI) operations, is the last remaining category of ferroics to be observed after the ferroelectric, ferromagnetic, and ferro-toroidal orders. This order has become increasingly popular in many new quantum materials, especially in complex oxides, and is considered responsible for a number of novel phenomena such as polar vortices, giant magnetoelectric coupling, and type-II multiferroics. However, physical properties of the ferro-rotational order have been rarely studied either theoretically or experimentally. Here, using high sensitivity rotational anisotropy second harmonic generation (RA SHG), we have, for the first time, exploited the electric quadrupole (EQ) contribution to the SHG to directly couple to this centrosymmetric ferro-rotational order in an archetype of type-II multiferroics, RbFe(MoO4)2. Surprisingly, we have found that two types of domains with opposite ferro-rotational vectors emerge with distinct populations at the critical temperature Tc ~195 K and gradually evolve to reach an even ratio at lower temperatures. Moreover, we have identified the ferro-rotational order phase transition as weak first order, and have revealed its conjugate coupling field as a unique combination of the induced EQ SHG and the incident fundamental electric fields. Our results on physical properties of a ferro-rotational order provide crucial knowledge for understanding and searching for novel phases of matter built upon the ferro-rotational order. Further, these results open the possibility of revealing unconventional centrosymmetric orders and identifying their conjugate coupling fields with second order nonlinear optics., Comment: 20 pages, 4 figures

We conduct a comprehensive study of three different magnetic semiconductors, CrI$_3$, CrBr$_3$, and CrCl$_3$, by incorporating both few- and bi-layer samples in van der Waals tunnel junctions. We find that the interlayer magnetic ordering, exchange gap, magnetic anisotropy, as well as magnon excitations evolve systematically with changing halogen atom. By fitting to a spin wave theory that accounts for nearest neighbor exchange interactions, we are able to further determine a simple spin Hamiltonian describing all three systems. These results extend the 2D magnetism platform to Ising, Heisenberg, and XY spin classes in a single material family. Using magneto-optical measurements, we additionally demonstrate that ferromagnetism can be stabilized down to monolayer in more isotropic CrBr$_3$, with transition temperature still close to that of the bulk.

We have used rotational anisotropic polarized Raman spectroscopy to study the symmetries, the temperature and the doping dependence of the charge ordered state in metallic $(Sr_{1-x}La_{x})_{3}Ir_{2}O_{7}$. Although the Raman probe size is greater than the charge ordering length, we establish that the charge ordering breaks the fourfold rotational symmetry of the underlying tetragonal crystal lattice into twofold, as well as the translational symmetry, and forms short-range domains with $90^{\circ}$ rotated charge order wave vectors, as soon as the charge order sets in below $T_{CO} = \sim$ 200K and across the doping-induced insulator metal transition. We observe that this charge order mode frequency remains nearly constant over a wide temperature range and up to the highest doping level. These above features are highly reminiscent of the ubiquitous unidirectional charge order in underdoped high-$T_C$ copper-oxide-based superconductors (cuprates). We further resolve that the charge order damping rate diverges when approaching $T_{CO}$ from below and increases significantly as increasing the La doping level, which resembles the behaviors for a disorder-interrupted ordered phase and has not been observed for the charge order in cuprates., Comment: 17 pages, 4 figures + supplementary material

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., Comment: 25 pages, 4 figures + 8 supplementary figures