We study ferromagnetism and its stability in twisted bilayer graphene. We work with a Hubbard-like interaction that corresponds to the screened Coulomb interaction in a well-defined limit where the Thomas-Fermi screening length $l_\text{TF}$ is much larger than monolayer graphene's lattice spacing $l_g \ll l_\text{TF}$ and much smaller than the Moiré super lattice's spacing $ l_\text{TF} \ll l_{\text{Moiré}}$. We show that in the perfectly flat band "chiral" limit and at filling fractions $\pm 3/4$, the saturated ferromagnetic (spin and valley polarized) states are ideal ground states candidates in the large band-gap limit. By assuming a large enough substrate (hBN) induced sub-lattice potential, the same argument can be applied to filling fractions $\pm 1/4$. We estimate the regime of stability of the ferromagnetic phase around the chiral limit by studying the exactly calculated spectrum of one-magnon excitations. The instability of the ferromagnetic state is signaled by a negative magnon excitation energy. This approach allows us to deform the results of the idealized chiral model (by increasing the bandwidth and/or modified interactions) towards more realistic systems. Furthermore, we use the low energy part of the exact one-magnon spectrum to calculate the spin-stiffness of the Goldstone modes throughout the ferromagnetic phase. The calculated value of spin-stiffness can determine the excitation energy of charged skyrmions.
We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $θ\sim1.05^\circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also…
Search for higher-order topological insulators, characterized by topologically protected gapless boundary states of codimension higher than one, in bosonic systems has attracted growing interest. Here, we establish twisted bilayer honeycomb magnets as a new platform for hosting second-order topological magnon insulators (SOTMIs) without fine-tuning. We employ a simple, minimal Heisenberg spin model to describe misaligned bilayer sheets of honeycomb ferromagnetic magnets with a large commensurate twist angle. We found that the higher-order topology in this bilayer system shows a significant dep…
We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structur…
When two sheets of graphene are stacked at a small twist angle, the resulting flat superlattice minibands are expected to strongly enhance electron-electron interactions. Here we present evidence that near three-quarters ($3/4$) filling of the conduction miniband these enhanced interactions drive the twisted bilayer graphene into a ferromagnetic state. We observe emergent ferromagnetic hysteresis, with a giant anomalous Hall (AH) effect as large as $10.4\ \mathrm{kΩ}$ and signs of chiral edge states in a narrow density range around an apparent insulating state at $3/4$. Surprisingly, the magne…
CoSi single crystal is a known realization of a chiral topological semimetal with simultaneously broken mirror and inversion symmetries. In addition to the symmetry-induced spin-orbit coupling, surface ferromagnetism is known in nominally diamagnetic CoSi structures, which appears due to the distorted bonds and ordered vacancies near the surface. We experimentally investigate electron transport through a thin CoSi flake at high current density. Surprisingly, we demonstrate $dV/dI(I)$ curves which are qualitatively similar to ones for ferromagnetic multilayers with characteristic $dV/dI$ magnon…
Bilayer Heisenberg ferromagnetic insulators hold degenerate terahertz Dirac magnon modes associated with two opposite valleys of the hexagonal Brillouin zone. We show that this energy degeneracy can be removed by breaking of the inversion symmetry (I), leading to a topological magnon valley current. We show furthermore that this current leads to valley Seebeck effect for magnons and is thereby detectable. We perform calculations in the specific example of bilayer CrBr3, where I can be broken by electrostatic doping.
We have previously reported ferromagnetism evinced by a large hysteretic anomalous Hall effect in twisted bilayer graphene (tBLG). Subsequent measurements of a quantized Hall resistance and small longitudinal resistance confirmed that this magnetic state is a Chern insulator. Here we report that, when tilting the sample in an external magnetic field, the ferromagnetism is highly anisotropic. Because spin-orbit coupling is negligible in graphene such anisotropy is unlikely to come from spin, but rather favors theories in which the ferromagnetism is orbital. We know of no other case in which fer…
We study a bilayer structure consisting of an antiferromagnetic insulator and a normal metal. An electron current is driven in the normal metal with direction parallel to the interface between the materials. Due to interfacial exchange coupling between the localized spins in the antiferromagnet and the itinerant electrons in the normal metal, a magnon current can then be induced in the antiferromagnet. Using an uncompensated antiferromagnetic interface, creating an asymmetry in the interfacial coupling to the two degenerate magnon modes, we find that it is possible to generate a magnon spin-cu…
Several moiré systems created by various twisted bilayers have manifested magnetism under flatband conditions leading to enhanced interaction effects. We theoretically study stability of moiré flatband ferromagnetism against collective excitations, with a focus on the effects of Bloch band quantum geometry. The spin magnon spectrum is calculated using different approaches, including Bethe-Salpeter equation, single mode approximation, and an analytical theory. One of our main results is an analytical expression for the spin stiffness in terms of the Coulomb interaction potential, the Berry curv…
The interfacial coupling between electrons and magnons in adjacent layers can mediate an attractive electron-electron interaction and induce superconductivity. We consider magic-angle twisted bilayer graphene sandwiched between two ferromagnetic insulators to optimize this effect. As a result, magnons induce an interlayer superconducting state characterized by $p$-wave symmetry. We investigate two candidate ferromagnets. The van der Waals ferromagnet CrI$_3$ stands out because it allows compression to tune the superconducting state with an exponential sensitivity. This control adds a new dimen…
We develop a comprehensive theory of twisted bilayer magnetism. Starting from the first-principles calculations of two-dimensional honeycomb magnet CrI3, we construct the generic spin models that represent a broad class of twisted bilayer magnetic systems. Using Monte-Carlo method, we discover a variety of non-collinear magnetic orders and topological magnons that have been overlooked in the previous theoretical and experimental studies. As a function of the twist angle, the collinear magnetic order undergoes the phase transitions to the non-collinear order and the magnetic domain phase. In th…
We demonstrate the magnetically-induced transparency (MIT) effect in Y$_3$Fe$_5$O$_{12}$(YIG)/Permalloy(Py) coupled bilayers. The measurement is achieved via a heterodyne detection of the coupled magnetization dynamics using a single wavelength that probes the magneto-optical Kerr and Faraday effects of Py and YIG, respectively. Clear features of the MIT effect are evident from the deeply modulated ferromagnetic resonance of Py due to the perpendicular-standing-spin-wave of YIG. We develop a phenomenological model that nicely reproduces the experimental results including the induced amplitude …
We explore the moiré magnon bands in twisted bilayer magnets with next-nearest neighboring Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By calculating the magnonic band structures and the topological Chern numbers for four representative cases, we find that (i) the valley moiré bands are extremely flat over a wide range of continuous twist angles; (ii) the topological Chern numbers of the lowest few flat bands vary significantly with the twist angle; and (iii) the lowest few topological flat bands in bi…
We reveal the rich magnon topology in honeycomb bilayer ferromagnets (HBF) induced by the combined effect of interlayer exchange, Dzyaloshinskii-Moriya interaction (DMI), and electrostatic doping (ED). In particular, we present a systematic study of the Hamiltonian non-adiabatic evolution in the HBF parametric space, spanned by the symmetry-breaking terms (DMI and ED) and interlayer exchange. We determine the band closure manifolds which are found to divide the parametric space into six distinct regions, matched with five distinct topological phases and one topologically trivial phase. The cha…
The rich and unconventional physics in layered 2D magnets can open new avenues for topological magnonics and magnon valleytronics. In particular, two-dimensional (2D) bilayer quantum magnets are gaining increasing attention due to their intriguing stacking-dependent magnetism, controllable ground states, and topological excitations induced by magnetic spin-orbit couplings (SOCs). Despite the substantial research on these materials, their topological features remain widely unexplored to date. The present study comprehensively investigates the magnon topology and magnon valley-polarization in ho…
Twistronics is currently one of the most active research fields in condensed matter physics, following the discovery of correlated insulating and superconducting phases in twisted bilayer graphene (tBLG). Here, we present a magnonic analogue of tBLG. We study magnons in twisted ferromagnetic bilayers (tFBL), including exchange and Dzyaloshinskii-Moriya interactions (DMI). For negligible DMI, tFBL presents discrete magnon magic angles and flat moiré minibands analogous to tBLG. The DMI, however, changes the picture and renders the system much more exotic. The DMI in tFBL induces a rich topologi…
Recent experiments have observed possible spin- and valley-polarized insulators and spin-triplet superconductivity in twisted double bilayer graphene, a moire structure consisting of a pair of Bernal-stacked bilayer graphene. Besides the continuously tunable band widths controlled by an applied displacement field and twist angle, these moire bands also possess van Hove singularities near the Fermi surface and a field-dependent nesting which is far from perfect. Here we carry out a perturbative renormalization group analysis to unbiasedly study the competition among all possible instabilities i…
Valleytronics is a pioneering technological field relying on the valley degree of freedom to achieve novel electronic functionalities. Topological valley-polarized electrons confined to domain walls in bilayer graphene were extensively studied in view of their potentials in valleytronics. Here, we study the magnonic version of domain wall excitations in 2D honeycomb ferromagnetic bilayers (FBL) with collinear order. In particular, we explore the implications of Dzyaloshinskii-Moriya interaction (DMI) and electrostatic doping (ED) on the existence and characteristics of 1D magnons confined to l…
We conducted a systematic angular dependence study of nonlinear magnetoresistance in NiFe/Pt bilayers at variable temperature and field using the Wheatstone bridge method. We successfully disentangled magnon magnetoresistance from other types of magnetoresistances based on their different temperature and field dependences. Both the spin Hall/anisotropic and magnon magnetoresistances contain sine phi and sine 3 phi components with phi the angle between current and magnetization, but they exhibit different field and temperature dependence. The competition between different types of magnetoresist…
Tripartite Phonon-Magnon-Plasmon Coupling, Parametric Amplification, and Formation of a Phonon-Magnon-Plasmon Polariton in a Two-Dimensional Periodic Array of Magnetostrictive/Plasmonic Bilayered Nanodots
Chiral antiferromagnets are currently considered for broad range of applications in spintronics, spin-orbitronics and magnonics. In contrast to the established approach relying on materials screening, the anisotropic and chiral responses of low-dimensional antifferromagnets can be tailored relying on the geometrical curvature. Here, we consider an achiral, anisotropic antiferromagnetic spin chain and demonstrate that these systems possess geometry-driven effects stemming not only from the exchange interaction but also from the anisotropy. Peculiarly, the anisotropy-driven effects are complemen…
In bilayer graphene rotationally faulted to theta=1.1 degrees, interlayer tunneling and rotational misalignment conspire to create a pair of low energy flat band that have been found to host various correlated phenomena at partial filling. Most work to date has focused on the zero magnetic field phase diagram, with magnetic field (B) used as a probe of the B=0 band structure. Here, we show that twisted bilayer graphene (tBLG) in a B as low as 2T hosts a cascade of ferromagnetic Chern insulators with Chern number |C|=1,2 and 3. We argue that the emergence of the Chern insulators is driven by th…
Recent inelastic neutron diffraction measurements on Cr$_2$(Te, W, Mo)O$_6$ have revealed that these systems consist of bilayers of spin-3/2 Cr$^{3+}$ ions with strong antiferromagnetic inter-bilayer coupling and tuneable intra-bilayer coupling from ferro (for W and Mo) to antiferro (for Te). These measurements have determined the ground state spin structure and the values of sublattice magnetization, which shows significant reduction of sublattice magnetization from the atomic spin value of 3.0$μ_B$ for Cr$^{3+}$ atoms. In an earlier paper we theoretically investigated the low temperature spi…
When interacting spins in condensed matter order ferromagnetically, their ground state wave function is topologically trivial. Nonetheless, in two dimensions, the ferromagnetic state can support spin excitations with nontrivial topology, an exotic state known as topological magnon insulator (TMI). Here, we theoretically unveil and numerically confirm a novel ferromagnetic state in three dimensions dubbed second-order TMI, whose hallmarks are excitations at its hinges, where facets intersect. Since ferromagnetism naturally comes with broken time-reversal symmetry, the hinge magnons are chiral, …
We develop a model for the magnonic contribution to the unidirectional spin Hall magnetoresistance (USMR) of heavy metal/ferromagnetic insulator bilayer films. We show that diffusive transport of Holstein-Primakoff magnons leads to an accumulation of spin near the bilayer interface, giving rise to a magnoresistance which is not invariant under inversion of the current direction. Unlike the electronic contribution described by Zhang and Vignale [Phys. Rev. B 94, 140411 (2016)], which requires an electrically conductive ferromagnet, the magnonic contribution can occur in ferromagnetic insulators…
We report broadband spectroscopy and numerical analysis by which we explore propagating spin waves in a magnetic bilayer consisting of a 23 nm thick permalloy film deposited on 130 nm thick $Y_{3}Fe_{5}O_{12}$. In the bilayer, we observe a characteristic mode that exhibits a considerably larger group velocity at small in-plane magnetic field than both the magnetostatic and perpendicular standing spin waves. Using the finite element method, we confirm the observations by simulating the mode profiles and dispersion relations. They illustrate the hybridization of spin wave modes due to exchange c…
We study the magnon-mediated pairing between fermions on the surface of a topological insulator (TI) coupled to a ferromagnetic insulator with a tilted mean field magnetization. Tilting the magnetization towards the interfacial plane reduces the magnetic band gap and leads to a shift in the effective TI dispersions. We derive and solve the self-consistency equation for the superconducting gap in two different situations, where we neglect or include the frequency dependence of the magnon propagator. Neglecting the frequency dependence results in p-wave Amperean solutions. We also find that tilt…
Ferromagnetic honeycomb systems are known to exhibit a magnonic topological phase under the existence of the next-nearest neighbor Dzyaloshinskii-Moriya interaction (DMI). Motivated by the recent progress in the sublattice-specific control of magnetic anisotropy, we study the topological phase of magnon bands of honeycomb ferromagnetic monolayer and bilayer with the sublattice symmetry breaking due to the different anisotropy energy in the presence of the DMI. We show that there is a topological phase transition between the topological magnon insulator and the topologically trivial magnon phas…
We theoretically investigate topological spin transport of the magnon-polarons in bilayer magnet with two-dimensional square lattices. Our theory is motivated by recent reports on the van der Waals magnets which show the reversible electrical switching of the interlayer magnetic order between antiferromagnetic and ferromagnetic orders. The magnetoelastic interaction opens band gaps and allows the interband transition between different excitation states. In the layered antiferromagnet, due to the interband transition between the magnon-polaron states, the spin Berry curvature which allows the t…
Magic-angle twisted bilayer graphene (MATBG) is notable as a highly tunable platform for investigating strongly correlated phenomena such as high-$T_c$ superconductivity and quantum spin liquids, due to easy control of doping level through gating and sensitive dependence of the magic angle on hydrostatic pressure. Experimental observations of correlated insulating states, unconventional superconductivity and ferromagnetism in MATBG indicate that this system exhibits rich exotic phases. In this work, using density functional theory calculations in conjunction with the effective screening medium…
