Observation of Standing Spin Waves in a van der Waals Magnetic Material

Theory for magnetic impurity modes in two-dimensional van der Waals ferromagnetic films

A spin-wave analysis is developed to calculate the energies of the localized excitations occurring in two-dimensional ferromagnetic van der Waals monolayers when a substitutional magnetic impurity is introduced. The magnetic ions lie on a bipartite honeycomb lattice (similar to that for graphene) and the theory includes the effects of both Ising anisotropy and single-ion anisotropy to stabilize the magnetic ordering perpendicular to the atomic plane at low temperatures. A Dyson-equation formalism, together with the spin-dependent Green's functions derived for van der Waals monolayers, is employed to evaluate the existence conditions and energies for the impurity modes, which lie above the band of spin-wave states of the pure host material. For realistic parameter values it is found that typically two impurity modes may exist, depending on the spin quantum number for the magnetic impurity atom. Numerical applications are made to CrI3and Cr2Ge2Te6as the host materials.

Direct Observation of Propagating Spin Waves in the 2D van der Waals Ferromagnet Fe5GeTe2

Magnetism in reduced dimensionalities is of great fundamental interest while also providing perspectives for applications of materials with novel functionalities. In particular, spin dynamics in two dimensions (2D) have become a focus of recent research. Here, we report the observation of coherent propagating spin-wave dynamics in a ∼30 nm thick flake of 2D van der Waals ferromagnet Fe5GeTe2 using X-ray microscopy. Both phase and amplitude information were obtained by direct imaging below TC for frequencies from 2.77 to 3.84 GHz, and the corresponding spin-wave wavelengths were measured to be between 1.5 and 0.5 μm. Thus, parts of the magnonic dispersion relation were determined despite a relatively high magnetic damping of the material. Numerically solving an analytic multilayer model allowed us to corroborate the experimental dispersion relation and predict the influence of changes in the saturation magnetization or interlayer coupling, which could be exploited in future applications by temperature control or stacking of 2D-heterostructures.

Probing spin dynamics of ultra-thin van der Waals magnets via photon-magnon coupling

Layered van der Waals (vdW) magnets can maintain a magnetic order even down to the single-layer regime and hold promise for integrated spintronic devices. While the magnetic ground state of vdW magnets was extensively studied, key parameters of spin dynamics, like the Gilbert damping, crucial for designing ultra-fast spintronic devices, remains largely unexplored. Despite recent studies by optical excitation and detection, achieving spin wave control with microwaves is highly desirable, as modern integrated information technologies predominantly are operated with these. The intrinsically small numbers of spins, however, poses a major challenge to this. Here, we present a hybrid approach to detect spin dynamics mediated by photon-magnon coupling between high-Q superconducting resonators and ultra-thin flakes of Cr₂Ge₂Te₆ (CGT) as thin as 11 nm. We test and benchmark our technique with 23 individual CGT flakes and extract an upper limit for the Gilbert damping parameter. These results are crucial in designing on-chip integrated circuits using vdW magnets and offer prospects for probing spin dynamics of monolayer vdW magnets.

Dipole-exchange spin waves in two-dimensional van der Waals ferromagnetic films and stripes

A spin-wave (SW) theory that includes the long-range dipole-dipole interactions is presented for monolayers of van der Waals (vdW) ferromagnets for which the magnetic ions lie on a two-dimensional honeycomb lattice. The dipolar interactions provide an additional anisotropy in these materials, along with the Ising exchange interaction and/or single-ion anisotropies that typically stabilize the two-dimensional magnetic ordering. Analytical results for the linearized SW energies are obtained for the ferromagnets in two geometries: complete films and finite-width stripes (or ribbons). In both cases it is found that the inclusion of the dipole-dipole interactions leads to a shift and sometimes a splitting of the magnetic modes in the vdW structure. Also, in the latter case, where the edges are assumed to be along the zigzag lattice directions, the dipole-dipole interactions are found to play a role, as well as the exchange interactions, in modifying the localized edge SWs. Numerical examples are given, including applications to the ferromagnet CrI₃.

Monolayer CrCl_{3} as an Ideal Test Bed for the Universality Classes of 2D Magnetism

The monolayer halides CrX_{3} (X=Cl, Br, I) attract significant attention for realizing 2D magnets with genuine long-range order (LRO), challenging the Mermin-Wagner theorem. Here, we show that monolayer CrCl_{3} has the unique benefit of exhibiting tunable magnetic anisotropy upon applying a compressive strain. This opens the possibility to use CrCl_{3} for producing and studying both ferromagnetic and antiferromagnetic 2D Ising-type LRO as well as the Berezinskii-Kosterlitz-Thouless (BKT) regime of 2D magnetism with quasi-LRO. Using state-of-the-art density functional theory, we explain how realistic compressive strain could be used to tune the monolayer's magnetic properties so that it could exhibit any of these phases. Building on large-scale quantum Monte Carlo simulations, we compute the phase diagram of strained CrCl_{3}, as well as the magnon spectrum with spin-wave theory. Our results highlight the eminent suitability of monolayer CrCl_{3} to achieve very high BKT transition temperatures, around 50 K, due to their singular dependence on the weak easy-plane anisotropy of the material.