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Magnetic inertia has emerged as a possible way to manipulate ferromagnetic spins at a higher frequency e.g., THz. Theoretical treatments so far have considered the magnetic inertia as a scalar quantity. Here, we explore the magnetic inertial dynamics with a magnetic inertia tensor as macroscopic derivations predicted it to be a tensor. First, the inertia tensor has been decomposed into three terms: (a) scalar and isotropic inertia, (b) anisotropic and symmetric inertia tensor, (c) chiral and antisymmetric tensor. Further, we employ linear response theory to the inertial Landau-Lifshitz-Gilbert equation with the inertia tensor and calculate the effect of chiral and anisotropic inertia on ferromagnets, antiferromagnets, and ferrimagnets. It is established that the precession and nutation resonance frequencies decrease with scalar magnetic inertia. Our results suggest that the nutation resonance frequencies further reduce due to inertia tensor. However, the effective damping of the nutation resonance increases with the chiral and antisymmetric part of the inertia tensor. We show that the precession resonances remain unaffected, while the nutation resonances are modified with the chiral magnetic inertia., Comment: 13 pages, 8 figures

Nanomagnets are the building blocks of many existing and emergent spintronic technologies. Magnetization dynamics of nanomagnets is often dominated by nonlinear processes, which have been recently shown to have many surprising features and far-reaching implications for applications. Here we develop a theoretical framework uncovering the selection rules for multimagnon processes and discuss their underlying mechanisms. For its technological relevance, we focus on the degenerate three-magnon process in thin elliptical nanodisks to illustrate our findings. We parameterize the selection rules through a set of magnon interaction coefficients which we calculate using micromagnetic simulations. We postulate the selection rules and investigate how they are altered by perturbations, that break the symmetry of static magnetization configuration and spatial spin-wave profiles and that can be realized by applying off-symmetry-axis or nonuniform magnetic fields. Our work provides the phenomenological understanding into the mechanics of magnon interaction as well as the formalism for determining the interaction coefficients from simulations and experimental data. Our results serve as a guide to analyze magnon processes inherently present in spin-torque devices for boosting their performance or to engineer a specific nonlinear response of a nanomagnet used in neuromorphic or quantum magnonic application., Comment: 15 pages, 8 figures

Hybrid light-matter coupled states, or polaritons, in magnetic materials have attracted significant attention due to their potential for enabling novel applications in spintronics and quantum information processing. However, most studies to date have been carried out for ferromagnetic materials with magnon excitations at gigahertz frequencies. Here, we have investigated strong resonant photon-magnon coupling at frequencies above 1 terahertz for the first time in a prototypical room-temperature antiferromagnetic insulator, NiO, inside a Fabry-P\'erot cavity. The cavity was formed by the crystal itself when it was thinned down to an optimized thickness. By using terahertz time-domain spectroscopy in high magnetic fields up to 25 T, we swept the magnon frequency through Fabry-P\'erot cavity modes and observed photon-magnon anticrossing behavior, demonstrating clear vacuum Rabi splittings exceeding the polariton linewidths. These results show that NiO is a promising platform for exploring antiferromagnetic spintronics and cavity magnonics in the terahertz frequency range.

Recent experimental observation of inertial spin dynamics calls upon holistic reevaluation of the theoretical framework of magnetic resonance in ferromagnets. Here, we derive the secular equation of an inertial spin system in analogy to the ubiquitous Smit-Beljers formalism. We find that the frequency of precessional ferromagnetic resonances is decreased as compared to non-inertial case. We also find that the frequency of nutational resonances is generally increased due to the presence of magnetic anisotropy and applied magnetic field. We obtain exact solutions of the secular equation and approximations that employ the terminology of non-inertial theory and thus allow for convenient estimates of the inertial effects.

Understanding and tailoring static and dynamic properties of magnetic insulator thin films is important for spintronic device applications. Here, we grow atomically flat epitaxial europium iron garnet (EuIG) thin films by pulsed laser deposition on (111)-oriented garnet substrates with a range of lattice parameters. By controlling the lattice mismatch between EuIG and the substrates, we tune the strain in EuIG films from compressive to tensile regime, which is characterized by X-ray diffraction. Using ferromagnetic resonance, we find that in addition to the first-order perpendicular magnetic anisotropy which depends linearly on the strain, there is a significant second-order one that has a quadratic strain dependence. Inhomogeneous linewidth of the ferromagnetic resonance increases notably with increasing strain, while the Gilbert damping parameter remains nearly constant (~ 2x10^-2). These results provide valuable insight into the spin dynamics in ferrimagnetic insulators and useful guidance for material synthesis and engineering of next-generation spintronics applications.

Next-generation spintronic applications require material properties that can be hardly met by one material candidate. Here we demonstrate that by combining insulating and metallic magnets, enhanced spin-charge conversion and energy-efficient thermal spin currents can be realized. We develop a nanowire device consisting of an yttrium iron garnet and permalloy bi-layer. An interfacial temperature gradient drives the nanowire magnetization into auto-oscillations at gigahertz frequencies. Interfacial spin coupling and magnetoresistance of the permalloy layer translate spin dynamics into sizable microwave signals. The results show prospect for energy-efficient spintronic devices and present an experimental realization of magnon condensation in a heterogeneous magnetic system.

Magnetic resonance plays an important role in today's science, engineering, and medical diagnostics. Learning and teaching magnetic resonance is challenging since it requires advanced knowledge of condensed matter physics and quantum mechanics. Driven by the need to popularize this technologically impactful phenomenon, we develop an inexpensive table-top demonstration experiment. It unveils the magnetic resonance of a hand-held compass in the magnetic fields of a permanent magnet. The setup provides an immediate visualization of the underlying physical concepts and allows for their translation to broad student audiences.

The magnetic analogue of the Josephson effect can be exploited to develop a new class of nano-spin oscillators that we denote as spin superfluid Josephson oscillators. Such a device, consisting of two exchange coupled easy-plane metallic ferromagnets separated by a thin normal metal spacer, is proposed and analyzed. A spin chemical potential difference drives a $2\pi$ precession of the in-plane magnetization of each ferromagnet. The $2 \pi$ precession angle gives maximum values of the giant magnetoresistance, resulting in large output power compared to conventional spin Hall oscillators. An applied ac current results in a time-averaged magnetoresistance with Shapiro-like steps. The multistate mode-locking behavior exhibited by the spin Shapiro steps may be explored for applications in neuromorphic computing. As an experimental characterization method, electrical measurements of spin superfluid Josephson junctions can provide additional signatures of spin superfluidity.

Manipulation of magnetization by electric field is a central goal of spintronics because it enables energy-efficient operation of spin-based devices. Spin wave devices are promising candidates for low-power information processing but a method for energy-efficient excitation of short-wavelength spin waves has been lacking. Here we show that spin waves in nanoscale magnetic tunnel junctions can be generated via parametric resonance induced by electric field. Parametric excitation of magnetization is a versatile method of short-wavelength spin wave generation, and thus our results pave the way towards energy-efficient nanomagnonic devices.

Energy loss due to ohmic heating is a major bottleneck limiting down-scaling and speed of nano-electronic devices, and harvesting ohmic heat for signal processing is a major challenge in modern electronics. Here we demonstrate that thermal gradients arising from ohmic heating can be utilized for excitation of coherent auto-oscillations of magnetization and for generation of tunable microwave signals. The heat-driven dynamics is observed in $\mathrm{Y_{3}Fe_{5}O_{12}/Pt}$ bilayer nanowires where ohmic heating of the Pt layer results in injection of pure spin current into the $\mathrm{Y_{3}Fe_{5}O_{12}}$ layer. This leads to excitation of auto-oscillations of the $\mathrm{Y_{3}Fe_{5}O_{12}}$ magnetization and generation of coherent microwave radiation. Our work paves the way towards spin caloritronic devices for microwave and magnonic applications.