The recent thrust in ultrafast magnetization dynamics aims at extending spintronic functionalities to terahertz frequencies. Deterministic manipulation of magnetization at the corresponding ultrashort timescales requires minute control not only over the magnetization itself but also the reservoirs it is interacting with. Although the various intricate couplings between spins, phonons, and electrons-all of which are susceptible to ultrashort laser pulses-lead to many (often nonlinear) coupling routes, magnetization-dynamical nonlinearities have remained largely underexplored. In this Perspective, we highlight recent advances and foresee future developments in the rapidly evolving field of nonlinear magnetization dynamics. Given the elementary character of coherent excitations, we put particular emphasis on their nonlinearities. We briefly review theoretical aspects and assess excitation mechanisms to reach the nonlinear regime of magnetic excitations in a broad class of magnetic materials, such as ferromagnets, antiferromagnets, and ferrimagnets. We present an overview of the groundbreaking experiments that showcase the unique insights provided by magnetic nonlinearities. We conclude by discussing open challenges and opportunities that underpin the potential of nonlinear magnetization dynamics for the advancement of spintronics and cavity quantum electrodynamics with spin waves at terahertz frequencies.

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With growing interest in exploring fundamental phenomena at terahertz (THz) frequencies, the need for controlling the polarization state of THz radiation is indispensable. However, simple optical elements, such as waveplates that allow to create circularly-polarized THz radiation, are scarce. Here, we present THz quarter-wave plates (QWPs) made out of (110)-cut and (001)-cut DyScO 3 (DSO) crystals. We examine the complex refractive indices along the in-plane axes and map the birefringence of both DSO crystals. Further, we demonstrate that both a 50-µm-thick (110)-cut DSO and a 370-µm-thick (001)-cut DSO crystals behave like a QWP over a broad frequency range of 0.50 -0.70 THz and 0.50 -0.61 THz, respectively, with a phase tolerance of ±3 %.The so-called terahertz (1 THz = 10 12 Hz) frequency range of the electromagnetic spectrum spans from 0.1 to 10 THz. This spectral range has remained unexplored for a long time due to the lack of intense radiation sources and sensitive detectors. Over the past few decades, extensive progress has been made towards the development and application of THz technology 1-3 . In particular, these include intense single-cycle THz pulse generation 4-7 and THz time-domain spectroscopy (THz-TDS) [8][9][10][11] . From the fundamental point of view, light-matter interaction in this range is an ideal tool for studying collective excitations in solid-state systems, such as phonons 12 , magnons 13 , and heavy fermions [14][15][16] . In addition, the non-destructive nature of THz radiation makes it ideal for investigating the dynamic properties (conductivity, dielectric function, etc.) in a contactless manner for thin films 17,18 where mechanical contacts are detrimental. Recently, THz-TDS has been used to investigate soft vibrational modes in thin ferroelectric SrTiO 3 19 and PbTiO 3 films 20 and the non-Fermiliquid behavior in thin films of heavy-fermion material, YbRh 2 Si 2 21 . While these investigations can be performed using linearly-polarized (LP) THz light, there are certain phenomena where the helicity inherent for circularlypolarized (CP) THz light is indispensable, such as in measuring circular dichroism 22 , the quasi-particle Hall-effect in superconductors 23 , ionization of Rydberg atoms 24 , generation of nanoscopic toroidal moments 25 , etc. In addition, CP THz light is of great importance for investigating chiral structures in bio-molecules with promising applications, such as drug delivery and biological sensing 1,26 . Quarter-wave plates (QWPs) for generating CP THz light can be designed in different ways, such as form birefringence, liquid crystals, and the intrinsic crystal anisotropy. Form birefringence, based on an anisotropic periodic structure, can be induced in artificial manners using gratings, stack of papers 27 or Pancharatnam-Berry metasurfaces 28,29 . Optical elements that incorporate liqa