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The coupling between spin and charge degrees of freedom in a crystal gives rise to magneto-optical effects with applications in the sensitive detection of local magnetic order, optical modulation and data storage. In two-dimensional magnets these effects manifest themselves in the large magneto-optical Kerr effect1,2, spontaneous helical light emission3,4 from ferromagnetic (FM) monolayers and electric-field induced Kerr rotation5–7 and giant second-order non-reciprocal optical effects8 in antiferromagnetic (AFM) bilayers. Here we demonstrate the tuning of inelastically scattered light through symmetry control in atomically thin chromium triiodide (CrI3). In monolayers, we found an extraordinarily large magneto-optical Raman effect from an A1g phonon mode due to the emergence of FM order. The linearly polarized, inelastically scattered light rotates by ~40°, more than two orders of magnitude larger than the rotation from the magneto-optical Kerr effect under the same experimental conditions. In CrI3 bilayers, the same phonon mode becomes Davydov-split into two modes of opposite parity, which exhibit divergent selection rules that depend on inversion symmetry and the underlying magnetic order. We demonstrate the magneto-electrical control over these selection rules by activating or suppressing Raman activity for the odd-parity phonon mode and the magneto-optical rotation of scattered light from the even-parity phonon mode. Our work underlines the unique opportunities provided by two-dimensional magnets to control the combined time-reversal and inversion symmetries to manipulate Raman optical selection rules and for exploring emergent magneto-optical effects and spin–phonon coupled physics.Symmetry control in atomically thin chromium triiodide enables the observation of tunable magneto-optical Raman effects in the 2D limit.

In this paper, we study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, we establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. We also use the miraculous property (quoting Chandrasekhar) - that the Dirac equation can be separated into radial and angular ordinary differential equations - to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, we use this expression of the scattering matrix to study the uniqueness property in the associated inverse scattering problem at fixed energy. Using essentially the particular form of the angular equation (that can be solved explicitly by Frobenius method) and the Complex Angular Momentum technique on the radial equation, we are finally able to determine uniquely the metric of the black hole from the knowledge of the scattering matrix at a fixed energy.

Magneto-optical Kerr effect microscopy is used to show that monolayer chromium triiodide is an Ising ferromagnet with out-of-plane spin orientation. Magnetism in flatland The question of what happens to the properties of a material when it is thinned down to atomic-scale thickness has for a long time been a largely hypothetical one. In the past decade, new experimental methods have made it possible to isolate and measure a range of two-dimensional structures, enabling many theoretical predictions to be tested. But it has been a particular challenge to observe intrinsic magnetic effects, which could shed light on the longstanding fundamental question of whether intrinsic long-range magnetic order can robustly exist in two dimensions. In this issue of Nature , two groups address this challenge and report ferromagnetism in atomically thin crystals. Xiang Zhang and colleagues measured atomic layers of Cr 2 Ge 2 Te 6 and observed ferromagnetic ordering with a transition temperature that, unusually, can be controlled using small magnetic fields. Xiaodong Xu and colleagues measured atomic layers of CrI 3 and observed ferromagnetic ordering that, remarkably, was suppressed in double layers of CrI 3 , but restored in triple layers. The two studies demonstrate a platform with which to test fundamental properties of purely two-dimensional magnets. Since the discovery of graphene 1 , the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent additions include semiconductors with spin–valley coupling 2 , Ising superconductors 3 , 4 , 5 that can be tuned into a quantum metal 6 , possible Mott insulators with tunable charge-density waves 7 , and topological semimetals with edge transport 8 , 9 . However, no two-dimensional crystal with intrinsic magnetism has yet been discovered 10 , 11 , 12 , 13 , 14 ; such a crystal would be useful in many technologies from sensing to data storage 15 . Theoretically, magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temperatures by the Mermin–Wagner theorem 16 . Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI 3 ) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 kelvin is only slightly lower than that of the bulk crystal, 61 kelvin, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent physical properties typical of van der Waals crystals 17 , 18 , 19 . Remarkably, bilayer CrI 3 displays suppressed magnetization with a metamagnetic effect 20 , whereas in trilayer CrI 3 the interlayer ferromagnetism observed in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as electrical control for realizing magnetoelectronics 12 , and van der Waals engineering to produce interface phenomena 15 .

Semiconducting ferromagnet-nonmagnet interfaces in van der Waals heterostructures present a unique opportunity to investigate magnetic proximity interactions dependent upon a multitude of phenomena including valley and layer pseudospins, moiré periodicity, or exceptionally strong Coulomb binding. Here, we report a charge-state dependency of the magnetic proximity effects between MoSe 2 and CrBr 3 in photoluminescence, whereby the valley polarization of the MoSe 2 trion state conforms closely to the local CrBr 3 magnetization, while the neutral exciton state remains insensitive to the ferromagnet. We attribute this to spin-dependent interlayer charge transfer occurring on timescales between the exciton and trion radiative lifetimes. Going further, we uncover by both the magneto-optical Kerr effect and photoluminescence a domain-like spatial topography of contrasting valley polarization, which we infer to be labyrinthine or otherwise highly intricate, with features smaller than 400 nm corresponding to our optical resolution. Our findings offer a unique insight into the interplay between short-lived valley excitons and spin-dependent interlayer tunneling, while also highlighting MoSe 2 as a promising candidate to optically interface with exotic spin textures in van der Waals structures. One advantage of van der Waals materials is the ability to combine different materials in layers to form new heterostructures. Here, the authors investigate heterostructures of CrBr 3 and MoSe 2 , and find that the ferromagnetism of CrBr 3 enhances the valley dependent optical response of the MoSe 2 .

\"Maryland-raised Cayce Kerr began his caddying career at the storied Congressional Country Club in 1986 and within a year had managed to work his way onto the PGA Tour, rubbing shoulders with the biggest names in the world of golf. Armed with quick wit and deep golf knowledge, he quickly established himself in the top echelon of his profession and never looked back, partnering with more than two dozen major champions and even working 30 Masters tournaments in a row from 1987 until 2016. In Walking with Greatness, Kerr reveals what really goes on inside and outside the ropes at the highest levels of golf. With a cast of characters including Ernie Els, Fred Couples, Vijay Singh, Fuzzy Zoeller, and Tiger Woods, this true insider's memoir pulls no punches in portraying life on the PGA Tour. Spanning indelible triumphs, improbable mishaps, and no shortage of hijinks, Kerr's adventures and observations will leave golf fans illuminated, entertained, and often literally laughing out loud\"-- Provided by publisher.

Interferometry has long been used to measure the phase of light signals. Combined with a heterodyne detection scheme, it allows to simultaneously and unambiguously record amplitude and phase variations. In this work, we exploit these well-known techniques to evaluate the nonlinear phase induced by the optical Kerr effect during the propagation of a laser pulse in a nonlinear medium. We show that the nonlinear index can easily be retrieved when the accumulated phase remains small, but counter-intuitive results can be observed at higher powers.