Preface xiii Acknowledgments xv 1 Introduction 1 1.1 Faraday and Voigt geometries; longitudinal and transverse magnetooptical effects 1.2 The Faraday effect 1.3 The Cotton-Mouton or Voigt effect 1.4 The magnetooptical Kerr effect (MOKE) 1.5 The permittivity tensor and the sign convention 1.6 Other physical aspects 1.6.1 Time-reversal symmetry, and circular anisotropy in a rotating medium 1.6.2 Light-induced magnetooptical effects; the angular momentum of a light beam

Multiferroics are compounds that show ferroelectricity and magnetism. BiFeO3, by far the most studied, has outstanding ferroelectric properties, a cycloidal magnetic order in the bulk, and many unexpected virtues such as conductive domain walls or a low bandgap of interest for photovoltaics. Although this flurry of properties makes BiFeO3 a paradigmatic multifunctional material, most are related to its ferroelectric character, and its other ferroic property--antiferromagnetism--has not been investigated extensively, especially in thin films. Here we bring insight into the rich spin physics of BiFeO3 in a detailed study of the static and dynamic magnetic response of strain-engineered films. Using Mössbauer and Raman spectroscopies combined with Landau-Ginzburg theory and effective Hamiltonian calculations, we show that the bulk-like cycloidal spin modulation that exists at low compressive strain is driven towards pseudo-collinear antiferromagnetism at high strain, both tensile and compressive. For moderate tensile strain we also predict and observe indications of a new cycloid. Accordingly, we find that the magnonic response is entirely modified, with low-energy magnon modes being suppressed as strain increases. Finally, we reveal that strain progressively drives the average spin angle from in-plane to out-of-plane, a property we use to tune the exchange bias and giant-magnetoresistive response of spin valves.

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We report field-induced switchable polarization (P ~ 0.2 -0.8 µC/cm 2 ) below the Néel temperature of chromium (T N Cr ) in weakly ferromagnetic rare-earth orthochromites, RCrO 3 (R=rare-earth) but only when the rare-earth ion is magnetic.Intriguingly, the polarization in ErCrO 3 (T C = 133 K) disappears at a spinreorientation (Morin) transition (T SR ~ 22 K) below which the weak ferromagnetism associated with the Cr-sublattice also disappears, demonstrating the crucial role of weak ferromagnetism in inducing the polar order. Further, the polarization (P) is strongly influenced by applied magnetic field, indicating a strong magnetoelectric effect. We suggest that the polar order occurs in RCrO 3 , due to the combined effect of poling field that breaks the symmetry and the exchange field on R-ion from Crsublattice stabilizes the polar state. We propose that a similar mechanism could work in the isostructural rare-earth orthoferrites, RFeO 3 as well.

In BiFeO3 films, it has been found that epitaxial constraint results in the destruction of a space modulated spin structure. For (111)c films, relative to corresponding bulk crystals, it is shown (i) that the induced magnetization is enhanced at low applied fields; (ii) that the polarization is dramatically enhanced; whereas, (iii) the lattice structure for (111)c films and crystals is nearly identical. Our results evidence that eptiaxial constraint induces a transition between cycloidal and homogeneous antiferromagnetic spin states, releasing a latent antiferromagnetic component locked within the cycloid.

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Future information technologies, such as ultrafast data recording, quantum computation or spintronics, call for ever faster spin control by light [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . Intense terahertz pulses can couple to spins on the intrinsic energy scale of magnetic excitations 5,11 . Here, we explore a novel electric dipole-mediated mechanism of nonlinear terahertz-spin coupling that is much stronger than linear Zeeman coupling to the terahertz magnetic field 5,10 . Using the prototypical antiferromagnet thulium orthoferrite (TmFeO 3 ), we demonstrate that resonant terahertz pumping of electronic orbital transitions modifies the magnetic anisotropy for ordered Fe 3+ spins and triggers large-amplitude coherent spin oscillations. This mechanism is inherently nonlinear, it can be tailored by spectral shaping of the terahertz waveforms and its efficiency outperforms the Zeeman torque by an order of magnitude. Because orbital states govern the magnetic anisotropy in all transition-metal oxides, the demonstrated control scheme is expected to be applicable to many magnetic materials.Ultrafast magnetization control has become a key goal of modern photonics, with a broad variety of successful concepts emerging at a fast pace. Examples include light-induced spin reorientation in canted antiferromagnets 3 , vectorial control of magnetization by light 6 , photoinduced antiferromagnet-ferromagnet phase transitions 9 , optical modification of the exchange energy 4,14 and driving spin precessions via nonlinear magneto-phononic coupling 7,16 . Despite this remarkable progress, most of the photon energy in all known concepts using visible and near-infrared light is inactive with respect to the light-spin interaction, and avoiding dissipation of large excess energies requires special care.In contrast, intense electromagnetic pulses at terahertz frequencies may interface spin dynamics directly on their intrinsic energy scales 5,11 . The magnetic field component of few-cycle terahertz pulses has been used to coherently control magnons in the electronic ground state by direct Zeeman interaction 5,11 . Because magnetic dipole coupling is typically weak, however, terahertz-driven spin excitation has been confined to the linear response regime. Massive nonlinearities, such as terahertz-induced phase transitions 17,18 and terahertz lightwave electronics [19][20][21][22]

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