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.