On ferroelectricity of magnets

Ferroelectric compounds possess a spontaneous and reversible electric polarization, P. Magnetic materials, on the other hand, display a spontaneous order of magnetic dipoles induced by electron spins. The cross-coupling between P and magnetism, which can potentially lead to novel memory storage devices, is found in magnetoelectric compounds, where magnetization can be induced by an applied electric field (or vice versa), and in so-called magnetic ferroelectrics, where a spontaneous polarization is induced by spin ordering. Understanding the physics underlying the rich variety of observed phenomena in these compounds is both of fundamental and technological interest. In this thesis we study model Hamiltonians for compounds in which magnetic ordering and electric polarization are coupled. Using symmetry considerations, the form of microscopic couplings between spins and electric polarization are obtained for different systems. These expressions are used to reveal the mechanism behind the magnetoelectric effect in Cr2O3 and to find the origin of so-called electromagnon excitations in YMn2O5. Furthermore, the theoretical analysis of materials with so-called magnetic spiral states allows us to explain a number of recently observed phenomena, in which electric polarization is controlled by an applied magnetic field. These include the rotation of electric polarization by rotating an applied magnetic field, and the clamping of ferromagnetic and ferroelectric domain walls. Finally, novel effects, such as the high-temperature induction of electric polarization by arrays of ferromagnetic domain walls, are predicted.

Strain-Induced Magnetic Anisotropy in Epitaxial Thin Films of the Spinel CoCr2_2O4_4

We show that the magnetic anisotropy in spinel-structure CoCr$_2$O$_4$ thin films exhibits a strain dependence in which compressive strain induces an out-of-plane magnetic easy axis and tensile strain an in-plane easy axis, exactly opposite to the behavior reported for the related compound CoFe$_2$O$_4$. We use density functional theory calculations within the LSDA+U approximation to reproduce and explain the observed behavior. Using second-order perturbation theory, we analyse the anisotropy tensor of the Co$^{2+}$ ions in both octahedral and tetrahedral coordination, allowing us to extend our results to spinels with general arrangements of Co$^{2+}$ ions.Comment: 8 pages, 7 figure

Spiral order from orientationally correlated random bonds in classical XY models

We discuss the stability of ferromagnetic long-range order in three-dimensional classical XY ferromagnets upon substitution of a small subset of equally oriented bonds by impurity bonds, on which the ferromagnetic exchange J_perp > 0 is replaced by a strong antiferromagnetic coupling J_imp < 0. In the presence of a single impurity bond, once the absolute value of the frustrating coupling J_imp 0, the ground state becomes two-fold degenerate, corresponding to either clockwise or anticlockwise canting of the spins in the vicinity of the impurity bond. In the presence of a small concentration of impurity bonds, the effective low-energy Hamiltonian is that of Ising variables encoding the sense of rotation of the local canting around the impurities. Those degrees of freedom interact through a dipolar interaction mediated by spin waves. A ferromagnetic Ising ground state indicates the instability of the XY ferromagnet towards a spiral state with a wave vector proportional to the concentration of impurity bonds. To analyze under which circumstances such a ground state arises, we study first impurities forming superlattices. For a subclass of those, we can rigorously establish the existence of spiral order. For another class of superlattices, the Ising variables order ferromagnetically in planes perpendicular to the orientation of impurity bonds, but antiferromagnetically parallel to it, which results in a fan-like XY ground state. Second, we consider the case when the impurity bonds are randomly distributed on the three-dimensional host lattice according to a Poisson process. We show the phenomenon of spiral order by disorder with an ordering wave vector proportional to the impurity concentration. The analytical predictions are confirmed by Monte Carlo simulations and are relevant for magnetic materials such as YBaCuFeO_5.Comment: 26 pages, 10 figures; Quantitative comparison with experiments added. Substantially improved manuscrip

Temperature-Dependent Magnetoelectric Effect from First Principles

We show that nonrelativistic exchange interactions and spin fluctuations can give rise to a linear magnetoelectric effect in collinear antiferromagnets at elevated temperatures that can exceed relativistic magnetoelectric responses by more than 1 order of magnitude. We show how symmetry arguments, ab initio methods, and Monte Carlo simulations can be combined to calculate temperature-dependent magnetoelectric susceptibilities entirely from first principles. The application of our method to Cr2O3 gives quantitative agreement with experiment.