An appealing mechanism for inducing multiferroicity in materials is the generation of electric polarization by a spatially varying magnetization that is coupled to the lattice through the spin-orbit interaction. Here we describe the reciprocal effect, in which a time-dependent electric polarization induces magnetization even in materials with no existing spin structure. We develop a formalism for this dynamical multiferroic effect in the case for which the polarization derives from optical phonons, and compute the strength of the phonon Zeeman effect, which is the solid-state equivalent of the well-established vibrational Zeeman effect in molecules, using density functional theory. We further show that a recently observed behavior -the resonant excitation of a magnon by optically driven phonons -is described by the formalism. Finally, we discuss examples of scenarios that are not driven by lattice dynamics and interpret the excitation of Dzyaloshinskii-Moriya-type electromagnons and the inverse Faraday effect from the viewpoint of dynamical multiferroicity.

In ionic materials, circularly polarized phonons carry orbital magnetic moments that arise from circular motions of the ions, and which interact with other magnetic moments or fields. Here, we calculate the orbital magnetic moments of phonons in 35 different materials using density functional theory, and we identify the factors that lead to, and materials that show, large responses. We compute the resulting macroscopic orbital magnetic moments that can be induced by the excitation of coherent phonons using mid-infrared laser pulses, and we evaluate the magnitudes of the phonon Zeeman effect in a strong magnetic field. Finally, we apply our formalism to chiral phonons, in which the motions of the ions are intrinsically circular. The zoology presented here may serve as a guide to finding materials for phonon and spin-phonon driven phenomena.

Electron paramagnetic resonance (EPR) spectroscopy is widely used to characterize paramagnetic complexes. Recently, EPR combined with scanning tunneling microscopy (STM) achieved single-spin sensitivity with sub-angstrom spatial resolution. The excitation mechanism of EPR in STM, however, is broadly debated, raising concerns about widespread application of this technique. We present an extensive experimental study and modeling of EPR-STM of Fe and hydrogenated Ti atoms on a MgO surface. Our results support a piezoelectric coupling mechanism, in which the EPR species oscillate adiabatically in the inhomogeneous magnetic field of the STM tip. An analysis based on Bloch equations combined with atomic-multiplet calculations identifies different EPR driving forces. Specifically, transverse magnetic field gradients drive the spin-1/2 hydrogenated Ti, whereas longitudinal magnetic field gradients drive the spin-2 Fe. Also, our results highlight the potential of piezoelectric coupling to induce electric dipole moments, thereby broadening the scope of EPR-STM to nonpolar species and nonlinear excitation schemes.

We describe an ultrafast coherent control of the transient structural distortion arising from nonlinear phononics in ErFeO3. Using density functional theory, we calculate the structural properties as input to an anharmonic phonon model that describes the response of the system to a pulsed optical excitation. We find that the trilinear coupling of two orthogonal infrared-active phonons to a Raman-active phonon causes a transient distortion of the lattice. The direction of the distortion is determined by the polarization of the exciting light, suggesting a route to nonlinear phononic lattice control and switching. Since the occurrence of the coupling is determined by the symmetry of the system we propose that it is a universal feature of orthorhombic and tetragonal perovskites.Over the last decade it has been shown repeatedly that laser excitation of infrared-active phonons is a powerful tool for modifying the properties of materials. This dynamical materials design approach has been used to drive metal-insulator transitions [1,2], to melt orbital order [3,4] and to induce superconductivity or modify superconducting transition temperatures [5,6] in a range of complex oxides. Particularly intriguing is the case in which the laser intensity is so high that the usual harmonic approximation for the lattice dynamics breaks down and anharmonic phonon-phonon interactions become important. Recent experimental and theoretical studies [7,8] have clarified that quadratic-linear cubic coupling of the form Q 2 IR Q R between a driven infraredactive mode, Q IR , and a Raman-active mode, Q R , causes a shift in the equilibrium structure to a nonzero value of the Raman mode normal coordinates. This nonlinear phononic effect has most notably been associated with the observation of coherent transport, an indicator of superconductivity, far above the usual superconducting Curie temperature in underdoped YBaCu 3 O 6+δ [9-11].Here we investigate theoretically a different kind of cubic phononic coupling of the trilinear form Q IR1 Q IR2 Q R , in which two different infrared-active (IR) modes are excited simultaneously and couple anharmonically to a single Raman mode. Our motivation is provided by recent experimental work on the perovskite-structure orthoferrite ErFeO 3 [12], in which two polar modes of similar frequencies with atomic displacement patterns along the inequivalent a and b orthorhombic axes were simultaneously excited. Ref. [12] reported and analyzed the resulting excitation of a magnon; here our focus is on the changes caused by and the implications of the nonlinear phonon dynamics.ErFeO 3 is a distorted perovskite with the orthorhombic P nma structure and the typical G-type antiferromagnetic ordering of the Fe 3+ magnetic moments [13] (Fig. 1). The primitive magnetic unit cell contains 20 atoms, resulting in 60 phonon modes characterised by representations (within the orthorhombic point group mmm) A g , B (1,2,3)g , A u and B (1,2,3)u . Of the polar "u" modes, only B 1u , B 2u and B 3u have dipole moments and are therefo...