Light fields at terahertz and mid-infrared frequencies allow for the direct excitation of collective modes in condensed matter, which can be driven to large amplitudes. For example, excitation of the crystal lattice 1,2 has been shown to stimulate insulator-metal transitions 3,4 , melt magnetic order 5,6 or enhance superconductivity [7][8][9] . Here, we generalize these ideas and explore the simultaneous excitation of more than one lattice mode, which are driven with controlled relative phases. This nonlinear mode mixing drives rotations as well as displacements of the crystal-field atoms, mimicking the application of a magnetic field and resulting in the excitation of spin precession in the rare-earth orthoferrite ErFeO 3 . Coherent control of lattice rotations may become applicable to other interesting problems in materials research-for example, as a way to a ect the topology of electronic phases.ErFeO 3 is an antiferromagnetic insulator that crystallizes in an orthorhombically distorted perovskite structure, as shown in Fig. 1a (space group: Pbnm). Because of the Dzyaloshinskii-Moriya interaction, the spins are canted and result in a small ferromagnetic moment (saturated by a 7.5 mT field 10 ) along the c axis (Fig. 1b). In our experiments, femtosecond mid-infrared pulses at 20 THz frequency were tuned to drive the in-plane B ua and B ub phonons 11 . The eigenvectors of these modes are shown in Fig. 1c. The pump was linearly polarized and aligned at variable angles with respect to the a and b crystallographic axes. Due to the orthorhombic distortion in ErFeO 3 , the infrared-active modes along the two axes exhibit different eigenfrequencies and oscillator strengths. As a consequence, even when the modes are excited simultaneously (for example, with the light polarization at a 45• angle from either crystal axes), the two modes start with a nonzero relative phase, and advance in time at different rates. Hence, the total lattice polarization inside the material is elliptical (Fig. 1d). This is interesting, as coherent atomic loops 12 can break time-reversal symmetry and stimulate a new class of opto-magnetic phenomena, which are independent of equilibrium multiferroicity [13][14][15] . These considerations are validated here by mid-infrared pump, optical probe experiments performed at 100 K. The Faraday rotation of a linearly polarized near-infrared pulse (800-nm wavelength) was measured as a function of time delay after direct lattice excitation. As shown in Fig. 2a, the polarization of the probe was found to oscillate in time, revealing the coherent excitation of a number of Ramanactive modes (Fig. 2b). These include Raman phonons of A 1g + B 1g and B 1g symmetry (3.36 THz and 4.85 THz, respectively).Strikingly, we also observed the excitation of a coherent quasiantiferromagnetic magnetic mode (q-AFM, 0.75 THz) (ref. 16), associated with a modulation of the ferromagnetic moment along the c axis (Fig. 2c) 17 . Figure 3a shows the pump-wavelength-dependent amplitude of this mode, plotted with the reflectivity of...

Fluctuating orders in solids are generally considered high-temperature precursors of broken symmetry phases. However, in some cases these fluctuations persist to zero temperature and prevent the emergence of long-range order, as for example observed in quantum spin and dipolar liquids. SrTiO3 is a quantum paraelectric in which dipolar fluctuations grow when the material is cooled, although a long-range ferroelectric order never sets in. We show that the nonlinear excitation of lattice vibrations with mid-infrared optical pulses can induce polar order in SrTiO3 up to temperatures in excess of 290 K. This metastable phase, which persists for hours after the optical pump is interrupted, is evidenced by the appearance of a large second-order optical nonlinearity that is absent in equilibrium. Hardening of a low-frequency mode indicates that the polar order may be associated with a photo-induced ferroelectric phase transition. The spatial distribution of the optically induced polar domains suggests that a new type of photo-flexoelectric coupling triggers this effect.

Strain engineering is widely used to manipulate the electronic and magnetic properties of complex materials 1, 2 . An attractive route to control magnetism with strain is provided by the piezomagnetic effect, whereby the staggered spin structure of an antiferromagnet is decompensated by breaking the crystal field symmetry, which induces a ferrimagnetic polarization. Piezomagnetism is especially attractive because unlike magnetostriction it couples strain and magnetization at linear order 3 , and allows for bi-directional control suitable for memory and spintronics applications 4, 5 . However, its use in functional devices has so far been hindered by the slow speed and large uniaxial strains required. Here, we show that the essential features of piezomagnetism can be reproduced with optical phonons alone, which can be driven by light to large amplitudes without changing the volume and hence beyond the elastic limits of the material. We exploit nonlinear, three-phonon mixing to induce the desired crystal field distortions in the antiferromagnet CoF2. Through this effect, we generate a ferrimagnetic moment of 0.2 μB per unit cell, nearly three orders of magnitude larger than achieved with mechanical strain 6 .

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