Multiferroicity in plastically deformed SrTiO3

Abstract

Quantum materials have a fascinating tendency to manifest novel and unexpected electronic states upon proper manipulation. Ideally, such manipulation should induce strong and irreversible changes and lead to new relevant length scales. Plastic deformation introduces large numbers of dislocations into a material, which can organize into extended structures and give rise to qualitatively new physics as a result of the huge localized strains. However, this approach is largely unexplored in the context of quantum materials, which are traditionally grown to be as pristine and clean as possible. Here we show that plastic deformation induces robust magnetism in the quantum paraelectric SrTiO₃, a property that is completely absent in the pristine material. We combine scanning magnetic measurements and near-field optical microscopy to find that the magnetic order is localized along dislocation walls and coexists with ferroelectric order along the walls. The magnetic signals can be switched on and off via external stress and altered by external electric fields, which demonstrates that plastically deformed SrTiO₃ is a quantum multiferroic. These results establish plastic deformation as a versatile knob for the manipulation of the electronic properties of quantum materials.

Fig. 1. Scanning SQUID measurement and stripy magnetic order in plastically deformed SrTiO₃ observed by scanning in contact with the surface of the sample.

a Illustration of scanning SQUID measurement in contact mode (Note that our axes choice is different from that in ref. , where the deformation axis was [010] or $\widehat{y}$). b Optical images of the sample. The deformation stripes are visible on the surface. c–e Scanning SQUID images of capacitive surface sensing, susceptibility, spontaneous magnetism, respectively, in an undoped sample (sample 4). The magnetic stripe direction coincides with that of the deformed stripes shown in (b). f, g Susceptibility and spontaneous magnetism, respectively, in a conducting sample (Nb doped, sample 2). h Stress dependence of the magnetism exhibits linear behavior (see also Fig. 2a). The capacitive reading is proportional to the force exerted on the sample, see section “Methods”. i The strength of the magnetism (see also 2b) increases with increasing temperature. Both the stress and the temperature dependence are explained by the phenomenological model we suggest.

Fig. 2. Stress, temperature, and electric field dependence of magnetic signal in undoped, plastically deformed SrTiO₃.

a Stress dependence of magnetic stripes in susceptibility and magetometry at 8 K in undoped sample 4. Before contact (lift-off height of 0.6 μm) with the surface by the SQUID tip, we observe only background noise. The magnetic response increases with the applied force. b Temperature dependence of magnetic stripes by scanning in contact, in undoped sample 4. The applied force is estimated to be 0.1–1 μN (Note: this range is rather uncertain because of the nonuniform surface). The magnetic response increases with the temperature. (Further temperature ranges can be found in the SI Figs. S2 and S3). c Electric field dependence of magnetic stripes in the gated sample 5. The arrow indicates that the electric field is applied in-plane, perpendicular to the direction of the deformation stripes. The details of the gate dependence require further investigation. See SI Fig. S1.

Fig. 3. Nano-infrared imaging of optical phonon contrasts at an energy of 100 meV along the surface of an undoped 2.4% deformed crystal.

Variations of the absorption coefficient amplitude (a) and phase (b) in a 1000 nm × 100 nm strip (see section “Methods” for details). Striped contrast made clearly visible by the Grüneisen effect show that stresses and strains are localized to dislocation walls. The inferred strain variations (averaged over the experimental spot size and penetration depth; see SI) are of order 0.1%, implying localized strains of order unity near the dislocations (see section “Methods”). c A histogram of the nearest-neighbor separation of the absorption amplitude peaks, revealing that the typical dislocation separation is approximately 100 nm. The data for the phase is qualitatively the same (see SI). d A histogram of the typical width of a peak, showing that the peak width is approximately 10 nm, which is comparable with the resolution of our experiment, confirming that strain is highly localized to the stripes.

Fig. 4. Depiction of the theoretically expected magnetic configuration from several different perspectives.

a Sketch of the randomly distributed dislocation walls and the Burgers vector orientations (Note that our axes choice is different from that in ref. , where the deformation axis was [010] or $\widehat{y}$). b Magnetic order along a dislocation wall. The dislocation wall consists of a repeating unit cell (dashed lines) of two dislocations (purple Burgers vectors), and elastomagnetic coupling induces a nonzero magnetic moment m whose magnitude is strongly localized in “puddles” near the dislocations (heatmap, arbitrary units). The planar projection (m_x, m_z) of m (black arrows) is shown in an “antiferromagnetic” configuration of m_z, and “ferromagnetic” configuration of m_x. This order is nearly degenerate with a fully ferromagnetic one. c Magnetic order in a region occupied by a random series of dislocation walls. The dashed region marks the area in the unit cell of (b). d Illustration of a possible spin-spiral structure of the coarse-grained spin-chain model of the dislocation wall. Blue arrows denote the constant background FE field direction, and red arrows the rotating magnetic moments. Only m_x remains ferromagnetic, which explains why there is no out-of-contact magnetic signal.

Fig. 5

Almost degeneracy of the free energy for ferromagnetic and antiferromagnetic puddle configurations.

Fig. 6. The FE order along the dislocation walls.

The intensity map corresponds to u_y (arbitrary units). For simplicity we set c_u = 0. At nonzero c_u the ordered regions will merge together and create long-range order.