Introduction

Magnetoelectric (ME) multiferroics have attracted much recent attention, largely due to the scarcity of naturally occurring materials in which magnetic and electric order coexist1,2,3,4. However, the microscopic mechanisms underlying ME coupling between these order parameters have been difficult to unravel, hindering the development of single-phase multiferroics with strong ME coupling at useful temperatures1,2,5. Artificial multiferroic composites6,7,8,9 offer an appealing alternative, in which the ME coupling can be engineered through proper choice of the interface geometry and constituent materials4. The most well-known approach for achieving strong ME coupling in these systems uses strain to indirectly couple ferroelectric (FE) and ferromagnetic (FM) order in two-phase-layered composites5,7,10. In these composites, the ME effect is essentially a product of the magnetostrictive effect in the FM layer and the piezoelectric effect in the FE layer5,10,11,12,13. A magnetic (B) field is used to modify the spin alignment in the FM layer, which changes the lattice constant through magnetostriction. This in turn applies stress on the FE layer and modifies the FE polarization through the piezoelectric effect12,13,14, significantly increasing the ME coupling as compared with single-phase multiferroics5,10. Several reviews describing the ME effect in these composites have been recently published5,10,12,15.

Despite these impressive advances, an important aspect of multiferroics has received relatively little attention: namely, their dynamic properties2,3,10, which will impact many of their potential applications. In fact, the ultimate timescales limiting the speed of ME coupling in these materials, as well as the physical processses governing them, remain relatively unexplored. Femtosecond optical pulses are particularly useful in this regard16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31, since they can be used to both interrogate and control the ME response in a non-contact manner on ultrafast timescales, much faster than by directly applying magnetic or electric fields. Furthermore, specific order parameters can be directly accessed using time-resolved second-harmonic generation (TR-SHG), making it especially attractive for studying both magnetically20 and orbitally ordered32 materials, as well as multiferroics18 and interfacial properties of novel layered materials19 in the time domain.

Here, we use TR-SHG to explore and optically manipulate the coupling between FE and FM order in an oxide heterostructure for the first time, inspired by the strain/stress-based approach described above. By separating the different contributions to the TR-SHG signal in the time domain, we discovered that the timescale dominating the ME response is governed by demagnetization of the FM layer through spin–lattice relaxation. More specifically, optically perturbing magnetic order in the FM layer imposes lateral stress on the FE layer through magnetostriction, modifying FE order within tens of picoseconds. This demonstrates that femtosecond optical pulses can be used not only to give insight into the microscopic mechanisms underlying ME coupling in complex oxide heterostructures, but also to manipulate the ME response in these systems on ultrafast timescales.

Results

Static and TR-SHG experiments

The heterostructure studied here consists of a 50-nm-thick film of FE Ba0.1Sr0.9TiO3 (BSTO) and a 50-nm-thick film of FM La0.7Ca0.3MnO3 (LCMO), grown on a MgO substrate; more detail on sample fabrication is given in Methods and in ref. 33. We chose BSTO with this specific composition since lattice strain introduced through heteroepitaxial growth can enhance ferroelectricity and the FE transition temperature (TFE), as theoretically predicted34,35 and experimentally observed33. This coupling between strain and FE order makes it a good candidate for inducing indirect ME effects through elastic coupling with a magnetic material. Similarly, LCMO was chosen since a strong ME effect was previously obtained through magnetostriction under an applied d.c. magnetic field, when it was incorporated into a bilayer structure with lead zirconate titanate5,14,36. The concept behind our experiment is thus to demagnetize LCMO with femtosecond optical pulses, modifying its lattice constant through magnetostriction; the resulting stress on BSTO activates its piezoelectric response, changing FE order and indirectly inducing ME coupling within the demagnetization time.

Photoinduced changes in the static FE polarization of BSTO, Ps, can be measured using SHG (Fig. 1a,b,d), which is well known to directly probe FE order37,38,39,40. The SHG polarization generated by the fundamental light fields Ej and Ek is Pi(2ω)=ε0dijkEj (ω) Ek(ω), where ω is the frequency and dijk is the nonlinear optical susceptibility tensor39,40,41. Our BSTO films have C4v symmetry and a FE polarization along the sample normal (z in Fig. 1a) due to the in-plane compressive strain induced by lattice matching to LCMO33. There are only three non-vanishing tensor components for this crystal symmetry: d15, d31 and d33. By varying the polarization of the incident fundamental and detected SHG light (Fig. 1a) while measuring the SHG intensity I (Fig. 1b), these different components can be extracted, as discussed in Methods.

Figure 1: Experimental set-up, static SHG characterization and piezoelectric response to in-plane stress.
figure 1

(a) Experimental schematic for TR-SHG in reflection. θ is the angle between the sample normal and the light propagation direction. φ is the incident polarization of the fundamental light, which is controlled by a half-wave (λ/2) plate. Incident p and s polarizations correspond to φ=0° (180°) and 90° (270°), respectively. (b) Polar plot of the measured SHG intensity at 10 K. The blue and red symbols are the p- and s-polarized SHG signals, Ip and Is, respectively, plotted as a function of the incident light polarization. The cyan dashed and green solid lines are numerical fits to Ip and Is with d31=−1, d15=−1.2 and d33=7. (c) Schematic diagram of piezoelectric response along z to applied in-plane stress (εxx and εyy). (d) Static temperature-dependent SHG for (p, p) and (s, p) polarization combinations. In LCMO, TC~240 K, while in BSTO, TFE~215 K (ref. 33), as indicated by the arrow.

Full size image

To optically explore the ME response of our BSTO/LCMO heterostructure, we use the majority of the output laser intensity to photoexcite LCMO (at 1.59 eV, far below the BSTO band gap of ~3.3–3.6 eV; ref. 33) and the remainder to measure the resulting changes in Ps using SHG. Photoexcited quasiparticles (unbound electrons and holes) in LCMO will relax through different processes that have been extensively studied using pump–probe spectroscopy42,43,44. Initially, the non-equilibrium quasiparticles rapidly lose energy through electron–phonon (e−ph) coupling (within ~1 ps), after which the lattice exchanges energy with the spins through spin–lattice (s−l) coupling on a timescale of tens to hundreds of ps. On longer timescales (>1 ns), LCMO returns to equilibrium as the remaining energy is dissipated through the substrate. More detail on quasiparticle dynamics in manganites is provided in Supplementary Note 1.

Data analysis

We can relate this to the timescales on which the FE polarization changes in our TR-SHG experiments (Fig. 2). Figure 2a schematically shows the different processes occurring for different pump–probe delays t. Before t=0, a small negative change in the p-polarized SHG intensity (ΔIp) is observed in all polar combinations at low temperatures (P0), corresponding to residual heating that is not completely dissipated before the arrival of the next pump pulse. This change in Ip, where the SHG intensity decreases for all incident light polarizations, as more clearly seen in Figs 2b and 3a for negative time delays, is equivalent to increasing the sample temperature in the SHG polar plot of Fig. 1b (or the temperature-dependent plots in Fig. 1d), since before t=0 the electron, spin and lattice subsystems share a common temperature.

Figure 2: Photoinduced coupling between ferroelectric and ferromagnetic order.
figure 2

(a) Schematic diagram of the interplay between the lattice, the magnetization M and the FE polarization P at various pump–probe delays. After photoexcitation, thermal stress on BSTO (thin red arrows) initially results from e−ph coupling in LCMO within 1 ps. Its magnitude gradually increases after relaxation of the lattice contraction in LCMO through magnetostriction (thin blue arrows) on a timescale of ~50 ps, causing P to decrease. Thermal diffusion from LCMO to both BSTO and the substrate then takes place at longer timescales, t>0.5 ns, finally dissipating through the substrate. (b) Time-resolved p-polarized SHG as a function of the incident light polarization at 10 K. P0−P3 are the FE polarization responses at different times to changes in the magnetization (arising from M0−M3 in a).

Full size image
Figure 3: Evidence for a non-equilibrium, nonlinear origin of the TR-SHG response.
figure 3

(a) Polarization-dependent changes in Ip measured at 10 K for various time delays. The data are plotted as symbols and numerical calculations for t=−10; 50 ps are plotted as dashed lines. Before t=0, the change is due to long-lived residual heating from LCMO to BSTO. After t=0, the change arises from reductions in d31 and d33 (more detail is given in Methods). (b) Polarization-dependent changes in Ip measured at t=200 ps for different temperatures.

Full size image

In contrast, at early times (t~1–2 ps), we observe a polarization-dependent change in Ip (P1), where the SHG intensity both increases and decreases for different polarizations, as shown in Figs 2b and 3. This cannot be obtained by simply changing the sample temperature; it is a non-equilibrium effect, occurring before the different subsystems can reach a common temperature. This is due to the elevated temperature of the lattice in LCMO after e−ph coupling, causing it to expand, which in turn initiates an in-plane thermal stress εxx and εyy on BSTO (without changing its temperature) (Fig. 2a). This then initiates an out-of-plane piezoelectric response through Di=eijkεjk, where Di is the dielectric displacement and eijk is the piezoelectric coefficient. In the C4v symmetry, e31 is non-zero (more detail is given in Methods), linking εxx and εyy to Dz (Fig. 1c) and leading to a photoinduced change in the SHG intensity. It takes ~7 ps for the strain induced by in-plane stress to propagate through the BSTO layer (estimated from the speed of sound in BSTO), which agrees relatively well with the timescale of the initial rise in ΔIp, as shown in Fig. 4 (that is, there is no rapid ~1 ps rise time, unlike the photoinduced change in reflectivity, ΔR/R). However, the maximum change in Ip (represented by P2) does not occur on this timescale, but on a much slower timescale of ~50–100 ps (Figs 2b and 3a).

Figure 4: Comparison of ΔR/R and ΔI/I.
figure 4

Comparison at (a) 10 K and (b) above 250 K. ΔR/R is measured with a p-polarized probe and ΔI/I is taken in the (p, p) configuration. The solid lines are the experimental data and the dashed lines represent a double exponential fit. Additional discussion of the comparison between the ΔR/R and ΔI/I data is given in Methods and Supplementary Note 1.

Full size image

We can gain insight into the origin of this large change in Ip (and thus Ps) by first noting that it primarily occurs below the FM ordering temperature, TC~240 K (Fig. 3b), indicating that FM order in LCMO is linked to the observed ΔIp. In addition, the timescale is comparable to that for s−l relaxation in LCMO, as determined through comparison of our TR-SHG data to optical pump–probe measurements on our BSTO/LCMO heterostructure (Fig. 4). This suggests that the observed photoinduced ME response is initiated by a change in the lattice constant through magnetostriction45, which arises from photoinduced demagnetization of LCMO. More specifically, s−l relaxation reduces the magnetization in the FM-ordered state, gradually decreasing the magnitude of the existing in-plane lattice contraction due to spin–spin interactions and applying stress to BSTO (Fig. 2a, t~50 ps); more detail on general magnetostriction is given in Supplementary Note 2. Then, as for the early time dynamics, the resulting increase in the in-plane tensile stress on BSTO initiates a piezoelectric effect along the z direction (Fig. 1c), reducing the dielectric displacement Dz and modifying the FE polarization Ps (Fig. 2a).

Additional experimental evidence enables us to rule out other possibilities that could lead to the observed change in ΔIp. First, ΔIp at low temperatures does not originate from a photoinduced modulation in the reflectivity due to changes in the optical constants; ΔR/R is an order of magnitude smaller than ΔI/I (the normalized photoinduced change in SHG intensity for a given polarization configuration) at low temperatures (Fig. 4), and unlike ΔI/I, it does not vary with the incident probe polarization (Supplementary Fig. 1). Second, there is no observable SHG signal, either static (Ip) or photoinduced (ΔI/I), from a single LCMO film, verifying that ΔIp in our BSTO/LCMO heterostructure does not result from SHG in LCMO. Third, there is no measurable ΔI/I signal from a single BSTO film upon 1.59 eV excitation, since the pump is far below the gap33. Fourth, we note that the observed features are independent of the pump polarization, consistent with photoinduced demagnetization in LCMO. Fifth, Kerr rotation of the reflected light at both 1.55 and 3.1 eV, induced by demagnetization in LCMO, does not contribute to ΔIp. Previous work has shown that the Kerr rotation in manganites for similar pump fluences is ~0.01–0.1 degrees44,46. This small rotation is unlikely to result in the large changes in SHG intensity that we observed. In addition, if it were to contribute significantly to ΔI/I, it would also be observed in TR-SHG measurements on a single LCMO film, where Kerr rotation dominates polarization-dependent measurements44,46. Moreover, in the unlikely case that Kerr rotation in this heterostructure is larger than that of a single LCMO layer upon photoexcitation, the rotated fundamental or SHG polarizations would induce phase shifts in our polarization-dependent TR-SHG measurements, which are not observed (Figs 2b and 3).

Finally, any contributions from surface SHG, including any potential time-dependent interference with the contribution from FE order, are expected to be negligible. The temperature-dependent static SHG signal (Fig. 1d) originates primarily from bulk FE order in BSTO33. Surface and interface contributions from this layer have the same symmetry, C4v, as the bulk FE order. Any interference between these contributions will be either in-phase or 180° out-of-phase, but will remain constant over the entire sample, as a spatially homogeneous SHG intensity is observed after SHG saturation33. Well above TFE, the residual SHG signal likely originates from the surface or interface and mixes with other potential contributions, such as slow carrier transfer33 and size effects37,47 in thin films. Upon photoexcitation, surface SHG does not contribute to the ΔI/I signal, since the BSTO surface is not excited. Furthermore, we can exclude any contribution from changes in interfacial SHG due to demagnetization of LCMO, because no TR-SHG signal was obtained from the interface between LCMO and the MgO substrate. These considerations allow us to conclude that the ΔI/I signal from our heterostructure originates from changes in Ps that are initiated by photoinduced changes in LCMO.

Discussion

It is worth re-emphasizing that, as discussed in the introduction, the photoinduced ME response measured here is analogous to the ME effect observed when an external B field is applied to enhance the lattice contraction through magnetostriction in a FE/FM bilayer, inducing a piezoelectric response in the FE layer14. The major advantage of our approach lies in the temporal degree of freedom offered by femtosecond laser pulses, enabling us to optically manipulate the ME response in the time domain and also discriminate between different contributions to the ME response. For example, we can temporally separate the comparatively small changes in Ps at early times due to heating-induced expansion of LCMO (Fig. 2, t~1 ps) from the larger changes in Ps on longer timescales due to the reduction in the LCMO lattice contraction by magnetostriction (Fig. 2, t~50 ps). The difference in the magnitude of these changes is likely due to the strong interaction between the ordered spins in LCMO (causing the lattice to contract through magnetostriction), which only permits a small amount of heating-induced thermal stress at early times. As a result, the in-plane tensile stress does not significantly increase before s−l relaxation takes place. Therefore, strain relaxation throughout the entire BSTO film only occurs after tens of ps, setting the timescale for the maximum changes in FE polarization (Fig. 3a). Finally, we note that at long (hundreds of ps to ns) timescales, the remaining changes in the FE polarization are due to thermal diffusion from LCMO to BSTO.

In conclusion, we used femtosecond optical pulses to manipulate the coupling between FE and FM order in a complex oxide heterostructure, employing TR-SHG to optically perturb the magnetization in LCMO and selectively probe the associated change in the FE properties of BSTO. We find that, although lattice heating in LCMO occurs within ~1 ps, the resulting lateral stress on BSTO is relatively small compared to the strong lattice contraction originating from spin–spin interactions in LCMO. This lattice contraction is reduced through spin–lattice relaxation, increasing the tensile stress on BSTO through magnetostriction in LCMO and leading to a piezoelectric response that changes the FE polarization. Therefore, coupling between FE and FM order in BSTO/LCMO is induced within tens of picoseconds, mediated through elastic coupling between the BSTO and LCMO layers. Femtosecond optical spectroscopy can thus shed light on the mechanisms underlying ME coupling in complex oxide heterostructures, while presenting intriguing possibilities for future high-speed optically controlled ME devices (for example, through coherent spin control48,49,50, which would enable faster manipulation of spin dynamics and minimize undesired heat flow in device applications.)

Methods

Sample fabrication and characterization

The samples used in our studies are 50-nm-thick BSTO films grown by pulsed laser deposition on 50-nm-thick optimally doped manganite films (LCMO), using (100) MgO substrates. The substrate temperature during film growth is initially optimized and maintained at 750 °C. The oxygen pressure during deposition is 100 mTorr. The samples are cooled to room temperature in pure oxygen (at a pressure of 350 Torr) without further thermal treatment. X-ray diffraction measurements reveal a compressive strain in epitaxially grown BSTO, while LCMO on MgO is relaxed. This causes an increase in tetragonality, even at room temperature, enhancing the FE TC to ~215 K, which is significantly higher than the bulk TC~75 K. More detailed characterization of these samples is discussed in ref. 33.

TR-SHG experimental details

Our TR-SHG experiments are based on an amplified Ti:sapphire laser system producing pulses at a 250-kHz repetition rate with ~100-fs duration and energies of ~4 μJ at a centre wavelength of 780 nm (1.59 eV). SHG is generated from BSTO at 3.18 eV using a 1.59-eV probe beam, after which it is detected by a photomultiplier tube using lock-in detection after filtering out the fundamental signal. The fundamental light polarization is controlled by a half-wave plate (λ/2 in Fig. 1a) and the SHG signal is detected for either p or s polarizations. The standard laser fluence used for SHG in our measurements is F0~0.25 mJ cm−2 and the pump fluence is ~1 mJ cm−2, creating a carrier density of ~1020 cm−3 (~10−2 per unit cell). In the C4v symmetry, SHG can be generated and probed when the fundamental light is incident at an angle away from the sample normal, thus exhibiting a sinusoidal dependence on the incident angle θ (as observed in separate angle-dependent measurements on our samples). Therefore, we used a reflection geometry in which the fundamental light was incident at a ~20° angle to obtain the data shown in our manuscript. The pump beam was incident at a smaller angle of ~10–15°, and its specular reflection was completely separated from the probe beam path. The temporal delay is achieved by a mechanical delay stage that allows us to vary the probe path length. Finally, ref. 33 gives a detailed static SHG characterization of these samples. Here, all time-resolved data were taken after saturation of the static SHG signal33.

SHG analysis

For the third-rank tensor dijk, the indices jk can be replaced by l=1, 2, ..., 6, corresponding to xx, yy, zz, yz, xz and xy, respectively, using simple symmetry arguments that reduce 27 tensor components to 18. Further reduction can be achieved by noting that the C4v symmetry has d31=dzxx=d32=dzyy, d15=dxxz=d24=dyyz and d33=dzzz. Therefore, we use the three independent indices 15, 31 and 33 here. To represent the fourth-rank stress tensor eijk, the first i=1, 2, ..., 6 as defined above, and j, k=1, 2, 3 correspond to the Cartesian coordinate x, y, z, respectively. It also can be reduced according to the above discussion of indices j, k.

Figure 1b depicts the static SHG signals for p and s polarizations, Ip and Is. In reflection (Fig. 1a), φ determines the polarization of the fundamental light that generates SHG. With a unit E field of the fundamental light incident at an angle θ (Fig. 1a), we have components (Ex(ω), Ey(ω), Ez(ω))=(cos φ cos θ,sin φ,−cos φ sin θ), where θ=0 is along z and φ=0° and 90° represent p and s polarizations of the incident fundamental light, respectively. When the detection polarizer is set to p or s, we detect the SHG dipole components (Px(2ω), Py(2ω), Pz(2ω)) along (1, 0, 1) and (0, 1, 0), respectively, with each component linked to (d15=d24, d31=d32, d33) by

We thus can derive the SHG intensities Ip and Is as functions of φ (Fig. 1b):

where a, b and c are functions of θ and linear combinations of d15, d31 and d33. This enables us to detect different components of dijk through different polarization combinations of (incident light, SHG). The combination of (45°, s) probes c, associated with d15, while (s, p) detects b, associated with d31. The (p, p) configuration measures a as a linear combination of all three independent components of dijk, allowing us to extract d33 (Supplementary Table 1) from the measurements in the (45°, s) and (s, p) configurations.

We can use the above analysis methods to numerically fit our TR-SHG data (Fig. 3a). To do this, we need to know the new values of a and b after photoexcitation, which can then be inserted into equation (4). First, we note that the polarization dependence of ΔIp for t>0 (that is, ΔIp decreases for (s, p) and increases for (p, p)) (Fig. 3) implies that a decrease in b is accompanied by an increase in a. The TR-SHG signal in the (s, p) configuration is solely due to b (originating from d31 (equation (4))),which has the opposite sign of a (Supplementary Table 1). Therefore, the photoinduced decrease in d31 implies an increase in a, as observed for the (p, p) configuration in Fig. 3. Next, we consider the coefficient c, which solely originates from d15. There are three significant features we notice from the photoinduced change in d15. First, ΔI/I is much smaller than that measured for the (p, p) and (s, p) configurations (Supplementary Fig. 1). Second, the change is comparable to the modulation arising from the change in optical constants (Supplementary Fig. 1c; Fig. 4). Third, it does not have significant temperature dependence, unlike the other two polar combinations (Supplementary Fig. 1).

We conclude that d15 has an insignificant contribution to a, and the photoinduced changes in d15 could be strongly influenced by photoinduced reflectivity changes in BSTO. These considerations allowed us to simulate the photoinduced changes in d33 and d31, revealing that Δd33/d33~−4% and Δd31/d31~−6%. We thus can use these reductions in d31 and d33, together with the isotropic reduction of d31, d33 and d15 due to residual heating, to numerically fit ΔIp (dashed lines in Fig. 3a). These transient changes lead to the feature observed in Ip after t0=0 (Fig. 3a,b).

Additional information

How to cite this article: Sheu, Y. M. et al. Using ultrashort optical pulses to couple ferroelectric and ferromagnetic order in an oxide heterostructure. Nat. Commun. 5:5832 doi: 10.1038/ncomms6832 (2014).