Letter | Published:

# Femtosecond activation of magnetoelectricity

## Abstract

In magnetoelectric and multiferroic materials, the magnetic degree of freedom can be controlled by electric field, and vice versa. A significant amount of research has been devoted to exploiting this effect for magnetoelectric data storage and manipulation devices driven by d.c. electric fields1,2,3,4. Aiming at ever-faster schemes of magnetoelectric manipulation, a promising alternative approach offers similar control on a femtosecond timescale, relying on laser pulses4,5,6 to control both the charge7,8 and the magnetic9,10 order of solids. Here we photo-induce magnetoelectricity and multiferroicity in CuB2O4 on a sub-picosecond timescale. This process is triggered by the resonant optical generation of the highest-energy magnetic excitations—magnons with wavevectors near the edges of the Brillouin zone. The most striking consequence of the photo-excitation is that the absorption of light becomes non-reciprocal, which means that the material exhibits a different transparency for two opposite directions of propagation of light. The photo-induced magnetoelectricity does not show any decay on the picosecond timescale. Our findings uncover a path for ultrafast manipulations of the intrinsic coupling between charges and spins in multiferroics4, which may reveal unexplored magnetic configurations and unravel new functionalities in terms of femtosecond optical control of magnetism.

## Main

The tetragonal dielectric magnetic material CuB2O4 (space group I$$\bar{4}$$2d, point group $$\bar{4}2m$$)11 has a rich phase diagram (see Fig. 1a). If the temperature is higher than 21 K, CuB2O4 is paramagnetic. A weak ferromagnetic phase (II) and a spiral antiferromagnetic phase (I) appear in the temperature ranges 9–21 K and below 9 K, respectively12, in the absence of an external magnetic field. The magnetic ground state is defined by two interactions, which can be expressed in a general way by means of the following Hamiltonian:13

$$H=J\sum _{i,j}{\hat{{\bf{S}}}}_{i}\cdot {\hat{{\bf{S}}}}_{j}+\sum _{i,j}{{\bf{D}}}_{ij}\cdot {\hat{{\bf{S}}}}_{i}\times {\hat{{\bf{S}}}}_{j}$$
(1)

where J is the Heisenberg exchange interaction, $${\hat{{\bf{S}}}}_{i,j}$$ are spin operators at sites i,j and D ij is the Dzyaloshinskii–Moriya (DM) vector. The competition between the Heisenberg exchange and DM interaction determines the phase diagram of CuB2O4. This material is magnetoelectric, and the origin of the magnetoelectric coupling is the hybridization between the d orbitals of copper and the p orbitals of oxygen14. The magnetoelectricity is limited to phase II, owing to the lack of time-reversal symmetry breaking in phase I (ref.14).

Our choice of sample is motivated by two remarkable features of this material. First, extensive experimental evidence and theoretical analysis have demonstrated that the magnetoelectricity in CuB2O4 can be directly probed through its optical properties. The magnetoelectric phase exhibits an effect called ‘non-reciprocal directional dichroism’ (NDD): a different absorption coefficient for light propagating along two opposite directions through the material15,16. Second, the photoluminescence spectrum of CuB2O4 reveals that a light beam can generate high-energy magnons with wavevectors lying near the edges of the Brillouin zone, by means of radiative decay of an optically induced 3d-electronic transition of the copper atoms17. As a consequence, given the correspondence between the symmetries and conservation laws of photoluminescence and absorption18, the optical stimulus can simultaneously induce a 3d-electronic transition and high-energy magnons by absorption. This process has been widely studied and is known in the literature as ‘exciton–magnon’19,20,21. Because a magnon is in essence a perturbation of the magnetic system originating from a spin-flip event, the optical pumping of such elementary excitations causes a modification of the total spin of the medium, which affects both spin-dependent terms in the Hamiltonian in equation (1). In particular, magnons near the edges of the Brillouin zone have the highest frequency in the dispersion of CuB2O4 (ref. 13). A resonant optical generation of these spin excitations thus has the potential to modify the magnetic configuration and induce magnetoelectricity in CuB2O4 on the shortest timescale.

Our experiment relies on the pump–probe scheme, which allows one to detect only the effects induced by an intense pump beam (see Fig. 1b). In particular, we excite a zero-phonon d−d transition of copper atoms via the resonant pumping of phonon sidebands (see Fig. 2). By monitoring the modification of the optical transmissivity, we are able to ascertain whether, in the transient state, a photo-induced NDD (PI-NDD) is present. Therefore, our strategy consists in cooling the sample down to phase I, photoexciting it and verifying whether the magnetic phase transition to phase II is triggered. Because the pump–probe approach is exclusively sensitive to pump-induced effects, it can reveal whether the magnetoelectricity is photoinduced, whereas it is not sensitive to the magnetoelectricity if the material is already in the magnetoelectric phase before illumination by the pump beam. Earlier experiments proved that the NDD in CuB2O4 can be measured by reversing the externally applied magnetic field, and thus the magnetization of the medium, instead of the wavevector of light15. The reason lies in a change of sign of the magnetic dipole term in the light–matter interaction energy, which can be caused by reversing either the magnetization of CuB2O4 or the direction of propagation of light16. Hence we plan to measure the transient transmissivity by applying an external magnetic field along opposite directions. The experimental procedure and the data analysis used to disclose the PI-NDD are described in the Methods section.

The typical time-dependence of the optical transmissivity can be observed in the pump–probe traces in Fig. 3a: a plateau is established at a 600 fs delay and does not decay in a time-window of 40 ps. Additional experiments reveal that the level of the plateau is constant up to 500 ps (see Supplementary Fig. 1). After cooling the sample to phase I, we performed measurements as a function of the excitation fluence by using a pump beam linearly polarized along the a(b)-axis. The time-traces in Fig. 3a show the effect of the orientation of the magnetic field on the dynamics of the optical transmissivity for a few selected values of the pump fluence. A field-dependent and fluence-dependent contribution is visible in the data. We average the normalized transient transmissivities in the delay range from 600 fs to 40 ps. To quantify the effect of the magnetic field, we consider the difference of the average values obtained for the same excitation fluence and opposite orientations of the field. This difference corresponds to the definition of NDD16 in the photo-excited state, PI-NDD. Possible photo-induced modifications of the magnitude of the magnetization would not invalidate this procedure: such a phenomenon would affect both the time-traces used to evaluate the PI-NDD dynamics in an equivalent way, being determined only by the pump parameters (fluence and polarization). The results, shown by the orange dots in Fig. 3b, display a non-vanishing value of the PI-NDD in the fluence range 4.5–9 mJ cm−2. The values obtained using lower and higher (10.5 mJ cm−2) pump fluence are below the sensitivity level shown in Fig. 3b (see discussion of the sensitivity in the Methods section).

The non-trivial experimental trend is consistent with the idea of a photo-induced phase-transition to phase II, according to the following picture. If the fluence is too low, the magnetic system is not perturbed enough to undergo the phase transition and thus no PI-NDD can be detected. Once the pump beam is intense enough, the medium is driven into the magnetoelectric phase and the PI-NDD is observed. If the sample is heated even further, the transition to the paramagnetic phase occurs and once again no PI-NDD is measured. The time-traces of the PI-NDD (see Supplementary Fig. 2) confirm that the effect is established in 600 fs. Below, we will confirm the suggested picture with three additional and independent experiments represented by the other datasets in Fig. 3b and by Fig. 4.

Let us recall that the pump–probe experimental scheme is sensitive exclusively to effects triggered by the pump beam. Although we can detect the light-induced magnetoelectricity (via the PI-NDD) in the measurements just described, this should not be the case if a similar experiment was performed with the sample already in phase II before the photo-excitation. This argument is supported by the magenta data points in Fig. 3b, which show the results of experiments in which the temperature of the sample was set to 15 K (phase II). No PI-NDD is detected when CuB2O4 is in the magnetoelectric phase before the photo-excitation, supporting our interpretation of the results.

The optical properties of CuB2O4 along the a(b)-axis are different from the properties along the c-axis, consistent with the tetragonal structure of the sample. Figure 2 shows that if the electric field of the pump beam is parallel to the a(b)-axis, optical absorption is stronger than for light linearly polarized along the c-axis. Thus we investigate the fluence-dependence of the transient transmissivity by using a pump beam linearly polarized along the c-axis, which should not heat the material intensively. More specifically, a light beam linearly polarized along the c-axis does not induce the exciton-magnon process (no sharp peak at 1.4 eV in Fig. 2), whereas this transition is photo-activated if the linear polarization of light is along the a(b)-axis. The results of this experiment (green dots in Fig. 3b) are consistent with our expectation and further corroborate our interpretation: no PI-NDD is observed in this data set, as the light–matter interaction takes place in a non-dissipative regime and the exciton-magnon transition is not induced.

Seeking further substantiation, we conceived an additional experiment. The phase diagram in Fig. 1a shows that the magnetic phase transition can be triggered by an external field with critical value of the order of Hc ≈ 2 T, if the sample temperature is 5 K (ref. 22). Consequently, measuring the transient transmissivity as a function of the external magnetic field should disclose a non-vanishing PI-NDD as long as Hext < Hc. Increasing the field above the critical value is expected to suppress the PI-NDD signal, because the transition to phase II is induced by the field before the interaction with the pump pulses. Using a pump fluence and polarization that allowed a successful observation of the PI-NDD in Fig. 3b, we studied the field dependence of the effect. The results confirm our physical interpretation (see Fig. 4). Measurements performed by applying an external field of intensity lower than 2 T show PI-NDD and are in quantitative agreement with the data in Fig. 3b (within the error bars). If the external field is more intense, the PI-NDD is suppressed.

Our extensive experimental investigation demonstrates overall a non-vanishing PI-NDD, implying a contribution to the optical transient transmissivity that is dependent on the orientation of the magnetic field and, consequently, linearly dependent on Hext. This observation demonstrates that magnetoelectricity is photo-induced. In fact, the optical transmissivity is defined by the symmetric components of the dielectric tensor: symmetry considerations show that, in a non-magnetoelectric material, these terms depend quadratically (at the lowest order) on an externally applied magnetic field23. On the other hand, it is experimentally assessed that the optical transmissivity of CuB2O4 in the magnetoelectric phase exhibits a contribution linearly dependent on an external magnetic field15,16. Our data in Fig. 4b reveal a contribution dependent on the sign of the field (that is, linear), although a linear increase of the PI-NDD as a function of the field is not visible, because this effect is in competition with the proximity of the phase-transition induced by Hext, which quenches the signal.

Having provided robust experimental evidence of the photo-induced magnetic phase transition, we must address a fundamental question: how does light couple to spins in CuB2O4 on a 600 fs timescale? It is known that laser pulses can increase the effective spin temperature in dielectrics24,25 and even trigger magnetic phase transitions26. These phenomena have been observed on the 10–100 ps timescale, consistent with the characteristic timescale of the magnetic excitations photo-induced in those experiments, which are typically magnons with wavevectors near the centre of the Brillouin zone26. In our case, the magnetic phase transition in CuB2O4 occurs in 600 fs, pointing to the involvement of magnons with wavevectors near the edges of the Brillouin zone. Because of the femtosecond period and nanometre wavelength of these elementary excitations, they are known as femto-nanomagnons27. The characteristic timescales of femto-nanomagnons are typically shorter than those of zone-centre magnetic excitations10,28, and this holds for CuB2O4 as well13. Although non-resonant impulsive stimulated Raman scattering of the femto-nanomagnons has been demonstrated, this process is not relevant in our experiment: no coherent oscillations at the magnonic frequency have been observed27.

As previously mentioned, the photo-excitation in our experiment induces optical phonons (sidebands), a dd transition and magnons near the edges of the Brillouin zone. Although the phonon non-radiative relaxation heats the lattice18 on an estimated timescale below our time resolution (see Fig. 5), this process alone cannot drive the phase transition, as no structural modification takes place when CuB2O4 evolves from phase I to II. We observe that the ground and excited states shown in Fig. 5 have different spin16, making an electric dipole contribution to this transition spin-forbidden. The parity-forbiddance of the dd transition is weakly removed by the hybridization of the excited state with different d orbitals16,17. However, the simultaneous generation of excited 3d electrons and femto-nanomagnons can result in a pair-excitation transition within an electric dipole framework, restoring the conservation of spin: this is the canonical interpretation of the exciton-magnon process19,20,21. The resonant generation of high-energy magnons strongly perturbs the magnetic system, not solely because of the difference in spin between the ground and the excited states. In fact, the femto-nanomagnons in CuB2O4 exhibit a strong magnon–magnon interaction leading to an estimated characteristic lifetime of about 670 fs. This number is derived from the bandwidth of the two-magnon mode detected in the Raman spectrum of this compound29. A pronounced magnon–magnon interaction entails considerable energy dissipations in the spin system and short lifetime of the magnons, inducing ultrafast heating of spins. In the present case, the photogeneration of electrons and lattice provides two additional scattering channels for the high-energy magnons, shortening the lifetime of the magnetic quasiparticles below the 670 fs estimation. We ascribe the cause of the magnetic phase-transition to the excitation and subsequent dissipations of high-energy magnons. Although femto-nanomagnons are induced also via the radiative relaxation of the 3d electrons17, this process is not relevant on the sub-picosecond timescale. In fact, our measurements of time-resolved photoluminescence (see Supplementary Fig. 3) demonstrate a characteristic relaxation time in the microsecond regime, consistent with the constant value of the plateau observed in the transient transmissivity up to a 500 ps delay (see Supplementary Fig. 1).

We note that also a non-radiative decay channel of the photo-excitation involving phonon–magnon scattering may result in the generation of magnons near the edges of the Brillouin zone. Recent experiments show that an energy transfer from the lattice to the spin excitations can occur if the phononic and magnonic dispersion relations are close30. This situation occurs in CuB2O4 near the edges of the Brillouin zone in the case of magnons13 and optical phonons, here photo-excited and generated during the non-radiative lattice relaxation18.

Our findings have implications not only in terms of ultrafast optical manipulation of magnetoelectric and multiferroic materials4, but also for the development of new concepts for photonic technologies, given the femtosecond photo-activation of a nanosecond-long directional transparency demonstrated here.

## Methods

### Sample preparation and optical characterization

A single crystal of CuB2O4 was grown by the flux method. The orientation of the single crystal was determined by X-ray diffraction. The sample was cut into thin plates with wide faces orthogonal to the (b)a-axis. Each wide face was polished to obtain a flat surface. The thickness of the sample was approximately 100 μm. A halogen lamp was used for the optical absorption measurements. A monochromatic light beam was obtained by using a grating-type monochromator. The intensity of the transmitted beam was detected by a photodiode. The optical absorption spectrum was calculated from the intensity spectrum of the transmitted light. Note that CuB2O4 has a transparency window in correspondence of the probe photon energy31. The onset of the charge-transfer transition, which is the bandgap, arises at 3.7 eV (ref. 31).

### Pump–probe set-up

The light source used for our pump–probe experiments is a regeneratively amplified mode-locked Ti:sapphire laser, delivering 100 fs, 700 μJ pulses with central photon energy of 1.55 eV and 5 kHz repetition rate. The output of the laser system is split into two beams: the pump beam (1.55 eV) and the probe beam, which has central photon energy of 3.1 eV. The probe beam is obtained by second-harmonic generation of the fundamental wavelength of the laser system, by means of a β-barium borate crystal. The pulse durations for pump and probe pulses were 100 fs and 300 fs, respectively. The two beams impinged on the sample with a relative angle smaller than 10°. The pump and probe were focused on the sample down to spot diameters of approximately 480 μm and 50 μm, respectively. The delay between pump and probe pulses was continuously tuned by a mechanical delay line, able to access the 0–500 ps range. The intensity of the pump beam was modulated by a mechanical chopper operating at 2.5 kHz, synchronized with the train of pump pulses. The angle between the pump and the probe beam is wide enough to avoid the pump beam impinging on the detector, ruling out any possible contribution to the signal originating from a second harmonic generation process of the pump. The scattered pump radiation did not affect our detection, as we had placed a colour filter in front of the photodiode to block any scattered 1.55 eV radiation while letting the 3.1 eV probe beam propagate to the detector. The sample was placed in a magneto-optical cryostat, allowing us to change the temperature of the medium in the range 4 K to 300 K. A split-coil superconducting magnet is able to generate a magnetic field up to 5 T along the b(a) axis of the sample, as shown in Fig. 1b.

### Data analysis

The normalized transient transmissivity represented by each pump–probe trace was averaged in the range 600 fs to 40 ps to evaluate the plateau. We do not consider the data at shorter delays, because coherent nonlinear optical effects (‘coherent artifacts’32) due to the overlap of the pump and probe beams obscure the real value of the transient transmissivity. The PI-NDD (dotted curves in Figs. 3b and 4) is then expressed by the absolute value of the difference between measurements performed by applying the external magnetic field in opposite orientations along the b(a)-axis (see Fig. 1b). The experimental uncertainty of each pump-probe measurement is defined by the standard deviation of the data points used to evaluate the average of ΔT/T. The errorbars of the PI-NDD are then obtained by the sum of squared errors of the two average values of ΔT/T, as the two measurements are independent. However, the error bars calculated in this way do not take into account all the experimental sources of errors, such as mechanical drift of the sample during the time interval between the two measurements involved in calculating the PI-NDD (typically 2–3 hours). We identify the sensitivity of our experimental apparatus in Fig. 3b with the data point obtained for 1.5 mJ cm−2 fluence and pump polarization parallel to the a(b)-axis. In fact, we calculated the laser-heating of the sample, using the experimentally determined12 specific heat of CuB2O4 at T = 5 K. The increase of temperature induced by a pump beam linearly polarized along the a(b)-axis and with a fluence of 1.5 mJ cm−2 is estimated to be 1.5 K. In this configuration, no PI-NDD is thus expected, motivating our choice for the sensitivity value. The data points obtained below this level are not ascribed to the PI-NDD. This choice is motivated and its validity is confirmed by the results obtained and shown in Figs. 3b and 4b. We stress that, in these two figures, measurements performed under the same conditions provide values of the PI-NDD that are in quantitative agreement (within error bars).

### Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon request.

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## Acknowledgements

We thank J. Omachi for the time-resolved photoluminescence measurements and N. Nemoto, Y. Arashida and H. Sakurai for technical support. This work was supported by JSPS KAKENHI grant no. 26247049 and the Photon Frontier Network Program funded by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan. D.B was supported by the Japanese Society for Promotion of Science (JSPS) ‘Postdoctoral Fellowship for Overseas Researcher’ no. P16326. S.T was also supported by JSPS through the Program for Leading Graduate Schools (MERIT) and a Grant-in-Aid for JSPS Fellows (14J06840).

## Author information

### Author notes

• D. Bossini

Present address: Experimentelle Physik VI, TU-Dortmund, Dortmund, Germany

### Affiliations

1. #### Institute for Photon Science and Technology, Graduate School of Science, The University of Tokyo, Tokyo, Japan

• D. Bossini
• , K. Konishi
• , J. Yumoto
•  & M. Kuwata-Gonokami
2. #### Department of Advanced Materials Science, The University of Tokyo, Kashiwa, Japan

• S. Toyoda
•  & T. Arima

• S. Toyoda
4. #### Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan

• J. Yumoto
•  & M. Kuwata-Gonokami
5. #### Photon Science Center, Graduate School of Engineering, The University of Tokyo , Tokyo, Japan

• M. Kuwata-Gonokami

### Contributions

D.B. conceived the project with contributions from K.K., T.A. and M.K-G. The sample was grown and characterized by S.T. D.B. performed the time-resolved experiments and analysed the data. All the authors took part in regular discussions and contributed to the writing of the manuscript.

### Competing interests

The authors declare no competing financial interests.

### Corresponding author

Correspondence to D. Bossini.

## Supplementary information

1. ### Supplementary Notes

Supplementary Notes 1–3, Supplementary References.