Electric field control of terahertz polarization in a multiferroic manganite with electromagnons

TL;DR

This study demonstrates the all-electrical control of terahertz polarization in a multiferroic manganite through electromagnons, enabling dynamic tuning of terahertz light polarization via magnetoelectric coupling.

Contribution

It introduces a method to electrically manipulate terahertz polarization in a multiferroic material using electromagnons, showcasing dynamic control of the magnetoelectric effect.

Findings

Terahertz polarization rotation can be controlled by ferroelectric domain orientation.

Voltage can switch the amplitude and direction of polarization rotation.

The dynamic magnetoelectric effect enables tunable terahertz polarization.

Abstract

All-electrical control of a dynamic magnetoelectric effect is demonstrated in a classical multiferroic manganite DyMnO3, a material containing coupled antiferromagnetic and ferroelectric orders. Due to intrinsic magnetoelectric coupling with electromagnons a linearly polarized terahertz light rotates upon passing through the sample. The amplitude and the direction of the polarization rotation are defined by the orientation of ferroelectric domains and can be switched by static voltage. These experiments allow the terahertz polarization to be tuned using the dynamic magnetoelectric effect.

Equations

$${\mathbf{P}}_0\sim {\delta }_{j\to j+1}\times ({\mathbf{S}}_j\times {\mathbf{S}}_{j+1}).$$

Full text

Electric and magnetic field control of the propagation and the polarization state of terahertz radiation is one of the prerequisites for continuous progress of modern electronics. A number of recent developments in this direction have been achieved using multiferroics, i.e. materials simultaneously revealing electric and magnetic ordering fiebig_jpd_2005 ; ramesh_nmat_2007 ; eerenstein_nature_2006 ; tokura_science_2006 ; cheong_nmat_2007 . Several multiferroics provide not only a direct coupling between static electric and magnetic properties but also give a possibility to modify dynamic susceptibilities by external fields. Application of a static magnetic field to the multiferroic materials leads to dichroism in the terahertz range pimenov_nphys_2006 ; kida_prb_2011 or even to more complex effects like controlled chirality bordacs_nphys_2012 or directional dichroism kezsmarki_prl_2011 ; takahashi_nphys_2012 ; takahashi_prl_2013 . Electric control of terahertz radiation is more difficult to realize and it has been recently demonstrated in Raman scattering experiments rovillain_nmat_2010 .

Dynamical properties of several multiferroic materials in the terahertz range are governed by novel magnetoelectric modes called electromagnons tokura_phil_2011 ; shuvaev_jpcm_2011 ; sushkov_jpcm_2008 ; smolenskii_ufn_1982 . Electromagnons may be defined as collective excitations of the magnetic structure which are coupled to the electric dipole moment.They may be regarded as a mixture of magnons and phonons. In orthorhombic rare earth manganites RMnO3 one generally observes several electromagnons in the terahertz and sub-terahertz range. A strong high frequency mode around 2-3 THz is well understood on the basis of a symmetric Heisenberg exchange (HE) coupling aguilar_prl_2009 ; lee_prb_2009 as a zone edge magnon which can be excited by electric component of the electromagnetic radiation. A second intensive mode existing at 0.5-1 THz has been explained using the same mechanism but including a Brillouin zone folding due to modulation of the magnetic cycloid lee_prb_2009 ; stenberg_prb_2009 . In the sub- terahertz frequency range a series of weaker modes is observed in optical pimenov_jpcm_2008 ; shuvaev_jpcm_2011 and neutron scattering experiments senff_jpcm_2008 . These modes are explained as the magnetic eigenmodes of the spin cycloid in RMnO3. Some of these modes may get an electrical dipole activity due to the relativistic Dzyaloshinskii-Moriya (DM) mechanism. Dynamic contributions due to this mechanism have been investigated both experimentally and theoretically katsura_prl_2007 ; pimenov_jpcm_2008 ; pimenov_prl_2009 ; cano_prb_2009 ; senff_prl_2007 . In spite of its weakness, the DM interaction is a promising mechanism especially in application to spiral magnets as it connects static spontaneous polarization and magnetic structure katsura_prl_2007 ; mostovoy_prl_2006 . This mechanism is responsible for the switching of ferroelectric polarization by magnetic field and for the control of magnetic structure by electric voltage in spiral magnets cheong_nmat_2007 . It may be expected that in the frequency range where the dynamics is governed by the DM mechanism, the terahertz light will be controlled by electric field as well. In present experiments we utilize this idea for two purposes: we obtain a direct evidence of dynamical magnetoelectric coupling within the DM electromagnon and we demonstrate a possibility to control the polarization of terahertz light by applying static electric fields.

DyMnO3 is a multiferroic manganite with orthorhombic structure. The high-temperature paramagnetic state in this material transfers into an incommensurate antiferromagnetic structure below $T_{\textrm{N}}\simeq 39$ K. At lower temperatures a second phase transition into a ferroelectric phase takes place at $T_{c}\simeq 19$ K. By analogy to TbMnO3 this phase is most probably a cycloidal antiferromagnet kenzelmann_prl_2005 with an incommensurate propagation vector. Below the transition to the cycloidal state DyMnO3 reveals static electric polarization which is aligned along the $c$-axis ($Pbnm$ crystallographic setting is used throughout this paper). This polarization is well described by the DM coupling which leads to a simple expression mostovoy_prl_2006 :

[TABLE]

Here $\mathbf{S}_{j}$ and $\mathbf{S}_{j+1}$ are the neighbor Mn3+ spins within $ab$-planes and $\mathbf{\delta}_{j\rightarrow j+1}$ is the vector connecting them (see Fig. 1a). The spin cycloid breaks the space inversion symmetry and has two possible rotation directions of the spins ($\circlearrowleft$ and $\circlearrowright$). According to Eq. (1), the sign of the static polarization is opposite in these two cases (see Fig. 1a). Therefore, the antiferromagnetic domains are simultaneously ferroelectric domains, and the orientation of the spin cycloid is also affected by external electric field.

The idea of the present experiment is based on the DM coupling between static and dynamic properties in DyMnO3. A schematic picture of the cycloidal magnetic structure in DyMnO3 is shown in Fig. 1a. Due to an incommensurate character of the cycloid, the solution of the dynamic equations for this structure reveals three eigenmodes (see Supplementary Information for more details). For the present experiment only one mode is the most promising. Within this mode magnetization and electric polarization oscillate along the $b$ and $a$ axes, respectively (DM electromagnon in Fig. 1a). Therefore, this mode can be excited either via electric channel by $e\|a$ and via magnetic channel by $h\|b$. Moreover, these two channels are not independent. The electric excitation drives also the magnetic moment and vice versa. As discussed in more details in the Supplementary Information, this cross coupling is manifested in the existence of the nonzero dynamic magnetoelectric susceptibility $\chi_{ab}^{me}$.

The main experimental difficulty to observe dynamic magnetoelectric effect in DyMnO3 is that it cannot be detected in an experiment with an $ab$-plane cut crystal. In such geometry the ac fields of the incident wave are either $e\|b$ and $h\|a$ and do not excite the electromagnon at all, or they are $e\|a$ and $h\|b$ and, therefore, they both excite the electromagnon at the same time. The existence of the magnetoelectric effect in such geometry does not lead to an emergence of a wave with the perpendicular polarization but only slightly changes the absorption of light. In order to overcome this difficulty, the sample with tilted axes has to be used. The geometry of such an experiment is shown in Fig. 1b. In the following arguments we assume incident wave with electric field component $e\|ab$-plane of the crystal which excite the DM electromagnon via electric channel. This geometry is equivalent to $e\bot c$ in Fig. 1b and contains both components of the electric field $e\|a$ and $e\|b$. Because the DM electromagnon has nonzero magnetoelectric component $\chi_{ab}^{me}$, an ac magnetic field $h\|b$ will be induced by this excitation. This electromagnetic field corresponds to a wave with polarization perpendicular to the incident wave with $h\|c$. Thus, an appearance of a signal in crossed polarizers is a characteristic of a nonzero magnetoelectric susceptibility. These qualitative arguments are supported by rigorous calculations given in the Supplementary Information.

We note that within the present experiment the existence of DM electromagnon which can be excited at the center of the Brillouin zone is crucial. As shown in the rigorous solution Supplementary Eq. (5), the electrically and magnetoelectrically active mode can be represented as a symmetric superposition of two magnons with wavevectors $\mathbf{q}=+\mathbf{Q}$ and $\mathbf{q}=-\mathbf{Q}$. Here $\mathbf{Q}$ is the modulation vector of the magnetic cycloid aguilar_prl_2009 . The symmetric mode represents an electromagnon which have nonzero dynamic polarization along the $x$ axis and, therefore, can be excited by electromagnetic wave with $e\|a$.

In case of (although much stronger) Heisenberg electromagnons aguilar_prl_2009 ; lee_prb_2009 which are excited as a zone edge magnons, the present experiment would not work. For the zone edge electromagnon the neighbor spins oscillate out-of-phase, which cancels the resulting magnetic moment. Although this mode reveals strong electric contribution, the magnetic and magnetoelectric susceptibilities are zero. As will be shown in more detail below (Fig. 3), the dynamic magnetoelectric effects observed in DyMnO3 are indeed centered around the weak DM electromagnon at 210 GHz and they are absent around strong Heisenberg electromagnon around 550 GHz.

The remaining point is the requirement of an electrical poling of DyMnO3 crystal. Without poling, two types of domains (Fig. 1a) coexist in the sample. The domains with the opposite ($\circlearrowleft$ or $\circlearrowright$) rotation of the spin cycloid reveal the opposite sign of the magnetoelectric susceptibility, canceling the effect. In order to avoid the signal compensation from different domains, the sample has been poled in static electric fields $E||c$. Such poling orients the majority of the domains along one direction.

Figure 2a shows a typical result of the experiment in crossed polarizers geometry. We note that crossed polarizers separate the incident polarization from the induced one. As expected, no signal could be be detected in the paraelectric phase. Immediately upon the onset of the ferroelectric phase, distinct polarization rotation is observed with the sign of the signal correlating with the sign of the static field (Fig. 2a). Here we plot clockwise rotation of the polarization as positive signal and the counterclockwise rotation as negative signal. Equivalently, the positive and negative sign of $t_{\bot}$ reflect the 180∘ phase difference between the experimental signal for different sign of static electric field. No signal is observed without poling of the sample. These results demonstrate the validity of the qualitative arguments given above.

Another important result of this work is shown in Figs. 2b,c. Here, not far from the phase transition into the ordered state, the ferroelectric domains may be switched by moderate static field. Due to direct coupling of static and dynamic properties, the sign of the magnetoelectric susceptibility is switched as well. Therefore, in this range we can directly influence the signal $t_{\perp}$ and the polarization rotation of the terahertz radiation by static electric field.

A significant difference between the experiments in Figs. 2a,c is that a field-cooling experiment is performed in the fist case and a zero-field-cooled experiment in the second case. Because in the field-cooled case the sample is cooled starting from the paraelectric state, it is much easier to align the ferroelectric domains by static field. In the zero-field-cooled sample the electric domains are not oriented. Especially at low temperatures the coercive field is strong and the static electric field cannot reorient the domains. The reorientation of the domains takes place close to the ferroelectric transition only, which explains the maxima observed in Figs. 2c. Finally, we note that the effects in Figs. 2a,b are due to the same microscopic mechanism, but a direct switching of polarization in Fig. 2b is more relevant from the point of view of possible applications.

In order to prove the proposed mechanism of the polarization rotation, a series of spectroscopic experiments has been carried out. The terahertz dynamics in our frequency range is dominated by a strong electromagnon at about 550 GHz (18 cm*-1*). This electromagnon is responsible for a relatively low transmission in the geometry with $e\|a$, seen as blue symbols in Fig. 3a. This excitation most probably originates from a symmetric Heisenberg exchange mechanism aguilar_prl_2009 ; lee_prb_2009 ; kida_prb_2008 and it does not contribute to the effects described in this work.

In the transmission spectra $e\|a$ another weaker excitation can be seen close to 210 GHz. This mode is observed both in the geometry $e\|a$ (Fig. 3a, red curve) as well as in the perpendicular geometry $e\|c$ (Fig. 3c). In the latter geometry the sample is more transparent as the main absorption mechanism due to the Heisenberg exchange with the component $e\|a$ is absent. In close analogy to a similar spectral analysis pimenov_prl_2009 in TbMnO3, we attribute the 210 GHz mode to the zone-center eigenmode of the cycloidal structure. This mode gets its intensity predominantly due to the Dzyaloshinskii-Moriya mechanism. Because static electric polarization is governed by the same mechanism, static and dynamic properties are strongly correlated for the 210 GHz mode. As discussed above, this connection is the basic mechanism to produce electrically controlled rotation of the terahertz polarization.

As presented in more details in the Supplementary Materials, the 210 GHz mode of the cycloidal spin structure reveals nonzero electric $\chi_{a}^{e}$, magnetic $\chi_{b}^{m}$, and magnetoelectric $\chi_{ab}^{me}$ susceptibilities. This mode can be excited by both, an ac electric field $e\|a$ and ac magnetic field $h\|b$ and can be therefore called a DM electromagnon. In agreement with these arguments, a rotation of the polarization is the strongest close to 210 GHz and fades away on both sides of the resonance. This result is shown in Fig. 3a with black squares. Green solid line represents the result of calculations of the transmission in crossed polarizers assuming Lorentz line shape of the DM electromagnon at 210 GHz. Tiny oscillations in this curve reflect the Fabry-Pérot resonances on the sample surfaces. In order to obtain the magnetoelectric susceptibility directly from the measured transmission, the complex transmission matrix has been inverted numerically. The frequency dependence of a resulting magnetoelectric susceptibility in DyMnO3 is shown in Fig. 3b by black symbols. We note that in spite of the complexity of the data treatment, a nonzero signal in crossed polarizers is to a leading term directly proportional to $\chi^{me}$ shuvaev_epjb_2011 . This explains qualitative similarity of the frequency dependencies of $t_{\bot}(\nu)$ and $\chi^{me}(\nu)$ in Fig. 3a,b.

From the Lorentzian fits in Fig. 3 the intensities of the DM electromagnon are obtained as follows: electric contribution (Fig. 3a) $\Delta\varepsilon_{a}=1.7\pm 0.3$; magnetic contribution (Fig. 3c) $\Delta\mu_{b}=0.010\pm 0.002$; Magnetoelectric contribution: (Fig. 3b) $\Delta\chi_{ab}^{me}=0.03\pm 0.01$. We see that the universality condition Supplementary Eq. (10) is not fulfilled in DyMnO3: $\sqrt{\Delta\varepsilon_{a}\Delta\mu_{b}}=0.13>\chi_{ab}^{me}$. This disagreement most probably indicates that large part of the DM electromagnon spectral weight is provided by the Heisenberg exchange mechanism. Indeed, a theoretical estimate of electric contribution aguilar_prl_2009 from Supplementary Eq. (8) gives the value $\Delta\varepsilon_{a}\sim 0.2$ substantially smaller than the experimental result.

In orthorhombic rare earth manganites (RMnO3, R = Dy, Tb, Eu:Y) strong zone edge electromagnons in the terahertz spectra are due to symmetric Heisenberg exchange mechanism. However, their properties do not correlate with the behavior of static electric polarization, because the latter is due to antisymmetric Dzyaloshinskii-Moriya coupling. On the contrary, in present experiments static and dynamic properties are controlled by the same DM mechanism, which explains the observed voltage control of terahertz light.

Finally, the observed results differ from such well-known effect like electro-optical modulationlandau_book8 (Pockels effect). Several arguments support this statement: i) the observed signal qualitatively follow the ferroelectric polarization (Fig. 2a) and disappear in unpoled sample at low temperatures (Fig. 2c); ii) in poling experiment the same signal is observed if only half as intensive electric voltage is applied, i.e. the effect saturates in field; iii) the frequency dependence of the observed magnetoelectric signal follows the Lorentzian line shape of the DM electromagnon.

In conclusion, we investigate dynamic magnetoelectric effect based on DM electromagnon in DyMnO3. Due to off-diagonal elements of the magnetoelectric susceptibility a polarization plane rotation of the transmitted radiation is observed. The amplitude and the direction of the polarization rotation can be controlled and switched by static electric voltage. From the spectral analysis a full set of magnetic, electric, and magnetoelectric susceptibilities of the DM electromagnon in DyMnO3is obtained.

Acknowledgements

We thank K. Hradil for the help in sample orientation. This work was supported by the by the German Research Foundation DFG, by Russian Foundation for Basic Researches (N 12-02-01261), and by the Austrian Science Funds (I815-N16, W1243).