Emission of coherent THz magnons in an antiferromagnetic insulator triggered by ultrafast spin–phonon interactions

Antiferromagnetic materials have been proposed as new types of narrowband THz spintronic devices owing to their ultrafast spin dynamics. Manipulating coherently their spin dynamics, however, remains a key challenge that is envisioned to be accomplished by spin-orbit torques or direct optical excitations. Here, we demonstrate the combined generation of broadband THz (incoherent) magnons and narrowband (coherent) magnons at 1 THz in low damping thin films of NiO/Pt. We evidence, experimentally and through modeling, two excitation processes of spin dynamics in NiO: an off-resonant instantaneous optical spin torque in (111) oriented films and a strain-wave-induced THz torque induced by ultrafast Pt excitation in (001) oriented films. Both phenomena lead to the emission of a THz signal through the inverse spin Hall effect in the adjacent heavy metal layer. We unravel the characteristic timescales of the two excitation processes found to be < 50 fs and > 300 fs, respectively, and thus open new routes towards the development of fast opto-spintronic devices based on antiferromagnetic materials.


S1. THz signals in different NiO(001)(10nm)/Pt(2nm) samples
We present in Fig. S1 THz measurements for two different batch of NiO(001)(10nm)/Pt(2nm) samples. On the second sample (denoted as sample B, grown at 1.5 sccm of O2), we could not measure any 1 THz oscillations as mapped in sample A (grown at 0.7 sccm of O2). This evidence the crucial role of optimizing the NiO growth conditions, whilst the origin of this different behavior can arise from either a larger damping coefficient in NiO or a change of the magnetostrictive coefficient 11 .

S2. Kerr imagery on NiO antiferromagnetic twin domains
To obtain domain arrangement and orientation on NiO thin films, we performed optical imaging of the antiferromagnetic T-domains using magneto-optical effects in an adapted Kerr microscope (following the approach described in Ref. [1]) as shown in Fig. S2 for a NiO(001)(10nm)/Pt(2nm) sample. We identify three small as-grown antiferromagnetic Tdomain (white contrast) oriented at 90° from the largest majority T-domain (grey contrast). The black spots are defects also imaged in the sample morphology. The thin film therefore presents large uniaxial domains that we estimate to be in average larger than 100 x 100 μm². Birefringence difference imaging presenting two T-domains orientation with white contrast (circled in red) and grey (majority orientation, largest domain) and (b) sample morphology imaging indicating the defects at the surface of the sample (circled in black). The majority domain orientation (grey contrast) has an area estimated to be larger than 100 x 100 μm².

S3. Pump power dependence of the NiO/Pt THz emission
We present in Fig. S3 the fluence dependence on the THz emission for NiO/Pt bilayers which shows linear trend as expected from spintronic based THz emission mediated by spin-charge conversion (SCC) emission mechanism [2]. In our study, we worked below the damage threshold.

S4. THz emission mechanism originating from inverse spin Hall effect
To clearly identify the inverse spin Hall effect (ISHE) as the main mechanism allowing the THz emission from generated magnon flow from NiO, we performed two experimental checks. First, on (001) oriented thin films, Fig. S4a presents the THz emission from NiO/Pt, and NiO/W and NiO/Ta bilayers on a same (001) thin film. The presence of a phase reversal of the generated THz signal for Pt ( Fig. S4a-b), and W (Fig. S4a) and Ta (Fig. S4b) based bilayers, indicates that the spin-charge conversion (SCC) occurring via ISHE is responsible for the detected THz emission according to ∝ SHE ( × ) and given the opposite spin-Hall angle between Pt, and W and Ta. The smaller amplitude obtained in NiO/W and NiO/Ta arises potentially from i) a different spin-mixing conductance and/or ii) a smaller value of the spin Hall angle. One can nevertheless notice here that the presence of the oscillations also in the W case despite the lower signal amplitude. Secondly, we also collected the THz emission with different pumping direction to discriminate between electric or magnetic dipolar emission. Fig. S4c presents the THz emission when pumping from either the front (Pt) or substrate (MgO) side. It appears the generated THz polarization is reversed, which is also in line with a THz emission emerging from SCC in the Pt layer and not with a potential dipolar emission from the dynamics of the AFM moments. One must notice the crucial role of the spin-transparency of the NiO/Pt interface in this SCC process, with a measured spin-mixing conductance of about 10 14 Ω -1 .m -1 (Ref. [3]) as large as for ferromagnetic materials.
Lastly, we have replaced, for a (111) oriented NiO sample, the capping layer Pt(10nm) by W(10nm), which has a negative spin Hall angle SHE W about the same amplitude as the positive spin Hall angle of Pt SHE Pt . We also observed a phase reversal (see Fig. S5), in line with spin-tocharge conversion processes.

S5. Magnetic field dependence of the THz emission
We performed the magnetic field dependence measurement of the THz emission by applying a static magnetic field of about 200 mT in the sample plane (along and direction) as shown in Fig. S6. We measured an identical THz trace when applying (or not) an external magnetic field. The THz-emission signal shows a time-domain 1 ps oscillations in all cases. This independence of THz emission with respect to applied magnetic field is in line with antiferromagnetic origin of the THz emission. It allows us to discard the presence of an uncompensated interface, which could have resulted in spin current injection via ultrafast demagnetization. One must also notice that only X-ray magnetic linear dichroism (XMLD) (and not X-ray magnetic circular dichroism -XMCD -) signals were measured on these samples [4].

S6. Modelling of the NiO spin dynamics under various torque excitations
In this section, we introduce NiO antiferromagnetic ordering before considering the dynamics of the Néel vector. We then introduce magneto-optical torque and thermo-magneto-elastic effect and their respective symmetries which allow THz emission.

NiO material description.
NiO is an easy-plane antiferromagnet with the Néel temperature of 523 K (Ref. [5]). Below the Néel temperature, the magnetic spins lie in (111) planes where 1 and 2 describe opposite spin ordering between adjacent planes in equilibrium state. Magnetic structure can be realized in form of four possible T domains that are distinguished by orientation of easy magnetic planes [6]. Orientation of the magnetic moments in easy magnetic plane and T-domain structure depend on the film orientation. In NiO(111) samples, the growth conditions favor formation of a single T domain with 1 ↑↓ 2 aligned along one of the three equivalent [112 ̅ ] directions in (111) plane, thus forming three equivalent S domains. NiO(001) films show multidomain structure with all four possible T domains. However, pronounced out-of-plane deformation [4] removes S domains and stabilizes the single equilibrium orientation along [5 5 1 ̅ 9] within each of T domain. We thus consider this initial AFM state in our theoretical modelling.

Equation of motion of the antiferromagnetic order
Under excitation, we described the antiferromagnetic order dynamics by: where AF 2 = 2 ex an is the angular frequency of the magnetic oscillations depending on the temperature with the gyromagnetic ratio, ex the exchange field that keeps the magnetic sublattice moments antiparallel, an ( ) = − ∂ an / ∂ the magnetic anisotropy field, an is the density of the magnetic energy, /2 is the sublattice magnetization, AF is the damping constant and is the limiting magnon velocity. Eq. (1) of the main text is defined by linearization of Eq. (S1) with respect to small deviations of the Néel vector from equilibrium orientation . We picture in Fig. S7 the projection of the initial Néel vector and small deviations into the (11 ̅ 0) and (001) plane. We associate the spin current injected in the Pt with the spin accumulation produced by magnetization at the NiO/Pt interface. The polarization of the emitted THz signal out is then parallel to the current density i.e. we have ∝ ∝ 2 SH ⋅ × ( × ⊥ )/ℏ in the Pt layer [7], where SH is the spin Hall angle, is the electron charge, ℏ is the reduced Planck constant. We further display in this part the two contributions allowing the excitation of THz dynamics depending on the two studied orientations (001) or (111). Either the excitation mechanism needs to have the appropriate symmetry with respect to the orientation to excite the Néel mode or the generated spin current would need to have the correct symmetry (i.e. injection of angular momentum along the interface normal) to be efficiently converted via ISHE. We display in Fig. S8 the out-of-plane mode excitation configurations leading to the generation of charge current in Pt from NiO (001) and (111). In order to induce the THz mode, the torque should have a component parallel to ⊥ (otherwise, the low frequency mode is excited) while in order to excite a charge current in the Pt layer, the magnetization should have an in-plane component, which is achieved only for the 1 THz mode in the case of (111) oriented films.
We describe theoretically below in more detail the three different torques discussed in the main text, i.e. an off-resonant optical spin torque with the symmetry of the inverse Cotton-Mouton effect (ICME) and thermo-magneto-elastic effects which can generate a dynamical net moment leading to the generation of a non-zero THz signal by the inverse spin-Hall effect: Off-resonant optical spin torque via Inverse Cotton-Mouton effect (ICME). The interaction between light and matter is described phenomenologically by the Hamiltonian The structure of the fourth rank tensor of phenomenological coefficients is defined by the , and 12 = 23 = 31 (Voigt notation). The torque between optical pump and antiferromagnetic order is defined as = ∂ int / ∂ , so that: (S3) The out-of-plane mode (1 THz) can be excited either in NiO(111) and in NiO(001) samples. For NiO(111), the component of the torque in ⊥ direction is: [ 44 + (3 44 − 2 11 + 4 12 where we assume that the light is linearly polarized and is the angle with respect to equilibrium orientation of the Néel vector. This result is consistent with that of Ref. [8]. For NiO(001), we have: [2( 11 − 2 12 ) + 4 44 sin2 ]. (S5) By introducing the notations 1 ≡ 2( 11 − 2 12 ), 2 ≡ 44 and in = in 2 light , we get: (111), Furthermore, we then expect the amplitude of the emitted THz signal out to scale with the NiO thickness (up to the magnon spin-diffusion length of around 100 nm in NiO [9]) and with the incoming laser power as in which are both in line with the observations of Fig. 3. Though ICME is non-zero for both NiO(001) and NiO(111), its value and angular dependence is defined by different combinations of the coefficients Hence, we expect a different ICME contribution for NiO(001). We recall that inverse Faraday contribution can be excluded from the pump polarization dependence. Our experimental results are, in this regard, in line with Refs. [8,10], and demonstrate the stronger off-resonant optical spin torque contributions from (111) samples.
Thermo-magneto-elastic effect. Magneto-elastic coupling between the components of the Néel vector and strain tensor is described by the Hamiltonian where the fourth rank tensor of magneto-elastic constants has the same structure as tensor . Inhomogeneous laser-induced heating creates an out-of-plane strain component ( , ) whose time dependence NiO ( ) (integrated over the NiO thickness) is shown in Fig.  4b of the main text. The corresponding local component of the torque in ⊥ direction is: In NiO, we have 11 = 3 × 10 7 J.m -3 according to Schmitt et. al. [4]. In case of (111) NiO samples, 0 = 0 and thermo-magneto-elastic torque vanishes as shown in Fig. S9. For (001) films 0 ⋅ ⊥ = 0.46, and the thermo-magneto-elastic torque produces a pronounced effect. From the amplitude of the maximum out-of-plane strain wavefront = 6 × 10 −6 , we estimated the tilt of the Néel vector to be around = arccos ( ( ) ⋅ ) = NiO 11 /(2 AF ) ≃ 0.3° for the THz-TDS measurements. In this case, the magnetization should be of the order of 1 A/m following the data from Ref. [4]. Its spin signal then depends on the orientation of the Néel vector with respect to crystallographic axes. The sign of the out-coming signal, however, changes sign for the reversed film orientation (as shown in Fig. 2b and pictured in Fig. S7), leading to the opposite direction of the spin current into Pt layer (in line with SM4). On the contrary, the emitted signal is proportional to the intensity of pump pulse and does not depend on orientation of light polarization. The amplitude of the effect is inversely proportional to the thickness of NiO layer, as excitation of magnons takes place at the NiO/Pt interface. The timescale is defined by the slowest process, thermal heating of Pt and falls into picosecond range in line with the observations of Fig. 4b.

Spin-Seebeck effect contributions (SSE).
First, it should be noted that the standard bulk spin-Seebeck effect, present in magnetic systems for which a magnon flux carries angular momentum (ferromagnets, easy-axis antiferromagnets under applied field), seems to be irrelevant in the NiO/Pt system. A generated thermal gradient in the NiO (hot interface with Pt and cold interface with MgO) is a necessary factor but not the only element that needs to be considered for the spin-Seebeck effect. In NiO, although it possesses a sizeable macroscopic AFM ordering [11], the two magnon branches are non-degenerate at zero magnetic field [12,13], which excludes the spin-Seebeck excitation mechanism for building a net spin current. Moreover, the weak temperature dependence of the NiO(001)(10nm)/Pt(2nm) THz emission (see SM9) does not fit the theoretical expectations for SSE [13].
It should then be noted that the symmetry of (001) films allows for a second spin-Seebeck contribution proportional to the temperature gradient at the NiO/Pt interface and to spin-spin correlations, with the same symmetry as the thermo-magneto-elastic effect. In order to describe this contribution, we follow the approach of Ref. [14] used for YIG/Pt systems and consider a torque induced by spin fluctuations Pt in the Pt layer: where curr is a phenomenological constant whose value depends on the properties of the NiO/Pt interface. The average of the spin fluctuations is ⟨ Pt ( )⟩ = 0, however, they produce non-zero fluctuations of the Néel vector. In the frequency domain, we have: (ω) = Numerical simulations. We then model the magnetization dynamics of the NiO triggered by the torque contributions associated with non-linear (interfacial) SSE and thermo-magnetoelastic effect in the (001) films using the Eq. (S1). To model the THz response, we use as input parameters the temperature and strain profile extracted by fitting the URSM data using the strain model presented in SM7. We used the strain profile ( , ) to calculate the thermomagneto-elastic torque (S10) in NiO layer and plug it into dynamic Eq. (S4) to calculate the corresponding magnetization = ×̇/( ) of the several near-interface NiO layers that contribute into the optical response MAS . We separately calculated the non-linear (interfacial) spin-Seebeck effect using the temperature profile extracted from the modelling in SM7.
We then present in Fig. S10 the numerical simulations presenting the THz response of both component contributing to the overall modelling shown in Fig. 1b. It reads THz = MAS + T where MAS and T represent respectively the magneto-acoustic strain (Fig. S10a) and the temperature contributions according to the non-linear (interfacial) SSE (Fig. S10b) estimated in the presented fitting for =-0.3 and =0.7. It is to be noted that both components present a THz response centred around the out-of-plane magnon mode. The presence of oscillations at long timescale is assured by the magneto-acoustic strain contribution while the broadband contribution is fitted mainly via the temperature contribution. One must notice that the timescales of the modelled magnetization response are in line with the experimental THz response (Fig. 4b) and with the modelled ultrafast strain and temperature responses (Fig. 4b  and SM8).

S7. Linear pump polarization dependence on (111) films
Complementary to (001) oriented NiO films linear pump polarization dependence, we performed the same polarization dependence on NiO(111)(110nm)/Pt(2nm) sample as illustrated in Fig. S11. Contrary to the polarization independent THz emission measured for (001) films, we measured a cos(2 ) dependence on the linear pump polarization, in line with magneto-optic excitation as discussed in the main manuscript and in Refs. [10,15]. Here, = 0° corresponds to a p-polarized pump while we detect p-polarized THz component. The sample is placed so that [12 ̅ 1] is along the s-direction. In this view, the reduced THz amplitude found for the circular pump polarization arises from the fact that pump electric field can be written as = √ ( + ). Thus, as we only map the p-polarized THz component, we measure a THz signal which is half the amplitude recovered for a fully p-polarized pump.

Determination of transient strain in NiO
The time-resolved out-of-plane strain of the NiO layer is given by the relative change of the Bragg peak position in reciprocal space with the time delay :  The rising intensity at the small angle side of the RSM originates from the MgO substrate Bragg peak, which is cut from the figure due to its 100 times higher intensity. The left panel displays the extraction of the NiO Bragg peak (blue circles) by integrating the intensity along the -direction in reciprocal space (grey circles) and subtracting the modelled background provided by the MgO substrate (black dashed line). The blue and grey solid line describe the fitted NiO Bragg peak and its superposition with the background, respectively. The vertical dashed grey line denotes the determined position of the NiO Bragg peak along which determines the out-of-plane strain of the NiO layer NiO .

Transient strain modelling
We use the modular Python toolbox udkm1Dsim [16] to model the measured mean strain of the NiO layer, which provides access to the spatio-temporal temperature and strain used for the simulation of the THz signal. The absorbed energy in the Pt capping layer drives a transient out-of-plane strain where refers to the sound velocity. In general, the laser-induced stress is given by the product of the energy density ( , ) = • ∆ and the material-specific Grüneisen constant Γ for each subsystem, i.e. electrons and phonons [17]. We use the literature values of the thermoelastic constants for the considered materials in Table S1. Since the electronic subsystem is only relevant in the Pt capping layer, we simplify the model by only considering one spatiotemporal temperature rise denoted as Δ ( , ). We model the laser-induced temperature rise (see Fig. S13a) by first calculating the deposited energy in Pt and the subsequent transport via 1D heat diffusion. To account for a finite stress rise time in Pt due to electron-phonon coupling, we model the stress in Pt driving the strain wave by [18]: Inserting the resulting spatio-temporal laser-induced stress into Eq. (S12) results in the spatiotemporal strain displayed in Fig. S13b. We use dynamical X-ray diffraction theory to calculate a NiO Bragg peak from the modelled spatio-temporal strain in NiO. The results of this modelling correspond to the modelled transient mean strain of NiO represented as a blue line in Fig. 4b, which is in line with the experimental data points obtained by UXRD (from the timedependent shift of the Bragg peak in reciprocal space).  Table S1. Thermoelastic constants table for Pt, NiO and MgO. is the phonon heat capacity, is the heat conductivity, is the mass density, is the sound velocity (for NiO, we used a different sound velocity value given in brackets), Γ el and Γ ph are respectively the electronic (phononic) Grüneisen constant and el−ph is the electronphonon coupling time.

S9. Temperature dependence below and above Néel order on the THz emission
We performed in Fig. S14 temperature dependence on the NiO(001)(10nm)/Pt(2nm) THz emission. The obtained dependence is not in in line with spin Seebeck effect as described in Ref. [13].