Impact of gigahertz and terahertz transport regimes on spin propagation and conversion in the antiferromagnet IrMn

Control over spin transport in antiferromagnetic systems is essential for future spintronic applications with operational speeds extending to ultrafast time scales. Here, we study the transition from the gigahertz (GHz) to terahertz (THz) regime of spin transport and spin-to-charge current conversion (S2C) in the prototypical antiferromagnet IrMn by employing spin pumping and THz spectroscopy techniques. We reveal a factor of 4 shorter characteristic propagation lengths of the spin current at THz frequencies (~ 0.5 nm) as compared to the GHz regime (~ 2 nm) which may be attributed to the ballistic and diffusive nature of electronic spin transport, respectively. The conclusion is supported by an extraction of sub-picosecond temporal dynamics of the THz spin current. We also report on a significant impact of the S2C originating from the IrMn/non-magnetic metal interface which is much more pronounced in the THz regime and opens the door for optimization of the spin control at ultrafast time scales.

Antiferromagnetic spintronic devices 1 provide many advantages such as robustness against external magnetic fields, a higher memory bit integration, two orders of magnitude faster manipulation of the magnetic order and new topological phenomena 2,3 . Their functionalities include pseudospin dynamics of magnons 4 and a wide spectrum of applications like memory [5][6][7][8][9] , spin logic 10 and terahertz (THz) emission devices using pinning of a hard magnetic layer 11 or gradual reorientation of the Néel-vector 12 . To exploit these advantages, we need to control (i) the injection, (ii) transport and (iii) conversion of the spin angular momentum in antiferromagnetic materials.
A model metallic antiferromagnet (AF) is IrMn in which spin-transfer effects 13 , spin-orbit effects 14 and ferromagnetic reversal by spin Hall torques 15, 16 have been exploited. It was shown that the AF ordering plays no significant role for spin transport in IrMn polycrystalline films 1,14 . This behavior was suggested to arise from the different direction of the moments averages out any anisotropic spin-relaxation contribution due to the magnetic order. Interestingly, the fact that the spin transport does not depend on the magnetic order parameter means that they can be obtained from the paramagnetic state and applied to the technologically relevant AF case, in line with earlier strategies used for AF spintronics 1,14 . In addition, regarding (i), an enhancement of the spin injection in IrMn by spin pumping due to spin fluctuations around the Néel temperature ( N ) at GHz frequencies may be possible 17 . The origin of the effect lies in the direct link between the spin mixing conductance and the linear dynamic spin susceptibility 18,19 .
In terms of (ii), in IrMn and structurally similar FeMn, two types of spin transport -electronic and magnonic -may exist at GHz frequencies 20,21 as indicated by spin-pumping techniques. Experiments in FeMn 20 suggest different spin-current penetration depths in both regimes (1 and 9 nm, respectively). Lastly, regarding (iii), spin-to-charge-current conversion (S2C) in IrMn was studied at DC and AC frequencies, giving a spin Hall angle of a few percent 14,[22][23][24] . A non-monotonic contribution to the temperature-dependent S2C signal due to nonlinear spin susceptibilities around N may also be possible, although not demonstrated so far, similar to findings in the PdNi weak ferromagnet 25 . This contribution relates to a different term that is the second order nonlinear dynamic susceptibility. To utilize the full potential of antiferromagnetic spin transport, spin currents have to be transferred to the ultrafast regime that matches the dynamics of the antiferromagnetic order parameter. So far, only a few recent studies focused on the spin transport at terahertz (THz) frequencies [26][27][28][29] .
In this paper, we explore the ultrafast (THz) spin injection, transport and S2C in Ir20Mn80 and directly compare them with transport experiments in the GHz range in equivalent samples. First, our results indicate a change in the nature of the spin transport when transiting from the GHz to the THz regime. Second, we show that S2C in IrMn at THz frequencies reaches similar efficiencies as in the GHz range. Interestingly, our observation suggests a strong influence of the interfaces between IrMn and the heavy-metal or the metallic magnet on the resulting in-plane charge current that is significantly more pronounced in the THz regime.
Our methodology is based on measuring S2C of spin currents injected from a layer of ferromagnetic Ni81Fe19 (F) into a bilayer of Ir20Mn80 (AF) and non-magnetic metal (N) [see Fig. 1(a,b)]. Spin angular momentum is injected in two different frequency ranges by (i) ferromagnetic spin pumping at 9.6 GHz (defined by the ferromagnetic resonance of NiFe), using a continuous-wave electron paramagnetic resonance spectrometer fitted with a three-loop-two-gap resonator 30 [ Fig.1(a)], and (ii) ultrafast spin-voltage generation in NiFe at 0.1-30 THz 31-33 by an optical femtosecond pump pulse [ Fig.1(b)]. In both techniques, the resulting out-of-plane spin current density s (ω, ) is converted to an in-plane charge current c (ω) by the local (layerdependent) spin Hall angle θ(ω, z), thus generating a detectable electric field . In the frequency domain, the complex-valued field amplitude is given by

FIG. 1. | Measuring inverse spin Hall effect at GHz and THz frequencies. (a)
Schematic of the GHz experiment. A microwave magnetic field (amplitude hrf ~ 0.05 mT, frequency 9.6 GHz) triggers the precession of magnetization in a magnetic layer (F = NiFe, thickness of 8 nm) and, due to spin pumping, launches a periodic spin current s through the antiferromagnetic layer IrMn (AF, thickness AF ) into a heavy metal layer (N, 3 nm) where it is converted into a detectable DC charge current c via the inverse spin Hall effect. We note that the generated electric field is constant over the entire thickness of the thin-film stack. (b) The analogous experiment performed at THz frequencies. A femtosecond optical pulse triggers an ultrafast s between the magnetic (F, 3 nm) and the AF layer. The converted serves as a source of an emitted THz pulse. (c, d) Typical raw experimental data, illustrated here by N = Pt: normalized voltage /ℎ rf 2 in the GHz (c) and the electro-optical signal in the THz (d) experiments for different AF (black arrows indicate increase of AF ). All waveforms in (d) were normalized by the amplitude corresponding to = 0. Inset: amplitude spectrum of the corresponding THz temporal waveforms.
Here, is the coordinate along the sample normal [see Fig. 1(a), (b)], ω is the angular frequency and c (ω) denotes the sheet charge current. (ω), related to c through the total sample impedance (ω), is detected (i) directly by electrical contacts on the sample, and (ii) contact-free by electro-optic sampling 34, 35 of the emitted THz pulse with a co-propagating probe pulse (0.6 nJ, 10 fs) in a 10µm-thick ZnTe(110) crystal under ambient conditions. We note that is -independent and represents the total impedance (i.e., the inverse of the sum of conductances of all layers). The electric field is constant and equals ( ) across the thin-film stack because it propagates through the stack several times due to back reflections on sample boundaries 36 (see Supplementary Fig. 6 for more details).
To investigate the propagation of s ( ) in both frequency regimes, we study thickness-dependent series of samples in the form of trilayers N|AF|F and F|AF|N. Each of them consists of a F = NiFe with thicknesses of 3 nm and 8 nm for THz and GHz experiments, respectively. The AF layer is Ir20Mn80 with varying thickness AF ranging from 0 nm up to 12 nm with a paramagnetic-to-antiferromagnetic phase transition expected at AF ≈ 2.7 nm at room temperature 17 . Finally, the sample structures contain a heavy metal layer with N = Pt, W or Ta (all 3 nm). All samples are deposited on thermally oxidized Si on glass substrates with thicknesses of Si(0.3mm)|SiO2(500nm) and SiO2(0.5mm) for GHz and THz experiments, respectively.
nm-thick Al cap was deposited on all samples to form a protective AlOx film after oxidation in air. We note that the different thicknesses of the F layer serve to increase the impedance and, thus, increase the emitted THz amplitudes [Eq. (1)] or to reduce damping and subsequently increase spin injection efficiency in the spin pumping experiments 37,38 . The impact of the F-dependent spin injection efficiency on the detected signals is removed by a normalization procedure described below.
Typical raw signals from the GHz and THz experiment are shown in Fig. 1(c)-(d) for various values of AF . In both experiments, the signal amplitudes decrease with increasing AF . The bandwidth of the THz setup is large enough to resolve sub-picosecond dynamics of the THz emission signal [ Fig. 1(d) inset]. We note that the additional oscillations after the main pulse in the THz raw data [ Fig. 1(d)] arise from water vapor absorption 39 . We also note that the GHz raw data gradually evolves from a Gaussian-to a Fano-like shape as AF increases because for thick AF layers the S2C predominantly takes place inside the AF layer, which is relatively weak than the initial large S2C in the N layer, as detailed below (see also Supplementary Figs. S1 and S2). To remove trivial AF -dependent photonic and electronic effects and, thus, make the data from the various samples directly comparable, we normalize 40 the signals by the independently measured (ω, AF ) and the absorbed powers of optical laser pulses or microwave GHz excitation (values for all samples are summarized in Supplementary Tab. S2), and take the root-mean square of the signals. The output of this procedure is the sheet charge-current amplitude c normalized by the excitation power in the respective frequency range. We also remove all method-specific impacts on the measured signal (e.g., the effect of different thickness of F layer) by normalizing the GHz and THz data sets to Pt|IrMn(0 nm)|NiFe at the respective frequency range. The raw GHz voltage [ Fig. 1(c)] was further treated to obtain its symmetric component as described in Fig. S1 and Ref. 30 . The resulting signals, shown in Fig. 2, directly capture the AF -dependence of c , which is a measure of the spin current S and the S2C efficiency [Eq. (1)]. The underlying raw data sets are provided in Fig. S2.
We first analyze qualitatively the data in the "forward-grown" samples N|IrMn|NiFe [ Fig. 2 (a)-(c)]. In both the GHz and THz regime, we observe a change in the signal polarity at AF = 0 when varying the N layer material, consistent with the sign and approximately the amplitudes of θ N known from literature (θ Pt > 0 and θ W , θ Ta < 0) 41 . With increasing AF and for a fixed N layer material, the signal decreases and, in the thick limit ( AF > 5 nm), saturates at approximately the same value for all THz and GHz experiments. The thick-limit values are also consistent with THz and GHz signals from control bilayer samples of NiFe|IrMn with AF = 12 nm (see supplementary Fig. S5). The striking observation is the different rate of signal decay in both regimes which can be, in general, understood as a consequence of the finite propagation length of s ( ).
The accurate modeling of s ( ) in multilayers is typically a complicated task and requires the determination of many unknown parameters such as the spin mixing conductance of each interface 42 . To compare GHz and THz regime, we simplify the model by neglecting the back-reflections of s ( ) and consider the IrMn layer a simple exponential spin-current attenuator 32, 43 , as illustrated for bilayer and trilayers by the sketches in Fig. 3. Consequently, the total sheet charge-current c from Eq. (1) can be separated into contributions of three individual layers and two interfaces: Here, s,0 is the total initial spin current launched by the excitation, is the characteristic propagation length for the spin current in the corresponding layer = F, AF, N, and θ * the effective spin Hall angle which includes all possible effects of spin memory loss (not shown in Fig. 3 for simplicity) and spin mixing conductance between the layers 44 . The last term c,a = c,F + c,I stands for an additional sheet charge current originating from S2C in the ferromagnetic layer and both interfaces 40 . Note that due to the simplifications, λ cannot be rigorously taken as the spin diffusion length but rather serves as a quantity to compare spin transport in both frequency regimes. Similarly, we can view the quantity (λθ * ) as the efficiency of the S2C that characterizes the practically achievable conversion in the layer including all mentioned spin injection losses.
We see that the model explains well the data in Fig. 2 On a quantitative level, we use the model and fit the data in Fig. 2 by a offset mono-exponential function 32,43 ( AF ) = 1 e − AF /λ AF + 0 where 1 and 0 stand for the relative conversion ( * ) N /( * ) Pt and the sum of all remaining relative S2C, respectively [Eq. (2)]. The obtained values are summarized in Tab. 1 and Tab. S1. We remind that the data shown in Fig. 2 are normalized to the signal from the Pt|NiFe reference sample in the respective frequency range. The average relative efficiency of the S2C in the thick limit 0,THz ≈ (8 ± 1)% and 0,GHz ≈ (10 ± 3)% in the THz and GHz regimes, respectively, are reaching consistently similar values. We can interpret the findings as a demonstration that the spin-current injection and propagation in IrMn are operative at ultrafast time-scales. In the thin AF limit, the layer behaves like a monoexponential spin current attenuator in the ultrafast THz regime 32,43 , qualitatively same as in the established GHz experiments 1, 45 . In the thick AF limit, when the ultrafast spin current does not reach the N layer, the role of IrMn as an attenuator changes to a converter, and the THz S2C efficiency signals saturate at very close averaged values as in the reference GHz measurements.

FIG. 4. | Broadband THz charge and spin currents. (a) Frequency dependence of the charge currents
c ( AF = 12 nm, ω)/ c (0, ω) for the thick limit normalized to the Pt|NiFe reference sample ( AF = 0). The data is extracted from the Pt|IrMn|NiFe series shown in panel Fig. 2 (a). The dotted red line depicts the mean value from the THz experiment corresponding to S2C in the thick limit (fitting parameter 0,THz , see Tab. S1) and the triangle symbol is the same quantity in the GHz range. (b) Comparison of the extracted THz spin current s ( ) for AF = 0 (blue curve), 3 nm (red curve) and 6 nm (green curve), all normalized to peak value −1 for better comparability.
We note that a possible contribution to the THz emission signal originating from magnetic dipole radiation 33 it is usually an order of magnitude smaller and we, correspondingly, do not observe any significant THz signal contributions that are even upon sample reversal. Another source of the S2C signal may be the conversion in the F layer c,F . Although this contribution is typically neglected in GHz experiments 1 , we should take the value of 0 ≈ 8 − 10% only as an upper bound of ( * ) IrMn /( * ) Pt , i.e., the practically achievable total conversion signal in heterostructures including IrMn compared to Pt.
In addition to time-averaged values, the high temporal resolution of the THz experiment allows us to extract the ω dependence of 0 taken from the THz data in Fig. 2(a). We observe a flat response between 0.5 and 30 THz and approximately the same value as in the GHz range [ Fig. 4(a)]. The good agreement of GHz and THz S2C efficiency in both thickness limits is consistent with previous studies that compared THz and low-frequency regimes of spin-orbit-coupling-based effects 32, 46, 47 .
As 0 ≪ 1 in most cases, the IrMn layer behaves like a simple spin-current attenuator, and we can justify the mono-exponential approximation in Eq. (2). Using the fitting values from Tab. 1, we obtain the mean λ AF,THz = 0.5 ± 0.1 nm and λ AF,GHz = 1.9 ± 0.6 nm, averaged over stacks with different N. Except for the THz data in Fig. 2(d), we also do not observe any significant irregularities in the GHz and THz signals around the ordering thickness at AF ≈ 2.7 nm at room temperature. We note that the pump laser pulse used in the THz experiments typically heats the electrons transiently by about 50-100 K 19 , which would imply only a slight increase of the ordering thickness to AF ≈ 3.2-3.6 nm 1, 17 .
Interestingly, the factor of 4 between λ AF,THz and λ AF,GHz may indicate a different regime of spin transport in the THz and GHz range. To test this hypothesis, we take advantage of the time-resolved nature of the THz experiment and extract the ultrafast spin-current dynamics of s ( ) from the THz signals from Pt|NiFe [blue curve in Fig. 4(b)] and Pt|IrMn( AF )|NiFe with AF = 3 and 6 nm (red and green curve), i.e., at AF where the IrMn is already antiferromagnetically ordered and allows for electronic and magnonic spin current. Data for more AF are displayed in Fig. S3. In all samples, the extracted s ( ) peaks at the same time and follows very similar dynamics as reported in previous works on fully metallic bilayer stacks (like F|Pt) 31,33,48 . Such behavior is in sharp contrast with what would be expected in a system with a significant contribution of magnon-mediated spin currents. As typical magnonic group velocities are of the order of 10 nm/ps and smaller 49,50 , the resulting dynamics of the total spin current of conduction electrons and magnons would be heavily deformed and, for increasing AF , exhibit an early electronic and delayed magnonic peak. The AFdependent relative delay would eventually leave our observation window (-0.4 … 0.8 ps). In addition, the recently observed ultrafast launching of magnonic currents, based on the spin Seebeck effect in metalsemimetal systems, would show a significantly slower dynamics, too. 51 As we do not observe any of these features and because our signals are not time-delayed with increasing AF we infer that the THz regime is dominated by a conduction-electron-mediated spin current. This conclusion is also consistent with a prior theoretical work 52 suggesting that the relevant characteristic spin-current decay length λ in F|Pt systems is at THz frequencies determined by the mean free path of electrons, implying ballistic transport.
At GHz frequencies, two types of spin transport regimes -electronic (diffusive) and magnonic -may exist. 20,21 Thickness-dependent spin-pumping experiments in F|FeMn( FeMn )|W 20 trilayers revealed non-monotonic S2C signals and, therefore, suggest a transition between spin transport regimes in FeMn. From our monotonic IrMn thickness-dependent S2C signals, we cannot disentangle electron and magnon contributions. If the magnonic component is not negligible, then a possible reason for why disentangling these contributions is more challenging for IrMn may be related with the shorter magnon characteristic lengths of 5 nm -as calculated in Ref. 53 -compared to 9 nm for FeMn. In that case, our data would infer that both the magnonic and electronic lengths are comparable (~2 nm).
Therefore, we can suggest the interpretation of the characteristic lengths λ AF , that differ by a factor of 4 between the THz and GHz data, as a consequence of different regimes of electronic spin transport: The ballistic regime at the THz frequencies where the electronic mean free path is the relevant quantity 31,33 , and the diffusive regime at the GHz frequencies characterized by the electron spin diffusion length 1 (typically longer than the mean free path 54,55 , implying slower dynamics). We cannot exclude though a magnonic contribution 14,20,21,56 in the GHz experiments.
Finally, we focus on the reversely grown samples [ Fig. 2 (d-f)]. If each stack NiFe|IrMn|Pt [ Fig. 2 (d-f)] is a mirror image of its forward-grown partner Pt|IrMn|NiFe [ Fig. 2 (a-c)], we would expect perfectly reversed signals since the spin and, thus, charge current flow is opposite and dominates over other THz-emission sources such as magnetic dipole radiation due to ultrafast demagnetization 33,57,58 . Because the excitation profile is nearly constant across the stacks 59 , any deviations from this behavior indicate deviations from the ideal mirror image, which can in particular arise from the interface 32, 60 and its quality 40 .
Although our simple model also well explains the reversely grown samples and they, therefore, provide values of AF and 0 very consistent with the forward-grown stacks [ Fig. 2 (a-c)], we do observe a significant change of signal amplitudes for thin AF layers ( AF < 2 nm) quantified by 1 + 0 (Tab. S1). For instance, by comparing Fig. 2(b) and Fig. 2(e), the GHz data show a reduction of 2.5 (and smaller in other pairs), whereas the THz data differ by more than a factor of 9.
However, we find more irregularities present only in the THz regime. Unlike in the GHz regime, the THz data from reversely grown samples does not only differ by thickness-independent factors from their forwardgrown counterparts, but it can also follow a non-monotonic trend, e.g. in the Pt-based trilayers [ Fig. 2(a) vs Fig. 2(d), or magnified in Fig. S4]. To test whether this might be an effect of growth-related differences in interfacial S2C, we make a linear combination of signals from the trilayer Pt|IrMn|NiFe (two interfaces present) and a control bilayer NiFe|IrMn (only F|AF interface present), shown in Fig. S4, which reasonably reproduces the non-monotonic trend from Fig. 2(d). This indicates that the signals from both interfaces changed their relative weights after reversing the growth without implying which one is more relevant, as detailed in the caption of Fig. S4.
Another striking signature of the interface impact that is manifested uniquely in the THz regime is observed at the thin limit of reversely grown Ta-based samples [ Fig. 2(f)], in which we find no polarity switching with increasing AF . Such observation is unexpected considering the typical magnitude of the S2C conversion in Ta (θ Ta ≈ −7% 41 comparing to small positive θ AF ).
Interestingly, the dramatic reduction of the S2C amplitude, the non-monotonic AF -dependence or even the change of polarity of the S2C in the thin limit of the reversed-grown series, represented by c,a , is much more profound in the THz regime. It can be understood in terms of the spin memory loss (represented by a finite size layer with spin-dependent spin-flip scattering such as a finite spin diffusion length) and spin asymmetry (represented by an infinitesimally thin layer with spin-dependent electronic scattering, i.e. with spin-dependent mean free path) introduced by one of the IrMn interfaces, as argued in Refs. 44,61,62 . The intrinsic nature of the above two processes is very different and may impact the THz and GHz experiments differently, considering their distinct λ AF . We note that the variations of c,a due to different N materials are much smaller in the thick limit than in the thin limit. This may be an indication of the prevailing role of the IrMn/N interface.
In conclusion, we have shown that the ultrafast spin injection and conversion in IrMn is operative up to ~30 THz and currently limited by the pump pulse duration and detection bandwidth. The upper bound of the spin-to-charge conversion efficiency in IrMn, ( * ) IrMn , amounts to roughly 10% of the conversion in Pt. The direct comparison of the THz to GHz regimes revealed that the characteristic length of the spin transport is 4 times larger at GHz frequencies. As the underlying mechanism, we suggest a dominating ballistic electron transport in the THz regime, compared to an electronic diffusive transport in the GHz regime mixed with an eventual magnonic contribution. We also showed that contributions of the interfaces to the spin-to-charge current conversion can be significant and even dominate the other conversion processes in the THz regime, thus making it useful in optimizing and engineering the ultrafast spintronic functionalities in antiferromagnets.
See the supplementary material for further details on the experiments.