Ultrafast THz emission spectroscopy of spin currents in the metamagnet FeRh Open Access

There has been considerable interest recently in establishing viable platforms for the ultrafast generation and detection of spin current through spin–charge interconversion. Notable examples of such platforms are heterostructures of ferromagnetic (FM) and noble metal (NM) materials in which the dynamics of spin current can, in principle, be probed using coherent time-domain THz emission spectroscopy.^1–6 When pumped by an ultrafast laser pulse, the FM layer, with its magnetization pointing in-plane, launches a spin current transverse to its magnetization direction. As the spin current propagates across the FM/NM interface, strong spin–orbit coupling in the NM layer converts it into a transient charge current via the inverse spin Hall effect (ISHE)^1–5 or the Rashba–Edelstein effect.⁶ 

In the case of ISHE, $jc⃗(z)=γ(2e/ℏ)[js⃗(z)×σ⃗]$⁠,⁷ where j_s and j_c denote the induced spin current and charge current, γ is the spin Hall angle, and $σ⃗$ is the spin direction. The lifetime of this transient charge current is on the order of a few ps, which results in a radiation spectrum with frequencies in the 0.1 to 10 THz range. This method of generating THz relies on the strong spin–orbit coupling strength of the adjacent NM capping layer. Although ISHE has been observed in -ferromagnets such as permalloy (Py) and yttrium iron garnet (YIG) through the spin Seebeck effect or spin pumping,^7,8 the study of THz generation from a single FM metal thin layer (without any adjacent NM layer) by ISHE remains quite limited⁹ and often results in very small THz emission.⁶ FM metals with large intrinsic spin–orbit coupling (SOC) can have a transverse charge current converted from a laser-induced spin current. This approach to measure spin currents through THz generation can also be extended to antiferromagnetic (AFM) metals with large spin–orbit coupling, in which large spin Hall effects (comparable to those of Pt) have been shown.^10–12 

FeRh is a metal which undergoes a first-order metamagnetic phase transition from antiferromagnet (AFM) to ferromagnetic ordering (FM) above room temperature, with an accompanying lattice expansion of about 1%.^13,14 Depending on the thickness of the FeRh film, chemical composition, and local strain, the transition temperature can vary by tens of Kelvin.^15–18 This metamagnetic transition makes FeRh a promising candidate for understanding coupled lattice and spin dynamics at ultrashort time scales. Seminal pump–probe and magneto-optical Kerr (MOKE) experiments have shown that laser pulses can induce FM domains in the AFM phase of FeRh within sub-picoseconds.^19,20 Later, several experimental and theoretical studies investigated the mechanism behind this transition from AFM to FM order.^21–24 Recent work using time-resolved photo-electron momentum microscopy suggests that a change in the electronic structure causes this first-order transition,²⁵ while another study using MOKE in high magnetic fields suggests that the magnetization formation and a structural change take place simultaneously.²⁶ 

Regardless of the mechanism of the transition from the AFM to the FM phase, the large SOC in FeRh allows for an investigation of light-induced spin currents and THz generation via ISHE in both the AFM and FM phases in a single material. THz emission from FeRh based heterostructures was recently reported by Seifert et al. at temperatures above the phase transition.² This THz emission decreases at a lower temperature but shows a lack of temperature hysteresis that is distinct from a SQUID magnetic moment measurement.²⁷ Li et al. further inspected the observed absence of temperature hysteresis and attributed it to the expansion of FM domains inside FeRh after photo-excitation.²⁸ In another recent study,³³ THz emission was observed in FeRh capped with gold using a double pump scheme. The study suggests that there is an intrinsic latency between laser-induced heating and emergent ferromagnetic order. Similarly, Awari et al.⁹ demonstrated that optical pump-THz emission can be a good probe for ultrafast magnetization dynamics in bare FeRh. Despite these studies, the origin of the THz emission in bare FeRh and whether the AFM phase of FeRh can host light-induced spin currents are not fully clear.

In this paper, we use ultrafast THz emission spectroscopy across a broad temperature range to study the dynamics of THz emission from a bare FeRh thin film in both the FM and AFM phases. We excite an epitaxial FeRh film grown on a MgO substrate with an ultrafast infrared pump, which transiently demagnetizes the sample and generates THz pulses. By examining the sample orientation and pump polarization dependence of the emitted THz, we attribute the ISHE to be the dominant contributor to THz emission in the FM and AFM phases of bare FeRh. THz emission spectroscopy in this fashion serves as a contact-less probe of the spin current in FeRh.

Epitaxial FeRh samples are grown using magnetron co-sputtering of FeRh from elemental targets on an (100) MgO substrate. First, the MgO substrate is pre-annealed in situ for 1 h at a temperature of 850 °C to ensure that the substrate is clean and dry. Then, the 15 nm FeRh film is co-sputtered at 450 °C. We sputter with a nominal composition of ∼47.5% Fe and 52.5% Rh, optimized to produce a robust metamagnetic transition in the FeRh. Finally, the film is annealed for 1 h at 650 °C to relax the film strain and allow the FeRh to develop a nicely ordered crystal structure. The sample is allowed to cool overnight in situ before use.

Figure 1(a) shows a schematic of the THz emission spectroscopy setup. When illuminated by a 1030 nm ultrashort optical pulse, the MgO/FeRh sample emits bursts of THz radiation, which we measure in the far-field using standard time-domain electro-optic sampling (EOS). The sample is kept in a closed-cycle helium optical cryostat under zero external magnetic field and is excited by linearly polarized laser pulses (a duration of 160 fs, a center wavelength of 1030 nm, and a fluence of 0.1–0.5 mJ/cm²). The IR pump is obtained from an Yb:KGW amplifier (PHAROS—Light Conversion) and is normally incident from either side of the sample (the beam diameter at the sample is 2 mm FWHM). The emitted THz field is collected by an off-axis parabolic mirror and focused onto a 0.5 mm thick CdTe(110) crystal. The THz electric field as a function of time is determined by EOS using a balanced detection scheme. Note that CdTe(110) has the same structure as the electro-optic crystal GaP but with a larger linear electro-optic coefficient.²⁹ As such, CdTe(110) has been used to measure the THz electric field using EOS in a variety of studies with a laser wavelength of 1030 nm.^30,31

Figure 1(b) shows the emitted THz field from a 15 nm FeRh thin film as a function of EOS time at room temperature in the absence of a magnetic field. The FeRh is in the FM phase (the metamagnetic transition point is estimated to be 285 K for our sample) and magnetized before the experiment. Blue and pink traces represent the THz emission when the sample is excited from the FeRh side (blue trace) and from the MgO substrate side (pink trace). When the pump is incident from the MgO side, a single-cycle THz pulse is produced with a negative maximum. When the sample is inverted about the magnetization axis, the generated waveform has the same shape but a reversed sign and a slightly larger magnitude, following the same behavior as observed in other NM/FM bilayer systems.^1,2 This observation implies that the dominant THz emission mechanism in bare FeRh is of an electric dipole nature instead of a magnetic dipole nature, as the latter should remain unchanged when flipping the sample and should be much smaller in magnitude than the electric counterpart.^28,32 However, we do notice a small difference in the amplitude of the THz emission before and after flipping the sample. This can be an indication of the co-existence of electric and magnetic dipole radiation, with electric dipole radiation being the dominant mechanism. Figure 1(c) shows the sample orientation dependence of the measured THz signal. As illustrated in the figure, we define 0° as when the FeRh magnetization is aligned parallel to the (1$1̄0$⁠) axis of the CdTe crystal. By making an in-plane rotation of the FeRh sample, we observe that the EO signal flips sign when the sample is rotated by 180° and reaches its maximum again after a full-cycle of rotation. The cosine dependence of the EO signal implies that the polarization of the emitted THz field is always perpendicular to the magnetization direction. We keep the sample orientation at 0° and pump from the FeRh side to achieve an optimal signal level for the rest of this study. Pump polarization-dependent THz emission in Fig. 1(d) shows that in the FM phase (300 K), near the metamagnetic transition point (240 K), and in the AFM phase (5 K), the FeRh THz emission strength is independent of the pump polarization. Both the sample orientation and pump polarization results show key features of the ISHE mechanism: the polarization of the emitted THz field from bare FeRh is always normal to the magnetization direction and independent of the pump polarization, as illustrated in Fig. 1(d). The pump fluence dependent study is also performed, as shown in Fig. 1(e). At room temperature, the strength of the THz field from the FeRh thin film scales linearly with pump fluence, in contrast to the quadratic dependence observed in Pt capped FM-order FeRh as reported in the previous study.² No saturation is observed up to the highest pump fluence of 0.5 mJ/cm²in our experiment.

To investigate spin dynamics in FeRh for both AFM and FM magnetic ordering, we first examined THz emission across a range of sample temperatures under zero external magnetic fields [Fig. 2(a)]. At room temperature, the emitted THz field strength is on the order of a few V/cm for a pump fluence of ∼0.4 mJ/cm². The strength of the THz field is found to decrease linearly as the temperature decreases [Fig. 2(c)]. Such an effect is in agreement with previous studies^21,33,34 in which AFM domains inside FeRh start to nucleate and expand during the first-order phase transition, leading to a drop in the net magnetization of the film. Below 285 K, we observed a sharp decrease in the emitted THz field strength, consistent with the onset of AFM order in bulk FeRh.

The corresponding charge current that leads to the THz emission can be derived by using the electric dipole approximation and integrating the measured THz field over time. The charge current follows the same temperature dependence as the THz field, which starts to quench around room temperature and suddenly reaches a small non-zero value for all temperatures below 285 K, i.e., in the AFM phase [Fig. 2(b)]. In the AFM phase, the emitted THz field is much smaller than that in the FM state. As shown in the inset of Figs. 2(a) and 2(b), the THz waveform and the associated transient current in the AFM state coincide with those in the FM state for the first picosecond of the emission. However, for later times, the transient current in the AFM state is out of phase with that in the FM state. This can be an indication of more than one THz emission mechanism in FeRh.^35,36 To make this trend clearer, we plot the integrated THz field strength as a function of temperature in Fig. 2(c). A clear hysteresis can be seen between the zero-field cooling (blue curve) and zero-field heating (red curve), with a temperature difference of about 20 K. Considering the low fluence of our pump pulse (∼0.4 mJ/cm ²), the photoexcitation is not strong enough to induce significant nucleation of FM domains inside the FeRh bulk. Hence, the observation of temperature hysteresis is in agreement with previous studies.⁹ 

In contrast to previous studies of THz emission in FeRh/Pt bilayers,^2,28 none of the bare FeRh samples we studied here show a complete quenching of THz emission at low temperatures. One possible mechanism for the non-vanishing THz emission at low temperatures is collinear magnetic difference frequency generation (DFG), a phenomenon observed in bare AFM insulators possessing zero magnetization, such as (111) oriented NiO.^37,38 A distinguishing feature of THz emission by magnetic DFG is a strong dependence on the pump polarization, attributed to the unequal nonlinear susceptibility tensor components at different pump polarizations. Yet, as shown in Fig. 1(c), the emitted THz field in bare FeRh is independent of pump polarization at all temperatures, which rules out magnetic DFG as the source of THz emission. Possible THz emission mechanisms obeying the same symmetry properties as we observe are the anomalous Nernst effect (ANE), anomalous Hall effect (AHE), and ISHE. The ANE accounts for a transient spin-polarized charge current induced by a sub-picosecond electron temperature gradient, which is commonly seen in a FM thin film.^35,39 The AHE accounts for the conversion of laser-induced longitudinal charge current to a transient transverse current, which generates THz emission and is observed at a FM/dielectric interface.⁴⁰ Previous THz emission studies have shown that it is challenging to disentangle the contribution from ANE, AHE, and ISHE, as all three mechanisms have the same symmetry properties for THz emission.³⁵ However, according to theory calculations,³⁶ both the AHE and ANE are expected to be suppressed once the FeRh is cooled down below the transition temperature, while the spin-Hall conductivity should remain non-zero and flip sign. Therefore, we rule out AHE and ANE as the THz emission mechanisms for the AFM phase of FeRh. As shown in the inset of Figs. 2(a) and 2(b), both the THz waveform and transient charge current change shape across the transition temperature. The THz field flips the sign after 0 ps, while the transient charge current flips the sign after 1 ps as the FeRh goes across the transition temperature. This observation can be explained by a shift in the weight of contributions from the three mechanisms. In the FM phase, ANE, AHE, and ISHE all contribute to the THz emission, while in the AFM phase, only ISHE contributes to the THz emission. At last, we exclude the possibility of a thermally induced AFM-FM phase transition at temperatures far below the transition temperature. The critical fluence required to drive the phase transition at a temperature 15 K below the transition temperature is ten times larger than the fluence used in our experiment^9,19,41 and should be larger at even lower temperatures.

We note that epitaxial FeRh grown on a MgO substrate has been known to exhibit a narrow FM layer at the substrate interface that persists well into the AFM phase.^16,18,42,43 Several groups have reported that a combination of strain and Fe deficiency leads to the formation of a few nm thick FM layers at the MgO–FeRh interface, even 80 K below the transition temperature.^{16,18,42–45} Based on this, one possibility for the temperature-independent THz emission below the transition temperature is the demagnetization of residual FM FeRh domains near the MgO substrate and the following spin-to-charge current conversion inside FeRh through ISHE. In this case, the ultra-fast IR pump demagnetizes the FM layer, creating a thermal gradient along the propagation direction. The combined effect of laser demagnetization and the spin Seebeck effect launches a spin current into the FeRh bulk within hundreds of fs, which is converted into a transient charge current via ISHE.^5,46,47 This interpretation is consistent with previous SQUID measurements⁴⁸ and the symmetry properties of our THz emission data.

The spin Hall angle of FeRh is taken from measurements done by Gibbons et al.⁵¹ Here, a DC-biased spin-torque ferromagnetic resonance (FMR) measurement on FeRh indicates that the FeRh samples have a surprisingly large spin Hall angle γ, and the spin direction in most of the samples is aligned with the magnetization direction. The value of γ is determined from the results measured between 170 and 300 K and extrapolated to a broader temperature range [Fig. 3(e)]. γ is measured to be 0.85 ± 0.3 for the AFM state of FeRh at 170 K and assumed to be constant at lower temperatures. Across the phase transition point, γ decreases by ∼3.5 times and decreases further with increasing temperature. The behavior of γ with temperature is roughly linear. Such a result is in agreement with a spin-torque FMR experiment done on the FM/AFM domains of FeRh,⁵² in which the product of γλ_rel is measured to be 0.7 nm for the AFM state and 0.3 nm for the FM state. In pure metals, the spin relaxation length λ_rel is limited by impurity and phonon scattering.⁵³ Studies of the noble metals Pt and Au show that λ_rel is qualitatively higher at low temperatures⁵⁴ and remains in the same order between 170 and 300 K. Therefore, we assume that λ_rel ∼ 1 nm for the above derivation.

By combining the above measured quantities, we can extract the light-induced spin current generated from a 15 nm FeRh thin film, as shown in Fig. 3(f). It is worth mentioning that we are overestimating the spin current in the FM phase of FeRh because our current model ignores the AHE and ANE contributions to the THz emission. In the AFM phase, the estimation is more accurate, and a small, temperature independent spin current is observed. This corresponds to the THz generated from the residual FM layer at the FeRh/MgO interface. The spin current undergoes a drastic enhancement across the phase transition point, becoming more pronounced and temperature dependent in the FM state due to a larger net magnetization of the bulk. Our study shows that the AFM state of FeRh, which exhibits no net magnetization, can still carry spin current, likely generated from the residual FM layer at the MgO–FeRh interface, and has a large SOC for the ISHE to occur to convert the spin current to a charge current. A possible future test for our hypothesis of the role of the residual FM later would consist of performing a systematic investigation of THz emission from FeRh grown on different substrates. Such future studies can help elucidate the origin of the spin current generation in the AFM phase of FeRh.

In summary, we performed temperature-dependent THz emission and time-domain THz spectroscopy in ferromagnetic and antiferromagnetic FeRh. We measured THz generation from bare FeRh thin film with no noble metal capping layer and extracted the light-induced spin current, j_s, for FeRh in both the AFM and the FM phases. Our findings provide insights into the ISHE mechanism inside magnetic materials, showing that for materials with strong spin–orbit coupling, the spin-to-charge current conversion can take place inside the FM layer and does not necessarily need a NM layer. This suggests that a careful evaluation of the ISHE process is needed for future studies of NM/FM THz emitters. Our findings and methods establish THz emission as a contact-less probe of spin current and spin current generation efficiency in magnetic materials. This method can be extended to study spin dynamics in more exotic condensed matter systems such as SC/FM heterostructures, hybrid magnon systems, and quantum spin liquids, which are otherwise hard to probe by conventional spectroscopic techniques.

We thank Barry Bradlyn, Matthew Gilbert, and David Cahill for fruitful discussions.

This study was performed as part of the Illinois Materials Research Science and Engineering Center, supported by the National Science Foundation MRSEC program under NSF Award No. DMR-1720633.

Y. L. and F. M. acknowledge the support from the NSF Career Award No. DMR-2144256 (data analysis and manuscript preparation).

The preparation of the FeRh samples was supported as part of Quantum Materials for Energy Efficient Neuromorphic Computing (Q-MEEN-C), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award No. DE-SC 0019273.

The authors have no conflicts to disclose.

Yinchuan Lv: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Soho Shim: Formal analysis (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). Jonathan Gibbons: Formal analysis (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). Axel Hoffmann: Formal analysis (equal); Funding acquisition (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). Nadya Mason: Formal analysis (equal); Funding acquisition (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). Fahad Mahmood: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.