Temperature dependent inverse spin Hall effect in Co/Pt spintronic emitters

Femtosecond laser excitation of ferromagnet/non-magnetic heavy metal bilayers yields surprisingly intense emission of THz radiation, despite their nanometer thickness.^1–3 It has been argued that this emission results from the combination of ultrafast demagnetization and the inverse spin Hall effect (ISHE). Specifically, laser excitation induces a subpicosecond quenching of magnetization in the ferromagnetic layer through the formation of a superdiffusive spin current $js$⁠, arising due to a larger mobility and lifetime of hot majority spins.^4–7 In the heavy metal, hot electrons of opposite spin undergo spatial deflection in opposite directions at a mean tangent $θsH≡ρsH/ρ$⁠, called the spin Hall angle, with $ρsH$ the spin Hall resistivity of the heavy metal and ρ its longitudinal resistivity. The heavy metal thereby acts as a spin-charge transducer, converting the injected pulsed spin current $js$ into a charge current $jc=θsHjs×m̂$⁠, with $m̂=M/M$ the magnetization direction. The pulsed charge current emits an electric pulse (⁠$ETHz$⁠) polarized perpendicularly to the initial in-plane magnetization of the sample. Due to the short timescale of demagnetization (⁠$0.2 ps$⁠), the spectral content of the emitted pulse lies in the THz band. In terms of the spin current density, the emission amplitude reads (see the supplementary material)

whereas the bracketed factor (which includes the resistivity of the full bilayer of thickness d) is nearly temperature independent of a bilayer of two similar metals, the THz emission amplitude may inherit a substantial temperature dependence from the remaining two quantities: the laser-induced pulsed spin current density $js$ supplied by the ferromagnet, and the spin Hall resistivity⁸ $ρsH=θsHρ$ of the heavy metal.

The temperature dependence of $ρsH$ (or $θsH$⁠) differs depending on the microscopic origin of the ISHE. The particular dependence can be ascribed either to spin-dependent scattering events (extrinsic origin), or to a geometric correction to the electron velocity arising from spin Berry curvature (intrinsic origin).^9,10 The temperature dependence of the spin current density $js$⁠, on the other hand, is set by the degree of demagnetization $ΔM/M0$ of the ferromagnet. Previous studies reported that the amplitude and timescale of demagnetization may depend on temperature when the ferromagnet is in proximity to a magnetic phase transition.^11–15 In this work, we use cobalt as a spin source because of its large Curie temperature (⁠$TC=1388 K$ in bulk¹⁶) meaning that below room temperature, the system is far from any magnetic transition. We show that the thermal variation in this case is not set by the spin source (Co), which exhibits temperature independent magnetization and demagnetization dynamics, but instead by the spin Hall resistivity of our chosen transduction layer (Pt).

A Co(⁠$10 nm$⁠)/Pt(⁠$3 nm$⁠) bilayer is deposited by dc magnetron sputtering at room temperature onto a glass substrate that is transparent to THz radiation. A small Ar deposition pressure (⁠$3 mTorr$⁠) leads to a low degree of interface roughness¹⁷ and a Pt residual resistivity (⁠$T→0$⁠) of $ρ0=29.4 μΩ cm$⁠. The experimental THz time-domain emission spectroscopy setup is depicted in Fig. 1. Subpicosecond laser pulses (central wavelength $1.2 μm$⁠, repetition rate $frep=1 kHz$⁠) are used to demagnetize the Co layer. The emitted pulse is collected by a parabolic mirror, focused, and detected with electro-optic sampling in a $0.5 mm$ thick $ZnTe$ crystal cut along the (110) crystallographic direction. Complementary measurements of the magnetization and ultrafast dynamics of demagnetization are obtained via the time-resolved Faraday effect. Electronic transport measurements are carried out on a $3 nm$ thick Pt film, deposited under the same conditions as the Co/Pt sample. These measurements are performed in a four-point van der Pauw geometry, sourcing a low frequency (⁠$17 Hz$⁠) $100 μA$ current and measuring the resulting voltage drop with a lock-in amplifier.

The peak amplitude (⁠$Ep$⁠) of the emitted pulse is measured in a temperature range of $10–280 K$⁠, as shown in Fig. 2. The pulse shape is constant with temperature, making $Ep$ an unambiguous measure of the emission amplitude. We observe a reduction of emission amplitude as the sample is cooled, eventually reaching a plateau at roughly $70 K$⁠. This decrease in $Ep$ is at striking variance with the temperature behavior of THz emitters based on optical rectification, such as $ZnTe$ and $LiNbO3$⁠, wherein lower temperatures reduce phonon reabsorption and enhance the emission amplitude.^18,19 The same is true for photoswitches made of $InSb$ or $GaAs$⁠, for which higher mobility at lower temperatures also contributes to enhanced THz emission.²⁰ 

To probe whether the observed temperature dependence of $Ep$ is due to variations in the excited spin current density $js$⁠, we measure the temperature dependence of the magneto-optical Faraday effect. In the presence of magnetization, this causes a static rotation (⁠$θF$⁠) of the probe pulse polarization plane [Fig. 3(a)], which is proportional to the total magnetization. We observe that the magnetization is independent of temperature in the $10–280 K$ range. The laser-induced change in rotation (⁠$ΔθF/θF$⁠) arising from demagnetization is presented in Fig. 3(b). For the various initial sample temperatures, we extract the degree of demagnetization. We see no significant temperature dependence of the demagnetization amplitude. These observations point to $ρsH$⁠, instead of j_s, as the origin of the temperature dependent THz emission amplitude.

The spin Hall resistivity $ρsH=θsHρPt$ is a measure of the magnitude of the ISHE for a system with longitudinal resistivity $ρPt$⁠. It is therefore necessary to consider the temperature dependence of the Pt resistivity. For this, we deposit a $3 nm$ Pt film on a glass substrate separately and measure the longitudinal resistivity as a function of temperature. We note that $ρsH$ and $ρPt$ both concern the static limit (⁠$ω→0$⁠), whereas the currents excited in the sample are transient. However, since interaction and scattering times are much shorter than the current dynamics $ω/2π≈1 THz$⁠, a quasi-static regime can be assumed (see the supplementary material). The measured resistivity $ρPt(T)$ of the bare Pt film decreases linearly from room temperature down to $30 K$⁠, below which a slight recovery occurs [Fig. 4(b)]. Additionally, we measure the temperature dependence of the resistivity of the Co/Pt bilayer, and note that the ratio $ρCo|Pt/ρPt$ is approximately constant to within $4%$ across the temperature range.

It is clear that $ρPt$ plays a central role in the temperature dependence of $Ep$⁠, a connection which requires consideration of the microscopic origin of spin Hall resistivity, $ρsH=σsHρPt2$⁠. The residual resistivity of the bare Pt film is $ρPt,0=29.4 μΩ cm$⁠, placing it at the boundary of two spin Hall regimes: the dominant contribution to the spin Hall resistivity arises, in one case, intrinsically from the band structure; in the other, from extrinsic skew (Mott) impurity scattering.²¹ The intrinsic effect occurs due to mixing of spin states near lifted degeneracies of the spin–orbit coupled band structure. This results in a finite spin Berry curvature $Ωσ,k$ that modifies the semiclassical electron velocity by an amount $−k×Ωσ,k$⁠.²² Thus, accumulation of transverse velocity takes place during propagation rather than during scattering events. Consequently, the intrinsic spin Hall conductivity $σsHint$ does not depend on the scattering rate, so that $ρSHint=σsHintρPt2$⁠. On the other hand, skew scattering is a relativistic effect in which electron spin–orbit coupled to an impurity experiences an effective magnetic field gradient in the scattering plane. This results in a net force toward, or away, from the scattering center depending on its spin angular momentum⁹ [Fig. 4(a)]. The skew scattering contribution to the spin Hall conductivity $σsHss=αss/ρPt,0$ relates inversely to the residual resistivity, with $αss$ the skew scattering angle. Furthermore, since skew scattering is impurity dependent, it is $ρPt,0$⁠, not $ρPt$⁠, that is the relevant resistivity. The spin Hall resistivity contribution therefore takes the form $ρsHss=σsHssρPt,02=αssρPt,0$⁠. From the above considerations, a temperature scaling of the total spin Hall resistivity has been motivated experimentally²³ and theoretically²⁴ to take the form

In Fig. 4, we display the quantity $(ρCo|Pt/ρPt)−1Ep∝ρsH$ as a function of $ρPt2$⁠. Comparing with Eq. (2), it is clear that the observed temperature dependence follows from the presence of a substantial intrinsic contribution to the spin Hall effect. A spin Hall effect of predominantly intrinsic origin is consistently observed for Pt in experiment^8,25 and is expected from relativistic band structure calculations.²⁶ 

While an approximately $ρPt2$-linear correlation is maintained across most of the temperature range, an unexpected amplitude recovery occurs below $T≈70 K$⁠. This is at variance with Eq. (2) and warrants discussion. One possible explanation is a rise in the spin current relaxation length at low temperatures. The decay of $js$ along the thickness of Pt yields a smaller effective spin current density $js∗≤js$ undergoing spin–charge conversion, resulting in reduced emission. However, assuming that this relaxation length is close to the spin diffusion length (⁠$λsd≈8 nm$⁠),²⁷ it is significantly longer than the thickness of our Pt film (⁠$dPt=3 nm$⁠). As such, variations in $λsd$ would have a negligible impact on $Ep$ (see the supplementary material). A more likely scenario is that the intrinsic spin Hall conductivity $σsHint$ has a temperature dependence, as predicted by Guo et al.²⁶ using first-principles relativistic band calculations for Pt. In this scenario, the Berry curvature results from the competition of two bands with contributions of opposite sign, one of which is unoccupied at T = 0. As the temperature is raised, the population of this band begins to reduce the net Berry curvature, thus decreasing the spin Hall conductivity. A similar temperature dependent competition between opposing sources of emergent magnetic field has been proposed recently for ultrathin $SrRuO3$⁠.²⁸ 

Using a combination of time-domain THz emission spectroscopy, transport measurements, and magneto-optics in a cryogenic setup, we demonstrate that the temperature response of the Co/Pt spintronic emitter is dictated by the spin Hall physics of Pt, the intrinsic origin of which leads to a proportionality between the emission amplitude and the squared resistivity of Pt. Our results highlight the relevance of cryogenic THz emission spectroscopy to the study of spin–charge conversion processes in spintronic emitters.

See the supplementary material for a discussion on Eq. (1), the effect of spin relaxation, and the assumption of the quasi-static limit.

This work was supported by The Netherlands Organization for Scientific Research (NWO/OCW) as part of the VIDI programme and by the European Research Council under the European Unions Horizon 2020 programme/ERC Grant Agreements No. 677458, and the project Quantox of QuantERA ERA-NET Cofund in Quantum Technologies. Work at UCSD was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0018237.