Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten

The emerging field of orbitronics exploits the electron orbital momentum L. Compared to spin-polarized electrons, L may allow the transfer of magnetic information with considerably higher density over longer distances in more materials. However, direct experimental observation of L currents, their extended propagation lengths and their conversion into charge currents has remained challenging. Here, we optically trigger ultrafast angular-momentum transport in Ni|W|SiO2 thin-film stacks. The resulting terahertz charge-current bursts exhibit a marked delay and width that grow linearly with the W thickness. We consistently ascribe these observations to a ballistic L current from Ni through W with a giant decay length (~80 nm) and low velocity (~0.1 nm fs−1). At the W/SiO2 interface, the L flow is efficiently converted into a charge current by the inverse orbital Rashba–Edelstein effect, consistent with ab initio calculations. Our findings establish orbitronic materials with long-distance ballistic L transport as possible candidates for future ultrafast devices and an approach to discriminate Hall-like and Rashba–Edelstein-like conversion processes.


Supplementary Information
Before showing the corresponding data, we summarize briefly the content of the Supplementary Materials:  Samples on Si show qualitatively the same THz emission waveforms for Ni with Pt, W and Ti.
Most importantly, the strong change in W dynamics is also observed on Si (Fig. S1).However, the THz waveforms of Si vs glass differ in the details, which might be related to slightly changed transport times. Drude scattering times are estimated to be ≪ 50 fs for all studied samples (Figs.S2).None of the samples show any indication of a drastically different Drude scattering time compared to all other samples. Emitted THz signals are found to be linearly polarized and perpendicular to the sample magnetization (Fig. S3). Pump-polarization dependent studies (pump helicity and linear polarization direction) show a minor impact on the measured THz emission signal (Figs.S4). Ni|Ti and Ni|W samples, all fluence dependencies are to a good approximation linear with minor sublinearities (Fig. S5).Likewise, only minor changes in the THz waveform dynamics can be observed for different pumping fluences (Fig. S5). We perform THz emission measurements upon reversing the sample.Only the pure Ni film shows a dominant contribution even in sample reversal, which we ascribe to SIA or magneticdipole radiation (Fig. S6) [1,2]. For all Py-based bilayer samples, we find almost identical THz emission waveform shapes even for elevated PM thicknesses of 20 nm (Fig. S7). For Ni|Ti samples, we find almost identical THz emission dynamics to Ni|Pt (Fig. S8). Ab-initio calculations of the orbital polarization close to the W-layer surface, the estimated velocity of the orbital current and the interface concentrated C in a W film are shown in Figs.S9-S11. A comparison of purely ballistic vs purely diffusive motion for orbitally polarized wavepackets is shown in Fig. S12. Currents driven by pump-intensity gradients in thick films of Ni|W and Ni|Ti can be neglected (Fig. S13). Cu has only a minor impact on the emitted THz waveforms (Fig. S14), either as a spacer layer or as a capping layer, as confirmed by comparison to the same sample without Cu. All data in the Supplementary Materials was measured with a ZnTe(110) detection crystal (thickness 1 mm).5)|W(20) samples, which are the thickest samples measured.However, even in these samples, the pump-light gradient is minor.The calculation is based on a transfer-matrix formalism [5].Film thicknesses in nanometers are given as numerals in parentheses.Table S1.Optical and properties of all studied samples.To obtain the absorbed fluence in the FM and PM layer, we assume imaginary parts of the dielectric constants (wavelength 800 nm) of 22.07 for Ni, 9.31 for Pt, 19.41 for Ti and 19.71 for W [6].All films are additionally capped with 4 nm SiO2.In the first column, film thicknesses in nanometers are given as numerals in parentheses.

FIGURE S2 :FIGURE S3 :
FIGURE S2: THz conductivities for samples on glass.Mean complex-valued THz conductivities obtained from THz-transmission measurements for a, Ni, b, Ni|Ti, c, Ni|Pt and d, Ni|W samples.The analysis is based on a thin-film formula[3] and assumes a THz refractive index of 2.1 for glass.Film thicknesses in nanometers are given as numerals in parentheses.In all panels, the extrapolated real (blue solid line) and imaginary parts (red) of the conductivity are expected to cross at frequencies /2 ≫ 3 THz.For a Drude-like conductivity, it follows that the current relaxation time 1/ is ≪ 50 fs[4].

FIGURE S4 :
FIGURE S4: Impact of pump polarization.a, b, Circular pump polarization.THz-emission signals even (LCP+RCP) and odd (LCP−RCP) with respect to the pump helicity, i.e., left-handed (LCP) and righthanded circular polarization (RCP).The THz emission is polarized along the p-direction (panel a) and s-direction (panel b).c, d, Linear pump polarization.THz emission signals even (s+p) and odd (s−p) with respect to linear pump polarization (s-and p-polarized).The THz emission is polarized along the p-direction (panel c) and s-direction (panel d), and samples are magnetized along the sdirection.Film thicknesses in nanometers are given as numerals in parenthesis.This figure implies that the THz-emission signal does neither depend on the pump helicity (left-vs right-circular; panels a, b) nor on the linear polarization direction (s vs p; panels c, d).

FIGURE S6 :
FIGURE S5: Pump-fluence dependence.a, Fluence dependence of the THz-emission signal from Ni capped with Pt, W or Ti.The data was contracted by taking the root mean square (RMS) of the timedomain traces.b-f, Normalized THz-emission signals for different pump fluences.The different colors correspond to the fluence levels applied (25%: red, 50%: orange, 75%: cyan and 100%: blue).Film thicknesses in nanometers are given as numerals in parentheses.
FIGURE S7: THz-emission signals for Py-based samples.a, THz-emission signals from thicker Ti and W layers on Py. b, Normalized THz-emission signals of the data shown in Fig. 2a in the main text.Film thicknesses in nanometers are given as numerals in parentheses, except for the Py layers, which are always 5 nm thick.

FIGURE S8 :
FIGURE S8: Ni|Pt vs Ni|Ti.THz-emission signals from Ni|Pt vs Ni|Ti.Film thicknesses in nanometers are given as numerals in parentheses.Note the rescaling of the Ni|Pt sample waveform.

FIGURE S9 :
FIGURE S9: Ab-initio calculation of the electronic structure and texture at the surface of a W thin film.The film consists of 19 layers of W atoms in bcc(110) stacking, and is evaluated for the two topmost surface atoms.a, Electronic band structure (grey lines) together with the expectation value of for individual states.b, -space texture of ,. c, d, Same as panels a, b, respectively, but for .

FIGURE S10 :FIGURE S11 :FIGURE S12 :
FIGURE S10: Calculated orbital velocity at the Fermi surface.The orbital velocity is calculated for states at the Fermi surface for bulk W in bcc structure for different values of the Fermi energy with respect to the true Fermi energy (see Methods).The coordinate system is defined such that ∥ [001], ∥ [11 0], ∥ [110].

FIGURE S13 :
FIGURE S13: Calculated pump-intensity gradient in Ni for Ni(5)|Ti(20) and Ni(5)|W(20) samples, which are the thickest samples measured.However, even in these samples, the pump-light gradient is minor.The calculation is based on a transfer-matrix formalism[5].Film thicknesses in nanometers are given as numerals in parentheses.

FIGURE S14 :
FIGURE S14: Impact of Cu interlayers and capping layers.THz-emission signals from a, reference samples without Cu, b, samples with Cu intermediate layer and c, samples with Cu capping layer.Film thicknesses in nanometers are given as numerals in parentheses.