1 Detection of long -range orbital -Hall torques Arnab Bose1 Fabian Kammerbauer1 Rahul Gupta1 Dongwook Go2 Yuriy Mokrousov12

2025-04-28 0 0 579.39KB 10 页 10玖币

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Detection of long-range orbital-Hall torques

Arnab Bose1, Fabian Kammerbauer1, Rahul Gupta1, Dongwook Go2, Yuriy Mokrousov1,2,

Gerhard Jakob1,3, Mathias Kläui1,3,4

1Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany

2Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425

Jülich, Germany

3Graduate School of Excellence Materials Science in Mainz, 55128 Mainz, Germany

4Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-

7491 Trondheim, Norway

Abstract

We report and quantify a large orbital-Hall torque generated by Nb and Ru, which we identify

from the strong dependence of torques on the ferromagnets. This is manifested as a sign-reversal and

strong enhancement in the damping-like torques measured in Nb (or Ru)/Ni bilayers as compared to Nb

(or Ru)/FeCoB bilayers. The long-range nature of orbital transport in the ferromagnet is revealed by

the thickness dependences of Ni in Nb (or Ru)/Ni bilayers which are markedly different from the regular

spin absorption in the ferromagnet that takes place within few angstroms and thus it uniquely

distinguishes the orbital Hall torque from the conventional spin Hall torque.

The nonequilibrium flow of angular momentum has been one of the key aspects of condensed

matter physics as it plays a major role in modern solid-state magnetic devices [1,2]. Nature provides two

different types of intrinsic angular momenta in a material that can be relatively easily accessible for

applications, which are: (1) orbital-momentum and (2) spin-momentum. In the past decade, the main

focus of spintronics has been to inject spin-momenta into a magnet for non-volatile memory

applications [1,2], which was triggered by the discovery of the spin-Hall effect (SHE) [3], a mechanism

that generates a transverse spin current (JSH) which can interact with the magnet directly via a spin-

transfer torque (STT) [1]. However, this scheme of strong JSH generation is mostly limited to certain

materials due to the requirement of large spin-orbit coupling (SOC) such as Pt, W etc [1]. Theory works

have predicted the generation of large orbital-Hall current (JOH) from orbital-Hall effect (OHE), not

relying on the SOC of the non-magnetic material (NM) [4–13]. However, JOH remain challenging for an

unambiguous experimental detection [14] since JOH does not interact directly with the magnetization of

commonly studied ferromagnets (FM) [7–9], unlike JSH which generates STT in a magnetic layer that

is largely independent of the FM [1]. So far, the orbital-Hall torques (OHT) have often been studied in

systems with the naturally grown oxides such as CuOx and AlOx as the non-magnetic layer [15–19], and

these oxide layers are often not well-controlled, making it difficult to compare the results with the

theoretical calculations. So, it is a prime interest to study this effect in the clean and well-defined

elements for a direct and unambiguous comparison.

While the spin-orbit torques (SOT) are essential ingredients for the memory application there

have been strong disagreements in the predicted and experimentally measured torques [1] in some

systems including the sign reversal [20–23], suggesting an important piece of physics is still missing.

By the SHE mechanism longitudinal electric current (JC) flowing along the x-direction in the heavy

metals (HM) generates the flow of spins perpendicular to it (along the z-axis, sample growth direction)

while the spins are polarized along y (Fig. 1(a)). Similarly, in certain nonmagnets it has been predicted

to have the flow of transverse orbital momenta (along the z-axis) from the JC (along the x-axis) with the

orbital quantization axis being along y [5] (Fig. 1(a), the orbital moment is normal to the drawn circles).

This is referred to as orbital-Hall current (JOH). Its advantage is that large values of JOH can be found in

abundant material uncorrelated to the SOC that could be used for practical application.

The actions of JSH and JOH are distinctly different on the FM. JSH can directly interact with the

static magnetization of the adjacent FM and thereby produces the damping-like torque (DLT) nearly

independent of the FM in the commonly studied HM/FM bilayers due to the comparable magnitude of

the spin-transparency [1]. On the other hand, JOH does not directly interact with the FM since the orbital

momentum is quenched in the equilibrium state. However, it is recently predicted that the injected JOH

can be converted into the spin-current (JOH

→

S) inside some of the FM using the SOC of the FM as

schematically shown in Fig. 1(b) and hence JOH

→

S would produce a torque on the FM, referred to as

orbital-Hall torque (OHT) [7–9]. Ni is predicted to be very efficient for OHT while Fe is quite inefficient,

suggesting a strong ferromagnet dependence as predicted in the recent theoretical [7–9] and reported in

the previous experimental work [23] and also corroborated in this work by comparing NM/Ni and

NM/Fe60Co20B20 bilayers.

Another key difference between JOH and JSH is the length scale of the angular momenta (spin

or/and orbital) transport inside the FM [9]. For example, the transverse component of the spins is

absorbed within the first few monolayers of the FM [1,24,25] whereas the JOH is predicted to be

transmitted over a long range inside the FM before it is fully converted into the spin-current (JOH

→

S) and

hence expected to result in a long-range torque effect [9]. By systematically varying the thickness of Ni

in NM/Ni bilayer we quantify the long-range torques which is an important outcome of this work and

has not been reported in previously studied systems [15,18,23,26–28]. In presence of both JOH and JSH

we can phenomenologically write the expression for the net damping-like torque () as follows:

    

  (1)

where  represents the conventional DLT as observed in the standard HM/FM bilayers in the absence

of JOH.  represents the DLT due to the JOH

→

S which is strongly FM dependent [7–9]. The term

 

  suggests the long-range action of the torques and uniquely distinguishes OHT

from the regular SHT as evident in our experiment.  is the thickness of the FM while  sets the

length scale of the long-range torques. We find that  of Ni is approximately 2.5 nm suggesting that

it takes 8-10 nm Ni-thickness to get the full strength of the OHT, nearly an order of magnitude larger

than the length scale of the conventional SHT [24,25].

While the long-range torque is the primary focus of this work, we have also explored the JOH

→

using the SOC of a HM (Pt in this case) rather than relying on the SOC of the FM by judiciously

designing the stack: NM/Pt(t)/FM/Pt(t)/cap (Fig. 1(c)). Our proposed device design eliminates the

contribution from the regular SHE due to the symmetric placement of Pt on both sides of the FM which

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1Detectionoflong-rangeorbital-HalltorquesArnabBose1,FabianKammerbauer1,RahulGupta1,DongwookGo2,YuriyMokrousov1,2,GerhardJakob1,3,MathiasKläui1,3,41InstituteofPhysics,JohannesGutenbergUniversityMainz,Staudingerweg7,55128Mainz,Germany2PeterGrünbergInstitutandInstituteforAdvancedSimulation,Forschungsze...

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1 Detection of long -range orbital -Hall torques Arnab Bose1 Fabian Kammerbauer1 Rahul Gupta1 Dongwook Go2 Yuriy Mokrousov12

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