Voltage control of frequency eective damping and threshold current in nano-constriction-based spin Hall nano-oscillators Victor H. Gonz alez1Roman Khymyn1Himanshu Fulara2Ahmad A. Awad1and Johan Akerman1a

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Voltage control of frequency, eﬀective damping and threshold current in

nano-constriction-based spin Hall nano-oscillators

Victor H. Gonz´alez,1Roman Khymyn,1Himanshu Fulara,2Ahmad A. Awad,1and Johan ˚

Akerman1, a)

1)Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden.

2)Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667,

India

(Dated: 4 October 2022)

Using micromagnetic simulations, we study the interplay between strongly voltage-controlled magnetic

anisotropy (VCMA), ∆K=±200 kJ/m3, and gate width, w= 10–400 nm, in voltage-gated W/CoFeB/MgO

based nano-constriction spin Hall nano-oscillators. The VCMA modiﬁes the local magnetic properties such

that the magnetodynamics transitions between regimes of i) conﬁnement, ii ) tuning, and iii) separation,

with qualitatively diﬀerent behavior. We ﬁnd that the strongest tuning is achieved for gate widths of the

same size as the the constriction width, for which the eﬀective damping can be increased an order of mag-

nitude compared to its intrinsic value. As a consequence, voltage control remains eﬃcient over a very large

frequency range, and subsequent manufacturing advances could allow SHNOs to be easily integrated into

next-generation electronics for further fundamental studies and industrial applications.

Spin Hall nano-oscillators (SHNOs)1–7are miniatur-

ized ultra-broadband microwave signal generators, typi-

cally based on bilayer stacks of nonmagnetic heavy-metal

(HM) and ferromagnetic (FM) thin ﬁlms, where the spin

Hall eﬀect8–10 converts a direct longitudinal current in

the HM into a pure transverse spin current injected into

the FM, where the associated spin transfer torque11–13

can drive auto-oscillations of the local magnetization.

Nanoconstriction-based SHNOs5,14–19 have a variety of

desirable properties, such as robust RF response19, ease

of injection locking20 and mutual synchronization14,21,

making them ideal candidates for broadband signal pro-

cessing and unconventional oscillator computing, where

multi-signal injection locking has shown potential for

neuromorphic computing21–24. SHNOs are also poten-

tially appealing for oscillator network-based Ising ma-

chines to solve combinatorial optimization problems.25,26

To unlock their potential for computing, eﬀective con-

trol of the functional properties of each individual SHNO

must be implemented. While optothermal SHNO con-

trol was very recently experimentally demonstrated27, a

more established approach has been to use gates and volt-

age controlled magnetic anisotropy (VCMA) to tune the

material properties of the active region of the SHNO,

and, through this, its microwave signal properties. Back-

gating a nanogap SHNOs achieved about 4.6 MHz/V

of frequency tuning28. In nanoconstriction SHNOs, a

frequency tuning of similar order of magnitude was re-

cently demonstrated for CoFeB sandwiched between W

and MgO29, which, thanks to the interplay between the

device geometry and the VCMA, also resulted in a giant

change in the eﬀective damping and the SHNO thresh-

old current. By adding a memristive behavior to the gate

dielectric, the tuning could also be made non-volatile.30

So far, only a relatively limited tuning range has been

explored. Very recently, Choi et al, presented giant

a)Electronic mail: johan.akerman@physics.gu.se

SHNO frequency tuning of up to 2.1 GHz using VCMA

tuning in Co/Ni multilayers, with a reported a change of

the perpendicular magnetic anisotropy (PMA) as large as

28.2 kJ/m3V.31 This hence raises the question of how the

damping, threshold current, and overall auto-oscillation

behavior would behave if such strong tuning could be

achieved with narrow gates, where geometrical eﬀects

should further amplify the eﬀect.

Here, we use micromagnetic simulations to study

voltage-gated SHNOs over a very wide range of PMA

tuning (∆K=±200 kJ/m3) and probe its eﬀect on the

damping, the resonant frequency, and the excited modes

for a wide range of gate widths (w= 10–400 nm). We ﬁnd

a broad range of tunability for both frequency and damp-

ing due to changes in mode localization both depending

on voltage and gate width. Our results demonstrate the

versatility of VCMA in SHNOs and suggest new phe-

nomena, not yet seen in experiments, which could be

employed in the eﬃcient design of purpose-built devices

for low-power electronics and unconventional computing

applications.

IDC

Bext

150 nm

FIG. 1. Schematic of the simulated voltage-controlled

W(5 nm)/CoFeB(1.7 nm)/MgO(2 nm) SHNO.

arXiv:2210.01042v1 [cond-mat.mes-hall] 3 Oct 2022

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Voltagecontroloffrequency,eectivedampingandthresholdcurrentinnano-constriction-basedspinHallnano-oscillatorsVictorH.Gonzalez,1RomanKhymyn,1HimanshuFulara,2AhmadA.Awad,1andJohanAkerman1,a)1)PhysicsDepartment,UniversityofGothenburg,41296Gothenburg,Sweden.2)DepartmentofPhysics,IndianInstituteofTechn...

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Voltage control of frequency eective damping and threshold current in nano-constriction-based spin Hall nano-oscillators Victor H. Gonz alez1Roman Khymyn1Himanshu Fulara2Ahmad A. Awad1and Johan Akerman1a

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