# Spatial Mapping of Torques within a Spin Hall Nano-oscillator

###### Abstract

Time-resolved scanning Kerr microscopy (TRSKM) was used to study the precessional magnetization dynamics induced by a microwave current within a AlO/Py(5 nm)/Pt(6 nm)/Au(150 nm) spin Hall nano-oscillator structure. The Au layer was patterned so as to form two needle-shaped electrical contacts that concentrated the current in the centre of a Py/Pt mesa of 4 m diameter. Due to the spin Hall effect, the current passing through the Pt layer generates a spin current that propagates into the Py layer, exerting a spin transfer torque (STT). By injecting an RF current, and exploiting the phase-sensitivity of TRSKM and the symmetry of the device structure, the STT and the torques due to the in-plane and out-of-plane components of the Oersted field have been separated and spatially mapped. TRSKM senses the magnetization directly and is able to probe the torques within measurement configurations for which the magnetoresistive response vanishes. The STT and the torque due to the in-plane Oersted field are found to be reduced at the centre of the device. While local heating might be expected to suppress the current density, a proportionately larger reduction of the STT suggests an additional suppression of the injected spin current. Knowledge of the local torques is essential for understanding the conditions under which auto-oscillations can be induced.

Spin torque oscillators (STOs)Chen et al. (2016) are nanoscale magnetoresistive devices of great promise for use in microwave assisted magnetic recording Shiroishi et al. (2009), microwave frequency telecommunications Chumak et al. (2015), and neuromorphic computing Grollier et al. (2016). Injection of DC current generates spin transfer torque (STT) that excites precessional oscillations of the constituent magnetic moments. The magnetoresistance (MR) therefore leads to an oscillatory voltage across the device. Within spin Hall nano-oscillator (SHNO) devices, charge current is first converted into a pure spin current, by means of the spin Hall effect (SHE) Kato et al. (2004); Hirsch (1999); Jungwirth et al. (2012); Hoffmann (2013), which then exerts STT upon the active magnetic layer. Decoupling of spin and charge currents provides additional freedom in device design, in the choice of the magnetic materials used Ranjbar et al. (2014); Dürrenfeld et al. (2015); Mazraati et al. (2016); Zahedinejad et al. (2018) (including electrical insulators Hamadeh et al. (2014)) and the precessional modes excited Dvornik et al. (2018). If the charge current flows parallel to the plane, without a top contact obscuring the active region, then optical techniques can probe the magnetization dynamics directly Demidov et al. (2012); Awad et al. (2016). However it is expected that the spatial current distribution is highly non-uniform, and that thermal effects may modify both the current distribution and the torques Liu et al. (2013); Demidov et al. (2014); Ulrichs et al. (2014). Knowledge of the Oersted torque and STT is critical for understanding the conditions under which auto-oscillations may be excited, and until now it has not been possible to probe their spatial distribution directly.

STT-ferromagnetic resonance (STT-FMR) is widely used to characterise spintronic devices. RF current is injected to excite the magnetisation, and mixes with the oscillatory MR response to generate a DC mixing voltage , which is recorded as the applied magnetic field or the frequency of the current is varied. Analysis of the resonance field, or frequency, and linewidth allows the torques acting upon the magnetization to be determinedSkinner et al. (2014); Tulapurkar et al. (2005); Kalarickal et al. (2006); Sankey et al. (2008); Kubota et al. (2008); Liu et al. (2011); Brataas et al. (2012); Dumas et al. (2014). However, vanishes for certain magnetic field configurations due to the symmetry of the MR mechanism, and represents a spatial average of magnetization dynamics that may in fact be highly inhomogeneous.

In the present study, time resolved scanning Kerr microscopy (TRSKM) is used to determine the torques generated by an RF current injected into an SHNO. The SHNO is formed on an extended magnetic disk, with the current and STT concentrated within a small central region. The spatial variation of both the STT and Oersted torques was mapped and found to diverge strongly, and by different amounts, from that expected for the current distribution calculated in the absence of Joule heating.

The SHNO devices shown in Figure 1 were fabricated on sapphire substrates by a combination of sputtering and electron-beam lithography Dürrenfeld et al. (2015). Triangular Au(150 nm) nano-contacts (NCs) with a tip separation of = 140 - 240 nm were defined on a 4 m diameter Py(5 nm)/Pt(6 nm) bi-layer disk. Current from the gold NCs is concentrated within a small region of the Pt layer between the tips, and generates a spin current, by means of the SHE, that flows into the Py layer beneath. The injected spin polarization lies parallel to the +ve direction along a horizontal line through the middle of the disk, Emori et al. (2013) and exerts a STT on the Py magnetization. The charge current also generates an Oersted field with both in and out of plane components. The distributions of the electric current and Oersted field plotted in figure 1 were calculated using COMSOL COM () . The STT amplitude is expected to have similar spatial distribution to the charge current within the Pt, while the Oersted field has a more complex structure that depends upon the current distribution in both the Pt and Au layers.

Conventional STT-FMR measurements were made by applying audio frequency modulation to the RF current injected through the the capacitative arm of a bias-tee, while was measured through the inductive arm using a lock-in amplifier. The out-of-plane component of the dynamic magnetization was also detected directly by means of TRSKM that has been described in detail elsewhere Keatley et al. (2017).

Both the dynamic magnetization and can be calculated in the macrospin limit. The equation of motion for the magnetization of a thin film driven by an external field and STT is

(1) |

where m̂ is the normalized magnetization vector, is the gyromagnetic ratio, is the Gilbert damping constant, is the injected spin polarisation, and and are the amplitudes of the “in-plane” or “anti-damping” STT, and the “out-of-plane” or ”field-like” STT respectively. A large in-plane torque is expected due to the SHE. However, since the Py layer is relatively thick and the current is shunted through the Pt layer, negligible torque is expected due to the Rashba. is the total effective field acting upon the magnetization, which may be written as , where is the static applied field, is the out of plane demagnetizing field, and h is the local Oersted field generated by the RF current. Other anisotropy fields are expected to be small and so have been neglected.

Equation (1) can be linearised to describe small amplitude precession, with the out of plane magnetization component written as where represents the phase of the RF current and is the complex amplitude. and the real and imaginary parts of have the forms

(2) |

(3) |

(4) |

where

(5) |

, and are the frequency and amplitude of the RF current, is the angle between and , and and represent effective fields, where the subscripts indicate the direction in which the associated torque acts. Finally, the linewidth , and the FMR frequency . is the change in electrical resistance when the magnetisation is rotated from orthogonal to parallel to the current, and has value of 0.03 Dürrenfeld ().

The above expressions yield at different positions within the SHNO when the observed dynamical magnetization is a response to local torques. This is a reasonable assumption when spin waves excited due to spatially varying STT and Oersted torques are similar in frequency. Dispersion due to dipolar interactions decreases with film thickness. For the 5 nm Py film, the frequency splitting, of the uniform mode and a spin wave with wavelength equal to the diameter of the disk, is no more than and lies within the measured linewidth.

The stroboscopic nature of TRSKM requires that measurements are made at an RF frequency that is a multiple of the laser repetition rate as and hence are varied. From equations (3 )and (4), the expressions for and are seen to contain a minimum in the the denominator at the resonance field, and terms in the numerator that are either slowly varying or antisymmetric (due to the factor ) about the resonance field. Hence both expressions consist of parts that are symmetric and antisymmetric about the resonance field. The microwave phase may be chosen in the experiment, so that is a weighted sum of and , and so also appears as a sum of symmetric and antisymmetric terms. TRSKM measures the polar Kerr rotation that may be written as where the constant is of order 0.1 mdeg cm emu. If the value of is known then, by recording the dependence of upon for a number of values of , and fitting to equations (3), (4) and (5), the values and can be determined at each position within the sample.

Conventional STT-FMR was first performed to obtain , as shown in figure 2a. The optical probe was then positioned at the centre of the disk, between the NC tips, and the polar Kerr signal recorded at three values of RF phase as a function of field, as shown in figure 2b. Both optical and electrical resonance curves are a superposition of components that are either symmetric or antisymmetric about the resonance field. The data, which does not depend upon , was fitted to equations (2) and (5), yielding values of Oe and Oe, while values of MHz/Oe, and Oe were found to best describe both the and optical data within the present studySup (). The relatively large value of has been attributed to spin pumping effects Liu et al. (2013). Since the average out-of-plane Oersted field is small due to the symmetry of the NCs, the large value of results from the anti-damping torque. From equation (5), if , has value of 12.1 Oe compared to 10.2 Oe calculated by COMSOL at the centre of the disk.

Due to the symmetry of the device, one may reasonably assume Sup () that the ratio determined from the optical measurements in figure 2b should be the same as that determined by fitting . Fixing this ratio and fitting the optical resonance curves then yields values for , that have been used to label each curve. The three phase values were found to be offset set by the same amount from the values set on the microwave synthesizer Sup (), justifying the assumed value of . The fitting also yields an estimate of , but his is less reliable because the areas sampled by the electrical and optical measurements are different, as will be discussed further.

The dependence of optical and electrical signal strength upon is shown in Figure 2c. Maximum optical signal amplitude is observed for , due to the sin factor in equation (5). In contrast vanishes for and , and is insensitive to the dynamics when . Finally, polar Kerr images are plotted in figure 2d for different values of . Due to the symmetry of the current distribution about a vertical line though the centre of the device, , and hence are expected to be symmetric about this centre line. On the other hand is antisymmetric so that has mixed symmetry. If terms in are neglected in equations (3) and (4), then at resonance, when , is symmetric about the centre line, while has mixed symmetry. Therefore, the most symmetric image is expected to occur for . The most striking feature of the images is the minimum observed between the tips of the NCs, which is unexpected from the calculations in Figure 1.

To further explore the spatial symmetry of the magnetic response, and hence the underlying torques, the field dependence of the polar Kerr rotation was measured at different points on a horizontal line through the middle of the disk, for values of , 85 and 130. The extracted values of and are plotted as a function of position in figure 3a. The field values obtained for the three values of are in good agreement confirming that the absolute phase has been determined correctly.

Since negligible out-of-plane STT is expected, should be proportional to and hence spatially symmetric. However, should contain both symmetric and antisymmetric components, (denoted as and ) due to the in-plane STT and respectively. These components can be separated by calculating the mirror image (reflection about ) of the data, calculating the sum and difference of the original data with its mirror image, and then dividing both by a factor of two. Both components are plotted in figure 3(b), together with convolutions of the Oersted field and current distributions of Figure 1 with a Gaussian function of 870 nm half maximum width (denoted Proc()Sup ()), to account for the finite size of the focused optical spot. In extracting field quantities from the experimental data, a value of = 0.3 mdeg cm emu was assumed so that the Oersted fields towards the edge of the disk were in agreement with those from Figure 1. However, the experimental and curves are seen to exhibit a minimum at m, in strong disagreement with the calculated curves.

As explained above, for and , time resolved images acquired at resonance reveal the spatial variation of and respectively. A similar procedure to that applied to the line scan in figure 3(b) was used to extract the symmetric and antisymmetric parts of the image acquired at . The resulting images of , and are plotted next to calculated images of , , and in Figure 3(d). Each calculated distribution has been convolved with a 2D Gaussian function of 870 nm half maximum diameter. The form of the and images are in reasonable agreement. However the and images possess a maximum at the centre of the disk, whereas the and images exhibit a minimum. The convolution with the spot profile takes into account the fact that the NCs partly obscure the underlying Py/Pt bilayer, so that the minimum corresponds to a reduction of the in-plane STT and the torque due to the in-plane Oersted field. Numerical simulations have shown that the temperature at the centre may increase by about for 20 mA of applied current Ulrichs et al. (2014). However, parameters such as thermal boundary resistance, for which values are not well known, can have a large effect upon the calculated temperature change, which could therefore be significantly larger. The resonance field appeared unchanged at the centre of the disk, compared to the surrounding area, suggesting minimal reduction of the Py magnetization. However both the spin Hall effect in Pt and the spin transparency of the Pt/Py interface may decrease with increasing temperature. Whatever the origin, the reduction of the in-plane STT at the centre of the SHNO will impact the critical value of the DC current required to induce auto-oscillations and influence the confinement of the resulting bullet mode.

In summary, it has been shown that TRSKM can be used to probe the local FMR driven by a combination of STT and Oersted field torques, and comparison has been made with a simple theory. By directly probing the local magnetization, this technique can be applied to magnetic materials or experimental configurations that exhibit weak MR response. Furthermore the phase and spatial symmetry of the different torques allows them to be separated and mapped. Unexpected minima of the in-plane STT and in-plane Oersted field torque at the centre of the device are most likely due to local heating that causes a reduction of the current density. However, the proportionately larger reduction of the STT suggests a further suppression of the injected spin current. Understanding the spatial distribution of the torques in spintronic devices provides greater insight into the physical processes that underlie their operation and is essential for optimising their performance.

###### Acknowledgements.

We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom, via the EPSRC Centre for Doctoral Training in Metamaterials (Grant No. EP/L015331/1), and grants EP/I038470/1 and EPSRC EP/P008550/1.## References

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