France



In the field of magnetism and spintronics chiral magnetic structures, such as spin spirals, chiral domain walls and skyrmions [1-2], are intensively investigated due to their fascinating properties such as potentially enhanced stability and efficient spin-orbit torque driven dynamics [3-4]. It has been shown that these structures are stabilized by the Dzyaloshinskii-Moriya interaction (DMI) that favours a chiral winding of the magnetisation. While the investigation of static structures and slow (ns) dynamics of chiral magnetic structures has been intensified recently, experimental studies addressing the ultimate fs-ps dynamics of the chirality have been elusive so far as ultrafast pump-probe experiments have so far concentrated on the collinear order in magnetic systems [5-7].&lt;br/&gt; &lt;br/&gt;In this work we employ circularly polarized light pulses from an XUV free-electron laser and investigate time-resolved the evolution of the chiral order of domain walls in magnetic thin film samples by an IR pump - X-ray magnetic scattering (XRMS) probe experiment (Fig. 1a) [8].&lt;br/&gt;Using samples with interfacial DMI and perpendicular magnetic anisotropy exhibiting labyrinth-like domain patterns (Fig. 1b), we measure in the same experiment both the (CL+CR) sum signal (Fig. 1d) corresponding to the ferromagnetic order in the domains (average collinear domain magnetisation m&lt;sub&gt;z&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;+m&lt;sub&gt;x&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;) and the difference signal (CL-CR) (Fig. 1e) corresponding to the average chiral order in the domain walls (chiral order correlator m&lt;sub&gt;z &lt;/sub&gt;m&lt;sub&gt;x&lt;/sub&gt;).&lt;br/&gt; &lt;br/&gt;In contrast to the (CL+CR) signal, phase information is preserved in the dichroic signal (CL-CR) allowing to determine the domain wall chirality (left/right-handed) and character (Bloch (helical), Néel (cycloidal)) [9-10]. Fig. 1f shows the orthoradial profile of the dichroic signal, which indeed confirms the prevalence of fully right-handed Néel-type domain walls [9-10]. This provides a tool to individually probe the time resolved dynamics of the chiral magnetic order in the domain walls [8].&lt;br/&gt; &lt;br/&gt;In a next step we investigated the time evolution of the scattering signals upon IR laser excitation. The key step is the comparison of the collinear ferromagnetic order dynamics and the chiral order dynamics. To ascertain both, we calculated the average intensity for the sum and the difference signal as a function of the wavevector Q&lt;sub&gt;r&lt;/sub&gt; for different time delays. With this the numerical integration of the radial profiles for each time delay leads to the data shown in Fig. 2a, which demonstrates the evolution of the total intensity of the sum and the difference signal as a function of delay time normalized to the unpumped total intensity. The data shown in Fig. 2b is the result of a second experimental run.&lt;br/&gt; &lt;br/&gt;We find an ultrafast intensity decrease of both signals in the sub-ps regime with similar time constants. However, a significantly faster recovery of the chiral signal in the sub-ns timescale is observed [8].&lt;br/&gt; &lt;br/&gt;In order to explain the key finding of the experimentally observed faster recovery of the chiral signal after laser excitation we can envisage two different mechanisms: (1) a change in the size ratio between domain walls and domains caused by an increase of the domain wall width during the whole investigated time frame or (2) a faster recovery dynamics of the chiral order within the domain walls compared to the ferromagnetic order in the domains leading to a faster build-up of the chiral magnetisation [8].&lt;br/&gt; &lt;br/&gt;We subsequently investigate the origin of the faster recovery of the chiral signal by performing numerical simulations of the scattering signal, which reproduce the experimental findings. We conclude from these that the main driver behind our experimental findings is likely mechanism (2) leading to a faster recovery of the chiral order in the domain walls in comparison to the ferromagnetic order in the domains.&lt;br/&gt; &lt;br/&gt;In the future further fundamental aspects will be studied in detail e.g. the dependence of the timescales of the chiral order build-up on the absolute strength of the DMI by varying the heavy metal layers. The better control of the DMI and the chirality of spin structures on the ultrafast timescale can finally allow for the controlled ultrafast manipulation of chiral magnetism, e.g. ultrafast writing of chiral topological objects such as skyrmions and pave the path to applications in the field of ultrafast chiral spintronics.

**References:**

[1] Jiang, W. J. et al. &lt;i&gt;Phys. Rev. &lt;/i&gt;704, 1–49 (2017).&lt;br/&gt;[2] Everschor-Sitte, K., Masell, J., Reeve, R. M. &amp; Kläui, M. &lt;i&gt;J. Appl. Phys.&lt;/i&gt; 124, 240901 (2018).&lt;br/&gt;[3] Fert, A., Cros, V. &amp; Sampaio, J. &lt;i&gt;Nat. Nanotech.&lt;/i&gt; 8, 152–156 (2013).&lt;br/&gt;[4] Woo, S. et al. &lt;i&gt;Nat. Mater&lt;/i&gt;. 15, 501–506 (2016).&lt;br/&gt;[5] Koopmans, B. et al. &lt;i&gt;Nat. Mater.&lt;/i&gt; 9, 259–265 (2010).&lt;br/&gt;[6] Battiato, M., Carva, K., &amp; Oppeneer, P. M. &lt;i&gt;Phys. Rev. Lett.&lt;/i&gt; 105, 027203 (2010).&lt;br/&gt;[7] Pfau, B. et al. &lt;i&gt;Nat. Commun.&lt;/i&gt; 3, 1100 (2012).&lt;br/&gt;[8] Kerber, N. et al. &lt;i&gt;Nat. Commun.&lt;/i&gt; 11, 6304 (2020).&lt;br/&gt;[9] Zhang, S. L. et al. &lt;i&gt;Phys. Rev. B&lt;/i&gt; 96, 094401 (2017).&lt;br/&gt;[10] Chauleau, J.-Y. et al. &lt;i&gt;Phys. Rev. Lett.&lt;/i&gt; 120, 037202 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0a6311ce5b2275e4d9718738f6370d87.jpg)
Figure 1: Experimental setup and diffraction images. (a) Measurement geometry: A magnetic thin film sample is pumped by an optical infrared laser pulse and probed by a circularly polarized X-ray FEL pulse. Afterwards an IR-protected CCD detector records the magnetic SAXS pattern. (b) MFM image of a typical labyrinth domain pattern of the [Ta(5.3 nm)/Co&lt;sub&gt;20&lt;/sub&gt;Fe&lt;sub&gt;60&lt;/sub&gt;B&lt;sub&gt;20&lt;/sub&gt;(0.93 nm)/Ta(0.08 nm)/MgO(2.0 nm)]&lt;sub&gt;x20&lt;/sub&gt;/Ta(1.6 nm) sample. (d) The resulting sum = CL+CR of the diffraction pattern confirms that the diffraction corresponds to the magnetic domains observed by MFM. (&lt;i&gt;e&lt;/i&gt;) The dichroic scattering signal = CL-CR and its azimuthal dependence (f) confirms the presence of (c) right-handed chiral Néel (cycloidal) domain walls [8].

![](https://assets.underline.io/uploads/markdown_image/1/image/6eaf4721a65ec4df5813cb74ec270cf9.jpg)
Figure 2: Time dependence of total scattering intensities and second moments. Time evolution of the (a,b) radially integrated intensity from two different experimental runs and (c,d) the 2&lt;sup&gt;nd&lt;/sup&gt; moments of the sum signal (ferromagnetic order) and the difference signal (chiral magnetic order) from the scan shown in (a). The solid lines in (c,d) provide a guide to the eye [8].

INTERMAG 2021

 Faster chiral versus collinear magnetic order recovery after optical excitation revealed by femtosecond XUV scattering INVITED

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In the field of magnetism and spintronics chiral magnetic structures, such as spin spirals, chiral domain walls and skyrmions [1-2], are intensively investigated due to their fascinating properties such as potentially enhanced stability and efficient spin-orbit torque driven dynamics [3-4]. It has been shown that these structures are stabilized by the Dzyaloshinskii-Moriya interaction (DMI) that favours a chiral winding of the magnetisation. While the investigation of static structures and slow (ns) dynamics of chiral magnetic structures has been intensified recently, experimental studies addressing the ultimate fs-ps dynamics of the chirality have been elusive so far as ultrafast pump-probe experiments have so far concentrated on the collinear order in magnetic systems [5-7]. In this work we employ circularly polarized light pulses from an XUV free-electron laser and investigate time-resolved the evolution of the chiral order of domain walls in magnetic thin film samples by an IR pump - X-ray magnetic scattering (XRMS) probe experiment (Fig. 1a) [8]. Using samples with interfacial DMI and perpendicular magnetic anisotropy exhibiting labyrinth-like domain patterns (Fig. 1b), we measure in the same experiment both the (CL+CR) sum signal (Fig. 1d) corresponding to the ferromagnetic order in the domains (average collinear domain magnetisation mz2+mx2) and the difference signal (CL-CR) (Fig. 1e) corresponding to the average chiral order in the domain walls (chiral order correlator mz mx). In contrast to the (CL+CR) signal, phase information is preserved in the dichroic signal (CL-CR) allowing to determine the domain wall chirality (left/right-handed) and character (Bloch (helical), Néel (cycloidal)) [9-10]. Fig. 1f shows the orthoradial profile of the dichroic signal, which indeed confirms the prevalence of fully right-handed Néel-type domain walls [9-10]. This provides a tool to individually probe the time resolved dynamics of the chiral magnetic order in the domain walls [8]. In a next step we investigated the time evolution of the scattering signals upon IR laser excitation. The key step is the comparison of the collinear ferromagnetic order dynamics and the chiral order dynamics. To ascertain both, we calculated the average intensity for the sum and the difference signal as a function of the wavevector Qr for different time delays. With this the numerical integration of the radial profiles for each time delay leads to the data shown in Fig. 2a, which demonstrates the evolution of the total intensity of the sum and the difference signal as a function of delay time normalized to the unpumped total intensity. The data shown in Fig. 2b is the result of a second experimental run. We find an ultrafast intensity decrease of both signals in the sub-ps regime with similar time constants. However, a significantly faster recovery of the chiral signal in the sub-ns timescale is observed [8]. In order to explain the key finding of the experimentally observed faster recovery of the chiral signal after laser excitation we can envisage two different mechanisms: (1) a change in the size ratio between domain walls and domains caused by an increase of the domain wall width during the whole investigated time frame or (2) a faster recovery dynamics of the chiral order within the domain walls compared to the ferromagnetic order in the domains leading to a faster build-up of the chiral magnetisation [8]. We subsequently investigate the origin of the faster recovery of the chiral signal by performing numerical simulations of the scattering signal, which reproduce the experimental findings. We conclude from these that the main driver behind our experimental findings is likely mechanism (2) leading to a faster recovery of the chiral order in the domain walls in comparison to the ferromagnetic order in the domains. In the future further fundamental aspects will be studied in detail e.g. the dependence of the timescales of the chiral order build-up on the absolute strength of the DMI by varying the heavy metal layers. The better control of the DMI and the chirality of spin structures on the ultrafast timescale can finally allow for the controlled ultrafast manipulation of chiral magnetism, e.g. ultrafast writing of chiral topological objects such as skyrmions and pave the path to applications in the field of ultrafast chiral spintronics.

**References:**

[1] Jiang, W. J. et al. Phys. Rev. 704, 1–49 (2017). [2] Everschor-Sitte, K., Masell, J., Reeve, R. M. & Kläui, M. J. Appl. Phys. 124, 240901 (2018). [3] Fert, A., Cros, V. & Sampaio, J. Nat. Nanotech. 8, 152–156 (2013). [4] Woo, S. et al. Nat. Mater. 15, 501–506 (2016). [5] Koopmans, B. et al. Nat. Mater. 9, 259–265 (2010). [6] Battiato, M., Carva, K., & Oppeneer, P. M. Phys. Rev. Lett. 105, 027203 (2010). [7] Pfau, B. et al. Nat. Commun. 3, 1100 (2012). [8] Kerber, N. et al. Nat. Commun. 11, 6304 (2020). [9] Zhang, S. L. et al. Phys. Rev. B 96, 094401 (2017). [10] Chauleau, J.-Y. et al. Phys. Rev. Lett. 120, 037202 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0a6311ce5b2275e4d9718738f6370d87.jpg)
Figure 1: Experimental setup and diffraction images. (a) Measurement geometry: A magnetic thin film sample is pumped by an optical infrared laser pulse and probed by a circularly polarized X-ray FEL pulse. Afterwards an IR-protected CCD detector records the magnetic SAXS pattern. (b) MFM image of a typical labyrinth domain pattern of the [Ta(5.3 nm)/Co20Fe60B20(0.93 nm)/Ta(0.08 nm)/MgO(2.0 nm)]x20/Ta(1.6 nm) sample. (d) The resulting sum = CL+CR of the diffraction pattern confirms that the diffraction corresponds to the magnetic domains observed by MFM. (e) The dichroic scattering signal = CL-CR and its azimuthal dependence (f) confirms the presence of (c) right-handed chiral Néel (cycloidal) domain walls [8].

![](https://assets.underline.io/uploads/markdown_image/1/image/6eaf4721a65ec4df5813cb74ec270cf9.jpg)
Figure 2: Time dependence of total scattering intensities and second moments. Time evolution of the (a,b) radially integrated intensity from two different experimental runs and (c,d) the 2nd moments of the sum signal (ferromagnetic order) and the difference signal (chiral magnetic order) from the scan shown in (a). The solid lines in (c,d) provide a guide to the eye [8].

technical paper

The ability to generate and control pulses of terahertz (THz) radiation has revolutionised a multitude of critical technologies, from medical imaging [1] to the detection of explosives [2]. Furthermore, sub-picosecond pulses of THz radiation have future application in the ultrafast control of electron spin states [3] and picosecond magnetisation switching in ferromagnets [4], ferrimagnets [5] and antiferromagnets [6]. To exploit the full potential of THz technology, broadband emitters are required which can generate radiation over a spectral range of 1-10 THz [7]. Spintronic emitters, consisting of ferromagnetic (FM)/non-magnetic (NM) heavy metal thin films, have been shown to produce THz pulses with large electric field amplitudes and gapless bandwidths of up to 30 THz [8]. This THz emission is produced when the spintronic structure is excited by femtosecond laser pulses, demonstrating their potential as low-cost sources of broadband radiation. Whilst it has been well established that particular combinations of FM/NM materials, such as Co20Fe60B20/Pt, produce pulses of THz radiation with high electric field amplitudes (300 kV/cm) [8], a detailed understanding of the role that material properties contribute to the generation process of THz radiation has yet to be fully explored in order to inform the future design of optimum performance spintronic emitters. In particular, post deposition annealing of CoFeB based structures has been shown to enhance the emission of THz radiation by up to a factor of 3 [9,10] further increasing the potential utility of these emitters. This enhanced electrical field amplitude has been attributed to two possible effects: 1) diffusion of Boron into the heavy metal layer, leading to an increased number of scattering centres and a reduced hot electron relaxation length, λNM [9]; or 2) local crystallisation of CoFeB leading to an increase in mean free path of hot electrons travelling through the FM layer [9,10]. In order to explore the electric field enhancement, we present a systematic study which investigates the effects of inducing defects in the NM layer and crystallisation of the FM/NM interface upon the emission of THz radiation from Co20Fe60B20 (2.5 nm)/Pt (3 nm) spintronic thin films. The films have been grown onto fused silica substrates using magnetron sputtering where the base pressure was better than 5 x10-8 Torr. We present results from two series of films. In the first series, the dc sputtering power for Pt was varied between 25 W and 100 W in order to control defects in the Pt layer [11]. In the second series, the films were annealed post deposition between 200°C and 400°C to induce crystallisation at the CoFeB/Pt interface. For all films, the Co20Fe60B20 layer was sputtered at 100 W dc power to enable direct comparison. The structural properties of Co20Fe60B20/Pt films were characterised via X-ray diffraction (Fig. 1a) and atomic force microscopy (Fig. 1b-e), from which the crystalline ordering and the surface roughness of the Pt were observed to change with varying sputtering power (series 1) and annealing temperature (series 2). X-ray reflectivity analysis of Co20Fe60B20/Pt films (series 2) shows a decrease in density of the Pt layer and increase in interfacial roughness of the CoFeB layer, indicating diffusion at the CoFeB/Pt interface with post deposition annealing above 200°C. We have used terahertz time-domain spectroscopy to measure the electric field amplitude of the emitted THz pulses from Co20Fe60B20/Pt films (see Fig. 2). Initial analysis shows that interfacial interdiffusion has a significant influence on the THz electric field amplitude. A full analysis of our results will be presented at the conference.

**References:**

[1] R. M. Woodward et. al., J.Biol.Phys. 29, 257 (2003); [2] K. Kawase et. al., Opt. Express 11, 2549 (2003); [3] S. Baierl et. al., Nat. Photonics 10, 715 (2016); [4] D. Polley et. al., J. Phys. D: Appl. Phys. 51, 084001 (2018); [5] S. Wienholdt et. al. Phys. Rev. Let. 108, 247207 (2012); [6] T. Kampfrath et. al., Nat. Photonics 5, 31 (2001); [7] M. T. Hibberd et. al., Appl. Phys. Let. 114, 031101 (2019); [8] T. Seifert et. al., Nat. Photonics 10, 483 (2016); [9] Y. Sasaki et. al., J. Phys. Soc. Jpn. 111, 102401 (2017); [10] Y. Gao et. al., IRMMW-THz Paris, France, 1-3 (2019) DOI: 10.1109/IRMMW-THz.2019.8874416; [11] S. Mahieu et. al. Thin Solid Films 515, 1229 (2006).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e1893bb8b173d49ae6661079e92079f8.jpg)
Fig. 1: Structural analysis of Co20Fe60B20 (2.5 nm)/Pt (3 nm) thin films deposited onto fused silica substrates. (a) X-ray diffraction spectra for Co20Fe60B20/Pt films with increasing Pt sputtering power (series 1 = pink - 25 W, and green - 50 W) and annealing temperature (series 2 = black - unannealed, red - Tann = 300°C and blue - Tann = 400°C). (b)-(e) Atomic force microscopy images of (series 2) b) unannealed Co20Fe60B20/Pt film, and films annealed at c) Tann = 200°C, d) Tann = 300°C and e) Tann = 400°C. RMS roughness observed to increase with annealing temperature from 0.81 nm (unannealed) to 2.06 nm (Tann = 400°C).

![](https://assets.underline.io/uploads/markdown_image/1/image/848c3f049ddc56bf9bbf0df330871380.jpg)
Fig. 2: Example of THz pulses generated from FS-CoFeB/Pt and FS-Pt/CoFeB thin films (capped with MgO), measured using terahertz time-domain spectroscopy. Inset shows the corresponding frequency spectrum for the FS-CoFeB/Pt thin film.

 Emission of THz Radiation from Co20Fe60B20/Pt Spintronic Thin Films with Varying Microstructural Properties

In recent years, magnon-phonon coupling has attracted renewed interest[1] both from the physics and technological perspectives owing to its efficient conversion of energy between magnon and phonon. In particular, the magneto-acoustic resonance, has become a focal point, partly owing to the possibility for rapid switching, which is significant for applications in cloud storage, advanced spin memory, logic, and other spintronic devices. An ultrafast optical approach, specifically femtosecond laser pulses, is a powerful tool to initiate the coupling and its successive detection. The laser pulse simultaneously generates the phonon and magnon, through thermal expansion and fast demagnetization. The thermal expansion produces a local strain or phonon, whose frequency is tunable by both the material composition and geometry. At the same time, the fast demagnetization excites the magnetization out of equilibrium and creates magnons. The femtosecond time scale of the laser pulse benefits the detection of both magnon and phonon, as their dynamics endure longer than the pulse time scale. However, research reported in the literature mostly launch strain electrically in piezoelectric materials, which leads to a different phonon propagation direction. In addition, the literature study of the coupling is confined to materials unsuitable for spintronic applications. These materials, limit the resonance frequency or require low temperature for the magnetoacoustic resonance. To date, direct demonstration of magnon-phonon coupling remains elusive in materials with high perpendicular magnetic anisotropy, which are capable of achieving ultrahigh frequency resonance at room temperature. Here, we report an extremely high frequency magnetoacoustic resonance up to 60 GHz, originating from magnon-phonon coupling in [Co/Pd]n multilayer with perpendicular magnetic anisotropy. Our theory uncovers the physics of resonance in a coupled system, and is based on the equation of motion for both magnon and phonon, with coupling introduced in the Hamiltonian through the magnetostrictive energy. Owing to the magnon and phonon possessing the same symmetry, the physics at resonance presents an enhanced wave envelope in the time domain, an anticrossing in the frequency domain, and significant hybridization of both magnons and phonons. When the frequencies of magnon and phonon approach each other in the resonance regime, these two modes hybridize into a quasiparticle contributed by both magnon and phonon. This hybridization generates an anticrossing in the dispersion with a frequency gap Δf in Fig. (a), which is quantitatively determined by the coupling coefficient in our model and consistent with our experiment. The amplitudes of both modes increase in the hybridization regime in Fig. (b): the original phonon mode is now highly visible owing to the admixed magnon, the original magnon mode is enhanced owing to the pumping from phonons. In addition, the resonance in the time domain (an enhanced wave envelope) indicates the strain substantially influences the spin dynamics at an ultrafast picosecond time scale. All these physical features are demonstrated in both ultrafast optical measurements and micromagnetic simulations. The ultrafast optical measurements [3] of the time-resolved magneto-optical Kerr effect (TR-MOKE) and time-domain thermoreflectance (TDTR) directly observe the dynamics of magnon and phonon. The frequency and the amplitude of TR-MOKE and TDTR signals are consistent with the modeling, which indicates the transition of the system from hybridization to de-hybridization, controlled by the external applied field. The simulations apply the properties of the [Co/Pd]n multilayers, whose structures are optimized to achieve a maximum resonance frequency allowable with current experimental settings. All the [Co/Pd]n multilayers samples were prepared in an ultra-high vacuum magnetron sputtering system. With an appropriate strain, the simulation predicts that the system is able to undergo a large-angle magnetization precession and achieve a rapid switching. In summary, our work demonstrates an efficient energy transfer among magnon and phonon at an ultrafast picosecond scale, which paves a potential pathway for enabling an ultrahigh speed strain-assisted magnetization switching in a technologically relevant magnetic system.

**References:**

[1] A. Kirilyuk, A. V. Kimel, T. Rasing, Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731–2784 (2010). [2] D.-L. Zhang, J. Zhu, T. Qu, D. M. Lattery, R. H. Victora, X. Wang, J.-P. Wang, High frequency magnetoacoustic resonance through strain-spin coupling in perpendicular magnetic multilayers. Sci. Adv. 6, eabb4607 (2020) [3] D. B. Huang, D. Lattery, X. Wang, Materials Engineering Enabled by Time-Resolved Magneto-Optical Kerr Effect for Spintronic Applications, ACS Appl. Electron. Mater., 2020 (appears online).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/da1d7a3d7e4d08d14d19d9c77f1710f1.jpg)
The frequency of the [Co(0.8 nm)/Pd(1.5 nm)]11 multilayers as a function of Hext. Two frequencies of spin precession (mode 1, open black circles; mode 2, open red diamonds) are derived by fitting the experimental data of TR-MOKE. The figure also includes the frequency of acoustic waves measured from TDTR (blue stars). The anticrossing point of mode 1 and mode 2 occur at the resonance field (Hext ≈ 21 kOe), where the frequencies of modes 1 and 2 split and open a gap Δf. We assign the strain mode as the one with field-independent frequencies that are nearly identical to the acoustic wave frequencies from TDTR. The frequency of the FMR mode increases linearly with Hext.

![](https://assets.underline.io/uploads/markdown_image/1/image/33d75b34edaa03dce17f237aff203cd9.jpg)
The individual Mz amplitudes of modes 1 and 2 as a function of Hext for the [Co(0.8nm)/Pd(1.5nm)]11 multilayers. There exists an apparent amplification of both modes due to the coupling between these two modes near the anticrossing point. (Figure is taken from Ref. 2.)

 High-frequency magnetoacoustic resonance through strain-spin coupling in perpendicular magnetic multilayers INVITED

We study coupling of electromagnetic waves to an antiferromagnetic resonance at THz frequencies [1,2]. In ferromagnetic materials, the Purcell effect and magnon-polaritons were shown [3], allowing single magnon detection [4] or observation of level attraction due to dissipative coupling [5]. Antiferromagnetic materials, in contrast to ferromagnets, are interesting due to their high-frequency dynamics, while they are still characterized by low coupling of spins to the lattice. For applicational reasons their abundance, huge number of existing materials and lack of stray fields are also advantages. However, in the case of antiferromagnets, there are only a few examples of an indirect strong coupling of spin waves with electromagnetic waves [6, 7] or at GHz frequencies [8]. Here, we report a direct and strong magnon-phonon coupling in high-temperature antiferromagnet hematite α-Fe2O3. A cube of hematite (0.2 mm edge length) was placed inside a gold-plated tube (2 mm long, 0.58 mm internal diameter). This cavity has the lowest mode at about 0.24 THz, as predicted by electrodynamic simulations. The cavity was placed inside a double-cone holder that allowed focusing THz beam into the cavity and collecting the transmitted THz beam form it. We measured transmission spectra in the 0.2-0.3 THz frequency band using a continuous wave spectrometer based on extenders to a vector network analyser. This system is characterized by very high dynamic range and very high frequency resolution. We used temperature as a tuning parameter, because the frequency of the antiferromagnetic resonance in hematite rises monotically with it from room temperature until about 700 K. Our data (Fig. 1) show very clear avoided crossing of the cavity mode and the antiferromagnetic resonance with the minimum splitting of about 6 GHz and the cooperativity factor of about 40. The splitting predicted by a microscopic model [3] is about 15 GHz. The difference is caused by imperfect matching of the cavity magnetic field with the magnetic moment of the antiferromagnetic resonance in the cube, that is confirmed by elecrodynamic simulations. We notice that we can tune the coupling between the experimental setup and the cavity that results in different lineshapes of the cavity mode. We fitted observed spectra with a model based on the input-output theory [3]. We also observed coupling with higher order modes of the cavity that is not as clear as with the lowest mode. We acknowledged support by the Sino-Swiss Science and Technology Cooperation (SSSTC) grant no. EG-CN_02_032019, EPFL and the SNF R'Equip under Grant No. 206021_144983.

**References:**

[1] M. Bialek, J. Zhang, H. Yu et al, arXiv:2012.10910 [2] D. L. Mills and E. Burstein, Rep. Prog. Phys. 37, 817 (1974). [3] H. Huebl, Ch. W. Zollitsch, J. Lotze et al, Phys. Rev. Lett. 111, 127003 (2013). [4] D. Lachance-Quirion, S. P. Wolski, Y. Tabuchi et al, Science 367, 425 (2020). [5] M. Harder, Y. Yang, B. M. Yao et al, Phys. Rev. Lett. 121, 137203 (2018). [6] X. Li, M. Bamba, N. Yuan et al, Science 361, 794 (2018). [7] P. Sivarajah, A. Steinbacher, B. Dastrup et al, J. Appl. Phys. 125, 213103 (2019). [8] J. R. Everts, G. G. G. King, N. J. Lambert et al, Physical Review B 101, 214414 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/803040ba5ac649ea7e6e3374d83e2c49.jpg)
(a) Normalized transmission spectra at different temperatures. (b) Normalized transmission spectra in a form of map.

 Strong coupling of antiferromagnetic resonance with sub-THz cavity fields

The phenomena of interlayer exchange coupling (JIEC) between thin ferromagnetic (FM) layers allows materials with precisely tailored properties to be created, and is key to the future development of spintronics. Synthetic ferromagnets (SFMs) have the same FM/Non-magnetic(NM)/FM structure as the widely studied Synthetic Antiferromagnet (SAF) [1], but describe the case where the magnetisation of the two FM layers are aligned in parallel. The structure of a SFM and its resonant dynamics is shown in Fig.1a. It is known that the formation of a double resonance consisting of an Acoustic Mode (AM) and an Optic Mode (OM) requires a difference in layer magnetisation (MDiff) and a FM JIEC [2] [3]. However, to date, a comprehensive description of the resonant properties as a function of JIEC and difference in layer magnetisation has not been reported despite their widespread use in quasi-static devices [4]. Here, we investigate, both experimentally and via numerical simulations, the hitherto uncharted dependence of the observed double resonance on MDiff and JIEC [5]. The samples were fabricated using magnetron sputtering and characterized by X-ray Reflectivity (XRR) to measure layer thickness, vector Vibrating Sample Magnetometry (VSM) to verify AF coupling and a Vector Network Analyser – Ferromagnetic Resonance (VNA-FMR) setup which allows fundamental dynamic properties to be explored. These SFMs exhibited a JIEC consistent with coupling on the 1st FM RKKY coupling peak and have structure Ta(2 nm)/CoFeB(5 nm)/Ru(tRu)/CoFeB(5 nm)/Pt(4 nm) where tRu is the thickness of the ruthenium layer, acting as the non-magnetic spacer layer. Our simulations, performed using MuMax3, show that MDiff and JIEC have orthogonal dependencies on the two resonant modes. We further demonstrate that the conventional understanding of the phases of these modes, described as possessing an in-phase or out-of-phase nature for the AM and OM respectively, does not capture fully the intricacy of the resonant dynamics. Comparison between experimental and simulated data allows MDiff, JIEC and the resonant phases of each mode to be accurately determined. These findings are directly applicable to the creation of tailored SFMs for spintronic devices with applications in STT/SOT-MRAM where control of these parameters is paramount [3] [6].

**References:**

[1] H. J. Waring, N. A. B. Johansson, I. J. Vera-Marun et al., Zero-field Optic Mode beyond 20 GHz in a Synthetic Antiferromagnet, Phys. Rev. Appl., Vol. 13, p. 034035 (2020) [2] B. Heinrich and J. F. Cochran, Ultrathin metallic magnetic films: magnetic anisotropies and exchange interactions, Adv. Phys., Vol. 42, p. 523–639 (1993) [3] T. McKinnon, P. Omelchenko, B. Heinrich et al., FMR study of interlayer exchange coupling in FeCoB|Ta|FeCoB trilayers with in-plane anisotropy, J. Appl. Phys., Vol. 123, p.223903 (2018) [4] T. Devolder, E. Liu, J. Swerts et al., Ferromagnetic resonance study of composite Co/Ni - FeCoB free layers with perpendicular anisotropy, Appl. Phys. Lett., Vol. 109, p.142408 (2016) [5] H. J. Waring, Y. Li, I. J. Vera-Marun et al. Phys. Rev. Lett., Manuscript In Preparation. [6] S. Yakata, H. Kubota, T. Seki et al., Enhancement of thermal stability using ferromagnetically coupled synthetic free layers in MgO-based magnetic tunnel junctions, IEEE Trans. Magn., Vol. 46, p. 2232–2235 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b5294be2ca537e2a7cb2e6695213d4ce.jpg)
Fig.1 a) The resonant dynamics of a synthetic ferromagnetic (SFM) system with a ferromagnetic (FM1)/non-magnetic (NM)/FM2 structure and a FM interlayer exchange coupling JIEC. An optic mode is seen in addition to the acoustic mode only in cases where the layer magnetization of FM1 (Ms,1) and FM2 (Ms,2) are different. b) 2D map of the resonant spectra of a SFM when the NM spacer layer, consisting of Ru, thickness tRu = 1.10nm.

 Characterizing Interlayer Coupling in Synthetic Ferromagnetic Thin Films

The Y3Fe5O12 (YIG) ferrimagnetic insulator is recognized as a model system for spintronic and magnonic phenomena, including spin pumping, spin Seebeck, proximity effects, and spin wave propagation. In these materials, the spin current is produced by spin-waves or magnons. Magnons can be electrically excited and sensed via the Spin Hall Effect (SHE) and Anomalous Spin Hall Effect (ASHE) or they can be thermally excited through the Spin Seebeck Effect (SSE). To detect the spin current, a thin non-magnetic layer such as Pt is deposited on top of the material of interest. This transforms the spin current into an observable thermoelectric voltage (VSSE) via the Inverse Spin Hall Effect (ISHE). Pt/YIG systems allow efficient spin-charge conversion and pure detection of spin-current effects, respectively, due to their unique magneto-optical and spin dynamic properties [1]. These properties allow a clean detection of the pure spin current thanks to the spin-orbit effects in the Pt/YIG microstructures [2]. Additionally, Rare Earth (RE) garnet films are magnetic and magnetoelastic, and their properties can be manipulated through choice of composition and substrate. When a proportion of bismuth (Bi) is added, the magneto-optical properties of YIG increase according to the concentration of bismuth (Bi) at the yttrium site [3]. But there are few studies on how the spin dynamic properties are modified due to this substitution. In this work we study different parameters in the manufacture of ferrimagnetic/non-magnetic bilayers to raise the thermoelectric spin voltage VSSE. Samples with different thicknesses of pure Y3Fe5O12 (YIG) films and a 5% Bi substitution, that is, thin films of BiY2Fe5O12 (BiYIG), were grown on Gd3Ga5O12 (111) and Gd3Sc2Ga3O12 (111) substrates by pulsed laser deposition (PLD). XRD, HR-TEM / STEM-HAADF and GPA measurements revealed high quality crystalline films as it can be seen in Figure 1. Ferromagnetic resonance (FMR) measurements were performed at room temperature for all heterostructures. A resonance field (Hres) and a resonance linewidth (FWHM) were extracted and are shown in Figure 2 as a function of frequency. These values allow the calculation of a Gilbert damping coefficient that is directly correlated with the SSE according to Chang et. Al [4]. In our case, the Gilbert damping coefficient is (5-14)x10-4 for the YIG//GGG samples and (18-19) x10-4 for the YIG//SGGG samples. The linewidth of BiYIG samples is much wider. After growth of an 8 nm-Pt coating layer by sputtering, the damping in all the samples increases due to the contribution due to spin pumping from the YIG or BiYIG to the metal film. The difference between the Heff result and the bulk value of 4πMS reported (1750 G [5]) demonstrates the existence of a perpendicular anisotropy. With a maximum 20K thermal difference across the entire structure, we measure longitudinal SSE voltages in both YIG and BiYIG samples with sputtered Pt. The YIG//SGGG combination reported to have the best voltage signal from the Inverse spin-Hall effect (VISHE) and Spin Seebeck Effect (VSSE), along with the co-occurrence of a positive perpendicular anisotropy. In the case of the BiYIG samples, the voltages induced in the BiYIG//SGGG bilayers were lower with respect to YIG//SGGG but higher with respect to YIG//GGG. The samples with the lowest perpendicular magnetic anisotropy showed the highest VSSE in both cases, YIG and BiYIG. This work is funded thanks to the SPICOLOST (GA 734187) project framed within “Horizon 2020 Funding” of the European Union with the MARIE SKLODOWSKA-CURIE - RISE Actions (Research and Innovation Staff Exchanges) program coordinated by the University of Zaragoza.

**References:**

[1] S. M. Rezende, R. L. Rodríguez-Suárez, and R. O. Cunha, Physical Review B, Vol. 89, p. 014416 (2014) [2] C. Du, H. Wang, and P. C. Hammel, Journal of Applied Physics, Vol. 117, p. 172603 (2015) [3] R. Kumar, B. Samantaray, and Z. Hossain, Journal of Physics: Condensed Matter, Vol. 31, p. 435802 (2019) [4] H. Chang, P. P. Janantha, and J. Ding, Science advances, Vol. 3, p. e1601614 (2017) [5] Bhoi B., Journal of Alloys and Compounds, Vol. 797, p. 523-528 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ea513c609599a29b0c52d36018d33073.jpg)
Figure 1: Structural characterization at room temperature of the Y3Fe5O12 film grown on Gd3Sc2Ga3O12 (111) crystal by PLD with an 8 nm-Pt coating layer grown by sputtering. Measurements were made by HRTEM / STEM-HAADF.

![](https://assets.underline.io/uploads/markdown_image/1/image/00ba5bba922754ea9aa452f7776f4cb0.jpg)
Figure 2: Room temperature ferromagnetic resonance measurements (FMR) of raw 66nm - Y3Fe5O12 film grown on Gd3Ga5O12 (111) crystal by PLD. The resulting α value is 5.8 ± 0.2. The difference between Heff (2335 G) and the bulk value of 4πMS reported (1790 G) demonstrates the existence of a perpendicular anisotropy.

 FMR and Thermal Spin Pumping in Garnets|Pt Bilayers

Voltage controlled magnetic anisotropy (VCMA) has attracted much attention, since it can dramatically reduce the power consumption during the writing in magnetic random access memory (MRAM) [1]. The voltage-induced anisotropy change triggers the magnetization precession, and a stable magnetization switching is confirmed by the application of appropriate voltage pulses [1]. It is also reported that the stable switching is significantly influenced by the relaxation time of the magnetization precession [2], and thus the magnetization dynamics under the application of the electric field is an important topic to be understood [2]. In this study, we report the electric-field modulation of perpendicular magnetic anisotropy (PMA) and the magnetization dynamics in MgO/Co/Pt trilayers by using time-resolved magneto-optical Kerr effect (TRMOKE). ITO(20) /MgO(10)/Co(1.2)/Pt(1.6)/Ta(10)/oxidized Si substrate (thickness in nanometer) was prepared by using a magnetron spattering system. The film was microfabricated into a Hall-bar structure and a gate electrode of ITO(15 nm) was deposited on the junction. Gate voltage was applied from -3 V to 3 V corresponding to the electric field from -0.3 V/nm to 0.3 V/nm. To investigate PMA, we measured anomalous Hall effect (AHE). The magnetization dynamics was measured by TRMOKE using high-power fiber laser with λ=1040 nm, a pulse width of 500 fs, and a repetition frequency of 100 kHz. During the measurement, an external magnetic field Hext in the range of 5-14 kOe was applied in the direction of 73 deg from the film normal. The measured precession was fitted with the damped oscillation function, exp(-t/τ)sin(ωt), where τ and ω denote relaxation time and angular frequency of the precession. By fitting the Hext dependence ofω, we estimated effective magnetic anisotropy field Hk and g-factor. Figure 1 shows the electric field E dependence of Hk estimated from AHE and TRMOKE. Hk decreases linearly with increasing the electric field in both measurements. The variation of PMA with the electric field η obtained from AHE and TRMOKE were -32 fJ/Vm and -47 fJ/Vm, respectively. Figure 2 (a) shows the electric field dependence of the inverse of relaxation time 1/τ obtained at Hext=14 kOe. 1/τ is known to consist of four contributions; effective Gilbert damping αeff, anisotropy axis distribution ΔθH, anisotropy distribution ΔHk and two-magnon scattering (TMS). The four contributions depend on Hext and E, since Hk depends on E, and we fitted Hext and E dependences of 1/τ by assuming material-dependent parameters which are independent of Hext and E. The extracted four contributions at Hext=14 kOe are also shown in Fig. 2 (a). The results indicate a large electric-field modification of 1/τ is caused by the two contributions: effective Gilbert damping and ΔθH, which have the same trend as the electric-field modification of 1/τ. Figure 2 (b) shows the electric field dependence of αeff. αeff is found to decrease with increasing electric field with a ratio of -13 % per 1 V/nm. Okada et al. reported a ferromagnetic resonance (FMR) study on MgO/CoFeB/Ta trilayers, and they showed PMA variation of η=-60 fJ/Vm and α modulation of -21 % per 1 V/nm [3]. These results are similar to our results, however their samples have MgO(001)/bcc-CoFe interface. Our study indicates similar PMA and α modulations are found in MgO/Co/Pt trilayers having MgO(111)/fcc-Co interface.

**References:**

[1] Y. Shiota, et al., Nat. Mater., 11, 39 (2011). [2] R. Matsumoto, et al., Appl. Phys. Express 12, 053003 (2019) [3] A. Okada, et al., Appl. Phys. Lett. 105, 052415 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/121663ae9205bffe840fa6e0e620c23c.jpg)
Fig.1 Electric field dependence of effective magnetic anisotropy field Hk of the MgO/Co/Pt trilayers.

![](https://assets.underline.io/uploads/markdown_image/1/image/03117393df9d4f663c79f64c0cda057f.jpg)
Fig.2 (a)Electric field dependence of the inverse of relaxation time 1/τ at an applied magnetic field Hext=14 kOe. Four contributions to 1/τ: effective Gilbert damping αeff, anisotropy axis distribution ΔθH, anisotropy distribution ΔHk and two-magnon scattering, are extracted by the fitting of Hext and E dependences of 1/τ, and are plotted in the same figure. (b)Electric field dependence of the effective damping constant αeff of the MgO/Co/Pt trilayers.

 Electric-field modulation of perpendicular magnetic anisotropy and damping constant in MgO/Co/Pt trilayers

Thin films with perpendicular magnetic anisotropy (PMA) have been widely studied for perpendicular recording media since the middle of the 1970s when Prof. Iwasaki suggested this approach [1]. Since them, a great effort has been done by the research community for the use of this kind of nanostructures with PMA in other technological applications such as in high-density spin-transfer torque magnetic random access memories (STT-MRAM) [2], skyrmion-based devices [3] or even in synthetic antiferromagnets for biomedical applications [4]. PMA in thin films can be usually achieved through different strategies such as by using materials with large magnetocrystalline anisotropy energy [5] as well as multilayer thin films with high surface anisotropy energy contributions [6]. Regarding the last alternative, Ikeda et al. [2] demonstrated in 2010 that amorphous CoFeB ultrathin films can show PMA and it is supported by the CoFeB/MgO interfacial anisotropy contribution. Since then, the development of non-magnetic/ferromagnetic superlattices with PMA, using CoFeB alloys as the ferromagnetic element, has received great attention. In particular, PMA in CoFeB/Pd was first demonstrated in bilayers by Fowley et al. [7] as well as in multilayers by Jung et al. [8]. Literature has reported that the effective anisotropy energy depends on the thickness of magnetic (tCoFeB) and non-magnetic (tPd) layers as well as on the number of bilayers (N). In this work, the dynamical response of [CoFeB (tCoFeB) / Pd (10 Å)]5 multilayered ultrathin films (1 Å ≤ tCoFeB ≤ 5 Å) were studied by using two complementary methods: broadband ferromagnetic resonance (Figure 1 a) and time-resolved magneto-optical Kerr effect (Figure 1 b). The perpendicular magnetization was confirmed for multilayers with tCoFeB ≤ 4 Å, while magnetization became in-plane oriented for tCoFeB ≥ 5 Å. This behaviour was explained by considering competing contributions from surface and magnetoelastic anisotropies. In addition, we have observed that the effective damping parameter is reduced with increasing tCoFeB (Figure 1 c), and the lower parameter, αeff ≈ (0.019 ± 0.001), was determined for the multilayer with 4 Å CoFeB thickness. We have suggested that for tCoFeB ≥ 4 Å the layer is continuous and the main contribution to effective damping is coming from spin-pumping when for lower thicknesses αeff is dominated by two-magnon scattering. Afterwards, we have studied the magnetic behaviour of ultrathin [CoFeB(tCoFeB)/Pd(10 Å)]N films. Intending to ensure that the system shows PMA, tCoFeB (3 or 4 Å) was fixed, while the number of bilayers (N) was ranged from 3 to 15. We observed that our samples show PMA and it is generally improved with N. In addition, we studied the dependence of αeff with the number of CoFeB/Pd repeats (N). Up today, literature in superlattices with PMA reported that αeff is proportional, inversely proportional or even, independent of N [9]. Therefore, the reported relationship between the damping parameter and N in superlattices with PMA is still unclear. We show that the evolution of αeff with N shows a complex behaviour that we have correlated with the magnetization process: larger αeff for samples with square hysteresis loops while αeff is independent of N for samples with bow-tie-shaped hysteresis loops.

**References:**

1. S. Iwasaki, Y. Nakamura and K. Ouchi, IEEE Trans. Magn., MAG-61, 1456 (1979). 2. S. Ikeda et al., Nat. Mater, 9, 721 (2010). 3. C. Moreau-Luchaire et al., Nature Nanotechnology, 11, 444 (2016). 4. R. Mansell et al., Sci. Rep,. 7, 4257 (2017). 5. N. Inaba , Y. Uesaka, and M. Futamoto , IEEE Trans. Magn., 36, 54 (2000). 6. C. J. Tatnall et al., J. Magn. Magn. Mater., 165, 391 (1997). 7. C. Fowley et al., IEEE Trans. Magn., 46, 2116 (2010). 8. J. H. Jung et al., Appl. Phys. Express, 3, 023001 (2010). 9. A. Barman et al., J. Appl. Phys., 101, 09D102 (2007); S. Mizukami et al., Appl. Phys. Express, 4, 013005 (2011); H.-S. Song et al., Appl. Phys. Lett., 102, 102401 (2013).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dc5eba45a2ba94ed3193f118e071a51e.jpg)
Fig. 1. (a) VNA-FMR spectra of the [CoFeB (4 Å) / Pd (10 Å)]5 multilayer thin film with the external magnetic field applied perpendicularly to the sample plane. (b) Time-resolved magneto-optical Kerr effect (TR-MOKE) signals of a [CoFeB (2 Å) / Pd (10 Å)]5 multilayer thin film under different external applied fields (H = 5650, 5060, 4695, 4310 Oe and 3900 Oe) and when H was applied at θH = 78°. Theoretical curves (solid curves) are fits to the experimental data (open symbols). Data was moved along the vertical axis for clarity. (c) Evolution of the effective damping (αeff) vs tCoFeB and determined from the TR-MOKE measurements (Δ), the perpendicular VNA-FMR (●) and the in-plane VNA-FMR (○) measurements.

 Magnetization Dynamics of ultrathin [CoFeB (tCoFeB) / Pd]N films with perpendicular magnetic anisotropy

Tailoring and control of electromagnetic properties of synthetic magnetic structures is advantageous for high frequency applications, such as shielding materials in magnetic recording, where characterisation in the gigahertz frequency range is necessary to determine parameters for simulations and aid component design. In such applications it is desirable to have a high saturation magnetization, low coercivity, high permeability and close to zero magnetostriction. Meeting almost all of these requirements, NiFe is the material of choice for many high frequency applications. We present a systematic study of the effects of process settings, dopants and composition on the ferromagnetic resonance (FMR) and spin wave properties of NixFe100-x alloy thin films fabricated by magnetron sputtering and investigated using a coplanar waveguide, vector network analyser (VNA) [1], vibrating sample magnetometer (VSM) and x-ray diffraction (XRD), with the aim to determine any relation between microstructure and the static and dynamic magnetic properties. It has been found that changes in the NiFe crystal structure and deposition can have significant impact on the magnetic properties, examples of which can be seen in Fig. 1 and 2. This work extends into compositionally modulated superlattice structures to explore further possibilities with respect to material design and optimization [2]. VAMPIRE [3] atomistic simulations have been employed in conjunction with these experiments and to provide parameters for FMR simulations using the micromagnetic model, OOMMF [4].

**References:**

[1] Y. Ding et al. J. Appl. Phys. 96. (2004) [2] C.B. Hill et al. Meas. Sci. Technol. 24. (2013) [3] R.F.L. Evans et al. J. Phys.: Condens. Matter 26, 103202 (2014) [4] M. J. Donahue and D. G. Porter, “OOMMF User’s Guide, Version 1.0,” NISTIR 6376, National Institute of Standards and Technology, Gaithersburg, MD (Sept 1999).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ca3c03d9e435df9d90ed1b8a3bcadece.jpg)
Fig. 1 : FMR spectra at an applied field of 253Oe showing the broadening of the FMR and therefore increased damping with increasing Fe content in NixFe100-x thin films. Note particularly the most significant changes occur at x=40 which marks the fcc/bcc transition.

![](https://assets.underline.io/uploads/markdown_image/1/image/f564dafe40ca24a0b86a77ae748d9a43.jpg)
Fig. 2 : FMR spectra at an applied field of 253Oe illustrating the effect of increasing substrate temperature during deposition on Ni80Fe20, where a supression of the FMR response is seen at 300°C and above.

 Control of Static and Dynamic Magnetic Properties of NixFe100-x Alloy Thin Films

Unconventional computing utilizing the probabilistic nature of physical systems – probabilistic computing – has recently gathered much attention for its potential to effectively address computationally complex problems [1]. A stochastic magnetic tunnel junction (MTJ) is a promising element to construct a probabilistic bit (p-bit), a fundamental building block of the probabilistic computers, owing to fast fluctuation rate and high controllability as well as the manufacturability based on current spin-transfer torque (STT) magnetoresistive random access memory (MRAM) technology. Recently, a proof of concept of the probabilistic computer using stochastic MTJs was presented, where integer factorization was demonstrated as an illustrative example of a combinatorial optimization problem [2]. Performance of stochastic MTJs is characterized by a time-varying fluctuation of magnetization and time-averaged response to the external field and current, and in this regard, understanding the physical mechanism governing these properties is of high importance. In this research, we investigate the mechanism governing the sigmoid-like time-averaged response to external field and current in stochastic MTJs with various sizes. We use the same stack structure used in the demonstration of integer factorization [2], i.e., Ta(5)/ Pt(5)/ syntheic ferrimagnet/ Ta(0.3)/ Co19Fe56B25(1)/ MgO(1.1)/ Co19Fe56B25(t)/ Ta(5)/ Ru(5) (thickness in nm), which is deposited by dc/rf magnetron sputtering on a thermally oxidized Si substrate. Both top and bottom CoFeB layers have perpendicular easy axis. We design the thickness of the free layer t so that the thermal stability factor Δ0 is low enough to show superparamagnetic behavior. All films are processed into MTJs with various junction diameters D by electron beam lithography and Ar ion milling. We determine D of each device from their electrically measured resistance R, with a resistance area product RA determined from several MTJs with D ~ 80 nm. Typical TMR ratio is 90% and RA = 6.3 Ωμm2. The measurement circuit for the time-averaged resistance 〈R〉 is shown in Fig. 1(a). We monitor the magnetization fluctuation of the MTJ by measuring R vs. time under dc bias current I with various magnitudes using an oscilloscope connected in parallel to the MTJ. The relaxation time τ of the studied MTJ is found to range from 1 ms to 1 s, corresponding to Δ0 of 14 to 21, by assuming the Néel-Arrhenius law, τ = τ0expΔ0 with τ0 being attempt time 1 ns [3]. The 〈R〉 against external perpendicular magnetic field H and I for the MTJ with nominal D = 50 nm are shown in Figs. 1(b) and (c), respectively. Clear sigmoidal-like characteristics with respect to H and I are observed as a result of the change of the ratio of τ in parallel (P) and anti-parallel (AP) states τP/τAP. We normalize 〈R〉 using resistances at P and AP states as 〈r〉 ≡ τP/(τP + τAP). The normalized sigmoid curves 〈r〉 against H and I are shown in Figs. 1(d) and (e), respectively. In order to characterize the external field and current dependences of stochasticity of MTJs, we derive an analytical expression of the slope of the sigmoidal curve around the center (〈r〉 = 1/2) [see Figs. 1(d) and (e)]. We define the shift current IS and the shift field HS as I and H to take 〈r〉 = 1/2 (P state probability of 50%), respectively. When MTJs are in P (AP) state, τ is given by τP(AP) = τ0 exp{Δ0[1 ± (I - IS)/IC0]nI}, where nI is a switching exponent for I and IC0 the intrinsic critical current. Here, we assume nI = 2, which was derived by analyzing the Fokker-Planck equation [4]. Then, the partial derivative of 〈r〉 (= τP/(τP + τAP)) with respect to I at I = IS is derived to be ∂〈r〉/∂I|I=Is = Δ0/IC0, which has been used as a figure of merit of STT switching in nonvolatile MTJs [5-7]. We apply the same procedure for ∂〈r〉/∂H and obtain ∂〈r〉/∂H|H=Hs = Δ0/HKeff with HKeff being the perpendicular effective anisotropy field. Experimentally measured ∂〈r〉/μ0∂H|H=Hs and ∂〈r〉/∂I|I=Is for MTJs with different t are plotted as a function of D in Figs. 2(a) and (b), respectively. The H derivative of sigmoid curve ∂〈r〉/∂H|H=Hs monotonically increases with increasing D. Since the analytical expression of the H derivative, Δ0/HKeff, can be converted to MSAefft/2kBT (Aeff denotes an effective area for thermal activation), where the spontaneous magnetization MS, thermal energy kBT, and thickness t are independent of D, this result indicates that Aeff increases with the device size; in other words, relatively coherent magnetization switching takes place in this D regime. On the other hand, the I derivative, ∂〈r〉/∂I|I=Is, decreases with increasing D. The reason for this behavior is not clear but we note that a similar result is also observed in the size dependence of Δ0/IC0 in nonvolatile MTJs [5-7]. In conclusion, this work has studied the physical mechanism governing the sigmoid-like response of stochastic MTJs, which strongly affects the performance of probabilistic computing. We derived an analytical expression of the slope of sigmoid curve and experimentally show that the slope varies with the device size. This work is supported in part by JST-CREST JP1082016.

**References:**

[1] P. R. Feynman, Int. J. Theor. Phys. 21, 467 (1982). [2] W. A. Borders et al, Nature 573, 390 (2019). [3] W. F. Brown Jr., Phys. Rev. 130, 1677 (1963). [4] T. Taniguchi et al., Phys. Rev. B 83, 054432 (2011). [5] J. Z. Sun et al, Phys. Rev. B 84, 064413 (2011). [6] H. Sato et al, Appl. Phys. Lett. 105, 062403 (2014). [7] B. Jinnai et al., IEEE IEDM 24.6 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dbe0f712d916203b266d2d43fc513b3a.jpg)
Fig. 1 (a) Measurement circuit and (b),(c) ((d),(e)) time averaged resistance 〈R〉 (sigmoid curve 〈r〉) as a function of external perpendicular magnetic field µ0H and bias current I, respectively (μ0 denotes a permeability in vacuum).

![](https://assets.underline.io/uploads/markdown_image/1/image/f482273c059d8cc39adbc62d2afcd307.jpg)
Fig. 2 (a)(b) Slopes of sigmoid curve 〈r〉 against μ0H and I, respectively, as a function of junction diameter D measured for the devices with different CoFeB free layer thicknesses t.

 Physical Mechanism Governing Sigmoid Curves of Stochastic Magnetic Tunnel Junctions

The magnetization reversal of a ferromagnetic layer using a single ultrashort optical pulse in a GdFeCo/Cu/[Co/Pt] spin-valve structure was first demonstrated in 2018 [1]. This work has attracted attention for future ultrafast and energy-efficient magnetic storage or memory devices. However, the mechanism and the role of the magnetic properties of the ferromagnet as well as the time scale of the magnetization switching are not fully understood. The single GdFeCo layer demonstrate all-optical helicity-independent switching (AO-HIS). In that case, the magnetization of this Rare-earth – Transition Metal alloy can be switched with one single femto-second pulse whatever light helicity is used. AO_HIS was attributed to the presence of two exchange coupled magnetic sublattices (the Rare Earth and the Transition Metal one) showing different relaxation times after the ultrafast laser excitation [2] in the GdFeCo/Cu/[Co/Pt] spin-valve studied in ref [1]. the switching of the [Co/Pt] ferromagnetic layer is observed after a single femto-second laser pulse. It has been carefully checked that no exchange coupling between the two magnetic layers exist. The [Co/Pt] switching would then result from the combined effect of the spin current generated by the AO-HIS of the GdFeCo layer [3] and the laser-induced heating of the ferromagnet. More recently single-shot all-optical magnetization switching was investigated in a GdFeCo/Cu/[CoxNi1-x/Pt] spin-valve structure. It was demonstrated that the threshold fluence for switching both the GdFeCo and the ferromagnetic layer depends on the laser pulse duration and the thickness and the Curie temperature of the ferromagnetic layer. We were able to explain most of the experimental results using a phenomenological model. This work provides a way to engineer ferromagnetic materials for energy efficient single-shot all-optical magnetization switching [4,5].

**References:**

[1] S. Iihama, Y. Xu,M. Deb, G. Malinowski, M. Hehn, J. Gorchon, E.E. Fullerton, S. Mangin, Single-Shot Multi-Level All-Optical Magnetization Switching Mediated by Spin Transport. Adv. Mater. 2018, 30 (51), 1804004. https://doi.org/10.1002/adma.201804004. [2] Radu, I.; Vahaplar, K.; Stamm, C.; Kachel, T.; Pontius, N.; Dürr, H. A.; Ostler, T. A.; Barker, J.; Evans, R. F. L.; Chantrell, R. W.; Tsukamoto, A.; Itoh, A.; Kirilyuk, A.; Rasing, T.; Kimel, A. V. Transient Ferromagnetic-like State Mediating Ultrafast Reversal of Antiferromagnetically Coupled Spins. Nature 2011, 472 (7342), 205–208. https://doi.org/10.1038/nature09901. [3] Choi, G.-M.; Min, B.-C. Laser-Driven Spin Generation in the Conduction Bands of Ferrimagnetic Metals. Phys. Rev. B2018, 97 (1), 014410. https://doi.org/10.1103/PhysRevB.97.014410. [4] Q. Remy, J. Igarashi, S. Iihama, G. Malinowski, M. Hehn, J. Gorchon, J. Hohlfeld, S. Fukami, H. Ohno and S. Mangin Energy Efficient Control of Ultrafast Spin Polarized Current to Induce Single Femtosecond Pulse Switching of a Ferromagnet Adv. Sci. 2001996 (2020) [5] J. Iigarasi, Q. Remy, S. Iihama, G. Malinowski, M. Hehn, J. Gorchon , J. Hohlfeld, S. Fukami, H. Ohno, S. Mangin, Engineering single-shot all-optical switching of ferromagnetic materials Nano Lett 20, 12, 8654–8660 (2020)

**Images:**

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By combining a single femtosecond laser pulse with an ultra-short spin current, generated by the demagnetization of a ferrimagnetic GdFeCo layer, it is possible to reverse the magnetization of a ferromagnetic Co / Pt multilayer. The energy required for this reversal can be controlled by modifying the properties of the different layers

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