France



Exchange bias is a well-known and very useful effect that occurs due to an interfacial coupling between adjacent thin films of an antiferromagnet and a ferro(ferri)magnet [1]. Controlling exchange bias in an antiferromagnet/ferro(ferri)magnet thin film system by application of a gate voltage is much sought-after for spintronic applications. However, since the exchange bias effect is related to the ordering of spins in both the antiferromagnet and the ferro(ferri)magnet, and electric fields have little influence over the spin order, electrical control of exchange bias is very hard to achieve practically.&lt;br/&gt;&lt;br/&gt;Recently, ionic gating of magnetic heterostructures, where a gate voltage is used to drive ions (O&lt;sup&gt;2-&lt;/sup&gt;, H&lt;sup&gt;+ &lt;/sup&gt;etc.) in or out of the active layers, has yielded very interesting and promising results. Due to the size of the H&lt;sup&gt;+&lt;/sup&gt; ion, protonic gating is potentially faster and more reversible compared to gating with other ions and is also able to cause large changes in magnetic properties in the underlying active layers, such as modulation of perpendicular magnetic anisotropy in ultra-thin Co films [2]. The utility of protonic gating was further demonstrated when it was shown that ferrimagnetic order in GdCo metal thin films can be dynamically controlled by this method [3].&lt;br/&gt;&lt;br/&gt;GdCo is comprised of two sub-lattices, one made up of Gd atoms and one of Co atoms, and the magnetic moments in each sub-lattice point in opposite directions, hence resulting in ferrimagnetic order. Experimental and theoretical analyses show that the protons being inserted into the GdCo reduce the effective magnetic moment of the Gd atoms, and by starting from a Gd-dominated magnetic state, the overall magnetization can be switched 180 degrees through proton gating.&lt;br/&gt;&lt;br/&gt;Harnessing this functionality, we have shown, in this work, that exchange bias toggling is possible when we incorporate the GdCo ferrimagnet in an exchange biased heterostructure with NiO serving as the antiferromagnet. Using sputter deposition we have engineered a stack with the structure NiO(33)/Pd(1)/GdCo(10)/Pd(10)/GdO&lt;sub&gt;x&lt;/sub&gt;(30)/Au(3) on thermalized Si, which has fully shifted loops, i.e. the exchange bias field is larger than the coercive field (H&lt;sub&gt;EB&lt;/sub&gt;&amp;gt;H&lt;sub&gt;C&lt;/sub&gt;), as depicted in Fig. 1(a). When a sufficiently high (&amp;gt;1.5V) positive voltage is applied to the Au top electrode (Pd serves as the bottom electrode), atmospheric water is split and the proton is transported through the GdO&lt;sub&gt;x&lt;/sub&gt; electrolyte, into the GdCo(10)/Pd(10) layers. Starting from a Gd-dominated state of the GdCo, upon enough insertion of hydron ions after applying +1.8V, the dominant sublattice of GdCo switches from Gd to Co, as expected from previous work, but is now also accompanied by a toggling of the exchange bias direction, as shown in Fig. 1(b). The effect is fully reversible, as shown in Fig. 1(c).&lt;br/&gt;&lt;br/&gt;We can understand this phenomena when we realize that although the gating does nothing to the relative spin orientation in either the ferrimagnet or the antiferromagnet, the ferrimagnet’s magnetization direction depends not only on the spin orientation of the sublattices but also on the relative magnitude. The magnetization direction flips 180 degrees during gating but the relative spin orientation across the interface remains the same. Essentially, if initially the pinned magnetization is +M&lt;sub&gt;z&lt;/sub&gt; (meaning H&lt;sub&gt;EB&lt;/sub&gt; is -ve) then after gating the pinned magnetization will be -M&lt;sub&gt;z&lt;/sub&gt; necessarily making H&lt;sub&gt;EB&lt;/sub&gt; +ve. To the best of our knowledge, this is the simplest demonstration of exchange bias toggling to date, since our system does not rely on any complex materials or growth processes and works at room temperature, as opposed to some previous works [4,5]. Due to the small size of the proton, our method is highly reversible, and initially we have shown full cycling toggling of the exchange bias up to 10 times, where the hysteresis loop remains fully shifted throughout the process (Fig. 2) as evidenced by H&lt;sub&gt;EB&lt;/sub&gt;/H&lt;sub&gt;C&lt;/sub&gt; being over 1.&lt;br/&gt;&lt;br/&gt;We believe our simple but robust method to toggle exchange bias can serve as a platform for demonstrating more functionalities and/or devices and can have broad implications for spintronics in general.&lt;br/&gt;&lt;br/&gt;This work is supported in part by SMART, one of seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by National Institute of Standards and Technology (NIST).

**References:**

[1]. Y. Fan et al., Nature Nanotechnology, Vol. 8, p. 438 (2013)&lt;br/&gt;[2]. A.J. Tan et al., Nature Materials, Vol. 18, p. 35 (2019)&lt;br/&gt;[3]. M. Huang et al., manuscript under review&lt;br/&gt;[4]. S. Wu et al., Physical Review Letters, Vol. 110, p. 067202 (2013)&lt;br/&gt;[5]. X. He et al., Nature Materials, Vol 9, p. 579 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/36bc1892deb385267892bf4aee4bb5dd.jpg)
Fig. 1. MOKE hysteresis loops of the structures described in the text in the (a) initial state, (b) after applying +1.8V for 180s  and (c) after applying 0V for 80s. The MOKE signal follows the Co magnetic moments, which is why in the Gd dominated state (a) and (c) the loops are inverted

![](https://assets.underline.io/uploads/markdown_image/1/image/ee59777b4e38f83110d076127ab1a339.jpg)
Fig. 2. Reversible toggling of exchange bias in sample with fully shifted loops, where the voltage was toggled between +1.8V and 0V with period of 40s. Note that the erratic oscillations in EB towards the latter cycles are due to noise during measurement of individual hysteresis loops

INTERMAG 2021

 Exchange Bias Toggling in GdCo/NiO Thin Film System by Solid-State Hydrogen Gating

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Exchange bias is a well-known and very useful effect that occurs due to an interfacial coupling between adjacent thin films of an antiferromagnet and a ferro(ferri)magnet [1]. Controlling exchange bias in an antiferromagnet/ferro(ferri)magnet thin film system by application of a gate voltage is much sought-after for spintronic applications. However, since the exchange bias effect is related to the ordering of spins in both the antiferromagnet and the ferro(ferri)magnet, and electric fields have little influence over the spin order, electrical control of exchange bias is very hard to achieve practically. Recently, ionic gating of magnetic heterostructures, where a gate voltage is used to drive ions (O2-, H+ etc.) in or out of the active layers, has yielded very interesting and promising results. Due to the size of the H+ ion, protonic gating is potentially faster and more reversible compared to gating with other ions and is also able to cause large changes in magnetic properties in the underlying active layers, such as modulation of perpendicular magnetic anisotropy in ultra-thin Co films [2]. The utility of protonic gating was further demonstrated when it was shown that ferrimagnetic order in GdCo metal thin films can be dynamically controlled by this method [3]. GdCo is comprised of two sub-lattices, one made up of Gd atoms and one of Co atoms, and the magnetic moments in each sub-lattice point in opposite directions, hence resulting in ferrimagnetic order. Experimental and theoretical analyses show that the protons being inserted into the GdCo reduce the effective magnetic moment of the Gd atoms, and by starting from a Gd-dominated magnetic state, the overall magnetization can be switched 180 degrees through proton gating. Harnessing this functionality, we have shown, in this work, that exchange bias toggling is possible when we incorporate the GdCo ferrimagnet in an exchange biased heterostructure with NiO serving as the antiferromagnet. Using sputter deposition we have engineered a stack with the structure NiO(33)/Pd(1)/GdCo(10)/Pd(10)/GdOx(30)/Au(3) on thermalized Si, which has fully shifted loops, i.e. the exchange bias field is larger than the coercive field (HEB&gt;HC), as depicted in Fig. 1(a). When a sufficiently high (&gt;1.5V) positive voltage is applied to the Au top electrode (Pd serves as the bottom electrode), atmospheric water is split and the proton is transported through the GdOx electrolyte, into the GdCo(10)/Pd(10) layers. Starting from a Gd-dominated state of the GdCo, upon enough insertion of hydron ions after applying +1.8V, the dominant sublattice of GdCo switches from Gd to Co, as expected from previous work, but is now also accompanied by a toggling of the exchange bias direction, as shown in Fig. 1(b). The effect is fully reversible, as shown in Fig. 1(c). We can understand this phenomena when we realize that although the gating does nothing to the relative spin orientation in either the ferrimagnet or the antiferromagnet, the ferrimagnet’s magnetization direction depends not only on the spin orientation of the sublattices but also on the relative magnitude. The magnetization direction flips 180 degrees during gating but the relative spin orientation across the interface remains the same. Essentially, if initially the pinned magnetization is +Mz (meaning HEB is -ve) then after gating the pinned magnetization will be -Mz necessarily making HEB +ve. To the best of our knowledge, this is the simplest demonstration of exchange bias toggling to date, since our system does not rely on any complex materials or growth processes and works at room temperature, as opposed to some previous works [4,5]. Due to the small size of the proton, our method is highly reversible, and initially we have shown full cycling toggling of the exchange bias up to 10 times, where the hysteresis loop remains fully shifted throughout the process (Fig. 2) as evidenced by HEB/HC being over 1. We believe our simple but robust method to toggle exchange bias can serve as a platform for demonstrating more functionalities and/or devices and can have broad implications for spintronics in general. This work is supported in part by SMART, one of seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by National Institute of Standards and Technology (NIST).

**References:**

[1]. Y. Fan et al., Nature Nanotechnology, Vol. 8, p. 438 (2013) [2]. A.J. Tan et al., Nature Materials, Vol. 18, p. 35 (2019) [3]. M. Huang et al., manuscript under review [4]. S. Wu et al., Physical Review Letters, Vol. 110, p. 067202 (2013) [5]. X. He et al., Nature Materials, Vol 9, p. 579 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/36bc1892deb385267892bf4aee4bb5dd.jpg)
Fig. 1. MOKE hysteresis loops of the structures described in the text in the (a) initial state, (b) after applying +1.8V for 180s and (c) after applying 0V for 80s. The MOKE signal follows the Co magnetic moments, which is why in the Gd dominated state (a) and (c) the loops are inverted

![](https://assets.underline.io/uploads/markdown_image/1/image/ee59777b4e38f83110d076127ab1a339.jpg)
Fig. 2. Reversible toggling of exchange bias in sample with fully shifted loops, where the voltage was toggled between +1.8V and 0V with period of 40s. Note that the erratic oscillations in EB towards the latter cycles are due to noise during measurement of individual hysteresis loops

technical paper

Ultrafast optical generation of chiral magnetic structure is one of the most promising and highly sought-after technology for next generation magnetic memory devices. Recent experimental demonstration of generation of skyrmions with ultrafast laser pulse [1] has revealed a new horizon in this field. However, a proper theoretical understanding of the underlying interactions taking place at different timescales as well as main stimulants of the process are still in darkness. Most of the existing studies focus on the magnetic interactions only and completely neglect the interaction between the electric field of the laser and the electronic wavefunction of the material and thus create a huge gap in the complete understanding of the laser assisted magnetization dynamics. We bridge this gap by employing a quantum-classical hybrid method [2] to study the evolution of quantum states as well as the magnetic moments on equal footing and demonstrate that how a stable spin spiral can be generated from a collinear anti-ferromagnetic spin chain with an ultrashort laser pulse [3] (Fig.1,2). We use a minimal tight binding model to define our antiferromagnetic chain with a scalar hopping and onsite magnetic exchange. The laser electric field is modelled as a Gaussian pulse which couples to the hopping. On being hit by the pulse several different mechanisms take place at different timescale starting with an instantaneous change in occupation of states resulting in a gradual buildup of effective torque which leads to the magnetization dynamics. The magnetization dynamics being a slower process compared to the quantum evolution lags by approximately 50fs behind the incident of laser. To initiate this process the initial state must deviate from an ideal collinear state. A stronger deviation shows a faster convergence to the steady state configuration. The mixing of quantum states gives rise to different emergent spin mixing interactions which drives the subsequent dynamics. The system finds its chiral state within a timescale of 1ps. The timeframe of the different steps of the spiralization process is of the same order of the timescales associated with the ultrafast demagnetization which indicates towards the similar underlying physics. After 1ps the dynamics becomes slower and the chain gradually attains a uniform steady chiral structure. We characterize this evolution in terms of the relative angle between adjacent magnetic moment and vector chirality which clearly distinguish different time frames. The relative angle and the induced chirality can be tuned by the strength of the amplitude field. We further show that these effects are fairly robust against thermal fluctuations. Our results thus reveal several salient features of optical manipulation of chirality which has not been revealed in existing literature and thus would be instrumental in their experimental realization.

**References:**

[1] F. Büttner et.al. Nat. Matter. 20, 30 (2021). [2] A. Ono and S. Ishihara, Phys. Rev. Lett. 119, 207202 (2017). M. D. Petrović, B. S. Popescu, U. Bajpai, P. Plecháč, and B. K. Nikolić, Phys. Rev. Applied 10, 054038 (2018). [3] S. Ghosh, F. Freimuth, O. Gomonay, S. Blügel and Y. Mokrousov, arXiv:2011.01670

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/87c5fef65fb042eaab838c75b45a688d.jpg)
Fig. 1: Formation of a spin spiral (solid arrows) from an collinear antiferromagnetic (transparent arrows) chain with 32 sites.

![](https://assets.underline.io/uploads/markdown_image/1/image/ed03b2ecc70a85f0fdc71272a0a68860.jpg)
Fig. 2: Time evolution of the components of magnetization over time for 1st (solid) and 17th (transparent) magnetic moment. The yellow line shows the laser pulse.

 Ultrafast electronic manipulation of antiferromagnetic spin spiral states

The observation of ultrafast and coherent control of spins in magnetic materials at room temperature [1-2] has prompted the experimental and theoretical efforts to understand the underlying mechanisms driving such magnetic phenomena. In order to understand the driving mechanisms, in this non-equilibrium regime, it is necessary to disentangle the relevant interactions (exchange, spin-lattice, electron-phonon, coulomb etc.). Stoichiometric B2 ordered epitaxial (001) FeRh undergoes a first order magnetic phase transition from antiferromagnetic (AFM) to ferromagnetic (FM) at ≈ 380K. In the AFM phase of FeRh, only Fe has net magnetic moment, whereas in the FM phase both Fe and Rh carry net moments. The phase transition is also accompanied by a ≈ 1% isotropic lattice expansion in the bulk BCC structure, and changes in electronic structure, see [3-5] and refs. therein. Since magnetic and structural dynamics can occur at different timescales, it makes FeRh an ideal candidate for disentangling relevant interaction mechanisms at different timescales. The phase transition has been extensively studied theoretically and experimentally [6-10], in thermal equilibrium (static heating) and at ultrafast time scales (fs- optical excitation), but a precise knowledge of the roles of the electronic, phononic and spin sub-systems remains elusive. We have studied the laser-driven AFM to FM phase transition in FeRh with X-ray absorption spectroscopy (tr-XAS) around the Fe L3 edge. The experiments were performed at the SCS Instrument of the European XFEL. We also performed the density functional theory (DFT) calculations to simulate the XAS spectra at different time delays including magnetic, lattice and temperature changes. Temperature modelling was done using two temperature model (2TM). In this contribution, we will discuss the changes in the electronic band structure of FeRh in the femto- and picosecond timescales, derived from the X-ray absorption spectroscopy measurements at the Fe L3 absorption and compare them with the density functional theory simulations.

**References:**

[1] E. Beaurepaire et al., Phys. Rev. Lett. 76, 4250 (1996) [2] J.-Y. Bigot et al., Nature Physics 5, 515 (2009) [3] J.-U. Thiele et al. Appl. Phys. Lett. 82, 2859 (2003) [4] A.X. Gray et al., Phys. Rev. Lett. 108, 257208 (2012). [5] C. Baldasseroni et al., Appl. Phys. Lett. 100, 262401 (2012). [6] J.-U. Thiele, M. Buess, C.H. Back, Appl. Phys. Lett 85, 2857 (2004). [7] G. Ju et al., Phys. Rev. Lett. 93, 197403 (2004) [8] I. Radu et al., PRB 81, 104415 (2010) [9] S. Mariager et al., Phys. Rev. Lett. 108, 87201 (2012) [10] F. Quirin et al., Phys. Rev. B 85, 020103(R) (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/92b1687e04e78b6abfbee5f8574ccb81.jpg)
Figure-1: a: X-ray absorption (XAS) changes: (dashed line: experiment) near the Fe L3 edge before and after laser excitation at a fixed time delay of 70 fs, (solid lines: DFT theory) XAS changes corresponding to temperature of 2000K 
 
b: a: X-ray absorption (XAS) changes: (dashed line: experiment) near the Fe L3 edge before and after laser excitation at a fixed time delay of 11.5 ps and 70 us, (solid lines: DFT theory) XAS changes corresponding to net changes including temperature (400K), lattice (0.5 % expansion) and magnetic changes (AFM->FM)

 Ultrafast dynamics in electronic band structure of optically excited epitaxial FeRh: X-ray absorption spectroscopy and density functional theory approach

The relaxation of the magnetisation in magnetic materials is of great importance from both an applied and fundamental point of view. Conventional modelling of magnetisation dynamics employs the Landau-Lifshitz-Gilbert (LLG) equation [1], where the damping is included phenomenologically by the Gilbert damping term. This describes the coupling of the magnetic modes (given primarily by the atomic spin) to the non-magnetic modes (lattice vibrations and electron orbits) which are assumed to be in equilibrium. Recent studies of the dynamics induced by THz laser pulses has highlighted the necessity of understanding magnetisation relaxation beyond this assumption. In reality the spin and lattice dynamics mutually influence one another, hence it is necessary to employ a unified model of molecular and spin dynamics [2,3,4], Spin-Lattice dynamics (SLD). In the present work we employ a model where the transfer of energy and angular momentum between the lattice and the spin system (Fig. 1) is realised by the pseudo-dipolar coupling [3,4], which arises from the spin-orbit interaction and can be parameterised by magneto-elastic experiments. The spin system exchange parameters are taken from ab-initio parameterisation for BCC iron [2], while for the phonon system interactions potential we compare the Harmonic and Morse potentials. Our results in Fig. 1 show that equilibration of both sub-systems can be obtained on a sub-nanosecond timescale in both the microcanonical and canonical ensembles, the relaxation time being governed by the energy initially deposited in the system. We also observe that the equilibrium magnetisation is independent of the thermostat and by coupling the spin system only to the lattice vibrations the magnetisation temperature dependence can be reproduced without the need of a phenomenological spin damping [3]. Our model allows the evaluation of the effective magnon-phonon damping (Fig. 2) which agrees well with the values measured in magnetic insulators where they depend predominantly on magnon-phonon coupling rather than on electronic effects. The functional form of the damping variation is quadratic, in accordance with the form of the pseudo-dipolar coupling term. The magnon-phonon damping has been also calculated for an alternate form of the coupling, where the pseudo-dipolar coupling is replaced by an on-site form, i.e a Néel-like anisotropy term. The latter leads to much smaller damping values, as shown in Ref. [3], suggesting that the magnon-phonon damping can clearly have complex behaviour depending on the properties of the system, especially the coupling term. Based on this remark, no universal behaviour of damping as a function of temperature can be deduced for spin lattice models. The model developed in this work [3] opens the possibility to describe the distinct dynamics of spins and phonons, necessary for the understanding of ultrafast magnetisation dynamics experiments and the subsequent angular momentum transfer between the two subsystems. We have demonstrated that the model works well in the absence of a phenomenological Gilbert damping, which consists mainly of electronic contributions, hence the SLD model can be employed to study magnetic insulators, such as YIG, where the principal contribution to damping is via magnon-phonon interactions.

**References:**

 [1] T. L. Gilbert, IEEE Trans. Magn. 40, 3443 (2004). [2] P.-W. Ma et al., Phys. Rev. B, vol. 78, no. 2, p. 024434, Jul. 2008. [3] M. Strungaru et al. arXiv preprint arXiv:2010.00642 (2020) (accepted in Phys. Rev. B) [4] M. Aßmann and U. Nowak, J. Magn. Magn. Mater 6 469 (2019): 217-223.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0415f635b3cb2e3e3855832e043401d0.jpg)
 
Fig.1: NVE (microcanonical – top panel) and NVT ( canonical – bottom panel) simulations for a 10 × 10 × 10 unit cell BCC Fe system. The spin system is initialised at a spin temperature TS = 0K corresponding to a saturated magnetic state in the z direction, while the lattice velocities are initialised by a Boltzmann distribution at T L = 1200 K (for NVE) and T L = 600 K (for NVT). In both cases we obtain equilibration of the two subsystems under 1ns.

![](https://assets.underline.io/uploads/markdown_image/1/image/6755da1be71fc906a6b75c124d5d162a.jpg)
 
Fig.2 Damping parameter extracted from fitting the z component of the magnetisation for two different choices of potential: HP- Harmonic Potential (green open squares) and MP-Morse Potential (black open circles) as a function of temperature - Panel a) and as a function of the coupling strength – Panel b); The effective damping in Panel a) is calculated for a constant coupling strength of C = 0.5, while in Panel b) the damping is calculated for a constant temperature of T = 300K. The black and green lines represent the average damping parameter obtained from the simulations using the Morse and the Harmonic Potentials, respectively.

 Magnon-phonon damping calculations in the spin-lattice dynamics model

Recently, the effects of inertia in the spin dynamics of ferromagnets were reported to cause nutation resonance [1-8] at the frequencies higher than the conventional ferromagnetic resonance. It was shown that spin-orbit induced inertia is responsible for nutation, which should be considered together with magnetization precession in a magnetic field. Recently nutation in ferromagnets was confirmed experimentally [1], since nutation and precession operate at substantially different time scales, and conventional microwave ferromagnetic resonance (FMR) spectroscopy techniques do not easily reach the high-frequency (sub-Terahertz) regime, required to observe the inertia effect which in addition yields much weaker signal. The interest in the ultrafast spin dynamics has inspired various theoretical studies. For instance, a relation between the Gilbert damping constant and the inertial regime characteristic time was elaborated in ref. [2]. The exchange interaction, damping, and moment of inertia can be calculated from the first principles as shown in [3]. In [4], the inertial regime was introduced in the framework of the mesoscopic nonequilibrium thermodynamics theory, and it was shown to be responsible for the nutation superimposed on the precession of magnetization. Wegrowe and Ciornei [5] discussed the equivalence between the inertia in the dynamics of uniform precession and a spinning top within the framework of the Landau–Lifshitz–Gilbert equation generalized to the inertial regime. This equation was studied analytically and numerically in ref. [6, 7]. In this digest we present new results on the frequency dependence of high-frequency magnetic susceptibility in ferromagnets taking inertia effects into account [8]. We performed calculations based on the Landau-Lifshitz-Gilbert equation with the additional inertia term and obtained an analytical solution. These results provide a basis for further studies of magnetocrystalline anisotropy and damping in magnetic materials in the sub-Terahertz range and furthermore a guideline for experimental research. Using circular variables of magnetization and magnetic field we obtained the dependence of the susceptibility on frequency for the right-hand precession, i.e. positive polarization (Fig. 1(a)). Due to the contribution of nutation, the frequency and linewidth of this resonance are slightly different from the ones of usual FMR. In Fig. 1(b) the nutation resonance possessing negative polarization is presented. Note that the polarizations of ferromagnetic and nutation resonances are reversed. In addition, we derived a general analytical expression for the linewidth of nutation resonance in ferromagnets, and will show its dependence on magnetization, the Gilbert damping, the inertial relaxation time and applied magnetic field. We find that the nutation linewidth can be tuned by the applied magnetic field, and this tunability breaks the direct relation between losses and the linewidth.

**References:**

[1] K. Neeraj, N. Awari, S. Kovalev et al., Nat. Phys. (2020), doi: 10.1038/s41567-020-01040-y [2] M. Fähnle, D. Steiauf, and C. Illg, Phys. Rev. B, Vol. 84, 172403 (2011). [3] S. Bhattacharjee, L. Nordström, and J. Fransson, Phys. Rev. Lett., Vol. 108, 057204 (2012). [4] M.-C. Ciornei, J. M. Rubí, and J.-E. Wegrowe, Phys. Rev. B, Vol. 83, 020410 (2011). [5] J.-E. Wegrowe and M.-C. Ciornei, Am. J. Phys., Vol. 80, p. 607 (2012). [6] E. Olive, Y. Lansac, and J.-E. Wegrowe, Appl. Phys. Lett., Vol. 100, 192407 (2012). [7] E. Olive, Y. Lansac, M. Meyer et al., J. Appl. Phys. 117, 213904 (2015). [8] M. Cherkasskii, M. Farle, and A. Semisalova, Phys. Rev. B 102, 184432 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/06be23fe2d97187eb18d84ec0746a005.jpg)
Fig. 1. (a) The FMR peak with nutation. (b) The nutation resonance. The calculation was performed for γ/(2π)=28 GHz T-1, μ0M0=1 T, μ0H0=100 mT, α=0.0065 and τ = 10-11 s.

 Nutation resonance in ferromagnets

Ferrimagnetic insulators (FIs) host an array of attractive properties for spintronics research and potential applications. Some prominent features are tunable saturation magnetization, perpendicular anisotropy, low damping, and highly ordered single crystal structure that could be beneficial for obstacle-free domain wall and skyrmion motion. However, electrically manipulating and detecting the magnetization in FIs, which is a prerequisite for spintronic devices, has been impossible for a long time due to the lack of physical phenomena to do so. Recent advances in spin current generation and detection have provided the relevant tools to detect the magnetization vector of FIs by purely electrical means [1,2]. Consequently, the research into MIs has gained significant momentum in the past decade. In this talk, we will discuss some of the recent efforts in controlling and detecting the magnetization vector via spin currents in FIs with perpendicular magnetic anisotropy. First, we will briefly overview the experiments of current-induced switching and electrical detection of magnetization vector in a FI, thulium iron garnet, with perpendicular anisotropy [3,4]. We will then discuss the emergent interfacial chiral magnetism, and current-driven dynamics of domain walls in rare-earth-based FIs. We will show that chiral magnetic interactions stabilize Néel-type domain walls in ultrathin FIs that can be propelled by spin-orbit torques with velocities ~0.8 km/s [5]. Finally, we will discuss a new thermoelectric effect that allows electrical detection of the out-of-plane magnetization component in FIs in a nonlocal device geometry [6]. We will show that, by using an engineered temperature gradient, we can convert a thermally-induced spin current in a FI into an electrical signal across a Pt detector that is proportional to the perpendicular component of the magnetization.

**References:**

[1] Uchida et al. Appl. Phys. Lett. 97, 172505 (2010) [2] Nakayama et al. Phys. Rev. Lett. 110, 206601 (2013). [3] Avci et al. Nat. Mater. 16, 309 (2017) [4] Avci et al., Appl. Phys. Lett. 111, 072406 (2017) [5] Avci et al. Nat. Nanotech. 14, 561 (2019) [6] Avci et al. Phys. Rev. Lett. 124, 027701 (2020)

**Images:**

 Spin current-driven control and detection of magnetization in ferrimagnetic insulators INVITED

While classical spintronics has traditionally relied on ferromagnetic metals as spin generators and spin detectors, spin-orbitronics exploits the interplay between charge and spin currents enabled by the spin-orbit coupling (SOC) in non-magnetic systems. The realization of magnetization switching induced by in-plane current injection in heavy metal/ferromagnetic heterostructures [1] has drawn increasing attention to spin-orbitronics, leading to the advent of spin-orbit torques magnetoresistive random access memories (SOT-MRAM). Compared to heavy metals, oxide 2D electron gases have emerged as alternative spin-orbitronics material systems. They benefit from an efficient spin-charge interconversion through the direct and inverse Edelstein effects, which appear at their interfaces where the broken inversion symmetry induces a Rashba SOC [1]. Recently, we have demonstrated an enhancement of the spin-to-charge conversion efficiency by two orders of magnitude in SrTiO3-based 2D gas compared to conventional heavy metals [2], along with a non-volatile electric-control of the spin-to-charge conversion [3]. While the sign and efficiency of the SOTs are fixed by the stack of materials in conventional SOT devices, achieving an electric-control of the mirror charge-to-spin conversion would be of great interest for developing reconfigurable SOT-MRAM and logic gates, offering the possibility of active manipulation of the torque by electric field for building new architectures. Here we report electric-field control of spin orbit torques with electrical remanence in a perpendicular ferromagnet - SrTiO3 system. Results are shown from a 1 µm wide Hall bar device made of a CoFeB ferromagnetic layer with perpendicular magnetization on top of a SrTiO3 substrate with a thin Ta insertion to protect the 2D electron gas at the interface (Figure 1). The perpendicular magnetization is achieved using an MgO capping layer that ensures high interfacial magnetic anisotropy along with compatibility for integration in magnetic tunnel junctions for SOT-MRAM. To modulate the 2D gas properties, voltage is applied to the devices via a back-gate. Non-volatile electric-field control of the sheet resistance is achieved with 1150% contrast (Figure 1c), with two switchable and remanent high and low resistivity states of the 2D electron gas. Spin-orbit torques effective fields are further measured using second harmonic Hall methods. A remanent electric-field control of the SOT efficiency is demonstrated, with inversion of the sign of the SOT anti-damping-like effective field (Figure 2). Anti-damping-like and field-like torque effective fields per 2D current density of 1.6 and 0.1 mT. A. cm-1 respectively are reached in the 2D gas low resistivity state. These results are consistent with a combination of both intrinsic modulation of the SOT efficiency together with extrinsic modulation due to the non-volatile electric-control of the current injection in the 2D gas. The non-volatile control of the SOT effective field is further evidenced in Figure 2b, which displays reproducible inversion of the SOT torques after initializing with negative or positive voltage pulses of ±130 V, opening the way to reconfigurable spin-orbit torque memory and logic gate architectures.

**References:**

[1] I. M. Miron et al., Nature 476, 189–193 (2011). [2] E. Lesne et al., Nature Materials, 15, 1261–1266 (2016). [3] D. C. Vaz et al., Nature Materials, 18, 1187–1193(2019). [4] P. Noel et al., Nature 580, 483–86 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/005ef5c4d7565a59c77e5faa647c55c7.jpg)
Schematic of the sample and magnetotransport properties. (a) Structure of the sample and measurement geometry. (b) Out-of-plane magnetic field dependence of the anomalous Hall resistance at zero electric field (Vg = 0 V). (c) Gate dependence of the sheet resistance at zero magnetic field after initializing the ferromagnet (FM) in the up (blue) and down (red) states. All data have been measured at 10K.

![](https://assets.underline.io/uploads/markdown_image/1/image/9e2388e262906d2be322591c09b882ed.jpg)
Electric-field control of spin orbit torques with electrical remanence. (a) Spin-orbit torques anti-damping-like effective field as a function of the gate voltage for j2D = 4 A.cm-1. (b) Normalized second harmonic Hall resistance at electrical remanence VR after initializing with negative (blue) or positive (red) voltage pulses of ±130 V. Dashed and dotted lines are linear fits, yielding SOT effective fields BAD = +0.29, -0.20, +0.32 and -0.18 mT. A. cm-1, respectively.

 SrTiO3 system

The presence of a Dzyaloshinskii-Moriya interaction (DMI) in perpendicular magnetized thin films stabilizes Néel type domain walls of fixed chirality, as opposed to the Bloch walls that are formed in the absence of a DMI [1]. Néel walls of fixed chirality have been shown to be driven efficiently in the same direction by electric currents through spin-orbit torques [2,3]. Later, a large tuning of the DMI with an applied voltage was demonstrated [4], which can be used for example for electric field control of magnetic domain wall motion via the modulation of the DMI [5]. Here, we demonstrate an alternative mechanism for the control of domain wall type: Using micromagnetic simulations and analytical modeling, we show that the presence of a uniaxial in-plane magnetic anisotropy can also lead to the formation of Néel walls in the absence of a DMI. It is possible to abruptly switch between Bloch and Néel walls via a small modulation of both the in-plane, but also the perpendicular magnetic anisotropy [6]. This opens up a route towards efficient electric field control of the domain wall type with tiny applied voltages, as the magnetic anisotropy can be modulated via the direct voltage controlled magnetic anisotropy (VCMA) mechanism [7], or via magnetoelastic anisotropy induced through coupling to a piezoelectric element [8].

**References:**

1. A. Thiaville, S. Rohart, E. Jué, V. Cros, and A. Fert, EPL (Europhysics Letters) 100, 57002 (2012). 2. K.-S. Ryu, L. Thomas, S.-H. Yang, and S. S. P. Parkin, Nat. Nanotech. 8, 527–533 (2013) 3. S. Emori, U. Bauer, S.-M. Ahn, E. Martinez, and G. S. D. Beach, Nat. Mater., 12, 611–616 (2013) 4. T. Srivastava, et al., Nano Letters 18, 4871 (2018) 5. T. Koyama, Y. Nakatani, J. Ieda, and D. Chiba, Science Advances 4 (2018) 6. K. J. A. Franke, et al., in preparation (2021) 7. T. Maruyama, et al., Nat. Nanotech. 4, 158 (2009). 8. S.Li, et al., J, Appl. Phys. 117, 17D702 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5815f993e947e36c366298e73960792b.jpg)
In a perpendiular magnetized thin film, domain walls (DWs) are generally of Bloch type (bottom left). The presence of a DMI (top left), stabilises Néel walls. Alternatively, and in-plane magnetic anisotropy can also form Néel walls (bottom right). An increase in the perpendicular magnetic anisotropy switches the DW type back to Bloch (top right).

 Control of Magnetic Domain Wall Type using Anisotropy Modulations

Mechanisms for voltage control of magnetism are often based on strain or charge effects. Recently, a new approach based on electrochemical mechanisms was discovered. Due to the ionic reactions involved, it is promising especially for large and non-volatile voltage induced effects on the magnetic properties.[1,2] In the charge-based or electrochemical approach, the fast majority of publications reports on Co-based thin films with perpendicular anisotropy. In our study, we focus on a distinctly different system, namely FeOx/Fe thin films with uniaxial in-plane anisotropy. Although films with uniaxial in-plane anisotropy hold great potential for switchable artificial magnetic stray field landscapes for lab-on-a-chip or for giant magnetoresistance sensors, there are no reports of electrochemical voltage control of such films yet. We demonstrate that significant effects on their magnetic properties can be achieved via electrolytic gating. The detailed analysis of the interplay between electrochemical processes and hysteresis, anisotropy and domain changes allow us to reveal an oxygen-based tuning of the Néel wall interactions as the underlying mechanism. The thin films are composed of 3nm FeOx and 5nm Fe. In-plane angular magnetometry measurements show the presence of a uniaxial anisotropy. Along the easy axis, the shape of the magnetization curve is close to rectangular. Nevertheless, the hysteresis along the hard axis is more rounded and the coercivity (HC) is comparable with the HC along the easy axis (red curve in Figure 1 a). This behavior is known to be caused by charged Néel domain wall interactions. These interactions block the rotation of the magnetization and lead to a large hysteresis along the hard axis. Upon voltage application, HC strongly decreases along every angle. In the vicinity of the hard axis, HC almost completely vanishes (blue curve in Fig. 1 a). As HC and anisotropy are strongly correlated, we investigate the anisotropy of the thin film via anhysteretic measurements. We find an increase of the uniaxial anisotropy energy density upon the voltage-triggered oxide-metallic transformation. This is an unusual finding as it is often assumed in voltage control of magnetism that HC and anisotropy are directly proportional to another. Obviously, this simple model is not applicable here. Instead, changes in the microstructure or the magnetic domain structure dominate over direct anisotropy effects. To evaluate how the magnetic domain structure is affected, we investigated the AC-demagnetized state, which resembles the equilibrium domain state. Upon a low voltage application (1V), and thus transforming the FeOx to metallic Fe, the domain size significantly increases, see Fig. 1 b and c. In order to understand the domain coarsening, we approximated the change in the surface energy density for the Néel walls. This calculation shows an increase in domain-wall energy of 40% upon the oxide-metal transformation, which could explain the decrease in the number of domain walls and the associated increase in the domain size. In order to propose a consistent mechanism which explains the observed changes, we focused on the specific properties of the magnetically charged Néel walls. The Néel domain wall interactions becomes a significant factor, as soon as their tails overlap which is when the domain width is smaller than two times the tail width. With the extracted domain size from Fig. 1, we calculated strong interactions for the oxidized state. For the oxide to metal transformation, the interactions are significantly decreased. A comparable trend is expected and also observed in the remanent state. As a result, the tails would not overlap and we thus expect significantly fewer interactions between the walls in the reduced state. This is consistent with the observed voltage controlled deblocking. To demonstrate the technological relevance, we demonstrated that our electrochemical based switching mechanism allows for 180° magnetization reversal along the easy axis. Purely magnetic field reversal shows the nucleation and growth of magnetic domains (Fig. 2 (a) red curve and (b)). In comparison, during voltage assisted switching, the magnetization reversal occurs at a lower field within seconds (Fig. 2 (a) blue curve and (c)). Assuming a linear relation between the electrode diameter and the switching energy, we estimate the energy efficiency of this process to be 5fJ for an electrode diameter of 3nm. These value approaches the same range as for the so far lowest reported switching energies. Interestingly, the domain evolution is similar to the reversal process induced by a magnetic field. This indicates that the nucleation sites and the local distribution of pinning sites that affect the reverse domain growth do not change substantially during the reduction process. However, the E-induced switching proceeds at much lower magnetic field, which points to a substantially reduced pinning strength during the FeOx to metal Fe transformation. The reversible and low voltage (1V) control of defect sites might be transferrable to other defect-controlled materials, such as type II superconductors or materials with specific mechanical properties.[3]

**References:**

[1] C. Navarro-Senent, A. Quintana, E. Menéndez, E. Pellicer, J. Sort, APL Materials 2019, 7, 030701. [2] C. Song, B. Cui, F. Li, X. Zhou, F. Pan, Progress in Materials Science 2017, 87, 33. [3] J. Zehner, I. Soldatov, S. Schneider, R. Heller, N. B. Khojasteh, S. Schiemenz, S. Fähler, K. Nielsch, R. Schäfer, K. Leistner, Adv. Electron. Mater. 2020, 6, 2000406.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d35959871426edaba9a12be7d3a1dbc5.jpg)
Fig.1: Magnetization curves and magnetic domains in the FeOx/Fe state (red curve in (a) and domains in (b)) and in the Fe state, blue curve in (b) and domains in (c).

![](https://assets.underline.io/uploads/markdown_image/1/image/5d4968e18040b7ba8b1145609a0e0b42.jpg)
Fig.2: E-induced 180° switching of magnetization (M). (a) pathway for H- and E-induced M-reversal. (b) H-induced and (c) E-induced M-reversal.

 Voltage control of Néel domain wall interactions and pinning sites

Gate voltage control of magnetic order is desirable for spintronic device applications [1], [2], but 180° magnetization switching is not straightforward since electric fields do not break time-reversal symmetry. Ferrimagnets have two sublattices with opposing magnetic moments, and by changing the relative amplitude of the magnetization of the two sublattice, magnetic reversal can be achieved. Here we show that ferrimagnetic order in rare earth-transition metal thin films can be dynamically controlled by voltage through solid-state hydrogen gating. We focus on GdCo ferrimagnetic structures with perpendicular magnetic anisotropy, and show that the dominant lattice of GdCo ferrimagnetic thin films at room temperature can be reversibly toggled by hydrogen loading/unloading into the material controlled using a solid-state hydrogen pump [3]. The loading/unloading of hydrogen is mediated by a positive gate bias applied to the top electrode generates protons through hydrolysis of ambient moisture in the air, as shown previously [3]. We find that hydrogen injection into the GdCo leads to a significant decrease in the compensation temperature. With a fixed perpendicular bias field, we show that a gate voltage can induce 180° magnetic switching of the sublattices by shifting the magnetic compensation temperature above and below room temperature. The localized nature of the hydrogen gating effect allows for gate-voltage generation of ferrimagnetic spin textures such as chiral domain walls in racetrack devices. The work provides a means to tune ferrimagnetic spin textures and dynamics, and provides a new direction in magnetoionic control of magnetism for data storage and computing.

**References:**

[1] F. Matsukura, Y. Tokura, and H. Ohno, “Control of magnetism by electric fields,” Nat. Nanotechnol., vol. 10, no. 3, pp. 209–220, 2015. [2] E. Y. Tsymbal, “Electric toggling of magnets,” Nat. Mater., vol. 11, no. 1, pp. 12–13, 2011. [3] A. J. Tan et al., “Magneto-ionic control of magnetism using a solid-state proton pump,” Nat. Mater., vol. 18, no. 1, pp. 35–41, 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a025e553f973e3a2bdc508401f7c457e.jpg)
Coercivity (Hc) versus temperature showing compensation temperature change of GdCo by solid-state ionic gating.

![](https://assets.underline.io/uploads/markdown_image/1/image/e240923efec7bf678cdf53c00f3dffa0.jpg)
Reversed domain generator based on hydrogen gating: a sequence of wide field MOKE contrast images showing the movement of the generated reversed domain.

 Voltage control of ferrimagnetic order and voltage-assisted spin texture writing by solid-state hydrogen gating

Magnetic random-access memory (MRAM) has recently emerged as a promising way for next generation memory due to its nonvolatility, low power consumption and high density. How to achieve energy-efficient magnetization switching is one of the main challenges for MRAM. Recent studies propose spin orbit torque (SOT) as a promising method for data writing [1]. However, an external magnetic field along current direction is usually needed to realize deterministic switching. It can be overcome by using antiferromagnet/ferromagnet structures in which exchange bias can replace external field [2]. Voltage controll of magnetic anisotropy (VCMA) is another candidate method for lowering down the energy height by inducing electron accumulation at the ferromagnet/oxide interface[3]. Combination of VCMA and SOT effect may lead to decrease of power consumption by a gate voltage lowering the energy barrier height. For example, Yoda et.al propose a new spintronics-based memory employing the VCMA effect as a bit selecting principle and the SOT effect as a writing principle. [4]. Back et al reported that a gate voltage can be used to manipulate both perpendicular magnetic anisotropy and spin orbit torque[5]. Hence, it is essential to make it clear whether the voltage-controlled spin-orbit effective torques (VCSOT) or voltage controlled magnetic anisotropy causes the decrease of critical current, or both. In this work, we investigate VCSOT effect and VCMA effect in the IrMn/CoFeB/MgO structures. The film structures were thermally oxidized Si substrate/Ta(2)/IrMn(5)/CoFeB(0.94)/MgO(2.5)Al2O3(5), (with film thickness in nm in the parentheses). The films were patterned into Hall bar by ion beam etching (IBE) and lithography as shown in Fig. 1(a). Fig. 1(b) shows the micrograph of the Hall bar and the measurement setup. Furthermore, to explore voltage-gated SOT switching, a gate voltage is applied at the top electrode and the switching loops are obtained with no external field applied as shown in Fig. 1(d). Figure 1(f) presents critical current densities with 5mT field under different gate voltages. The critical current density Jc shows a decreasing tendency with increasing VMgO. These results indicate that a gate voltage can be used to effectively modulate SOT-driven perpendicular magnetization switching and this is a feasible writing method for low energy consumption. Next, spin-orbit effective fields at the different voltage were measured by using a second harmonic method as shown in Fig. 2 (a). The damping-like torque efficiency decreases with positive voltage increasing, whereas the field-like torque efficiency shows weaker voltage dependence. These results demonstrate that VMgO can modulate spin torques in IrMn/CoFeB/MgO system. The damping-like torque efficiency under VMgO of -0.4 V is 1.5 times larger than that under VMgO of 0.4 V. A larger JC is required for the magnetization switching under positive voltage due to the reduction of θSHE. Through VCSOT effect, positive voltage tends to increase Jc, which is reverse to the experimental results in Fig. 1(f). In-plane hysteresis loops at different gate voltages are obtained as shown in Fig. 2(b). The dependence of anisotropy energy Keff(VMgO) on gate voltage is shown in Fig.2 (c). By linear fitting, Keff decreases by 55% when VMgO changes from -0.6V to 0.6V. According to theoretical research from Ref.[6], the Jc for SOT switching is proportional to Keff. Therefore, the decrease of Keff will lead to significant reduction of Jc. Figure 2(d) shows the interfacial anisotropy coefficient Ki. We can see that the Ki changes linearly with VMgO due to VCMA effect. From the slope of the linear fitting, the VCMA coefficient ξ of 34.3 fJ/Vm is obtained for IrMn/CoFeB/MgO structure. Therefore, VCSOT effect is not the reason for the reduction of Jc in the voltage-gated SOT switching. The decrease of Jc in the voltage-gate SOT switching is mainly caused by the reduction of PMA due to VCMA effect. In summary, we demonstrate field-free switching in the IrMn/CoFeB/MgO structures and show the critical switching current can be modulated by the control voltage. Moreover, VCSOT effect and VCMA effect are explored. We measured spin-orbit effective torques under different voltage. We concluded that through VCSOT effect, positive voltage tends to increase Jc, which is reverse to the experimental results. Next, we measured anomalous Hall resistance at different voltage to explore VCMA effect. From quantitative calculation, the critical switching current at different voltage is consistent with experiments. Therefore, we concluded VCSOT effect hindered the reduction of Jc, while the VCMA effect made a main contribution to the Jc reduction. This work provides comprehensive understanding of voltage-gated spin torque switching.

**References:**

[1] M. Miron, K.Garello and G. Gaudin., Nature, vol. 476, no. 7359, pp. 189–193. (2011). [2] S.Z. Peng, D. Q. Zhu and W S Zhao., Adv. Electron. Mater. Vol. 5 pp. 1100134. (2019). [3] W.G. Wang, M. Li and C.L.Chien., Nat.Mater, vol. 11, no. 1, pp. 64–68. (2012). [4] H. Yoda, N. Shimomura and A. Kurobe., IEEE Electron Devices Meet. (IEDM). pp. 27.6.1-27.6.1. (2016). [5] L. Chen, M.Gmitra and C.H.Back., Nat. Electron., vol. 1, no. 6, pp. 350–355, (2018). [6] K.S. Lee, S.W. Lee and K.J. Lee., Appl. Phys. Lett. vol.102, pp. 112410. (2013).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1ed57da223949489824ad933c4957076.jpg)
Fig.1 (a) Schematic of IrMn/CoFeB/MgO structures. (b) Micrograph of the Hall bar and the measurement setup. (c) SOT-driven magnetization switching with various in-plane external field. Voltage-gated SOT switching under different gate voltages with (d)no external field and (e)5 mT in-plane external field. (f) Critical current density Jc dependence on voltage applied to MgO (VMgO) with 5 mT field applied.

![](https://assets.underline.io/uploads/markdown_image/1/image/177e5ff0550d0f2846103ad2879572c8.jpg)
Fig.2 (a) The dependence of spin-orbit effective torques on voltage in MgO layer (VMgO). The error bars are standard deviations. (b) Anomalous Hall resistance (RHall) under different gate voltages (VMgO) (c) Keff and (d) Ki dependence on VMgO.

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