Session L6: Spin-Transport Phenomena: Oscillators and Spin-Injections I

Mutual synchronization of two spin transfer oscillators coupled through their self-emitted microwave currents

Here, we demonstrate the mutual synchronization of two vortex STOs through electrical coupling. We describe how in using a delay line, we can optimize the locking range of the synchronization. We also evidence that the coupling efficiency is tuned by the nonlinear parameters of STOs but also more originally through the ratio between the two components of spin transfer torques. This represents a definite advantage of our vortex-STNOs for their future implementation in large arrays of synchronized STOs. We find that the linewidth of the two synchronized STOs decreases by a factor 2 and the output power increases by factor 4 ($\sim $ 1.6 \textmu W) compared to non -interacting STOs. These results provide a solid basis towards the efficient synchronization of multiple STOs. EU FP7 grant (MOSAIC No. ICT-FP7-317950 is acknowledged.   

Toggling synchronization of nano-contact spin torque oscillators with spin wave beams

The synchronization of multiple nano-contact spin torque oscillators (NC-STOs) [1-3] is mediated by propagating spin waves (SWs) [4]. Furthermore, it has been shown that the Oersted field in the vicinity of the NC can induce highly directional SW beams [5, 6]. Not only have we recently demonstrated the robust synchronization between two oscillators separated by over 1 micron, but also the driven synchronization of up to five oscillators by purposefully taking advantage of such SW beams [7]. Here, we demonstrate that when the NC diameters differ by a significant amount, the Oersted field scale in such a way as to promote or block synchronization depending on the SW propagation direction, allowing one to easily toggle between synchronized and un-synchronized states by simply altering the applied field direction. [1] S. Kaka, \textit{et al.}, Nature \textbf{437}, 389 (2005). [2] F.B. Mancoff, \textit{et al.}, Nature \textbf{437}, 393 (2005). [3] S.R. Sani, \textit{et al.}, Nat. Comm. \textbf{4}, 2731 (2013). [4] M.R. Pufall, \textit{et al.}, Phys. Rev. Lett. \textbf{97}, 087206 (2006). [5] R.K. Dumas, \textit{et al.}, Phys. Rev. Lett. \textbf{110}, 257202 (2013). [6] M.A. Hoefer, \textit{et al.}, Phys. Rev. B, \textbf{77}, 144401 (2008). [7] A. Houshang, \textit{et al.}, \textit{Nature Nanotechnol., }in press$.$   

Theory of mode coupling in spin torque oscillators coupled to a thermal bath of magnons

Recently, numerous experimental investigations have shown that the dynamics of a single spin torque oscillator (STO) exhibits complex behavior stemming from interactions between two or more modes of the oscillator. Examples are the observed mode-hopping and mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In this work, we rigorously derive such a theory starting with the generalized Landau-Lifshitz-Gilbert equation in the presence of the current-driven spin transfer torques. We will first show, in general, that how a linear mode coupling would arise through the coupling of the system to a thermal bath of magnons, which implies that the manifold of orbits and fixed points may shift with temperature. We then apply our theory to two experimentally interesting systems: 1) a STO patterned into nano-pillar with circular or elliptical cross-sections and 2) a nano-contact STO. For both cases, we found that in order to get mode coupling, it would be necessary to have either a finite in-plane component of the external field or an Oersted field. We will also discuss the temperature dependence of the linear mode coupling.   

Nonlocal spin-transfer with low-resistance AlO$_{x}$ spin injection interface and ohmic spin absorption interface

Mesoscopic nonlocal spin valves are fabricated for the purpose of spin-transfer with pure spin current. The device consists of a 300 nm wide Py (NiFe alloy) spin injector (F1), an 80 nm wide Py spin detector (F2) and an 80 nm wide Cu channel. The thickness of F1, F2, and Cu is 15 nm, 3 nm, and 110 nm, respectively. A 3 nm layer of low-resistance AlO$_{x}$ is placed at the F1/Cu interface to mitigate the spin resistance mismatch between Py and Cu and to provide substantial injection spin polarization. The F1 injector and the F1/AlO$_{x}$/Cu interface are robust enough to sustain a d.c. injection current up to 6 mA. The F2/Cu interface remains ohmic to facilitate an efficient absorption of the pure spin current from the Cu channel into the F2. A nanoscale magnetic domain in F2 underneath the F2/Cu interface can be reversibly switched between 5 K and 150 K via spin-transfer by the pure spin current. The critical injection current for the reversal at 100 K is \textasciitilde 1.5 mA, which is significantly lower than those in previous studies for nonlocal spin-transfer.   

Spin current valve effect in normal metal/magnetic insulator/normal metal sandwiches

Pure spin current is generated in two common ways. One makes use of the spin Hall effect in normal metals (NM), the other utilizes spin waves with the quasi-particle excitations called magnons. A popular material for the latter is yttrium iron garnet (YIG), a magnetic insulator (MI). Here we demonstrate in NM/MI/NM sandwiches that these two types of spin current are interconvertible, which allows transmitting an electrical signal across the MI, predicted as the magnon-mediated current drag phenomenon. We show experimentally that the spin current can be switched “on” or “off” by controlling the magnetization orientation of MI, analogous to conventional spin valves for spin-polarized charge current. The transmitted current drag signal scales linearly with the driving current without any threshold and follows the power-law T$^{\mathrm{n}}$ with n ranging from 1.5 to 2.5. Our results indicate that the NM/MI/NM sandwich structure can serve as a scalable pure spin current valve device which is an essential ingredient in spintronics.   

Comparison of spin transfer mechanisms in three terminal spin-torque-oscillators

The manipulation of magnetization by electric current is one of the most active field of spintronics due to its interests for memory and logic applications. This control can be achieved through the transfer of angular momentum via a spin polarized current (the mechanism of spin-transfer torque - STT) or through a direct transfer of angular momentum from the crystal lattice through the spin-orbit interaction (the mechanism of spin-orbit torque - SOT). Over the five past years, SOT gained a lot of attention especially for the new possibilities that it offers for data storage application. However, the quantification and the comparison of both mechanisms' efficiencies remains uncertain. In this work, we compare for the first time the STT and SOT efficiencies in individual devices. For this, we created 3-terminal spin-torque oscillators (STO) composed of spin-valves (SV) on top of a Pt wires. The devices can be excited either by STT or by SOT depending on whether the current is applied through the SV or through the Pt wire. By varying the Pt width and the dimensions of the SV, we tune the SOT and STT and compare their efficiencies. We will discuss the complexity of such a structure and the differences in the magnetization dynamics induced by the different excitation mechanisms.   

Characterization of perpendicular STT-MRAM by spin torque ferromagnetic resonance

We describe a method for simple quantitative measurement of magnetic anisotropy and Gilbert damping of the MTJ free layer in individual perpendicular STT-MRAM devices by spin torque ferromagnetic resonance (ST-FMR) with magnetic field modulation. We first show the dependence of ST-FMR spectra of an STT-MRAM element on out-of-plane magnetic field. In these spectra, resonances arising from excitation of the quasi-uniform and higher order spin wave eigenmodes of the free layer as well as acoustic mode of the synthetic antiferromagnet (SAF) are clearly seen. The quasi-uniform mode frequency at zero field gives magnetic anisotropy field of the free layer. Then we show dependence of the quasi-uniform mode linewidth on frequency is linear over a range of frequencies but deviatesfrom linearity in the low and high frequency regimes. Comparison to ST-FMR spectrareveals that the high frequency line broadening is linked to the SAF mode softening near the SAF spin flop transition at 5 kG. In the low field regime, the SAF mode frequency approaches that of the quasi-uniform mode, and resonant coupling of the modes leads to the line broadening. A linear fit to the linewidth data outside of the high and low field regimes gives the Gilbert damping parameter of the free layer.   

Spin-torque ferromagnetic resonance (ST-FMR) spectroscopy of localized spin wave modes engineered by applied dipole-field localization

Maintaining efficient spin-Hall anti-damping torque in micron-scale devices is challenging near the critical current for auto-oscillation, likely due to spin wave mode degeneracies and nonlinear magnon scattering between them [1]. Localized spin wave modes confined by the strongly inhomogeneous dipole magnetic field of a nearby micro-spherical magnet [2] provides a potentially powerful tool to study these multi-mode interactions by allowing systematic tunability while avoiding potential spurious effects arising from imperfections in fabricating microscopic structures. We demonstrate electrical ST-FMR detection of well-resolved localized modes in a Py/Pt stripe. We find that magnon spectral engineering by means of a micromagnetic particle enables clear observation of damping control and significant reduction of linewidth by means of the anti-damping torque arising from an imposed DC current. The observed linewidth variation suggests that localized modes can be controlled as effectively as the uniform mode. References: [1] V. E. Demidov et al, Phys. Rev. Lett. 107, 107204 (2011) Z. Duan et al, Nat. Commun. 5, 5616 (2014) [2] I. Lee et al., Nature 466, 845 (2010) H.-J. Chia et al., Phys. Rev. Lett. 108, 087206 (2012)   

First-principles theory of current-induced spin torques in noncollinear antiferromagnets

We propose a new theoretical approach for calculating current induced torques in hybrid systems containing magnetic and heavy metal thin films. The theory is based on ab-initio density functional theory (DFT) and appeals explicitly to the local-spin-density approximation for exchange and correlation. Because the effective magnetic field from exchange and correlation is everywhere parallel to the spin-density in the ferromagnet, it does not contribute to the current-induced torque, which is due entirely to spin-orbit coupling near heterojunctions involving heavy metals. The theoretical picture can be combined with any theory of the electronic steady state produced by electrochemical potential gradients, and involves response of the single-particle density matrix that is partially diagonal and partially off-diagonal in an unperturbed eigenstate representation. The theory is formulated using the basis of Wannier functions and can be readily interfacing with existing DFT codes. This approach predicts strong current-induced torques due to either antiferromagnetic or non-magnetic heavy metal layers. As an illustration, we use it to calculate specifically the spin torque in a ferromagnet induced by an adjacent noncollinear antiferromagnet (Mn3Ir).   

Spin Torque Generated by the Spin Hall Effect in Ferromagnets

Ferromagnetic materials exhibit the anomalous Hall effect, the generation of a transverse charge current due to spin-orbit coupling. The anomalous Hall effect is closely related to the spin Hall effect, and hence this transverse charge current is expected to be accompanied by a strong transverse spin current, whose direction can be manipulated by rotating the magnetic moment. We measure the torque from this spin current generated by Gd-doped Fe and acting on an in-plane magnetized free layer. We use the harmonic measurement technique, applying a current to an in-plane pinned ferromagnet/spacer/in-plane free ferromagnet stack and measuring the second harmonic Hall voltage. We report the angular dependence of the spin torque for a variety of initial exchange bias directions, and as the spin torque changes with an external magnetic field.   

Enhanced spin orbit torques by oxygen incorporation in tungsten films

Spin orbit torques are generated by the conversion of charge to spin currents in non-magnetic materials. The origin of these torques is of considerable debate. One of the most interesting materials is metallic tungsten for which large spin orbit torques have been found in thin films that are stabilized in the A15 ($\beta $-phase) structure. Here we report, using spin transfer torque ferromagnetic resonance, large spin Hall angles of up to \textasciitilde --0.5 by incorporating oxygen into tungsten films. Whilst the incorporation of oxygen into the tungsten leads to significant changes in its microstructure and electrical resistivity, the large spin Hall angles measured are found to be remarkably insensitive to the oxygen doping level (12-44{\%}). This invariance of the spin Hall angle with the bulk W(O) properties for higher oxygen concentrations suggests that the spin orbit torques in this system may actually be partly interfacial in origin, and induced by scattering of the electrons at the W(O) \textbar CoFeB interface rather than from the interior of the W(O) film. Our results show an intriguing novel path towards enhanced spin orbit torques.   

Optically Detected Ferromagnetic Resonance in Metallic Ferromagnets Via Off-Resonant Detection of Nitrogen Vacancy Centers in Diamond

We report optical detection of ferromagnetic resonance in thin film metallic ferromagnets using a recently discovered approach employing nitrogen vacancy centers in nanodiamonds. While conventional optically detected magnetic resonance measures magnetic fields through their impact on the magnetic resonance frequency of the nitrogen vacancy center, we measure a change in the nitrogen vacancy center photoluminescence at the ferromagnet’s resonance condition without need to work at the NV resonance frequency. This measurement technique allows sensitive, local detection of ferromagnetic resonance and can enable the study of magnetic dynamics at the nanoscale in a wide range of materials. While this measurement protocol was first reported in the study of ferromagnetic resonance in YIG, here we demonstrate the measurement in commonly used metallic ferromagnets to establish the generality of the technique and open the possibility of measuring nanoscale patterned devices and magnetic textures based on metallic ferromagnets of both commercial and scientific interest.   

Phase-resolved ferromagnetic resonance detection using heterodyning

We have developed a new phase-resolved ferromagnetic (FMR) detection method using a heterodyne method. Phase resolution is important to determine the characteristics of spin transfer torques in magnetization dynamics under microwave excitation [1]. Specifically, field-like torques and damping-like torques result in magnetization precession with different phases. In this method, we drive spin precession in a Permalloy thin film using microwaves. The resulting precession is detected using 1550 nm laser light, that is modulated at a frequency slightly shifted with respect to the driving frequency. In the reflected light, beating of the spin precession and the light modulation produces an oscillating Kerr rotation signal with a phase equal to the precession phase plus a phase due to the path length difference between the excitation microwave and the optical signal. This detection method eliminates the need for field modulation and allows detection at higher frequencies where the 1/f noise floor is reduced. [1] M. Weiler, J. M. Shaw, H. T. Nembach, and T. J. Silva, Phys. Rev. Lett. 113, 157204 (2014).   

Anomalous Hall Effect in a Kagome Ferromagnet

The ferromagnetic kagome lattice is theoretically known to possess topological band structures [1,2]. We have synthesized large single crystals of a kagome ferromagnet Fe$_3$Sn$_2$ which orders ferromagnetically well above room temperature [3]. We have studied the electrical and magnetic properties of these crystals over a broad temperature and magnetic field range.  Both the scaling relation of anomalous Hall effect and anisotropic magnetic susceptibility show that the ferromagnetism of Fe$_3$Sn$_2$ is unconventional.  We discuss these results in the context of magnetism in kagome systems and relevance to the predicted topological properties in this class of compounds.  [1] \emph{Phys. Rev. B} 87 144101 (2013) [2] \emph{Phys. Rev. Lett.} 106 236802 (2011)  [3] \emph{J. Phys: Cond. Mat.} 21 452202 (2009)   

Interaction and multiband effects in the intrinsic spin-Hall effect of an interacting multiorbital metal

The spin-Hall effect is a spin-current version of the usual-Hall effect, and its potential for application may be great. For the efficient application utilizing the spin-Hall effect, an understanding of interaction effects may be helpful because the interaction effects sometimes become remarkable in transport phenomena (e.g., fractional-quantum-Hall effect). However, a lot of theoretical studies neglected the interaction effects, and the interaction effects in the spin-Hall effect had been little understood. To improve this situation, I developed a general formalism for the intrinsic spin-Hall effect including the interaction effects and multiband effects by using the linear-response theory with approximations appropriate for an interacting multiorbital metal (see arXiv:1510.03988). In this talk, I explain how the electron-electron interaction modifies the spin-Hall conductivity and show several new and remarkable interactions effects, new mechanisms of the damping dependence and a crossover of the damping dependence in a clean system and a temperature-dependent correction due to the spin-Coulomb drag. I also show guidelines useful for general formulations of other transport phenomena including the interaction effects and multiband effects.