Spin-Rotation Coupling: One Hundred Years After Einstein – de Haas and Barnett Experiments

• Eugene M. Chudnovsky (CUNY Lehman College and Graduate School)

Room: Mount Temple A Century-long studies of spin-rotation coupling will be reviewed, starting with Einstein - de Haas and Barnett experiments, and ending with modern-time experiments on torsional nano-oscillators and quantum Einstein – de Haas effect in magnetic molecules chemisorbed on surfaces and grafted on carbon nanotubes. Open questions related to microscopic mechanisms of the conservation of the total angular momentum in solids will be discussed.

Nanophotonic optomechanical devices: towards coupling photons, phonons and spins

• Paul Barclay (University of Calgary)

Room: Mount Temple A Optomechanical devices enhance the optical radiation pressure induced interaction between light and mechanical resonators. This interaction can be harnessed to enable coherent conversion of light to mesoscopic phonons with frequencies ranging from kHz to GHz. Through control of these phonons, new approaches for manipulating and probing solid state spin systems are feasible. In this talk I will present recent advances in creating such nanoscale "spin-optomechanical" devices. I will first present results demonstrating some of the first optomechanical devices fabricated from single crystal diamond [1, 2], which in addition to having remarkable mechanical properties (e.g. ultrahigh mechanical Q*f product), can be used for optomechanical control of single electron spins. I will then discuss silicon based nanophotonic devices that allow optomechanical probing of the magnetic properties of nanostructures, providing routine on-chip photonic readout of the nanomagnetic susceptibility of single magnetic defects [3]. Finally, I will comment on the prospect of cooling these devices into their quantum ground state, enabling studies coupling single phonons to electronic or magnetic spin systems. [1] B. Khanaliloo, H. Jayakumar, A. C. Hryciw, D. Lake, H. Kaviani, P. E. Barclay, "Single crystal diamond nanobeam waveguide optomechanics," Physical Review X 5, 041051 (2015) [2] M. Mitchell, B. Khanaliloo, D. Lake, P. E. Barclay, "Low-dissipation cavity optomechanics in single crystal diamond," Optica 3, 963 (2016) [3] M. Wu, N. L.-Y. Wu, T. Firdous, F. F. Sani, J. E. Losby, M. R. Freeman, P. E. Barclay, "Nanocavity optomechanical torque magnetometry and RF susceptometry," Nature Nanotechnology (Advanced Online Publication, doi:10.1038/nnano.2016.226, 2016)

Hybrid quantum systems with ultrahigh-Q nanomechanical resonators

• Albert Schliesser (Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Denmark)

Room: Mount Temple A We report a multimode optomechanical system with quantum cooperativity 𝐶_q = 4𝑔^2/𝜅𝛾 ≫ 1 already at moderate cryogenic temperature T~10 K [1]. Here, 𝛾 = 𝑘B𝑇/ℏ𝑄 is the quantum decoherence rate of the mechanical system, and Q~10^7 the mechanical quality factor. In this regime, the quantum backaction of the optical measurement dominates over the thermal Langevin noise. As a consequence, optical measurements create quantum correlations between the optical and mechanical degrees of freedom, which are measured as ponderomotive squeezing (-2.4 dB) of the light emerging from the cavity. In the multimode setting investigated here, we observe optically-induced hybridisation of mechanical modes, and the generation of squeezed light by hybrid modes [1]. Furthermore, we have implemented a hybrid system by combining this optomechanical system with a room-temperature atomic ensemble [2]. A light beam probes the spin state through Faraday interaction, and subsequently the motion of the nanomechanical membrane. We show that it is possible to cancel part of the measurement’s quantum backaction by appropriately tailoring the light-spin, and subsequent light-mechanical interaction. Finally, we report on the development of a novel type of membrane and string resonators with dramatically reduced decoherence [3]. By patterning a phononic crystal directly into a stressed SiN membrane we realise a “soft clamp” for a localised defect mode. Its engineered mode shape exhibits reduced curvature and therefore dissipation, reaching room-temperature Qf-products in excess of 10^{14} Hz—the highest reported to date—as well as Q~10^9 at T~4 K. The corresponding room temperature coherence time approaches that of optically trapped dielectric particles, and for cryogenic operation becomes comparable (~1 ms) to that of trapped ions. Extensive characterisation through laser-based imaging of mode shapes [3] and stress distribution [4] confirms a model that quantitatively predicts the quality factors over a wide parameter range. References [1] W. H. P. Nielsen, Y. Tsaturyan, C. B. Møller, E. S. Polzik, and A. Schliesser, PNAS 114, 62 (2017). [2] C. B. Møller, R. A. Thomas, G. Vasilakis, E. Zeuthen, Y. Tsaturyan, K. Jensen, A. Schliesser, K. Hammerer and E. S. Polzik, arXiv:1608.03613 [3] Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, arXiv:1608.00937 [4] A. Barg, Y. Tsaturyan, E. Belhage, H. P. W. Nielsen, C. B. Møller, and A. Schliesser, Applied Physics B 123, 8 (2017). [5] T. Capelle, Y. Tsaturyan, A. Barg, and A. Schliesser, in preparation.

Quantum Einstein de Haas Effect Studied With Molecular Spintronic Devices

• Franck Balestro (Institut Néel, CNRS, Grenoble Alpes University, BP 166, 38042 Grenoble, France)

Room: Mount Temple A One hundred years ago it has been discovered that a change of magnetization in a macroscopic magnetic object results in a mechanical rotation of this magnet [1]. The effect, known as Einstein de Haas or Richardson effect, demonstrates that a spin angular momentum in the magnet compensates for the mechanical angular momentum associated with its rotation. The experiment is therefore a macroscopic manifestation of the conservation of total angular momentum and energy in electronic spins. According to Noether's theorem, conservation of angular momentum follows from a system`s rotational invariance and would be valid for the ensemble of spins in a macroscopic ferromagnet as well as for an individual spin. It has been recently proposed that single spin systems would therefore manifest an Einstein de Haas effect at the quantum level [2]. Here we propose the first experimental realization of a quantum Einstein-de Haas experiment and describe a macroscopic manifestation of the conservation of total angular momentum in individual spins, using a single molecule magnet coupled to a nanomechanical resonator. We demonstrate that the spin associated with the single molecule magnet is then subject to conservation of total angular momentum and energy which results in a total suppression of the molecule’s quantum tunneling of magnetization [3]. 1. A. Einstein and W.J. de Haas, Deutsche Physikalische Gesellschaft, Verhandlungen, 1915, 17, 152. 2. E. M. Chudnovsky and D. A. Garanin, Phys. Rev. Lett., 1994, 72, 3433; Phys. Rev. B, 2010, 81, 214423; Phys. Rev. B, 2005 72, 094426;
 Phys. Rev. X, 2011, 1, 011005. 3. M. Ganzhorn, S. Klyatskaya, M. Ruben, W. Wernsdorfer, Nature Nanotechnol., 2013, 8, 165; Nature Comm., 2016.

Mechanical Effects on Spintronics

• Sadamichi Maekawa (Advanced Science Research Center, Japan Atomic Energy Agency)

Room: Mount Temple A We introduce mechanical effects on spintronics [1] and propose a variety of novel spintronics phenomena [2]. In particular, the coupling between nuclear spin and mechanical rotation is demonstrated [3]. Since the Bernett field is enhanced by three orders of magnitudes in nuclei more than electron spins, the nuclear-magnetic-resonance (NMR) with mechanical rotation introduces new applications. In addition to the Bernett effect, the mechanical rotation induces the spin-Berry phase which gives rise to additional resonance phenomena in NMR [4]. <br> We observe the generation of spin current by the flow of liquid metals. Combining this effect with the inverse spin Hall effect, the spin-hydrodynamic generation of electricity is obtained [5]. <br> The coupling between mechanical motion and a variety of spins may be identified as a quantum version of the Einstein-de・Haas effect and Bernett effect discovered in 1915. [1] M.Matuo, J.Ieda and S.Maekawa, Phys. Rev. Lett. 106, 076601 (2011). <br> [2] For example, M.Matsuo, E.Saitoh and S.Maekawa, to appear in J.Phys. Soc. Jpn. (2017).<br> [3] H.Chudo,M.Ono, K.Harii, M.Matsuo, J.Ieda, R.Haruki,S.Okayasu, S.Maekawa, H.Yasuoka and E.Saitoh, Appl. Phys. Express 7, 063004 (2014). <br> [4] M.Matsuo, H.Chudo, K.Harii, M.Sato, S.Maekawa and E.Saitoh, to be published. <br> [5] R.Takahashi, M.Ono, K.Harii, S.Okayasu, M.Matsuo, J.Ieda, S.Takahashi, S.Maekawa and E.Saitoh, Nature Phys. 12, 52 (2016).

Spintronics

• Sebastian Gönnenwein (Institut für Festkörperphysik, Technische Universität Dresden, D-01062 Dresden, Germany, and Center for Transport and Devices of Emergent Materials, Technische Universität Dresden, D-01062 Dresden)

Room: Mount Temple A The performance of modern electronic devices hinges on the transport, storage, amplification and/or detection of electronic charge. In close analogy, one can also envisage transporting, storing, sensing or amplifying spin angular momentum, taking advantage of spin-polarized charge currents or even pure spin currents. In general terms, the field of spintronics addresses the physics and the properties of structures featuring spin-based functionality. The tutorial shall give an introduction to spintronics and spin transport from an experimentalist’s perspective. I will discuss basic concepts behind charge and spin current transport, and address the interconversion between charge and spin currents based on spin Hall physics. The main focus of the tutorial will then be on spintronic devices and spin current transport-related phenomena.

Topological Antiferromagnetic Spin-orbitronics

• Jairo Sinova (Institut fur Physik, Johannes Gutenberg Universitat Mainz, 55128 Mainz, Germany)

Room: Mount Temple A Antiferromagnetic spintronics considers the active manipulation of the antiferromagnetic order parameter in spin-based devices. An additional concept that has emerged is that antiferromagnets provide a unifying platform for realizing synergies among three prominent fields of contemporary condensed matter physics: Dirac quasiparticles and topological phases. Here spintronic devices made of antiferromagnets with their unique symmetries will allow us to control the emergence and to study the properties of Dirac/Weyl fermion topological phases that are otherwise principally immune against external stimuli. In return, the resulting topological magneto-transport phenomena open the prospect of new, highly efficient means for operating the antiferromagnetic memory-logic devices. We discuss how these topological phases emerge and how their robustness depend on the relative orientation of the Neel order parameter that can be manipulated by Neel spin-orbit torques. If time allows, we will further discuss the generation and excitation of skyrmionic textures in simple geometries.

Spin - orbit coupling in ferro- and antiferromagnets

• Mathias Kläui (Johannes Gutenberg University Mainz)

Room: Mount Temple A The coupling of the mechanical lattice degree of freedom to the spin system by spin-orbit effects gives rise to a range of exciting mechanisms that can be key enablers for future low power GreenIT devices. The three main challenges that need to be met concern the stability of spin structures, their efficient manipulation and finally the low loss transport of spin information [1]. So firstly to obtain ultimate stability, topological spin structures that emerge due to the Dzyaloshinskii-Moriya interaction (DMI) at structurally asymmetric interfaces, such as chiral domain walls and skyrmions with enhanced topological protection can be used [2-4]. We have investigated in detail their dynamics and find that it is governed by the topology of their spin structures [3]. By designing the materials, we can even obtain a skyrmion lattice phase as the ground state of the thin films [3]. Secondly, for ultimately efficient spin manipulation in ferromagnets and antiferromagnets, we use spin-orbit torques, that can transfer more than 1ħ per electron by transferring not only spin but also orbital angular momentum. We combine ultimately stable skyrmions with spin orbit torques into a skyrmion racetrack device [3], where the real time imaging of the trajectories allows us to quantify the novel skyrmion Hall effect [4]. Finally to obtain efficient spin transport, we study the coupling between phonons and magnons in ferro- and antiferromagnetic insulators that can be used as spin conduits for long distance spin transport [5]. We establish that both, bulk and interface effects play a key role and together govern the measured spin transport signals in ferro-, ferri- and antiferromagnetic compounds [5,6] [1] Reviews: O. Boulle et al., Mater. Sci. Eng. R 72, 159 (2011); G. Finocchio et al., J. Phys. D: Appl. Phys. 49, 423001 (2016). [2] F. Büttner et al., Nature Phys. 11, 225 (2015). [3] S. Woo et al, Nature Mater. 15, 501 (2016); [4] K. Litzius et al., arxiv:1608.07216 (Nature Phys. in press (2016)). [5] A. Kehlberger et al., Phys. Rev. Lett. 115, 096602 (2015); [6] S. Geprägs et al., Nature Commun. 7, 10452 (2016); E.-J. Guo et al, Phys. Rev. X 6, 031012 (2016)

Magnon-mediated Dzyaloshinskii-Moriya torques, heat pumping, and spin Nernst effect.

• Alexey Kovalev (University of Nebraska-Lincoln)

Room: Mount Temple A We predict that a temperature gradient can induce a magnon-mediated spin Hall response in a collinear antiferromagnet with Dzyaloshinskii-Moriya interactions [1]. We have developed a linear response theory based on the Luttinger approach of the gravitational scalar potential which gives a general condition for a Hall current to be well defined, even when the thermal Hall response is forbidden by symmetry. We applied our theory to honeycomb lattice antiferromagnet and studied a role of magnon edge states in a finite geometry. As examples, we considered single and bi-layer honeycomb antiferromagnets where the nearest neighbor exchange interactions and the second nearest neighbor Dzyaloshinskii-Moriya interactions were present. From our analysis, we suggest to look for the magnon-mediated spin Nernst effect in insulating antiferromagnets that are invariant under (i) a global time reversal symmetry or under (ii) a combined operation of time reversal and inversion symmetries. In both cases, the thermal Hall effect is zero while the spin Nernst effect can be present. We have also considered transport of magnons and its relation to non-equilibrium magnon-mediated spin torques [2]. In particular, a temperature gradient can induce a magnon-mediated intrinsic torque in systems with broken inversion symmetry and spin-orbit interactions. With the help of a microscopic linear response theory of nonequilibrium magnon-mediated torques and spin currents we identify the interband and intraband components that manifest in ferromagnets with Dzyaloshinskii-Moriya interactions. To illustrate and assess the importance of such effects, we have applied the linear response theory to the magnon-mediated Nernst and torque responses in a kagome and honeycomb lattice ferromagnets. With the help of Onsager reciprocity principle we establish a connection to magnon-mediated contribution to Dzyaloshinskii-Moriya interactions. We suggest that magnons can lead to temperature dependence in Dzyaloshinskii-Moriya interactions. Finally, in a system with broken inversion symmetry and spin-orbit interactions we predict the magnon-mediated heat and spin pumping by magnetization precession. [1] arXiv:1606.03088 [2] Phys. Rev. B 93, 161106 (2016)

Evidence for a common origin of spin-orbit torque and the Dzyaloshinskii-Moriya interaction at a Py/Pt interface

• Thomas Silva (National Institute of Standards and Technology)

Room: Mount Temple A Harnessing spin-charge conversion through current-driven spin torques and spin precession-driven charge currents is widely regarded as a key for the development of scalable and efficient spintronic devices. These conversion processes occur across ferromagnet/normal metal (FM/NM) interfaces where there is strong spin-orbit coupling (SOC) but where details of the underlying physics are still much debated. SOC also underlies the interfacial Dzyaloshinskii-Moriya interaction (DMI). While efficient spin-charge conversion and large DMI often coincide, a causal connection between these two phenomena has not yet been experimentally established. It was recently proposed that a Rashba Hamiltonian operative at a FM/NM interface gives rise to both spin-orbit torques (SOT) and DMI, such that the presence one effect implies the other [1]. Despite the complexity of interfacial spin interactions, this theory provides a simple, testable quantitative relation between the DMI and SOT. Here, we use a powerful new microwave spectroscopy method to detect inverse spin-charge conversion processes in FM/NM bilayers [2] and demonstrate that the magnitude of the SOT is in good agreement with the theoretically-predicted value based on the previously measured value of DMI in identical bilayers [3]. [1] K.-W. Kim, H.-W. Lee, K.-J. Lee, and M. D. Stiles, Physical Review Letters 111, 216601 (2013). [2] A. J. Berger, E. R. J. Edwards, H. T. Nembach, J. M. Shaw, A. D. Karenowska, M. Weiler, T. J. Silva, arXiv:1611.05798 (2016). [3] H. T. Nembach, J. M. Shaw, M. Weiler, E. Jue, and T. J. Silva, Nature Physics 11, 825 (2015).

Fluid and mechanical spintronics

• Eiji Saitoh (ERATO-SQR, Tohoku University)

Room: Mount Temple A Spin current refers to a flow of electrons’ spin angular momentum in condensed matter, which is detectable by using the inverse spin Hall effect. Various phenomena induced by spin currents, such as spin-transfer torque and spin Seebeck effects have been discovered so far. Here I will give an introduction to phonon anomaly in spin Seebeck effects, spin current generated in a classical fluid, and spinon spin current generated in a quantum spin liquid state.

Hybrid quantum optomechanics

• Benjamin Pigeau (Institut Néel, CNRS and Université Grenoble Alpes)

Room: Mount Temple A A hybrid system consisting in a mechanical oscillator coupled to a purely quantum object is a powerful tool to study the quantum to macroscopic world interface. This is a unique route toward the creation of counter intuitive non classical states of motion. The emblematic signatures of quantum electrodynamics, such as Rabi oscillations of the quantum system population and Mollow triplet physics, are expected to arise from the hybrid coupling [2]. Here we investigate the dynamics of a SiC nanowire coupled to a nano-diamond hosting a single Nitrogen Vacancy defect. The SiC wire have intrinsically large oscillation amplitudes at high frequency and exhibit two orthogonal nearly degenerated polarisations. Regarding their ultra low masses they are very accurate vectorial force sensor, exhibiting room temperature sensitivities in the attoNewton range [1]. The NV centre contains a single electronic (S=1) spin that can be manipulated and readout using laser light. Similarly to a Stern-Gerlach experiment, the Zeeman energy of the spin is coupled to the oscillator position using a strong magnetic field gradient. The spin energy is therefore parametrically modulated at the mechanical frequency. It will be evidenced that this system has the potential to enter the strong coupling regime [1]. Moreover the parametric interaction can be turned resonant using a microwave dressing of the NV spin. In the dressed basis, the Rabi frequency of the spin population can be tuned to the mechanical frequency. As a result of this QED like interaction a phonon-dressed Mollow triplet is observed in the Rabi frequency of the spin [3]. These results pave the way to the observation quantum forces, namely the single spin back-action onto the mechanical oscillator. The outstanding sensitivity of SiC nanowires is also harnessed to probe other types of forces. In particular the vectorial nature of these force fields can be mapped with great accuracy. We have demonstrated the principle of such capability by mapping the electrostatic field created by a sharp metallic tip [4]. This experiment will lead to the measurement of fundamental vacuum fluctuation forces (or Casimir forces) in novel and unexplored geometries. [1] A. Gloppe et al., Nature Nanotechnology 9, 2014 [2] S. Rohr et al., Physical Review Letters 112, 2014 [3] B. Pigeau et al., Nature Communications 6, 2015 [4] L. Mercier de Lépinay et al., Nature Nanotechnology 11, 2016

Spin Transport by Collective Spin Excitations

• P. Chris Hammel (Department of Physics, The Ohio State University, 191 West Woodruff Avenue, Columbus, Ohio 43210-1117)

Room: Mount Temple A We report studies of angular momentum transport and magnetic dynamics in diverse insulating materials. We have shown that spin transport is exponentially suppressed by insulating diamagnetic barriers, but we find that collective spin excitations in various materials can enable robust spin transport in insulators. We present studies that reveal efficient spin transport in Yttrium Iron Garnet (YIG) even in the presence of magnetic-field defined barriers that require inter-conversion between magnons of dissimilar energy. Optical detection of Ferromagnetic Resonance (FMR) in YIG by means of nitrogen-vacancy (NV) defect centers in diamond reveals the role of spin waves in this dipole-mediated spin transfer process and presents a powerful approach to broadband, spatially resolved FMR detection for these and related studies. We find that fluctuating antiferromagnetic (AF) spin correlations also enable efficient spin transport having decay lengths approaching 10 nm in insulating antiferromagnets. While the spin decay length increases with the strength of the AF correlations, AF magnon spin transport is robust against the absence of long-range order. This research performed in collaboration with F.Y. Yang, V.P. Bhallamudi, C.H. Du, R. Adur, H.L. Wang, C.S. Wolfe, A.J. Berger and S.A. Manuilov, and is supported by the U.S. DOE through Grant DE-FG02-03ER46054, by the NSF MRSEC program through Grant 1420451 and by the Army Research Office through Grant W911NF-16-1-0547.

Quantum-limited and backaction evading measurements in optomechanics

• Aashish Clerk (McGill University)

Room: Mount Temple A In this tutorial-style talk, I’ll give an introduction to various aspects of how quantum mechanics constrains measurements in optomechanics. Among the topics I’ll cover include the formal definition of the quantum limit on continuous position measurement, techniques for beating the “standard” quantum limit, and back-action evading measurement strategies. Time permitting, I will end by discussing our recent work on two-mode backaction evading measurements and connections to autonomous feedback protocols (i.e. “reservoir engineering”) for stabilizing entangled mechanical (or magnonic) states.

The quantum limit of interacting magnetic waves

• Michael Flatté (University of Iowa)

Room: Mount Temple A The dynamic response of magnetic materials lacks time-reversal symmetry and can often be described through the propagation and evolution of waves of magnetic orientation, or spin waves. These spin waves, or magnons when quantized, can move without electric charge motion, yet spin-orbit interactions allow the spin waves to couple, sometimes very strongly, both to voltages and to illumination.  I will describe progress over the last several years in calculating and understanding, in collaboration with experimentalists, the coupling of magnons to microwave[1,2] and optical photons[3] as well as the manipulation of spin-wave propagation with a voltage[4]. In analogy with optomechanics, two photons will interact, within a cavity containing a ferrite, with a magnon mode to coherently modify the spontaneous emission rate, to exhibit electromagnetically-induced transparency and even to reach the strongly-coupled quantum regime[3]. Patterned magnetic media can also amplify voltage-dependent effects to produce voltage-tunable oscillators or filters[5]. Recently we have predicted a new effect called nonlocal magnon drag, whereby a flow of magnons in one sheet will drag magnons in a neighboring, disconnected sheet[6]. The presence of the magnetization in the two sheets introduces a twist in the drag, producing a transverse spin current. As a final example, we predict that quantum-coherent spin centers can sense the magnetic susceptibility of nearby materials, distinct from the magnetization of the material itself, and so this provides a potential method of detecting superconductors or magnetic dead layers without applied magnetic fields[7]. Work supported in part by ONR, AFOSR, DARPA, and NSF. \noindent [1] Ö. O. Soykal and M. E. Flatté, Phys. Rev. Lett. **104**, 077202 (2010). \noindent [2] Ö. O. Soykal and M. E. Flatté, Phys. Rev. B **82**, 104413 (2010). \noindent [3] T. Liu, X. Zhang, H. X. Tang, and M. E. Flatté, Phys. Rev. B **94**, 060405(R) (2016). \noindent [4] X. Zhang, T. Liu, M. E. Flatté and H. X. Tang, Phys. Rev. Lett. **113**, 037202 (2014). \noindent [5] G. Sietsema and M. E. Flatté, submitted. \noindent [6] T. Liu, G. Vignale and M. E. Flatté, Phys. Rev. Lett. **116**, 237202 (2016). \noindent [7] J. van Bree and M. E. Flatté, Phys. Rev. Lett. in press.

Cavity mediated non-local manipulation of spin current using cavity-magnon-polariton

• Lihui Bai (University of Manitoba)

Room: Mount Temple A As a strongly coupled magnon-photon system, the cavity-magnon-polariton (CMP) offers many potential applications for information processing. Typically such information processing applications would require manipulation of the energy exchange between the magnon and photon subsystems which, in a CMP system, relies on the cooperativity and can therefore be easily controlled. However in order to measure the extent of such an exchange, the spin subsystem must be locally detected. This obstacle can be overcome through electrical detection techniques. In our work we have combined electrical detection via the spin pumping effect with microwave transmission measurements in order to locally detect both the individual photon and spin subsystems of the CMP in a system comprised of one microwave cavity mode and two magnetic samples. Through controlling the cooperativity of one magnetic sample, while locally detecting another, we demonstrate a non-local spin current manipulation mediated by the cavity mode. We have demonstrated such a non-local spin current manipulation over a spatial separation up to 38 mm (limited only by the cavity size), which is orders of magnitude longer than either the spin coherence or diffusion length in materials. Therefore our work demonstrates the capability of strong spin-photon coupling for long range spin current manipulation, which we expect to play an important role in the development of cavity spintronics.

Magnon Kerr effect in a cavity quantum electrodynamics system

• Jian-Qiang You (Beijing Computational Science Research Center)

Room: Mount Temple A We report the experimental demonstration of the magnon Kerr effect in a cavity quantum electrodynamics system, where magnons in a small yttrium iron garnet (YIG) sphere are strongly but dispersively coupled to the microwave photons in a three-dimensional cavity. When considerable magnons are generated by pumping the YIG sphere, the Kerr effect gives rise to a shift of the cavity central frequency and yields more appreciable shifts of the magnon modes, including the Kittel mode (i.e., the ferromagnetic resonance mode), which holds homogeneous magnetization, and the magnetostatic (MS) modes, which have inhomogeneous magnetization. We derive an analytical relation between the magnon frequency shift and the pumping power for a uniformly magnetized YIG sphere and find that it agrees very well with the experimental results of the Kittel mode. In contrast, the experimental results of MS modes deviate from this relation owing to the spatial variations of the MS modes over the sample. To enhance the magnon Kerr effect, the pumping field is designed to directly drive the YIG sphere and its coupling to the magnons is strengthened using a loop antenna. Moreover, this field is tuned very off-resonance with the cavity mode to avoid producing any appreciable effects on the cavity. Our work is the first convincing study of a cavity QED system with magnon Kerr effect and paves the way to experimentally explore nonlinear effects in the cavity QED system with magnons.

High-Q and Novel Cavity Structures for Photon-Spin Strong Coupling

• Michael Tobar (ARC Centre of Excellence for Engineered Quantum Systems, University of Western Australia)

Room: Mount Temple A Strong coupling between microwave photons and spins at millikelvin temperatures is necessary to realise quantum information processing. We will present our most recent results in coupling strongly to a variety of cavity and spin systems. Novel cavity systems include whispering gallery modes, 3D lumped element meta-structures based on the reentrant cavity and dielectric TE modes. Spin systems include paramagnetic iron group and rare-earth impurities doped in low-loss crystalline materials (such as YSO, YAP and Silicon), P1 centers in diamond and magnons in ferrimagnetic YIG. In particular we will focus on new cavities, which couple photons and magnons in YIG spheres in a super- and ultra-strong way at around 20 mK in temperature. Few/Single photon couplings (or normal mode splitting, 2g) of more than 7 GHz at microwave frequencies are obtained for a 15.5 GHz mode. Types of cavities include multiple post reentrant cavities, which co-couple photons at different frequencies with a coupling greater that the free spectral range, as well as spherical loaded dielectric cavity resonators. In such cavities we show that the bare dielectric properties can be obtained by polarizing all ferromagnetic effects and magnon spin wave modes to high energy using a 7 Tesla magnet. We also show that at zero-field, collective effects of the spins significantly perturb the photon modes. Other effects like time-reversal symmetry breaking are observed.

Zero-field current switching of a single ferromagnetic layer

• Chia-Ling Chien (Johns Hopkins University)

Room: Mount Temple A Spin Hall effect (SHE) switching allows current switching of a single ferromagnetic (FM) layer in contact with a heavy metal (HM), where the pure spin current from the HM switches the adjacent FM layer via the spin orbit torque (SOT). However, this highly attractive scheme cannot occur unless a magnetic field is also applied along the current direction, or with some built-in asymmetry in the structure, thus greatly diminishing its utility. In this work, we describe the essential role of the magnetic field, which not only breaks geometrical symmetry and but also causes asymmetrical domain wall motion that accomplishes switching. More importantly, we demonstrate a new method of exploiting competing SOT by exploiting HMs with opposite spin Hall angles, different Dzyaloshinskii-Moriya interaction constants, and competing pure spin current. We describe the intricate physics that accomplishes current switching of a single ferromagnetic layer in zero magnetic field.

Spin dynamics of a magnetic antivortex

• Kristen Buchanan (Department of Physics, Colorado State University, Fort Collins, CO, USA)

Room: Mount Temple A Topological spin textures in patterned magnetic nanostructures including magnetic vortices and skyrmions are currently attracting a great deal of attention because they exhibit a variety of interesting properties, especially in the dynamic regime. The magnetic antivortex, the topological counterpart of a vortex that involves spins that sweep in from two opposite sides (e.g. the top and bottom) and out toward the other two (e.g., left and right), has received much less attention, in part because it is more difficult to stabilize. Here, we investigate the dynamic behavior of a magnetic antivortex stabilized at the intersection of orthogonal microstrips made of Permalloy using a combination of micro-focus Brillouin light scattering (micro-BLS) and micromagnetic simulations. The simulations show a rich dynamic response that includes analogs of the gyrotropic, azimuthal, and radial modes of a magnetic vortex. Additional complexities are, however, observed due to coupling between the antivortex excitations and propagating spin waves in the attached microstrips. We have detected several of these modes by micro-BLS [1]. A comparison of measurements made with an antivortex vs. a saturated spin configuration at the intersection shows that intersection spin state can be used to influence the mode structure in the microstrips, which suggests new possibilities for spin wave manipulation and generation. [1] G. A. Riley, H. J. Liu, M. A. Asmat-Uceda, A. Haldar, and K. S. Buchanan, Phys. Rev. B 92, 064423 (2015).

Electrical switching of an antiferromagnet

• Tomas Jungwirth (Institute of Physics, Czech Academy of Sciences and University of Nottingham, UK)

Room: Mount Temple A Louis Néel pointed out in his Nobel lecture that while abundant and interesting from theoretical viewpoint, antiferromagnets did not seem to have any applications. Indeed, the alternating directions of magnetic moments on individual atoms and the resulting zero net magnetization make antiferromagnets hard to control by tools common in ferromagnets. Strong coupling would be achieved if the externally generated field had a sign alternating on the scale of a lattice constant at which moments alternate in antiferromagnets. However, generating such a field has been regarded unfeasible, hindering the research and applications of these abundant magnetic materials. We will discuss a recent prediction that relativistic quantum mechanics may offer a staggered current induced field whose sign alternates within the magnetic unit cell. The staggered spin-orbit field can facilitate a reversible switching of an antiferromagnet with comparable efficiency to the switching of ferromagnets by conventional uniform magnetic fields. We will then discuss suitable antiferromagnetic materials and a demonstration of the complete writing/storage/readout functionality in PC compatible demonstrator device. The absence of dipolar fields in the zero net moment antiferromagnets allows for a multiple-stability of the memory states that are invisible to magnetic probes and robust against external magnetic field perturbations. Moreover, antiferromagnets have ultra-fast internal spin dynamics, opening the prospect of picosecond timescales for switching, both in the coherent single domain regime and by ultra-fast domain wall motion. References: [1] P. Wadley et al. Science 351, 587 (2016); C. Marrows (Editorial), Science 351, 558 (2016). [2] T. Jungwirth et al., Nature Nanotech. 11, 231 (2016); Editorial, Nature Nanotech. 11, 231 (2016).

Mechanics and spins in diamond

• Ania Jayich (Univ of California Santa Barbara)

Room: Mount Temple A Single crystal diamond mechanical resonators are a promising platform for hybrid quantum systems comprising spins and phonons. Diamond mechanical resonators exhibit exceptionally high quality factors and diamond plays host to a highly coherent atomic-scale spin system: the nitrogen vacancy (NV) center. Through its strain sensitivity, the NV can be coupled coherently to a mechanical degree of freedom. We have characterized the strain sensitivity of the NV center’s ground state spin, as well as its optical transitions. Through strain coupling, we show that mechanical control of individual spins in diamond is possible. These results are encouraging for proposals to use such a spin-mechanical platform for spin-squeezing, phonon-mediated spin-spin interactions, and phonon cooling of macroscopic mechanical resonators. We discuss the necessary steps needed to reach these goals and current progress including improvements in diamond fabrication, NV formation, and readout techniques.

Cavity-Optomechanical Torque Sensors

• John Davis (University of Alberta)

Room: Mount Temple A Reducing the moment of inertia improves the sensitivity of a mechanically-based torque sensor, the parallel of reducing the mass of a force sensor, yet the correspondingly small displacements can be difficult to measure. To resolve this, we incorporate cavity optomechanics, which involves co-localizing an optical and mechanical resonance. With the resulting enhanced readout, cavity-optomechanical torque sensors are now limited only by thermal noise. Further progress requires thermalizing such sensors to low temperatures, where sensitivity limitations are instead imposed by quantum noise. By cooling a cavity-optomechanical torque sensor to 25 mK, we have demonstrated a torque sensitivity of 2.9 yNm Hz^(-1/2). At just over a factor of ten above its quantum-limited sensitivity, such cryogenic optomechanical torque sensors will enable both static and dynamic measurements of integrated samples at the level of a few hundred spins.

"Trampoline" mechanical resonators for ultrasensitive force detection and optomechanics (plus some spin transfer)

• Jack Sankey (McGill University)

Room: Mount Temple A Mechanical systems are ubiquitous throughout society, from oscillators in timekeeping devices to accelerometers and electronic filters in automobiles and cell phones. They also comprise an indispensable set of tools for fundamental and applied science: using tiny mechanical elements, for example, it is possible to "feel around" surfaces at the atomic scale, and using human-scale masses, LIGO currently "listens" to gravitational waves emitted by violent events across the universe. In the field of optomechanics, we have exploited the forces exerted by radiation to gain a new level of control over these systems at all size scales. In this talk I will discuss our recent efforts to create pristine mechanical sensors and manipulate/enhance them with laser light. We have fabricated nanogram-scale "trampolines" having extremely low damping parameters (ringing for six minutes when struck) and record low force sensitivities (below 20 attonewtons at room temperature). These trampolines also have excellent optical properties and are well-suited for optomechanical applications. Of note, the combined mechanical and optical parameters will provide access to a regime in which an extraordinarily small amount of light -- at the level of a single photon -- exerts a profound influence over the trampoline's trajectory. I will discuss progress toward optically levitating these (and related) devices to further improve their performance, discuss progress toward realizing a new and weird type of optomechanical interaction wherein light strongly influences the geometry and mass of a mechanical mode. I will finish by briefly discussing an unrelated project to couple spin-transfer-controlled nanoscale magnetic circuits to atom-like defects in single-crystal diamond.

Friday Tutorial

• Michael Roukes (Kavli Nanoscience Institute and Departments of Physics & Applied Physics and Biological Engineering, California Institute of Technology, Pasadena, California 91125, USA)

Room: Mount Temple A

Force-detected magnetic resonance imaging and spectroscopy using silicon nanowire mechanical resonators

• Raffi Budakian (University of Waterloo)

Room: Mount Temple A Magnetic resonance imaging (MRI) has had a profound impact on biology and medicine. Key to its success has been the unique ability to combine imaging with nuclear magnetic resonance spectroscopy—a capability that has led to a host of powerful modalities for imaging spins. Although it remains a significant challenge, there is considerable interest to extend these powerful spectroscopic and imaging capabilities to the nanometer scale. In this talk, I will discuss a new platform for force-detected magnetic resonance detection that allows us to bring many aspects of NMR spectroscopy to the nanometer scale. In particular, I will focus on the development of optimal control theory (OCT) pulses that incorporate average Hamiltonian theory and realize high fidelity unitary operations. I will present recent results demonstrating the use of OCT-based line narrowing pulse sequences that suppress the dipolar evolution and increase the spin coherence time of proton spins in polystyrene at 4 K by a factor of 500, from 11 μs to 6 ms. This advance has allowed us to image proton spins in one dimension with 2-nm spatial resolution. More generally, through the use of OCT pulses, we now have the ability to perform high-resolution NMR spectroscopy on nanometer scale nuclear spin ensembles.

Nanowire Force Microscopy and Dynamic Cantilever Magnetometry

• Floris Braakman (University of Basel)

Room: Mount Temple A We describe the use of grown nanowires (NWs) as scanning directional force sensors. By virtue of slight asymmetries in geometry, a NW's flexural modes are split into doublets which oscillate along two orthogonal axes. By monitoring the frequency shift and direction of oscillation of both modes as we scan the NW above a surface, we construct a map of all in-plane tip-sample force derivatives. This capability, combined with the exquisite force sensitivity of NW sensors, allows for a type of atomic force microscopy especially suited to measuring the size and direction of weak tip-sample forces [1]. Due to their geometry, NWs are well-suited as scanning probes, when arranged in the pendulum geometry, i.e. with their long axis perpendicular to the sample surface. They can be grown in a variety of sizes and from different materials, allowing access to a wide range of mechanical frequencies and spring constants. Furthermore, NWs can be grown as heterostructures, making it possible to incorporate elements such as quantum dots. We present measurements of the vectorial electrostatic field of a sample with multi-edged gate electrodes and distinguish two different types of tip-sample forces. These results demonstrate the potential of NWs as highly tunable mechanical resonators that can be used as functional elements in a new type of scanning force microscopy. The detection of magnetic moments of individual nanoscale particles presents an additional experimental challenge. Here, we present measurements of nanometer-scale magnets based on sensitive mechanical detection of magnetic torque: dynamic cantilever magnetometry (DCM) [2]. With the use of ultrasensitive cantilevers, DCM allows us to collect information on the saturation magnetization, anisotropy, switching behavior, and magnetic phases. We discuss DCM measurements of the magnetic skyrmion phase in MnSi nanowires [3] and in GaVa$_4$S$_8$, which supports a Néel-type skyrmion phase. We also show results from experiments on ferromagnetic nanotubes [2, 3], interesting because of their potential flux-closure ground state at low applied magnetic fields. Using this technique, we were able to detect the entrance of vortices at the NT ends, nucleating the magnetization reversal. These features correspond well with micromagnetic simulations of the NT reversal process, showing that our samples can be described as idealized ferromagnetic NTs. [1] N. Rossi, F. R. Braakman, D. Cadeddu, D. Vasyukov, G. Tütüncuoglu, A. Fontcuberta I Morral, and M. Poggio, Nature Nano. AOP, doi:10.1038/nnano.2016.189 (2016).` [2] B. Gross, D. P. Weber, D. Rüffer, A. Buchter, F. Heimbach, A. Fontcuberta i Morral, D. Grundler, and M. Poggio, Phys. Rev. B 93, 064409 (2016). [3] A. Mehlin, F. Xue, D. Liang, H. F. Du, M. J. Stolt, S. Jin, M. L. Tian, and M. Poggio, Nano Lett. 15, 4839 (2015).

Frequency tuning and coherent dynamics of nanostring resonators

• Hans Huebl (Walther-Meissner-Institute of the Bavarian Academy of Sciences and Humanities)

Room: Mount Temple A Individual micro- and nanomechanical elements are extensively studied due to their importance in force and mass sensing applications, while resonator networks are key for the investigation of coupling physics and synchronization effects. In my talk I will discuss both cases: (i) utilizing the nanostring for sensing the magnetoelastic coupling constant of a magnetic thin and (ii) frequency control of a nanostring resonator network. Sensing requires that the mechanical properties of the vibrational element are altered by an external stimulus and thus become encoded in its resonance frequency and damping rate. In other words the property of interest has to couple to the mechanical degree of freedom. Here, the magnetostriction present in the in thin magnetic film modifies the total stress in the bilayer nanostring based on the magnetic film and a silicon nitride layer and hereby changes the resonance frequency of its fundamental vibrational mode. This allows for a quantitative determination of the magnetostriction constant of the magnetic material. I will discuss the measurement techniques as well as the sensitivity of the sensing platform. Nanomechanical resonator networks are ideal candidates for the investigation of strong coupling physics, synchronization, non-linear dynamics. Furthermore, they are discussed for all-mechanical information processing and quantum storage platforms. All of these applications, however, require the possibility to tune the relevant mode frequencies independently and to operate the resonators in the strong coupling regime. I will discuss how the fundamental mode frequencies of both nanostrings can be tuned independently using a strong drive tone resonant with one of the higher harmonic modes. This tuning concept relies on an effective increase of the pre-stress in a highly excited nanobeam, known as geometric nonlinearity. With the two nanobeams tuned in resonance, we observe coherent excitation exchange between the fundamental modes of the two nanostrings corresponding to Rabi oscillations of a quantum two-level systems. In addition, experimental investigation of classical Landau-Zener dynamics demonstrates that this coupling and tuning concept paves the way for a selective phonon transfer between two spatially separated mechanical resonators.

Dynamical dipolar coupling in pairs of 25 nm thick YIG nano-disks

• Olivier Klein (SPINTEC, CEA, CNRS, Universite Grenoble Alpes, CEA Grenoble, France)

Room: Mount Temple A In the past years, ultra-thin films of Yttrium Iron garnet (Y3Fe5O12, YIG) have become highly desirable in the context of magnonics [1] and its coupling to spintronics [2]. Due to its record low damping ( = 3x10^-5 in bulk), YIG is the magnetic material of choice to propagate and manipulate spin-waves. Having YIG films with thickness down to a few tens of nanometers is important to enhance interfacial effects with an adjacent metallic layer, e.g. to reach sizable spin-orbit torques at a YIG/Pt interface [3]. It is also required to pattern those films by standard nanofabrication techniques, e.g. to engineer the spin-wave spectrum of individual nanostructures [4]. Nanometer thick epitaxial YIG films with excellent dynamical quality ( down to 2x10^-4) have recently been grown by pulsed laser deposition [5]. Liquid phase epitaxy (LPE), the reference method to grow micrometer thick films with bulk-like dynamical properties, has long be thought to be inappropriate for thinner films, despite some encouraging results obtained on 200 nm thick films [6]. In this study, we will show that LPE can actually be used to grow YIG films with thickness from 17 nm to 200 nm and with damping parameters ranging from less than 4x10^-4 down to 7x10^-5 (extracted from broadband FMR between 1 GHz and 20 GHz). In order to characterize the dynamical dipolar interaction between YIG nanostructures, we have patterned from a 25 nm film pairs of YIG nano-disks with variable diameters and edge-to-edge separation. We use a magnetic resonance force microscope (MRFM) and take advantage of the stray field gradient produced by the magnetic tip to continuously tune and detune the resonance frequencies of adjacent nanodisks [7]. The magneto-dipolar interaction is revealed by the frequency anti-crossing and by the variation of the resonant peaks amplitude. In a pair of touching nano-disks with diameter of 470 nm, the strength of the dynamical dipolar coupling is Omega/gamma = 20 Oe, more than five times the resonance linewidth. This is a promising result to achieve control of the spin-wave dispersion in magnonic crystals based on YIG nanostructures. References [1] V. V. Kruglyak, S. O. Demokritov, and D. Grundler, J. Phys. D 43, 264001 (2010); A. A. Serga, A. V. Chumak, and B. Hillebrands, J. Phys. D 43, 264002 (2010). [2] Y. Kajiwara, et al., Nature 464, 262 (2010); A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Nature Phys. 11, 453 (2015). [3] A. Hamadeh, et al., Phys. Rev. Lett. 113, 197203 (2014); M. Collet, et al., Nature Comm. 7, 10377 (2016). [4] C. Hahn, et al., Appl. Phys. Lett. 104, 152410 (2014). [5] O. dAllivy Kelly, et al., Appl. Phys. Lett. 103, 082408 (2013). [6] C. Hahn, et al., Phys. Rev. B 87, 174417 (2013). [7] B. Pigeau, et al., Phys. Rev. Lett. 109, 247602 (2012)

Coherent spin physics in OLEDs

• John Lupton

Room: Mount Temple A The ability of some animals to navigate using Earth’s magnetic field is truly perplexing. How can tiny fields of one Gauss induce physiologically relevant reactions when Zeeman shifts are over a million times smaller than kT? The secret appears to lie in field-induced modifications to the effect of hyperfine interactions which become relevant because of the exceptionally long spin coherence times of radical pairs. OLEDs provide an unrivaled proving ground to explore the interplay between spin coherence, spin correlations and external fields through spin-dependent transport and luminescence. Spin-lattice relaxation in OLEDs is virtually independent of temperature and very slow. Spin dephasing over microseconds can be quantified by pulsed magnetic resonance using conventional echo schemes. Slow spin dephasing enables the direct observation of spin-Rabi flopping of both electron and hole species, which, under suitable resonance conditions, couple with each other to give spin beating. Such signals are, in principle, sensitive down to the single carrier within the OLED, since the measurement reports on spin permutation symmetry rather than on thermal spin polarization. As the sole parameter determining the resonance condition is the g-factor, compact OLED-based low-frequency resonance circuits can be designed to serve as versatile magnetometers. With novel dual singlet-triplet emitters, singlet-triplet oscillations in the radical-pair can now also be probed directly by a color change in emission. Recent highlights in exploiting coherent singlet-triplet oscillations in OLEDs include the demonstration of direct control of the hyperfine interaction by room-temperature NMR, quantification of the zero-field splitting of intermolecular carrier-pair species, and the direct manifestation of the elusive ac-Zeeman and spin-Dicke effects.

Non-degenerate Parametric Pumping of Spin Waves by Acoustic Waves

• Albrecht Jander (Oregon State Unirsity)

Room: Mount Temple A We demonstrate the parametric pumping of spin waves by longitudinal acoustic waves in YIG. Backward volume magnetostatic spin waves in the frequency range of 1.2 GHz – 1.3 GHz travelling in a YIG film have been amplified using an acoustic wave resonator driven at frequencies near twice the spin wave frequency. The existence of a distinct pump threshold that increases quadratically with frequency offset and the observation of a counter-propagating idler wave provide convincing evidence of the nonlinear parametric pumping process. Parametric pumping involves the nonlinear interaction between three waves, the signal spin wave at frequency f_s, the idler spin wave at frequency f_i, and the pump at frequency f_p. Energy conservation dictates that the three frequencies satisfy the relation f_p=f_s+ f_i. In the present experiments, the pump is a standing acoustic wave which couples to the spin waves via magnetoelastic coupling in the YIG. To conserve momentum, the idler wave propagates counter to the signal wave. In previous work \[1] we studied only the degenerate case, f_p=2f_s. Under this condition the signal and idler waves occur at the same frequency, making it difficult to distinguish the idler wave from the inevitable electromagnetic feedthrough of the signal wave excitation. In the present experiments, we extend the work to the non-degenerate case, where the counter-propagating idler as well as a distinct threshold for its appearance are clearly observed. The experimentally determined threshold for pumping, at an acoustic amplitude of 40 pm, is similar in magnitude to the threshold predicted by a recent theoretical treatment by Keshtgar et al. \[2]. The quadratic increase in threshold with frequency offset from the degenerate case indicates a spin wave damping linewidth of \delta H=1 Oe, which is typical for the films used. ![Plot of idler power versus pump power][1] 1. P. Chowdhury, P, Dhagat and A. Jander, IEEE Transactions on Magnetics 51, 1 (2015). 2. H. Keshtgar, M. Zareyan and G. E. W. Bauer, Solid State Communications 198, 30 (2014). [1]: http://web.engr.oregonstate.edu/~jander/Threshold%20Plots.PNG

Hybrid quantum optomechanics

• Benjamin Pigeau (Institut Neel, Universit Grenoble Alpes-CNRS:UPR2940, 38042 Grenoble, France)

Room: Mount Temple A A hybrid system consisting in a mechanical oscillator coupled to a purely quantum object is a powerful tool to study the quantum to macroscopic world interface. This is a unique route toward the creation of counter intuitive non classical states of motion. The emblematic signatures of quantum electrodynamics, such as Rabi oscillations of the quantum system population and Mollow triplet physics, are expected to arise from the hybrid coupling [2]. Here we investigate the dynamics of a SiC nanowire coupled to a nano-diamond hosting a single Nitrogen Vacancy defect. The SiC wire have intrinsically large oscillation amplitudes at high frequency and exhibit two orthogonal nearly degenerated polarisations. Regarding their ultra low masses they are very accurate vectorial force sensor, exhibiting room temperature sensitivities in the attoNewton range [1]. The NV centre contains a single electronic (S=1) spin that can be manipulated and readout using laser light. Similarly to a Stern-Gerlach experiment, the Zeeman energy of the spin is coupled to the oscillator position using a strong magnetic field gradient. The spin energy is therefore parametrically modulated at the mechanical frequency. It will be evidenced that this system has the potential to enter the strong coupling regime [1]. Moreover the parametric interaction can be turned resonant using a microwave dressing of the NV spin. In the dressed basis, the Rabi frequency of the spin population can be tuned to the mechanical frequency. As a result of this QED like interaction a phonondressed Mollow triplet is observed in the Rabi frequency of the spin [3]. These results pave the way to the observation quantum forces, namely the single spin back-action onto the mechanical oscillator. The outstanding sensitivity of SiC nanowires is also harnessed to probe other types of forces. In particular the vectorial nature of these force fields can be mapped with great accuracy. We have demonstrated the principle of such capability by mapping the electrostatic field created by a sharp metallic tip [4]. This experiment will lead to the measurement of fundamental vacuum fluctuation forces (or Casimir forces) in novel and unexplored geometries. References [1] A. Gloppe et al., Nature Nanotechnology 9, 2014 [2] S. Rohr et al., Physical Review Letters 112, 2014 [3] B. Pigeau et al., Nature Communications 6, 2015 [4] L. Mercier de Lpinay et al., Nature Nanotechnology 11, 2016

Cavity Electrodynamics of Magnons

• Hong Tang

Room: Mount Temple A Hybrid magnonic systems have emerged recently as an important approach for coherent information processing. The great tunability and long lifetime make magnon an ideal information carriers. We demonstrate, that particularly in magnetic insulator yttrium iron garnet (YIG), the coupling between magnon and microwave photons can reach the strong and even ultrastrong coupling regime thanks to the large spin density in YIG. Moreover, since YIG possesses excellent mechanical and optical properties, we show that by leveraging strongly coupled cavity magnonics system, coherent coupling between magnon and phonon, between magnon and optical photons can be all realized. Our work firmly establishes the great potential of magnons as an information transducer that can support coherent information inter-conversion of information carrier among different physics domains.

Accumulation of hybrid magneto-elastic quasi-particles in a ferrimagnet

• Alexander Serga

Room: Mount Temple A It is known that an ensemble of magnons, quanta of a spin wave, can be prepared as a Bose gas of weakly interacting quasi-particles with conservation of the particle number. The external pumping of magnons into the system causes an increase in the chemical potential of a thermalized magnon gas. When it becomes equal to the minimal magnon energy a magnon Bose-Einstein condensate (BEC) may form at this spectral point. However, magnon-phonon scattering processes can significantly modify this scenario. Our observations of the magnon BEC in a single-crystal film of yttrium iron garnet (Y3Fe5O12) by means of wavevector-resolved Brillouin Light Scattering (BLS) spectroscopy resulted in the discovery of a novel condensation phenomenon mediated by magneto-elastic interaction: A spontaneous accumulation of hybrid magneto-elastic bosonic quasi-particles at the intersection of the lowest spin-wave mode and a transversal acoustic wave. This accumulation is the result of a bottleneck in the downward spectral flow of the pumped magnons. The accumulation occurs in a spectral point whose position is determined by the passage from the magnon to the phonon branch and, thus, depends on the strength of the magneto-elastic interaction. As opposed to the classical magnon BEC, the accumulated magneto-elastic bosons have significantly non-zero group velocity (about 200 m/s in our experiment) and, thus, possess strong radiation losses. As a result, the density of these particles depends on their travel path through the thermalized cloud of the pumped magnons and consequently on the width of the pumping area. The developed theoretical model describes the experimentally observed peak of hybrid magneto-elastic quasi-particles. Moreover, it proves the saturation effect in accumulation of quasi-particles: An increase in the pumping power leads to the increase of the magnon BEC population and a following reduction of the bottleneck effect. The work is supported by the Deutsche Forschungsgemeinschaft within the SFB/TR 49 “Condensed Matter Systems with Variable Many-Body Interactions”, by EU-FET (Grant In-Spin 612759), and by the Graduate School Material Sciences in Mainz (MAINZ) through DFG funding of the Excellence Initiative (GSC-266).

Cavity Optomagnonics

• Yaroslav Blanter (Delft University of Technology)

Room: Mount Temple A Recently, seminal experiments of the Nakamura group demonstrated the coherent coupling of the elementary excitation of a ferromagnet (YIG sphere) with a superconducting qubit via cavity microwave photons. Other groups performed similar experiments with optical cavities, setting up the field of cavity optomagnonics, with the main focus on quantum coherence in ferromagnets. We will give a short overview of the field and then turn to the specific problem of photon-magnon interaction. In particular, we will demonstrate how magnons influence transmission through the optical cavity, show that there is a strong asymmetry between Stokes and anti-Stokes peaks for reflected light, and discuss how light can selectively create magnons.

Quantum magnonics in a ferromagnetic sphere

• Yasunobu Nakamura

Room: Mount Temple A A 1-mm$\phi$ sphere of yttrium iron garnet, a well-known ferro(ferri)magnetic insulator, contains $\sim 10^{19}$ net electron spins aligned in one direction. The spins, rigidly ordered by the exchange interaction and also interacting via the dipole forces, support collective excitations in the magnetostatic modes [1]. We control the quantum state of one of such modes coherently at the single magnon level by using a superconducting qubit. The qubit and the Kittel mode, the magnetostatic mode with spatially uniform spin precessions in the sphere, are strongly coupled via a microwave cavity mode, which results in the magnon-induced vacuum Rabi splitting of the qubit as well as Rabi oscillations between the qubit and the single-magnon excitation at resonance [2]. When the qubit and the Kittle mode are detuned, the dispersive interaction allows us to determine the magnon number distributions through the qubit spectroscopy [3]. These experiments demonstrate the potential of magnons as a quantum information carrier in the microwave domain. Coherent interaction of magnons with infrared light is also investigated [4,5]. [1] Y. Tabuchi *et al.*, Phys. Rev. Lett. **113**, 083603 (2014). [2] Y. Tabuchi *et al.*, Science **349**, 405 (2015); C. R. Phys. **17**, 729 (2016). [3] D. Lachance-Quirion *et al.*, arXiv:1610.00839. [4] R. Hisatomi *et al.*, Phys. Rev. B. **93**, 174427 (2016). [5] A. Osada *et al.*, Phys. Rev. Lett. **116**, 223601 (2016).

Spin Mechanics with YIG

• Gerrit Bauer (Tohoku University)

Room: Mount Temple A One of the subfields of spin mechanics addresses the interaction between spin and lattice waves. Magnetic insulators such as yttrium iron garnet (YIG) are very suitable materials to investigate the magnon-phonon coupling because of the combination of a high Curie temperature and a high quality of the magnetization and lattice dynamics. Incoherent magnon-phonon scattering is important to understand spin transport in magnetic insulators that are actuated electrically and thermally by heavy metal contacts, in local or non-local configurations. The coherent magnon-phonon interaction gives rise to hybrid states or “magnon-polarons” . These have been identified in spatiotemporally resolved Kerr rotation experiments that observe the magnetization waves generated by focussed fs optical excitation. The strong coupling of magnons and phonons to coherent magnon-polarons also gives rise to transport anomalies that are detected as sharp peaks or dips in the spin Seebeck effect as a function of applied magnetic field. This talk will review the progress in understanding magnon-phonon interactions in YIG with emphasis on the theoretical issues.