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The classical Einstein-de Haas (EdH) effect [1] is a AC mechanical torque arising from a time rate of change of net magnetization, and represents the intrinsic relationship between magnetism and mechanical angular momentum. Nanofabrication of torque sensing devices is opening new avenues for exploration and applications of the EdH effect. The scale-up of resonance frequencies with continued miniaturization of mechanical torque sensing resonators enhances EdH torques, which increase linearly with drive frequency, relative to frequency-independent magnetic cross-product torques. Previously, miniaturized EdH experiments have been performed at the microscale using mechanical modes in the audio frequency range (13 kHz) [2]. The present work brings the measurements to radio frequencies. 

Single-crystal Yttrium Iron Garnet (YIG) disks with magnetic vortex ground states are mounted on nano-scale mechanical resonators with a torsional resonance mode close to 3 MHz. For DC bias fields below about 200 A/m the maximum cross-product torques remain smaller than the EdH torques [3]; no control of the field geometry to null cross-product torques is required. Quadrature lock-in measurements allow cross-product and EdH torque signals to be recorded simultaneously, owing to a 90$^{\circ}$ relative phase shift arising between the driving torques, and referenced to the phase of the driving field. The simultaneous measurement scheme enables determination of the magnetomechanical ratio, $g\prime$, without requiring separate experimental inputs. Results from measurements around the full vortex hysteresis loop, and comparisons with micromagnetic simulations of cross-product and EdH torques, also will be discussed.

[1] A. Einstein and W.J. de Haas, Proceedings - KNAW **18**, 696 (1915).

[2] T.M. Wallis, J. Moreland, and P. Kabos, Appl. Phys. Lett. **89**, 122502 (2006)

[3] K. Mori, M.G. Dunsmore, J.E. Losby, D.M. Jenson, M. Belov, and M.R. Freeman, Phys. Rev. B **102**, 054415 (2020)

CAP Virtual Congress 2021

The Einstein-de Haas Effect in Yttrium Iron Garnet at 3 MHz

nanomechanics

yttrium iron garnet

magnetism

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poster

Morphogens (often acting as transcription activators or repressors) govern pattern formation and cell differentiation during early embryogenesis. Abnormal distributions of morphogens can result in developmental defects or even death. Oftentimes, thresholds of concentrations of morphogens behave like an ON/OFF switch for the activation or repression of downstream genes. Thus accurate measurements of morphogen concentration and mobility in space and time can help tackle the puzzle of how exactly cascades of hundreds of morphogens coordinate their targets precisely and promptly amidst crowded and complicated cellular environments. 

In principle, Fluorescence Correlation Spectroscopy (FCS) allow for accurate measurements of both protein dynamics and concentration. Here, we demonstrate how to use FCS and confocal imaging to achieve extremely low (~ nM) concentration measurements in live Drosophila embryos expressing recombinant fluorescent morphogens, by carefully taking account background noise and photobleaching effects. The dynamics of both an activator and a repressor morphogens were further studied using FCS and Fluorescence Recovery After Photobleaching. We found that both type of morphogens are very mobile in nuclei, explaining how that are able to turn on or off gene expression in only a few minutes.

Concentration and Mobility of Activator and Repressor Morphogens in live early Drosophila Embryos

Recently, there has been an increasing interest in the study of optical/microwave cavity-confined photon-magnon interaction due to their potential applications in quantum information processing
and spintronics [1,2]. In those studies, a number of unique features have been observed at frequencies in the GHz range. On the other hand, less is known about the dynamics of antiferromagnets, which are characterized by frequencies in the THz range [3].


We report results from an analytical study of the coupling of an antiferromagnetic domain wall to optical photons via the inverse Faraday effect. We consider spin canting and complex spin textures in antiferromagnetic materials that can arise from Dzyaloshinskii-Moriya interactions (DMI) [4]. DMI is not easily measurable and is often inferred from other quantities. In this work, we find that the presence of DMI enables spin interactions with cavity photons in a geometry which otherwise allows no magneto-optical coupling. This result may be used to measure the DMI constant in optomagnonic experiments by measuring the interaction of antiferromagnetic resonances to optical modes in a cavity.

**Keywords**: optomagnonic, DMI, antiferromagnet, domain wall, spin texture

*This work was supported by NSERC, CFI-JELF, Research Manitoba and the University of Manitoba, Canada.*

**References**
1. Harder, M. & Hu, C. M. Cavity Spintronics: An Early Review of Recent Progress in the Study of
Magnon–Photon Level Repulsion. in Solid State Physics - Advances in Research and Applications (eds. Camley, R. E. & Stamps, R. L.) vol. 69 47–121 (Academic Press, 2018).
2. Bozhko, D. A., Vasyuchka, V. I., Chumak, A. V & Serga, A. A. Magnon-phonon interactions in
magnon spintronics (Review article). Low Temp. Phys. 46, 383–399 (2020).
3. Kampfrath, T. et al. Coherent terahertz control of antiferromagnetic spin waves. Nat. Photonics 5, 31–34 (2011).
4. Conzelmann, T., Selzer, S. & Nowak, U. Domain walls in antiferromagnets: The effect of Dzyaloshinskii-Moriya interactions. J. Appl. Phys. 127, 223908 (2020).

Collective dynamics of antiferromagnetic domain walls in an optical cavity

Geometrical frustration arises in systems whose structures support multiple degenerate ground states. Artificial spin ice (ASI), has been built in diverse configurations which allows us to control frustration by experimentally tuning suitable parameters[1]. We present computational results on ASI systems consisting
of planar arrays of nanosized elongated ferromagnetic islands where geometrical frustration takes place at the vertices due to dipolar interactions between elements. To date, most studies have employed two-dimensional geometries in order to study magnetic charge dynamics, phase transitions, vertex-based frustration, and other interesting effects[2]. Recently, there has been a surge of interest in realizing three-dimensional artificial spin ice[3]. The use of a third dimension allows increased configurability and optimization of the magnetostatic interaction between different elements of the system. The work mentioned here concerns non-
equilibrium dynamics of a bilayer artificial spin ice structure consisting of two identical arrays separated by some distance and rotated at an angle between the two array axes. Introducing an angle between the layers enables the observation of novel, emergent phenomena as it changes the nature of the interactions between
the spins. We consider pinwheel variants of a square ice geometry for each
array[4]. Using different Monte Carlo techniques, we examine ground state ordering as a function of the interaction strength between layers for different relative orientations. Avalanche processes are also investigated and contrasted with those found in single-layer arrays.

References:
[1] RF Wang, C Nisoli, RS Freitas, J Li, W McConville, BJ Cooley, MS Lund, N Samarth, C Leighton, VH Crespi, et al. Artificial `spin ice' in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature, 439(7074):303{306, 2006.
[2] Cristiano Nisoli, Vassilios Kapaklis, and Peter Schier. Deliberate exotic magnetism via frustration and topology. Nature Physics, 13(3):200{203, 2017.
[3] Gia-Wei Chern, Charles Reichhardt, and Cristiano Nisoli. Realizing three-dimensional artificial spin ice by stacking planar nano-arrays. Applied Physics Letters, 104(1):013101, 2014.
[4] R. Mac^edo, G. M. Macauley, F. S. Nascimento, and Robert L. Stamps. Apparent ferromagnetism in the pinwheel artificial spin ice. Physical Review B,
98(1):014437, 2018.

Investigation of the dynamics of twisted bilayer artificial spin ice structure

Electron spins confined to quantum dots are a promising platform for scalable quantum computation. A necessary component of such a quantum processor is a microwave magnetic field (B$_1$) that implements single-qubit gate operations via electron spin resonance. A common method for generating a B$_1$ field is to place a micro-stripline close to the device. A second method is to place a micromagnet near the device and apply local voltage pulses to induce electric dipole spin resonance. Both methods involve elements that are bulky (> 1 µm) compared to the scale of an individual quantum dot (~60 nm), and are placed on the surface of the chip, taking up valuable space and preventing scalable, dense packing of qubits. Furthermore, the B$_1$ produced by both methods is local, limiting single-qubit rotations to only a few quantum dots per micro-stripline or micromagnet.

We have investigated a centimeter-scale bowtie-shaped microwave resonator design that produces a global B$_1$ field with minimal electric field over a relatively large area (~mm$^2$), which could enable single-qubit rotations for thousands of qubits. The design ensures that the magnetic field is maximal near the center of the resonator, whereas the electric field is expelled towards the edges of the resonator. A minimal electric field in the active area is necessary to prevent photon-assisted tunneling of the confined electrons. The resonator can be vertically integrated above the quantum device layer, removing the need for microwave interconnects or bulky components in the device layer. Individual qubits can be tuned in and out of resonance with this global B$_1$ field using the Stark effect, wherein the electronic $g$-factor shifts slightly as a function of applied electric field. Coupling an external microwave source to the resonator is achieved by an excitation stripline on the opposite side of a dielectric substrate. The resonator and stripline dimensions are optimized for operation at ~15 GHz, corresponding to a DC magnetic field of 0.53 T for a $g=2$ electron spin. At this field and a temperature of 100 mK, the spin qubit is initialized by relaxing into its ground state with a probability of 99.9 %. Our experimental implementation of lateral quantum dots in silicon will be discussed, along with progress in testing and integrating the global B$_1$ field resonator.

Microwave resonators for global control of electron spins qubits

Majorana zero modes (MZM) have been a focal point of the condensed matter physics
community in recent times due in part to their potential applications in quantum computation.
Most notably, the exotic exchange statistics of MZMs form the basis of
topologically protected quantum gates. The physical exchange, or braiding, of MZMs is often modeled in networks of 1D topological superconducting wires. A key ingredient of these braiding protocols is the transport of MZMs across a superconductor. We consider a “piano key model” of transport, where segments of a superconductor are adiabatically tuned between the topologically trivial and the topologically non-trivial phases via electric gates. We examine the time scales over which the piano key tuning should be performed in order to minimize the likelihood of unwanted excitations of the ground state. We also examine the dynamical phase accrued by the ground state, which is of importance in the context of braiding.

Transport of Majorana zero modes in 1D topological superconductors

The discovery of time-reversal symmetry(TRS) breaking in elemental Re has ignited fresh interest in the Re based superconductors. The recent studies show that role of Re concentration and crystal symmetry is crucial in understanding the unconventional superconductivity of these compounds. Therefore, we studied two Re-based superconductors Re$_3$B (<var>TC</var> = 5.19 K) and Re$_7$B$_3$ 
(<var>TC</var> = 3.2 K) having a centrosymmetric and non-centrosymmetric crystal structure, respectively. In this talk, we will present a comprehensive study on superconducting properties of Re$_7$B$_3$ and Re$_3$B through specific heat, magnetic susceptibility, resistivity, and transverse and zero-field muon rotation/relaxation ($\mu$SR) experiments. This will include the temperature dependence of penetration depth using transverse-field $\mu$SR measurements, which will be used to determine the symmetry of the superconducting gap. To further explore these materials, we performed the zero-field $\mu$SR measurements, which show the evidence for TRS preserving superconducting state for both materials in the limits of our measurements.

$\mu$SR study of superconducting Re-B compounds

The Kitaev model on the honeycomb lattice recently attracted considerable attention. However, in candidate materials, other interactions are present, and 
among them the off-diagonal $\Gamma$ interaction has been particularly challenging. While several numerical studies on a minimal Kitaev-$\Gamma$ $(K\Gamma)$ model found multiple quantum disordered phases, definite conclusions on existence of quantum spin liquids remain elusive due to various numerical limitations. Here we present a classical phase diagram of the $K\Gamma$ model in the presence of the bond-anisotropy, which reveals intriguing competing phases and extended frustration. The stability of the classical phases to quantum fluctuations using a linear spin wave theory will be also discussed.

Extent of Frustration in the Classical Kitaev-$\Gamma$ Model

Dynamical backaction resulting from radiation pressure forces in optomechanical systems has proven to be a versatile tool for manipulating mechanical vibrations. Notably, dynamical backaction has resulted in the cooling of a mechanical resonator to its ground-state, driving phonon lasing, and observing the optical-spring effect. In certain magnetic materials, mechanical vibrations can interact with magnetic excitations (magnons) via the magnetostrictive interaction, resulting in an analogous magnon-induced dynamical backaction. This talk will discuss the direct observation of magnon-induced dynamical backaction and its effect on a spherical magnetic sample's mechanical vibrations. Moreover, dynamical backaction effects play a crucial role in many recent theoretical proposals; thus, our work provides the foundation for future experimental work perusing many of these novel theoretical proposals. foundation for future experimental work perusing many of these novel theoretical proposals.

Dynamical Backaction Magnomechanics

By engineering an anti-parity-time (anti-PT) symmetric cavity magnonics system with precise eigenspace controllability, we observe two different singularities in the same system. One type of singularity, the exceptional point (EP), is produced by tuning the magnon damping. Between two EPs, the maximal coherent superposition of photon and magnon states is robustly sustained by the preserved anti-PT symmetry. The other type of singularity, arising from the dissipative coupling of two antiresonances, is a zero-damping condition (ZDC). At the settings of ZDCs, the coupled system exhibits infinite discontinuities in the group delay. We find that both singularities coexist at the equator of the Bloch sphere, which reveals a unique hybrid state that simultaneously exhibits the maximal coherent superposition and slow light capability.

Unconventional singularity in anti-parity-time symmetric cavity magnonics

The ability to image magnetodynamics has proved key to the advancement of spintronics technology [1]. As technological size scales reduce and speeds increase, there is a need to provide commensurate advancement in experimental tools to image magnetodynamics down to the atomic scale with ultrafast time resolution. In pursuit of this goal, we are developing a custom designed scanning tunneling microscope which will be paired with a THz light source to create a THz-STM that achieves ultrafast time resolution [2]. THz-STM experiments require significant acquisition time and present an extreme challenge. To make such an instrument practical, the STM must be designed with optical access, long-term stability, and rigidity in mind. Progress on the design and construction of a variable temperature scanning tunneling microscope purpose built for the observation of magnetodynamics will be presented. 

1 https://science.sciencemag.org/content/294/5546/1484
2 https://www.nature.com/articles/nphoton.2013.151

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The Einstein-de Haas Effect in Yttrium Iron Garnet at 3 MHz

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