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DOI:https://doi.org/10.1103/PhysRev.6.239

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... The mechanisms for the magnon-phonons interaction include, magnetostriction [1][2][3][4][5][6][7][8][9]16] and spin-rotation coupling [14,17,18]. The latter mechanism is a manifestation of the Einstein-de Haas and Barnett effects corresponding to the transfer of the angular momentum between spin and mechanical degrees of freedom [19][20][21]. In other words, the transfer between magnon-and phonon-angular momentum can be manipulated by magnetization dynamics [15,19,[21][22][23][24]. ...

... The latter mechanism is a manifestation of the Einstein-de Haas and Barnett effects corresponding to the transfer of the angular momentum between spin and mechanical degrees of freedom [19][20][21]. In other words, the transfer between magnon-and phonon-angular momentum can be manipulated by magnetization dynamics [15,19,[21][22][23][24]. These earlier research investigations shed light on the opportunity for phonon manipulation [25] and detection using magnetization dynamics. ...

... To model the phonons transport, we take into consideration both phonon attenuation and generation [28,29] manipulated by the magnetic dynamics, during the SAW-driven FMR. Angular momentum interconversion between magnons and phonons is related to the Einstein-de Haas effect [14,18] and the Barnett effect [21]. Due to the magnon-phonon interconversion during FMR, phonons will redistribute the angular momentum and energy between magnons and phonons [15,17], and thus macroscopic mechanical rotation can be strengthened, leading to an enhancement of the transmission of the SAW. ...

The resonant coupling of phonons and magnons is important for the interconversion of phononic and spin degrees of freedom. We study the phonon transmission in LiNbO3 manipulated by the dynamic magnetization in a Ni thin film. It is observed that the phonons can be absorbed strongly through resonant magnon-phonon coupling, which is realized by our modifying the magnon-phonon coupling within the Ni itself as well as our optimizing the interfacial coupling between Ni and LiNbO3. The line shapes of phonon transmission are further investigated considering the magnon-phonon interconversion in the elastically driven ferromagnetic resonance process. The results promote unique routes for phonon manipulation and detection in the presence of magnetization dynamics.

... The rotation can be induced by an externally applied transient magnetic field or temperature. The reverse effect, generation of a magnetic moment by mechanical rotation, called the Barnett effect, has also been realized [4]. The very first gyromagnetic ratio measurements were performed using the EdH effect. ...

... The equations of them are given by Eqs. (3) and (4). We show Berry curvature of magnon bands in Fig. 8. ...

We predict the existence of the Einstein-de Haas effect in topological magnon insulators. Temperature variation of angular momentum in the topological state shows a sign change behavior, akin to the low temperature thermal Hall conductance response. This manifests itself as a macroscopic mechanical rotation of the material hosting topological magnons. We show that an experimentally observable Einstein-de Haas effect can be measured in the square-octagon, the kagome, and the honeycomb lattices. Albeit, the effect is the strongest in the square-octagon lattice. We treat both the low and the high temperature phases using spin wave and Schwinger boson theory, respectively. We propose an experimental set up to detect our theoretical predictions. We suggest candidate square-octagon materials where our theory can be tested.

... Positivity of the thermal entropy requires µ eff < 4π 2 T 2 3 for κ > 0 and µ eff > 4π 2 T 2 3 for κ < 0. As the potentials (108) are obtained from (70), (71), and (74) they should satisfy the first law of thermodynamcis. This is verified straightforwardly ...

... These differences do not imply any contradiction as the axial component of the spin current in general is different than the axial charge current. All in all, the appearance of vorticity as a source of the spin current in (131) is interesting, implying magnetization by rotation, akin to the Barnett effect [71]. 17 Just as in regular hydrodynamics, we expect (132) to be frame dependent. ...

We explore the role of torsion as source of spin current in strongly interacting conformal fluids using holography. We establish the constitutive relations of the basic hydrodynamic variables, the energy-momentum tensor and the spin current based on the classification of the spin sources in irreducible Lorentz representations. The fluids we consider are assumed to be described by the five dimensional Lovelock-Chern-Simons gravity with independent vielbein and spin connection. We construct a hydrodynamic expansion that involves the stress tensor and the spin current and compute the corresponding one-point functions holographically. As a byproduct we find a class of interesting analytic solutions to the Lovelock-Chern-Simons gravity, including blackholes, by mapping the equations of motion into non-linear algebraic constraints for the sources. We also derive a Lee-Wald entropy formula for these blackholes in Chern-Simons theories with torsion. The blackhole solutions determine the thermodynamic potentials and the hydrodynamic constitutive relations in the corresponding fluid on the boundary. We observe novel spin induced transport in these holographic models: a dynamical version of the Barnett effect where vorticity generates a spin current and anomalous vortical transport transverse to a vector-like spin source.

... The amplitudes with winding number N = 2, C −0 and C 0− are also important in terms of the relative stability between the A-core and D-core vortex states, as discussed in Sec. . effect, [32] a substantial spin polarization in the form of the β phase, discussed in more detail in Sec. . Figure 4 shows a stationary solution of Eqs. 14 with axial symmetry which hosts both the chiral A-phase (C 0+ ) and β phase (C +0 ) with non-zero amplitudes in the vortex core. ...

... The bulk B phase is timereversal symmetric with s bulk ≡ 0. Thus, the gyromagnetic effect observed in rotating 3 He-B is a manifestation of intrinsic spin polarization of vortices, driven by vortex currents in the core region. This is a vortex manifestation of the Barnett effect [32], discussed in the context of vortices in the 3 P 2 neutron superfluid predicted to exist in the interiors of rotating neutron stars [38,39]. The intrinsic magnetization (spin polarization) for axially symmetric vortices takes a simple form when expressed in terms of amplitudes defined in the angular momentum basis, ...

We present the first theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid $^3$He-B. Based on a strong-coupling extension of the Ginzburg-Landau theory that accounts for the relative stability of the bulk A and B phases of $^3$He at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid $^3$He-B. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\,\mbox{G}$ parallel to the rotation axis, $\vec{H}\parallel\vec{\Omega}$, are reported, as well as the supercooling transition line, $T^{*}_ {v} (p,H)$. In zero field the vortex phases of $^3$He-B are separated by a first-order phase transition line $T_ {v} (p)$ that terminates on the bulk critical line $T_{c}(p)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly-quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $\beta$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, $T^{*}_ {v} (p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\gtrsim 60\,\mbox{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating $^3$He-B, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating $^3$He-B.

... More importantly we show that once one includes K 2 corrections, interesting spin transport phenomena emerge. An example of these includes the spontaneous magnetization of a rotating fluid, i.e. the Barnett effect [61]. ...

... Note that the dualization works in reverse as well and so we can write 16 S µνρ = µνρσS σ = −2 µνρσ ω σ . (7.58) Equation (7.58) shows that a spinning fluid can exhibit the Barnett effect [61], namely it states that fluid rotation leads to the polarization of the spin of the fluid in the direction parallel to ω µ . The Barnett effect can also be generated in 2 + 1 dimensions by an action of the form [188] ...

We employ the AdS/CFT correspondence and hydrodynamics to analyze the transport properties of \(2+1\) dimensional electron fluids. In this way, we use theoretical methods from both condensed matter and high-energy physics to derive tangible predictions that are directly verifiable in experiment. The first research topic we consider is strongly-coupled electron fluids. Motivated by early results by Gurzhi on the transport properties of weakly coupled fluids, we consider whether similar properties are manifest in strongly coupled fluids. More specifically, we focus on the hydrodynamic tail of the Gurzhi effect: A decrease in fluid resistance with increasing temperature due to the formation of a Poiseuille flow of electrons in the sample. We show that the hydrodynamic tail of the Gurzhi effect is also realized in strongly coupled and fully relativistic fluids, but with modified quantitative features. Namely, strongly-coupled fluids always exhibit a smaller resistance than weakly coupled ones and are, thus, far more efficient conductors. We also suggest that the coupling dependence of the resistance can be used to measure the coupling strength of the fluid. In view of these measurements, we provide analytical results for the resistance as a function of the shear viscosity over entropy density \(\eta/s\) of the fluid. \(\eta/s\) is itself a known function of the coupling strength in the weak and infinite coupling limits. In further analysis for strongly-coupled fluids, we propose a novel strongly coupled Dirac material based on a kagome lattice, Scandium-substituted Herbertsmithite (ScHb). The large coupling strength of this material, as well as its Dirac nature, provides us with theoretical and experimental access to non-perturbative relativistic and quantum critical physics. A highly suitable method for analyzing such a material's transport properties is the AdS/CFT correspondence. Concretely, using AdS/CFT we derive an estimate for ScHb's \(\eta/s\) and show that it takes a value much smaller than that observed in weakly coupled materials. In turn, the smallness of \(\eta/s\) implies that ScHb's Reynolds number, \(Re\), is large. In fact, \(Re\) is large enough for turbulence, the most prevalent feature of fluids in nature, to make its appearance for the first time in electronic fluids. Switching gears, we proceed to the second research topic considered in this thesis: Weakly coupled parity-breaking electron fluids. More precisely, we analyze the quantitative and qualitative changes to the classical Hall effect, for electrons propagating hydrodynamically in a lead. Apart from the Lorentz force, a parity-breaking fluid's motion is also impacted by the Hall-viscous force; the shear-stress force induced by the Hall-viscosity. We show that the interplay of these two forces leads to a hydrodynamic Hall voltage with non-linear dependence on the magnetic field. More importantly, the Lorentz and Hall-viscous forces become equal at a non-vanishing magnetic field, leading to a trivial hydrodynamic Hall voltage. Moreover, for small magnetic fields we provide analytic results for the dependence of the hydrodynamic Hall voltage on all experimentally-tuned parameters of our simulations, such as temperature and density. These dependences, along with the zero of the hydrodynamic Hall voltage, are distinct features of hydrodynamic transport and can be used to verify our predictions in experiments. Last but not least, we consider how a distinctly electronic property, spin, can be included into the hydrodynamic framework. In particular, we construct an effective action for non-dissipative spin hydrodynamics up to first order in a suitably defined derivative expansion. We also show that interesting spin-transport effects appear at second order in the derivative expansion. Namely, we show that the fluid's rotation polarizes its spin. This is the hydrodynamic manifestation of the Barnett effect and provides us with an example of hydrodynamic spintronics. To conclude this thesis, we discuss several possible extensions of our research, as well as proposals for research in related directions.

... The spin-spin coupling also gives rise to a magnetic field [34], in close analogy to the classical Barnett effect [35]. These (very large) magnetic fields, arising in peripheral but not central collisions, have been studied extensively: see for example [36][37][38][39]. ...

It is well known that an asymptotically flat four-dimensional Kerr black hole has a smaller (specific) entropy than a Schwarzschild black hole of the same mass. We show here that the same is true if the temperature, rather than the mass, is held fixed; and we also show that an asymptotically AdS$_5$-Kerr black hole has a smaller specific entropy than an AdS$_5$-Schwarzschild black hole of the same temperature, except in a negligibly small class of special examples. The AdS$_5$-Kerr case is particularly interesting, because here the gauge-gravity duality applies; if we further accept that there is a useful analogy between the strongly coupled field theories dual to AdS black holes and the best-understood example of a strongly coupled fluid (the Quark-Gluon Plasma), then we can apply QGP theory to predict the behaviour of black hole entropy in this case. The prediction agrees with our study of AdS$_5$-Kerr entropy. The hope is that such results might lead ultimately to an identification of black hole microstates.

... It is now suggested that this same mechanism determines the uniform straight-line inertial path by a process involving gyroscopic stability, out of which forms a surrounding centrifugal force field. This is in fact a weak magnetic field, similar in principle to that discovered by S.J. Barnett in 1915, [1], in connection with a spinning neutral body. When a strong gravitational field entrains the sea of aethereal vortices, hence bonding it to the gravitating object such as an orbiting planet, the centrifugal force field then begins at the edge of the entrained zone. ...

When a theory of electromagnetism promotes the idea that the medium for the propagation of light waves is an elastic solid comprised of electric particles, the question is always going to be asked as to why this medium would not generate friction in the planetary orbits, such as would cause the planets to spiral into the Sun. It would be impossible for a moving body to completely avoid any physical interaction with these electric particles, and so, in order to comply with Kepler’s Laws of Planetary Motion, this interaction must be the actual cause of the inertial forces, as opposed to being the cause of any dissipative friction.

... The problem of transfer of angular momentum between magnetic moments and macroscopic body goes back to seminal experiments of Einstein -de Haas [1] and Barnett [2]. The first established that the change in the magnetization of a freely suspended body is accompanied by mechanical rotation. ...

Exact conservation of the angular momentum is worked out for an elastic medium with spins. The intrinsic anharmonicity of the elastic theory is shown to be crucial for conserving the total momentum. As a result, any spin-lattice dynamics inevitably involves multiphonon processes and interaction between phonons. This makes transitions between spin states in a solid fundamentally different from transitions between atomic states in vacuum governed by linear electrodynamics. Consequences for using solid-state spins as qubits are discussed.

... A magnetic shielding factor f of 10 8 lowers this background to 10 −20 T √ Hz . Barnett Effect When an uncharged object is rotated on its axis, it will acquire a magnetization dependent on its magnetic susceptibility χ and frequency of rotation ω [24]: ...

The Axion Resonant InterAction Detection Experiment (ARIADNE) is a collaborative effort to search for the QCD axion using nuclear magnetic resonance (NMR), where the axion acts as a mediator of spin-dependent forces between an unpolarized tungsten source mass and a sample of polarized helium-3 gas. Since the experiment involves precision measurement of a small magnetization, it relies on limiting ordinary magnetic noise with superconducting magnetic shielding. In addition to the shielding, proper characterization of the noise level from other sources is crucial. We investigate one such noise source in detail: the magnetic noise due to impurities and Johnson noise in the tungsten source mass.

... The rotation can be induced by an externally applied transient magnetic field or temperature. The reverse effect, generation of a magnetic moment by mechanical rotation, called the Barnett effect has also been realized [4]. The very first gyromagnetic ratio measurements were performed using the EdH effect. ...

We predict the existence of Einstein-de Haas effect in topological magnon insulators. Temperature variation of angular momentum in the topological state shows a sign change behavior, akin to the low temperature thermal Hall conductance response. This manifests itself as a macroscopic mechanical rotation of the material hosting topological magnons. We show that an experimentally observable Einstein-de Haas effect can be measured in the square-octagon, the kagome, and the honeycomb lattices. Albeit, the effect is the strongest in the square-octagon lattice. We treat both the low and the high temperature phases using spin wave and Schwinger boson theory, respectively. We propose an experimental set up to detect our theoretical predictions. We suggest candidate square-octagon materials where our theory can be tested.

... As known from the Barnett effect [96], a rotating magnetic object is magnetized due to the coupling of angular velocity and spin. Similarly, the vorticity of a fluid couples to spin. ...

The interplay of spin-orbit coupling (SOC) and magnetism gives rise to a plethora of charge-to-spin conversion phenomena that harbor great potential for spintronics applications. In addition to the spin Hall effect, magnets may exhibit a magnetic spin Hall effect (MSHE), as was recently discovered [M. Kimata et al., Nature (London) 565, 627 (2019)]. To date, the MSHE is still awaiting its intuitive explanation. Here, we relate the MSHE to the vorticity of spin currents in the Fermi sea, which explains pictorially the origin of the MSHE. For all magnetic Laue groups that allow for nonzero spin current vorticities the related tensor elements of the MSH conductivity are given. Minimal requirements for the occurrence of a MSHE are compatibility with either a magnetization or a magnetic toroidal quadrupole. This finding implies in particular that the MSHE is expected in all ferromagnets with sufficiently large SOC. To substantiate our symmetry analysis, we present various models, in particular a two-dimensional magnetized Rashba electron gas, that corroborate an interpretation by means of spin current vortices. Considering thermally induced spin transport and the magnetic spin Nernst effect in magnetic insulators, which are brought about by magnons, our findings for electron transport can be carried over to the realm of spin caloritronics, heat-to-spin conversion, and energy harvesting.

... The spin polarization of emitted particles is believed to be induced by the coupling of the initial orbital ("mechanical") angular momentum of two nuclei colliding with a non-vanishing impact parameter and the spin distributed in the matter created in the collision. This is in analogy to the Barnett effect observed more than a century ago [10] when an electrically neutral un-magnetized metallic object became spontaneously magnetized after being set in rotation. The orbital angular momentum per nucleon in the system of two nuclei A colliding with the impact parameter b and the center-of-mass energy of two nucleons √ s N N can be easily estimated as ...

Heavy-ion collisions at center-of-mass nucleon collision energies 4.5--11.5 GeV are analyzed within the PHSD transport model. Spectator nucleons are separated, and the transfer of the initial angular momentum of colliding nuclei to the fireball formed by participants is studied. The maximal angular momentum is carried by the fireball in gold-gold collisions with the impact parameter about 5 fm corresponding to centrality class 10--20\%. The obtained participant distributions were fluidized and the energy and baryon number densities, temperature, and velocity fields are obtained in the Landau frame. It is shown that the velocity field has dominantly Hubble-like transversal and longitudinal expansion with the vortical motion being only a small correction on top of it. The vorticity field is calculated and illustrated in detail. The formation of two oppositely-rotating vortex rings moving in opposite directions along the $z$ axis is demonstrated. Other characteristics of the vortical motion such as the Lamb vector field and the kinematic vorticity number are considered. The magnitude of the latter one is found to be smaller than that for the Poiseuille flow and close to the pure shear deformation corresponding to just a flattening of fluid cells. The field of hydrodynamic helicity, which is responsible for the axial vortex effect, is calculated. The separation of positive and negative helicities localized upper and lower semi-planes with respect to the reaction plane is shown. It is proved that the areas with various helicity signs can be probed by the selection of $\Lambda$ hyperons with positive and negative projections of their momenta orthogonal to the reaction plane.

... The experiments showing the connection between angular momentum and magnetic moment in ferromagnets and superconductors are summarized in Table 1. These experimental results follow [3] superconductors gyromagnetic effect Kikoin and Gubar (1940) [26], see also Pry et al. (1952) [35] London moment Becker et al. (1933) [5], Hildebrandt (1964) [18] from conservation laws. However, the question of how angular momentum causes magnetization or magnetization causes angular momentum is a separate question that needs to be addressed and understood. ...

This paper is concerned with the motion of an unbalanced dynamically symmetric sphere rolling without slipping on a plane in the presence of an external magnetic field. It is assumed that the sphere can consist completely or partially of dielectric, ferromagnetic, superconducting and crystalline materials. According to the existing phenomenological theory, the analysis of the sphere's dynamics requires in this case taking into account the Lorentz torque, the Barnett-London effect and the Einstein-de Haas effect. Using this mathematical model, we have obtained conditions for the existence of integrals of motion which allow one to reduce integration of the equations of motion to a quadrature similar to the Lagrange quadrature for a heavy rigid body. MSC2010 numbers: 37J60, 70F25, 74F15

... Another, not less important, problem is that of the motion of a ferromagnetic or superconducting body in a magnetic field with magnetization during rotation [1,2,23,26,27,32,37]. In contrast to the Grioli problem, in the general case the equations of motion are not Hamiltonian and, generally speaking, possess no invariant measure and do not preserve the total mechanical energy of the body. ...

We consider the possibility of using Dirac’s ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable constraints in the model of a nonholonomic Chaplygin sphere on a plane. We prove that, when a solenoidal field is applied, the general mechanical energy, the invariant measure and the conformally Hamiltonian representation of the equations of motion are preserved. In addition, we consider the case of motion of the nonholonomic Chaplygin sphere in a constant magnetic field taking dielectric and ferromagnetic (superconducting) properties of the sphere into account. As a by-product we also obtain two new integrable cases of the Hamiltonian rigid body dynamics in a constant magnetic field taking the magnetization by rotation effect into account.

... Another, not less important, problem is that of the motion of a ferromagnetic or superconducting body in a magnetic field with magnetization during rotation [1,2,23,26,27,32,37]. In contrast to the Grioli problem, in the general case the equations of motion are not Hamiltonian and, generally speaking, possess no invariant measure and do not preserve the total mechanical energy of the body. ...

We consider the possibility of using Dirac's ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable constraints in the model of a nonholonomic Chaplygin sphere on a plane. We prove that, when a solenoidal field is applied, the general mechanical energy, the invariant measure and the conformally Hamiltonian representation of the equations of motion are preserved. In addition, we consider the case of motion of the nonholonomic Chaplygin sphere in a constant magnetic field taking dielectric and ferromagnetic (superconducting) properties of the sphere into account. As a by-product we also obtain two new integrable cases of the Hamiltonian rigid body dynamics in a constant magnetic field taking the magnetization by rotation effect into account.

... As known from the Barnett effect [96], a rotating magnetic object is magnetized due to the coupling of angular velocity and spin. Similarly, the vorticity of a fluid couples to spin. ...

The interplay of spin-orbit coupling (SOC) and magnetism gives rise to a plethora of charge-to-spin conversion phenomena that harbor great potential for spintronics applications. In addition to the spin Hall effect, magnets may exhibit a magnetic spin Hall effect (MSHE), as was recently discovered [Kimata \textit{et al.}, Nature \textbf{565}, 627-630 (2019)]. To date, the MSHE is still awaiting its intuitive explanation. Here we relate the MSHE to the vorticity of spin currents in the Fermi sea, which explains pictorially the origin of the MSHE. For all magnetic Laue groups that allow for nonzero spin current vorticities the related tensor elements of the MSH conductivity are given. Minimal requirements for the occurrence of a MSHE are compatibility with either a magnetization or a magnetic toroidal quadrupole. This finding implies in particular that the MSHE is expected in all ferromagnets with sufficiently large SOC. To substantiate our symmetry analysis, we present various models, in particular a two-dimensional magnetized Rashba electron gas, that corroborate an interpretation by means of spin current vortices. Considering thermally induced spin transport and the magnetic spin Nernst effect in magnetic insulators, which are brought about by magnons, our findings for electron transport can be carried over to the realm of spincaloritronics, heat-to-spin conversion, and energy harvesting.

... II, a correct description of the magnetization dynamics in rotating nanoparticles is achieved by introducing in Eq. (2.3) the Barnett field. This emergent magnetic field is responsible for the Barnett effect (magnetization by rotation) [34] and its existence has been recently confirmed experimentally for different spin systems [35][36][37]. In this context, it is of interest to analyze the role of the Barnett field in the dissipation-induced rotation of suspended ferromagnetic nanoparticles. ...

We report the precessional rotation of magnetically isotropic ferromagnetic nanoparticles in a viscous liquid that are subjected to a rotating magnetic field. In contrast to magnetically anisotropic nanoparticles, the rotation of which occurs due to coupling between the magnetic and lattice subsystems through magnetocrystalline anisotropy, the rotation of isotropic nanoparticles is induced only by magnetic dissipation processes. We propose a theory of this phenomenon based on a set of equations describing the deterministic magnetic and rotational dynamics of such particles. Neglecting inertial effects, we solve these equations analytically, find the magnetization and particle precessions in the steady state, determine the components of the particle angular velocity, and analyze their dependence on the model parameters. The possibility of experimental observation of this phenomenon is also discussed.

... II, a correct description of the magnetization dynamics in rotating nanoparticles is achieved by introducing in Eq. (2.3) the Barnett field. This emergent magnetic field is responsible for the Barnett effect (magnetization by rotation) 34 and its existence has been recently confirmed experimentally for different spin systems [35][36][37] . In this context, it is of interest to analyze the role of the Barnett field in the dissipation-induced rotation of suspended ferromagnetic nanoparticles. ...

We report a new phenomenon, the precessional rotation of magnetically isotropic ferromagnetic nanoparticles in a viscous liquid that are subjected to the rotating magnetic field. In contrast to magnetically anisotropic nanoparticles, whose rotation occurs due to coupling between the magnetic and lattice subsystems through magnetocrystalline anisotropy, the rotation of isotropic nanoparticles is induced only by magnetic dissipation processes. We propose a theory of this phenomenon based on a set of equations describing the deterministic magnetic and rotational dynamics of such particles. Neglecting inertial effects, we solve these equations analytically, find the magnetization and particle precessions in the steady state, determine the components of the particle angular velocity and analyze their dependence on the model parameters. The possibility of experimental observation of this phenomenon is also discussed.

... In ferromagnetic materials, such a conversion, i.e., the gyromagnetic effect, has been known already a century ago. [19][20][21][22] The conversion between the spin angular momentum and the mechanical torque has received recently renewed attention in the spintronics community. [23][24][25][26][27][28][29][30] In the presence of the SOI, the direction of an injected spin varies continuously during the transmission process. ...

We analyse the appearance of a mechanical torque that acts on a chiral molecule: a single-stranded DNA, in which the spin-orbit interaction is expected to induce a spin-selectivity effect. The mechanical torque is shown to appear as a result of the non-conservation of the spin current in the presence of the spin-orbit interaction. Adopting a simple microscopic model Hamiltonian for a chiral molecule connected to source and drain leads, and accounting for the mechanical torque acting on the chiral molecule as the back action on the electrons traversing the molecule, we derive the spin continuity-equation. It connects the spin current expressed by a Landauer-type formula and the mechanical torque. Thus, by injecting a spin-polarized current from the source electrode, it is possible to generate a torque, which will rotate the DNA molecule.

... In this work, we initiate a route to clarify the debate by introducing the atomic spin-mechanical coupling [10][11][12][13] that is the angular momentum transfer between magnetic and mechanical degrees of freedom. We are motivated by two phenomena observed in Ref. [8]: (i) The magnetosensor complex is strongly stretched in case of a good alignment between its long axis and the geomagnetic field, and (ii) the protein crystal would instantly flip 180 o when the polarity of the approaching magnetic field is inverted. ...

It is a well established notion that animals can detect the Earth's magnetic field, while the biophysical origin of such magnetoreception is still elusive. Recently, a magnetic receptor Drosophila CG8198 (MagR) with a rod-like protein complex is reported [Qin \emph{et al}., Nat. Mater. \textbf{15}, 217 (2016)] to act like a compass needle to guide the magnetic orientation of animals. This view, however, is challenged [Meister, Elife \textbf{5}, e17210 (2016)] by arguing that thermal fluctuations beat the Zeeman coupling of the proteins's magnetic moment with the rather weak geomagnetic field ($\sim25-65$ $\mu$T). In this work, we show that the spin-mechanical interaction at the atomic scale gives rise to a high blocking temperature which allows a good alignment of protein's magnetic moment with the Earth's magnetic field at room temperature. Our results provide a promising route to resolve the debate on the thermal behaviors of MagR, and may stimulate a broad interest on spin-mechanical couplings down to atomistic levels.

... Care has to be exercised when interpreting the phonon operators (9) and (8) (9) and (8) canonically. ...

We develop a microscopic theory of spin-lattice interactions in magnetic insulators, separating rigid-body rotations and the internal angular momentum, or spin, of the phonons, while conserving the total angular momentum. In the low-energy limit, the microscopic couplings are mapped onto experimentally accessible magnetoelastic constants. We show that the transient phonon spin contribution of the excited system can dominate over the magnon spin, leading to non-trivial Einstein-de Haas physics.

... In a quasi-2D ferrite disk, the dipole-dipole interaction couples the precessing electron spin and orbital angular momenta of magnetization. Since, in contrast to the Einstein-de Haas effect [23], we observe the angular momentum transferred not to rotation of a rigid body, the question arises about the stability of the MDMs. This contributes to the spontaneous formation of topological spin textures. ...

For dipole-carrying excitations observed in a high-quality resonator, strong-coupling modes can appear as composite bosons with the spontaneous formation of quantized vortices in the condensed phase of a polariton fluid. In exciton-polaritons, in particular, it leads to sustained trapping of the emitted photon. In this paper, we show that magnon-polaritons can be realized due to magnon condensation caused by magnetic dipole-dipole interaction. In a quasi-2D ferrite disk placed in a microwave cavity, one observes quantum confinement effects of magnetic-dipolar-mode (MDM) oscillations. These modes, characterized by energy eigenstates with rotational superflows and quantized vortices, are exhibited as spinor condensates. Along with the condensation of MDM magnons in the quasi-2D disk of the magnetic insulator, electric dipole condensation is also observed. At the MDM resonances, transfer between angular momenta in the magnetic insulator and in the vacuum cavity, demonstrates generation of vortex flows with fixed handedness. This indicates unique topological properties of polariton wavefronts. One observes curved wavefronts and effects of supperradiance in microwave structures. In an environment of scattering states of microwave waveguide, EM waves can carry the topological phases of MDM resonances.

... Previously, it was experimentally shown that the energies of the electronic ground states of NV centers in diamond will be shifted due to the rotation as a result of Barnett effect [66][67][68][69]. However, since the energies of the electronic excited states will be correspondingly shifted by the same amount, the energy spectra in Fig. 1 will not be modified by the rotation. ...

We theoretically propose a method to realize optical nonreciprocity in rotating nano-diamond with a nitrogen-vacancy (NV) center. Because of the relative motion of the NV center with respect to the propagating fields, the frequencies of the fields are shifted due to the Doppler effect. When the control and probe fields are incident to the NV center from the same direction, the two-photon resonance still holds as the Doppler shifts of the two fields are the same. Thus, due to the electromagnetically-induced transparency (EIT), the probe light can pass through the NV center nearly without absorption. However, when the two fields propagate in opposite directions, the probe light can not effectively pass through the NV center as a result of the breakdown of two-photon resonance.

... Barnett [16] noted that magnetic fields are induced by rotation and are proportional to the rotational speed. By appling the Barnett Ω for a single electron system where Ω is the angular velocity in revolution per second and 2 L g ≈ is the Lande factor. ...

An experiment reported by Podkletnov and Modanese, where gravitational radiation was purportedly emitted from the type II YBCO superconductor with voltage discharges greater than 500 kV is analyzed in relationship to the power radiated in gravitational waves. Due to the direction of the discharge, which was oppositely directed from the force measurements and the formation of an atomic cloud near the superconductor surface, helium atoms were suggested as the source of the gravitational energy. However, an analysis using the electromagnetic analog of gravitational waves showed that there would not be enough mass to produce gravitational waves unless the electron pair mass about pinned flux sites inside the superconductor is taken into account. The analysis shows that the acceleration distance required for the reported gravitational energy to move the test masses used in the experiment would be near that of the typical atom-to-atom bond length of 0.3 [nm] as would be expected for rapid motion inside a superconductor and suggest that the acceleration time t ∆ was on the order of 10-18 [s]. The rapid change in acceleration or "jerk" of the vortex plane of the cooper-pairs about the flux pinning sites is presented as the mechanism for the generating a gravitational wave and a model is presented. Such a jerk should give rise to energetic High-Frequency Gravitational Waves (HFGW) and if linked up to a computer logic system might have practical applications to communications and propulsion.

... The observed polarization is of a similar magnitude as predicted by 3D-fluid-dynamics and the UrQMD plus thermal vorticity model and significantly above results from the AMPT model. The conversion of orbital angular momentum of a rotating rigid body into the spins of the individual particles, is rooted back to the Barnett effect, discovered already in 1915 [1]. Recently, this effect of mechanically induced spin polarization has been observed for electrons in liquid mercury [2] and for protons in fast rotating water [3]. ...

The global polarization of Λ hyperons along the total orbital angular momentum of a relativistic heavy-ion collision is presented based on the high statistics data samples collected in Au+Au collisions at sNN=2.4 GeV and Ag+Ag at 2.55 GeV with the High-Acceptance Di-Electron Spectrometer (HADES) at GSI, Darmstadt. This is the first measurement below the strangeness production threshold in nucleon-nucleon collisions. Results are reported as a function of the collision centrality as well as a function of the hyperon's transverse momentum (pT) and rapidity (yCM) for the range of centrality 0–40%. We observe a strong centrality dependence of the polarization with an increasing signal towards peripheral collisions. For mid-central (20 – 40%) collisions the polarization magnitudes are 〈PΛ〉(%)=6.0±1.3(stat.)±2.0(syst.) for Au+Au and 〈PΛ〉(%)=4.6±0.4(stat.)±0.5(syst.) for Ag+Ag, which are the largest values observed so far. This observation thus provides a continuation of the increasing trend previously observed by STAR and contrasts expectations from recent theoretical calculations predicting a maximum in the region of collision energies about 3 GeV. The observed polarization is of a similar magnitude as predicted by 3D-fluid-dynamics and the UrQMD plus thermal vorticity model and significantly above results from the AMPT model.

... State-of-the-art gyromagnetic effects are based on the motion of spinning magnetic objects. In this case, the magnetization M stemming from the spin angular momentum can be controlled or manipulated by an external rotation to align M and via the spin-rotation coupling as shown in Fig. 1b [4][5][6][7] . In all these cases, an object subject to manipulation is initially spinning around a well-defined axis s in the laboratory frame. ...

The classical laws of physics are usually invariant under time reversal. Here, we reveal a novel class of magnetomechanical effects rigorously breaking time-reversal symmetry. These effects are based on the mechanical rotation of a hard magnet around its magnetization axis in the presence of friction and an external magnetic field, which we call spin revolution. The spin revolution leads to a variety of symmetry breaking phenomena including upward propulsion on vertical surfaces defying gravity as well as magnetic gyroscopic motion that is perpendicular to the applied force. The angular momentum of spin revolution differs from those of the magnetic field, the magnetic torque, the rolling axis, and the net torque about the rolling axis. The spin revolution emerges spontaneously, without external rotations, and offers various applications in areas such as magnetism, robotics and energy harvesting.

... Another interesting outcome of our analysis is the possibility to use the heat flow to propose an analogue of the Einstein-de Haas experiment. This is a famous experiments of the beginning of the twentieth century based on gyromagnetic phenomena [33][34][35]. A cylinder made of a non magnetized ferromagnetic material, suspended to a torsion wire, is subject to an external magnetic field along the cylinder's axis. ...

We study the diffusion processes of a real scalar field in the presence of the distorsion field induced by a chiral topological defect. The defect modifies the usual Euclidean background geometry into a non-diagonal Riemann-Cartan geometry characterized by a singular torsion field. The new form of the diffusion equation is established and the scalar field distribution in the vicinity of the defect is investigated numerically. Results show a high sensitivity to the boundary conditions. In the transient regime, we find that the defect vorticity generates an angular momentum associated to the diffusion flow and we discuss its main properties.

... The conversion of spin into orbital angular momentum and back has been of great interest since the early measurements of Einstein and deHass [1] and Barnett [2]. One recently posed question [3][4][5][6] is whether spin excitations, commonly called magnons, can have both spin and orbital angular momentum (OAM). ...

We obtain exact results for the orbital angular momentum (OAM) of magnons at the high symmetry points of ferromagnetic (FM) and antiferromagnetic (AF) honeycomb lattices. For the FM honeycomb lattice, the amplitude of the OAM at ${\bf k}_1^*=(0,2\sqrt{3}/9)2\pi/a $, ${\bf k}_2^*=(1/3,\sqrt{3}/9)2\pi/a $, and symmetry-related points is $3\hbar /16$ for both magnon bands. For the AF honeycomb lattice, the amplitudes of the OAM at those points are $0$ and $3\hbar /8$ for the two otherwise degenerate magnon bands.

... The conversion of orbital angular momentum of a rotating rigid body into the spins of the individual particles, is rooted back to the Barnett effect, discovered already in 1915 [1]. Recently, this effect of mechanically induced spin polarization has been observed for electrons in liquid mercury [2] and for protons in fast rotating water [3]. ...

The global polarization of {\Lambda} hyperons along the total orbital angular momentum of a relativistic heavy-ion collision is presented based on the high statistics data samples collected in Au+Au collisions at \sqrt{s_{NN}} = 2.4 GeV and Ag+Ag at 2.55 GeV with the High-Acceptance Di-Electron Spectrometer (HADES) at GSI, Darmstadt. This is the first measurement below the strangeness production threshold in nucleon-nucleon collisions. Results are reported as a function of the collision centrality as well as a function of the hyperon transverse momentum (p_T) and rapidity (y_{CM}) for the range of centrality 0--40%. We observe a strong centrality dependence of the polarization with an increasing signal towards peripheral collisions. For mid-central (20--40%) collisions the polarization magnitudes are <P_{\Lambda}>(%) = 6.0 \pm 1.3 (stat.) \pm 2.0 (syst.) for Au+Au and <P_{\Lambda}>(%) = 4.6 \pm 0.4 (stat.) \pm 0.5 (syst.) for Ag+Ag, which are the largest values observed so far. This observation thus provides a continuation of the increasing trend previously observed by STAR and contrasts expectations from recent theoretical calculations predicting a maximum in the region of collision energies about 3 GeV. The observed polarization is of a similar magnitude as predicted by 3D fluid dynamics and the UrQMD plus thermal vorticity model and significantly above results from the AMPT model.

... The coupling between a material's vibrational and spin degrees of freedom is a fundamental feature of magnetic materials. While the existence of this coupling has been known for over a century [1][2][3][4][5], most theoretical research has focused on the low frequency regime [6][7][8][9] while analytical studies emphasize simple geometries such as the bulk [10,11] or thin film [9] limits. Many of the magnetic devices that enable current and future spintronic/magnonic applications are multilayer stacks of magnetic and nonmagnetic materials [12][13][14]. ...

The direct calculation of magnetoelastic wave dispersion in layered media is presented using an efficient, accurate computational technique. The governing, coupled equations for elasticity and magnetism, the Navier and Landau-Lifshitz equations, respectively, are linearized to form a quadratic eigenvalue problem that determines a complex web of wavenumber-frequency dispersion branches and their corresponding mode profiles. Numerical discretization of the eigenvalue problem via a spectral collocation method (SCM) is employed to determine the complete dispersion maps for both a single, finite-thickness magnetic layer and a finite magnetic-nonmagnetic double-layer. The SCM, previously used to study elastic waves in non-magnetic media, is fast, accurate, and adaptable to a variety of sample configurations and geometries. Emphasis is placed on the extremely high frequency regimes being accessed in ultrafast magnetism experiments. The dispersion maps and modes provide insight into how energy propagates through the coupled system, including how energy can be transferred between elastic- and magnetic-dominated waves as well as between different layers. The numerical computations for a single layer are further understood by a simplified analytical calculation in the high-frequency, exchange-dominated regime where the resonance condition required for energy exchange (an anticrossing) between quasi-elastic and quasi-magnetic dispersion branches is determined. Nonresonant interactions are shown to be well approximated by the dispersion of uncoupled elastic and magnetic waves. The methods and results provide fundamental theoretical tools to model and understand current and future magnetic devices powering spintronic innovation.

... The close relation between electron angular momentum and mechanical angular momentum was revealed by Einstein and de Haas in 1915 by measuring the mechanical torque generated when reversing the magnetization of an iron cylinder. The reciprocal effect, i.e., the induced magnetization by mechanical rotation, was discovered by Barnett [471,472]. A rigid rotation with angular velocity that in a rotating framc corresponds to an effective Barnett field = ∕ that affects the magnetization by the Zeeman interaction − ⋅ . ...

Chirality or handedness is a digital relation between three vectors that distinguishes an object from its mirror image, such as the spread fingers of the right and left hand. The chirality of ground state magnetic textures defined by the vectors of magnetization, its gradient, and an electric field from broken inversion symmetry can be fixed by a strong relativistic spin-orbit interaction. This review focuses on the chirality observed in the excited states of the magnetic order, dielectrics, and conductors that hold transverse spins when they are evanescent. Even without any relativistic effect, the transverse spin of the evanescent waves are locked to the momentum and the surface normal of their propagation plane. This chirality thereby acts as a generalized spin-orbit interaction, which leads to the discovery of various chiral interactions between magnetic, phononic, electronic, photonic, and plasmonic excitations in spintronics that mediate the excitation of quasiparticles into a single direction, leading to phenomena such as chiral spin and phonon pumping, chiral spin Seebeck, spin skin, magnonic trap, magnon Doppler, and spin diode effects. Intriguing analogies with electric counterparts in the nano-optics and plasmonics exist.
After a brief review of the concepts of chirality that characterize the ground state chiral magnetic textures and chirally coupled magnets in spintronics, we turn to the chiral phenomena of excited states. We present a unified electrodynamic picture for dynamical chirality in spintronics in terms of generalized spin-orbit interaction and compare it with that in nano-optics and plasmonics. Based on the general theory, we subsequently review the theoretical progress and experimental evidence of chiral interaction, as well as the near-field transfer of the transverse spins, between various excitations in magnetic, photonic, electronic and phononic nanostructures at GHz time scales. We provide a perspective for future research before concluding this article.

... In his interview with Thomas Kuhn and John Heilbron, Landé would note [14] : In the context of the Paschen-Back effect and the Barnett [31,32] and Einstein-de Haas [33] experiments, Landé noted [34] : Back. [23] ...

Prompted by the centenary of Alfred Landé's g‐factor, we reconstruct Landé's path to his discovery of half‐integer angular momentum quantum numbers and of vector coupling of atomic angular momenta—both encapsulated in the g‐factor—as well as point to reverberations of Landé's breakthroughs in the work of other pioneers of quantum physics.

... The early works have one common feature: the particles are considered as point objects in space, so the motion in the field of centrifugal forces is an issue. In 1915, Barnett experimentally discovered magnetization of uncharged rotating body [4]. The inverse effect was described by Einstein and de Haas [5]. ...

We consider a statistical mechanics of rotating ideal gas consisting of classical non-relativistic spinning particles. The microscopic structure elements of the system are massive point particles with a nonzero proper angular momentum. The norm of proper angular momentum is determined by spin. The direction of proper angular momentum changes continuously. Applying the Gibbs canonical formalism for the rotating system, we construct the one-particle distribution function, generalising the usual Maxwell-Boltzmann distribution, and the partition function of the system. The model demonstrates a set of chiral effects caused by interaction of spin and macroscopic rotation, including the change of entropy, heat capacity, chemical potential and angular momentum.

... Recently, thermal gradient 3 and liquid-metal motion 4 have been demonstrated to generate spin separation. Furthermore, generation of spin current in a non-magnetic metal by mechanical rotation has been proposed 5,6 but has not yet been successfully achieved 7 due to the presence of the Barnett effect 8 . ...

The generation of spin-polarised carriers in a non-magnetic material holds the key to realise highly efficient spintronic devices. Recently, it has been shown that the large spin-orbit coupling can generate spin-polarised currents in noble metals such as tungsten and platinum. Especially, if small samples of such metals are rotated on a plane disc in the presence of a perpendicular magnetic field, the orbital angular momentum is altered leading to a segregation of spin up and spin down electrons, i.e., a spin current in the samples. This is manifested via an induced magnetic moment on the metal. In this letter, magneto-optical Kerr effect (MOKE) is used to detect induced magnetic moments which allows remote measurements on metal samples rotating at 100 ~ 210 Hz. Our results confirm the mechanical generation of spin-polarised currents via optical detection of spin accumulation.

... Since spin is a kind of angular momenta, it can be manipulated by mechanical rotation in accordance with the angular momentum conservation. Indeed, Barnett, Einstein and de Haas experimentally showed that rigidbody rotation interacts with magnetic moment originating from the spin angular momenta of electrons [13,14]. The mechanical manipulation of spin is demonstrated in a variety of systems, including micromechanical systems [15][16][17][18], microfluid systems [19][20][21], atomic nuclei [22,23], and quark-gluon plasma [24]. ...

We propose a spin transport induced by inertial motion. Our system is composed of two host media and a narrow vacuum gap in between. One of the hosts is sliding at a constant speed relative to the other. This mechanical motion causes the Doppler effect that shifts the density of states and the nonequilibrium distribution function in the moving medium. Those shifts induce the difference in the distribution function between the two media and result in tunnelling spin current. The spin current is calculated from the Schwinger-Keldysh formalism with a spin tunnelling Hamiltonian. This scheme does not require either temperature difference, voltage or chemical potential.

... State-of-the-art gyromagnetic effects are based on the motion of spinning magnetic objects. In this case, the magnetization ⃗ M stemming from the spin angular momentum can be controlled or manipulated by an external rotation ⃗ Ω to align ⃗ M and ⃗ Ω via the spin-rotation coupling as shown in Fig.1 (b) [4][5][6][7][8]. In all these cases, an object subject to manipulation is initially spinning around a well-defined axis ⃗ Ω s in the laboratory frame. ...

The classical laws of physics are usually invariant under time reversal. Here, we reveal a novel class of magnetomechanical effects rigorously breaking time-reversal symmetry. The effect is based on the mechanical rotation of a hard magnet around its magnetization axis in the presence of friction and an external magnetic field, which we call spin revolution. The physical reason for time-reversal symmetry breaking is the spin revolution and not the dissipation. The time-reversal symmetry breaking leads to a variety of unexpected effects including upward propulsion on vertical surfaces defying gravity as well as magnetic gyroscopic motion that is perpendicular to the applied force. In contrast to the spin, the angular momentum of spin revolution − → L R can be parallel or antiparallel to the equilibrium magnetization − → M eq. The spin revolution emerges spontaneously, without external rotations, and offers various applications in areas such as magnetism, robotics and energy harvesting.

... Barnett [16] noted that magnetic fields are induced by rotation and are proportional to the rotational speed. By appling the Barnett Ω for a single electron system where Ω is the angular velocity in revolution per second and 2 L g ≈ is the Lande factor. ...

An experiment reported by Podkletnov and Modanese, where gravitational radiation was purportedly emitted from the type II YBCO superconductor with voltage discharges greater than 500 kV is analyzed in relationship to the power radiated in gravitational waves. Due to the direction of the discharge, which was oppositely directed from the force measurements and the formation of an atomic cloud near the superconductor surface, helium atoms were suggested as the source of the gravitational energy. However, an analysis using the electromagnetic analog of gravitational waves showed that there would not be enough mass to produce gravitational waves unless the electron pair mass about pinned flux sites inside the superconductor is taken into account. The analysis shows that the acceleration distance required for the reported gravitational energy to move the test masses used in the experiment would be near that of the typical atom-to-atom bond length of 0.3 [nm] as would be expected for rapid motion inside a superconductor and suggest that the acceleration time t ∆ was on the order of 10-18 [s]. The rapid change in acceleration or "jerk" of the vortex plane of the cooper-pairs about the flux pinning sites is presented as the mechanism for the generating a gravitational wave and a model is presented. Such a jerk should give rise to energetic High-Frequency Gravitational Waves (HFGW) and if linked up to a computer logic system might have practical applications to communications and propulsion.

In order to commemorate Alfred Landé’s unriddling of the anomalous Zeeman Effect a century ago, we reconstruct his seminal contribution to atomic physics in light of the atomic models available at the time. Landé recognized that the coupling of quantized electronic angular momenta via their vector addition within an atom was the origin of all the apparent mysteries of atomic structure as manifested by the anomalous Zeeman effect. We show to which extent Landé’s ideas influenced the development of quantum physics, particularly Wolfgang Pauli’s path to the exclusion principle. We conclude with Landé’s brief biography.

Mechanical rotation of a crystal lattice in ferromagnetic materials can be energetically coupled with its magnetization via magnetoelastic coupling or spin rotation coupling. Surface acoustic wave (SAW) in piezoelectric materials is one of the promising candidates to realize the mechanical excitation of magnetization dynamics. In order to understand the mechanical rotation induced magnetization dynamics quantitatively, we examined the ferromagnetic resonance in an Ni film using a SAW in a LiNbO3 substrate. By decreasing a period of interdigital transducer as short as 4 μm which is one‐fifth of the previous work by Weiler [M. Weiler and co‐workers, Elastically driven ferromagnetic resonance in Nickel thin films. Phys Rev Lett 106, 117601 (2011)], the fundamental frequency of SAW could be higher than 800 MHz. From the dependence of microwave absorption on the angle between the magnetization and the wave vector of SAW, it was confirmed that the Rayleigh type SAW, which was significant to obtain a large mechanical coupling with the magnetization, was dominantly excited in the 800‐MHz‐SAW device.

The spin in a rotating frame has attracted a lot of attentions recently, as it deeply relates to both fundamental physics such as pseudo-magnetic field and geometric phase, and applications such as gyroscopic sensors. However, previous studies only focused on adiabatic limit, where the rotating frequency is much smaller than the spin frequency. Here we propose to use a levitated nano-diamond with a built-in nitrogen-vacancy (NV) center to study the dynamics and the geometric phase of a rotating electron spin without adiabatic approximation. We find that the transition between the spin levels appears when the rotating frequency is comparable to the spin frequency at zero magnetic field. Then we use Floquet theory to numerically solve the spin energy spectrum, study the spin dynamics and calculate the geometric phase under a finite magnetic field, where the rotating frequency to fulfill the resonant transition condition could be greatly reduced.

Interconversion between electron spin and other forms of angular momentum is useful for spin-based information processing. Well-studied examples of this are the conversion of photon angular momentum and rotation into ferromagnetic moment. Recently, several theoretical studies have suggested that the circular vibration of atoms work as phonon angular momentum; however, conversion between phonon angular momentum and spin-moment has yet to be demonstrated. Here, we demonstrate that the phonon angular momentum of surface acoustic wave can control the magnetization of a ferromagnetic Ni film by means of the phononic-to-electronic conversion of angular momentum in a Ni/LiNbO 3 hybrid device. The result clearly shows that the phonon angular momentum is useful for increasing the functionality of spintronic devices.

A novel experiment has been devised shedding new light on the phenomenon of unipolar induction, also known as “Faraday’s Paradox”. This is a topic which continues to fascinate scientists and engineers with much debate continuing to this day. In particular, the question of the field co-rotating with the magnet or remaining stationary remains unsettled and supporting evidence exists for both positions. In this study, we present a novel experimental apparatus that includes, for the first time, the relative motion of the measurement circuit including the closing wires, as well as the magnet and disc respectively. The results show that the closing wire needs to be considered as part of the problem, which enables the apparent paradox associated with this phenomenon to be resolved. However, it remains impossible to tell if the field co-rotates with the magnet or if it remains stationary. Instead, direct electron interaction is considered as a viable alternative to resolve remaining paradoxes.

We examine mechanical rotation of a levitated magnetic particle that is induced by ferromagnetic resonance under microwave irradiation. We show that two stable solutions appear in a certain range of parameters by bifurcation when the rotation frequency is comparable to the microwave frequency. This phenomenon originates from the coexistence of the Barnett and the Einstein-de Haas effects. We also reveal that this measurement is sensitive to the strength of the spin-rotation coupling. Our work provides a platform for accessing a microscopic relaxation process from spin to macroscopic rotation.

In Part I of this topical review, we discussed dynamical phenomena in nanomagnets, focusing primarily on magnetization reversal with an eye to digital applications. In this part, we address mostly wave-like phenomena in nanomagnets, with emphasis on spin waves in myriad nanomagnetic systems and methods of controlling magnetization dynamics in nanomagnet arrays which may have analog applications. We conclude with a discussion of some interesting spintronic phenomena that undergird the rich physics exhibited by nanomagnet assemblies.

In order to commemorate Alfred Land\'e's unriddling of the anomalous Zeeman Effect a century ago, we reconstruct his seminal contribution to atomic physics in light of the atomic models available at the time. Land\'e recognized that the coupling of quantized electronic angular momenta via their vector addition within an atom was the origin of all the apparent mysteries of atomic structure as manifested by the anomalous Zeeman effect. We show to which extent Land\'e's ideas influenced the development of quantum physics, particularly Wolfgang Pauli's path to the exclusion principle. We conclude with Land\'e's brief biography.

In condensed matter systems it is necessary to distinguish between the momentum of the constituents of the system and the pseudomomentum of quasiparticles. The same distinction is also valid for angular momentum and pseudoangular momentum. Based on Noether's theorem, we demonstrate that the recently discussed orbital angular momenta of phonons and magnons are pseudoangular momenta. This conceptual difference is important for a proper understanding of the transfer of angular momentum in condensed matter systems, especially in spintronics applications.

Einstein’s life-long effort to develop a theory that unifies gravitation and electromagnetism was not a purely theoretical enterprise. The technical environment of a gyrocompass factory triggered his search for a novel connection between the rotation of an electrically uncharged body and its magnetic field. The dimensional equality of the electric unit charge and the mass of a body multiplied by the square root of the gravitational constant hinted at a nonsensical electric charge, to which he gave the name “ghost charge.” He felt that he found a fundamental unity of gravitating mass and electricity, a hitherto undiscovered law of nature. Two physicists offered to assist him in finding evidence of this peculiar electric charge. Peter Pringsheim performed experiments with deionized gases and Teodor Schlomka made measurements of the earth’s magnetic field from balloons and airplanes; Schlomka also executed a thorough literature search and placed Einstein’s efforts in their historical context.

In the Einstein-de Haas effect [1] and the Barnett effect [2], magnetization and mechanical rotation of a whole crystal are mutually converted. The origin of spin conversion in these effects is considered to be the spin-rotation coupling [3, 4, 5, 6], which couples spin and a mechanical rotation. In spintronics, the mechanical generation of spin current via the spin-rotation coupling has been reported in various setups, such as a surface acoustic wave [7, 8], a twisting vibrational mode in a carbon nanotube [9], and a flow of a liquid metal [10]. Thus, the conversion between a spin and a mechanical rotation has been studied intensively. However, microscopic origins of the spin-rotation coupling are not well-known.

We study the orbital angular momentum of magnons for several collinear ferromagnet (FM) and antiferromagnetic (AF) systems with nontrivial networks of exchange interactions. Specifically, we consider AF and FM zig-zag and honeycomb lattices. Our work demonstrates that the arrangement of exchange interactions may play a more important role at producing the orbital angular momentum of magnons than the spin-orbit coupling energy and the resulting non-collinear spin arrangements.

We argue that certain (semi)conductors should exhibit asymmetry of their mechanical and conducting properties with respect to clockwise/counterclockwise rotation. We show that a cylinder made of a suitably chosen semiconductor coated in a metallic film and placed in the magnetic-field background can serve as a "rotational diode" which conducts electricity only at a specific range of angular frequencies. The critical angular frequency and the direction of rotation can be tuned with the magnetic field's strength. Mechanically, the rotational diode possesses different moments of inertia when rotated in clockwise and counterclockwise directions.

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