Memo
Towards an experimental proof of the magnonic Aharonov−Casher effect
Rostyslav O. Serha, Vitaliy I. Vasyuchka, Alexander A. Serga, Burkard Hillebrands
Controlling the phase and amplitude of spin waves in magnetic insulators with an electric field opens the way to fast logic circuits with ultra-low power consumption. One way to achieve such control is to manipulate the magnetization of the medium via magnetoelectric effects. In experiments with magnetostatic spin waves in an yttrium iron garnet film, we have obtained the first evidence of a theoretically predicted phenomenon: The change of the spin-wave phase due to the magnonic Aharonov−Casher effect−the geometric accumulation of the magnon phase as these quasiparticles propagate through an electric field region.
Magnon Landau-Zener tunnelling and spin current generation by electric field
YuanDong Wang, Zhen-Gang Zhu, Gang Su
To control the magnon transport in magnetic systems is of great interest in magnonics. Due to the feasibility of electric field, how to generate and manipulate magnon with pure electrical method is one of the most desired goals. Here we propose that the magnon spin current is generated by applying time-dependent electric field, where the coupling between the magnon and electric field is invoked via Aharonov-Casher effect. In particular, the magnon spin current is dominated by electric field component which perpendicular to the magnetization direction. We apply our theory to 1D ferromagnetic SSH model and show that the generated magnon spin current is closely related to the band geometry. Our findings expands the horizons of magnonics and electric-control-magnon mechanisms.
Topological Phases in Magnonics: A Review
Fengjun Zhuo, Jian Kang, Aurélien Manchon, Zhenxiang Cheng
Magnonics or magnon spintronics is an emerging field focusing on generating, detecting, and manipulating magnons. As charge-neutral quasi-particles, magnons are promising information carriers because of their low energy dissipation and long coherence length. In the past decade, topological phases in magnonics have attracted intensive attention due to their fundamental importance in condensed-matter physics and potential applications of spintronic devices. In this review, we mainly focus on recent progress in topological magnonics, such as the Hall effect of magnons, magnon Chern insulators, topological magnon semimetals, etc. In addition, the evidence supporting topological phases in magnonics and candidate materials are also discussed and summarized. The aim of this review is to provide readers with a comprehensive and systematic understanding of the recent developments in topological magnonics.
(Review)(magnon)(topological)
Breakdown of Chiral Edge Modes in Topological Magnon Insulators
Jonas Habel, Alexander Mook, Josef Willsher, Johannes Knolle
Topological magnon insulators (TMI) are ordered magnets supporting chiral edge magnon excitations. These edge states are envisioned to serve as topologically protected information channels in low-loss magnonic devices. The standard description of TMI is based on linear spin-wave theory (LSWT), which approximates magnons as free non-interacting particles. However, magnon excitations of TMI are genuinely interacting even at zero temperature, calling into question descriptions based on LSWT alone. Here we perform a detailed non-linear spin-wave analysis to investigate the stability of chiral edge magnons. We identify three general breakdown mechanisms: (1) The edge magnon couples to itself, generating a finite lifetime that can be large enough to lead to a spectral annihilation of the chiral state; (2) The edge magnon hybridizes with the extended bulk magnons and, as a consequence, delocalizes away from the edge; (3) Due to a bulk-magnon mediated edge-to-edge coupling, the chiral magnons at opposite edges hybridize. We argue that, in general, these breakdown mechanisms may invalidate predictions based on LSWT and violate the notion of topological protection. We discuss strategies how the breakdown of chiral edge magnons can be avoided, e.g. via the application of large magnetic fields. Our results highlight a challenge for the realization of chiral edge states in TMI and in other bosonic topological systems without particle number conservation.
Stable Bosonic Topological Edge Modes in the Presence of Many-Body Interactions
Niclas Heinsdorf, Darshan G. Joshi, Hosho Katsura, Andreas P. Schnyder
Many magnetic materials are predicted to exhibit bosonic topological edge modes in their excitation spectra, because of the nontrivial topology of their magnon, triplon or other quasi-particle band structures. However, there is a discrepancy between theory prediction and experimental observation, which suggests some underlying mechanism that intrinsically suppresses the expected experimental signatures, like the thermal Hall current. Many-body interactions that are not accounted for in the non-interacting quasi-particle picture are most often identified as the reason for the absence of the topological edge modes. Here we report stable bosonic edge modes at the boundaries of a ladder quantum paramagnet with gapped triplon excitations in the presence of the full many-body interaction. For the first time, we use tensor network methods to resolve topological edge modes in the time-dependent spin-spin correlations and the dynamical structure factor, which is directly accessible experimentally. We further show that these edge modes have anomalously long time coherence, discuss the topological phase diagram of the model, demonstrate the fractionalization of its low-lying excitations, and propose potential material candidates.
SU(3) altermagnetism: Lattice models, chiral magnons, and flavor-split bands
Pedro M. Cônsoli, Matthias Vojta
Altermagnetism, a type of magnetic order that combines properties of ferromagnets and antiferromagnets, has generated significant interest recently, in particular due to its potential spintronics applications. Here, we show that altermagnetic states, which typically involve collinear magnetic order of SU(2) spins, can be generalized to higher SU(N) symmetry groups. We construct a two-dimensional Heisenberg model for a three-sublattice SU(3) altermagnet and analyze its excitation spectrum via flavor-wave theory. By deriving a general formula for the chirality of the excitations, we show that the SU(3) altermagnet harbors chiral magnons that are split in energy. We also compute the electronic band structure for a metallic system of the same symmetry and map out the polarization of the resulting flavor-split bands. We conclude by discussing further generalizations.
Thermal Hall effects in quantum magnets
Xiao-Tian Zhang, Yong Hao Gao, Gang Chen
In the recent years, the thermal Hall transport has risen as an important diagnosis of the physical properties of the elementary excitations in various quantum materials, especially among the Mott insulating systems where the electronic transports are often featureless. Here we review the recent development of thermal Hall effects in quantum magnets where all the relevant excitations are charge-neutral. In addition to summarizing the existing experiments, we pay a special attention to the underlying mechanisms of the thermal Hall effects in various magnetic systems, and clarify the connection between the microscopic physical variables and the emergent degrees of freedom in different quantum phases. The external magnetic field is shown to modify the intrinsic Berry curvature properties of various emergent and/or exotic quasiparticle excitations in distinct fashions for different quantum systems and quantum phases, contributing to the thermal Hall transports. These include, for example, the conventional ones like the magnons in ordered magnets, the triplons in dimerized magnets, the exotic and fractionalized quasparticles such as the spinons and the magnetic monopoles in quantum spin liquids. We review their contribution and discuss their presence in the thermal Hall conductivity in different physical contexts. We expect this review to provide a useful guidance for the physical mechanism of the thermal Hall transports in quantum magnets.
(Review)(magnon)(Hall effect)
Topological magnon band structure of emergent Landau levels in a skyrmion lattice
T. Weber, D. M. Fobes, J. Waizner, P. Steffens, G. S. Tucker, M. Böhm, L. Beddrich, C. Franz, H. Gabold, R. Bewley, D. Voneshen, M. Skoulatos, R. Georgii, G. Ehlers, A. Bauer, C. Pfleiderer, P. Böni, M. Janoschek, M. Garst
The motion of a spin excitation across topologically non-trivial magnetic order exhibits a deflection that is analogous to the effect of the Lorentz force on an electrically charged particle in an orbital magnetic field. We used polarized inelastic neutron scattering to investigate the propagation of magnons (i.e., bosonic collective spin excitations) in a lattice of skyrmion tubes in manganese silicide. For wave vectors perpendicular to the skyrmion tubes, the magnon spectra are consistent with the formation of finely spaced emergent Landau levels that are characteristic of the fictitious magnetic field used to account for the nontrivial topological winding of the skyrmion lattice. This provides evidence of a topological magnon band structure in reciprocal space, which is borne out of the nontrivial real-space topology of a magnetic order.
(magnon)(topological)(experiment)
Topological Thermal Hall Effect of Magnons in Magnetic Skyrmion Lattice
Masatoshi Akazawa, Hyun-Yong Lee, Hikaru Takeda, Yuri Fujima, Yusuke Tokunaga, Taka-hisa Arima, Jung Hoon Han, Minoru Yamashita
Topological transports of fermions are governed by the Chern numbers of the energy bands lying below the Fermi energy. For bosons, e.g. phonons and magnons in a crystal, topological transport is dominated by the Chern number of the lowest energy band when the band gap is comparable to the thermal energy. Here, we demonstrate the presence of topological transport by bosonic magnons in a lattice of magnetic skyrmions - topological defects formed by a vortex-like texture of spins. We find a distinct thermal Hall signal in the magnetic skyrmion phase of an insulating polar magnet GaV4Se8, identified as the topological thermal Hall effect of magnons governed by the Chern number of the lowest energy band of the magnons in a triangular lattice of magnetic skyrmions. Our findings lay a foundation for studying topological phenomena of other bosonic excitations through thermal Hall probe.
(magnon)(topological)(Hall effect)(experiment)
Probing Complex-energy Topology via Non-Hermitian Absorption Spectroscopy in a Trapped Ion Simulator
Mingming Cao, Kai Li, Wending Zhao, Weixuan Guo, Bingxiag Qi, Xiuying Chang, Zichao Zhou, Yong Xu, Luming Duan
Non-Hermitian systems generically have complex energies, which may host topological structures, such as links or knots. While there has been great progress in experimentally engineering non-Hermitian models in quantum simulators, it remains a significant challenge to experimentally probe complex energies in these systems, thereby making it difficult to directly diagnose complex-energy topology. Here, we experimentally realize a two-band non-Hermitian model with a single trapped ion whose complex eigenenergies exhibit the unlink, unknot or Hopf link topological structures. Based on non-Hermitian absorption spectroscopy, we couple one system level to an auxiliary level through a laser beam and then experimentally measure the population of the ion on the auxiliary level after a long period of time. Complex eigenenergies are then extracted, illustrating the unlink, unknot or Hopf link topological structure. Our work demonstrates that complex energies can be experimentally measured in quantum simulators via non-Hermitian absorption spectroscopy, thereby opening the door for exploring various complex-energy properties in non-Hermitian quantum systems, such as trapped ions, cold atoms, superconducting circuits or solid-state spin systems.
(non-Hermitian)(experiment)
Non-Hermitian Topological Magnonics
Tao Yu, Ji Zou, Bowen Zeng, J. W. Rao, Ke Xia
Dissipation in mechanics, optics, acoustics, and electronic circuits is nowadays recognized to be not always detrimental but can be exploited to achieve non-Hermitian topological phases with functionalities for potential device applications, ranging from sensors with unprecedented sensitivity, light funneling, wave isolators, non-reciprocal amplification, to dissipation induced phase transition. As elementary excitations of ordered magnetic moments that exist in various magnetic materials, magnons are the information carrier in magnonic devices with low-energy consumption for reprogrammable logic, non-reciprocal communication, and non-volatile memory functionalities. Non-Hermitian topological magnonics deals with the engineering of dissipation for non-Hermitian topological phases in magnets that are not achievable in the conventional Hermitian scenario, with associated functionalities cross-fertilized with their electronic, acoustic, optic, and mechanic counterparts, such as giant enhancement of magnonic frequency combs, magnon amplification, (quantum) sensing of the magnetic field with unprecedented sensitivity, magnon accumulation, and perfect absorption of microwaves. In this review article, we introduce the unified basic physics and provide a comprehensive overview of the recent theoretical and experimental progress towards achieving distinct non-Hermitian topological phases in magnonic devices, including exceptional points, exceptional nodal phases, non-Hermitian magnonic SSH model, and non-Hermitian skin effect. We emphasize the non-Hermitian Hamiltonian approach based on the Lindbladian or self-energy of the magnonic subsystem but address the physics beyond it as well, such as the crucial quantum jump effect in the quantum regime and non-Markovian dynamics. We provide a perspective for future opportunities and challenges before concluding this article.
(Review)(magnon)(non-Hermitian)
Magnonic Superconductivity
Khachatur G. Nazaryan, Liang Fu
We uncover a new superconducting state with partial spin polarization induced by a magnetic field. This state, which we call "magnonic superconductor", lacks a conventional pairing order parameter, but is characterized instead by a composite order parameter that represents the binding of electron pairs and magnons. We rigorously demonstrate the existence of magnonic superconductivity with high transition temperature in a triangular lattice Hubbard model with repulsive interaction. We further show that magnonic Cooper pairs can attract to form higher-charge bound states, which can give rise to charge-6e superconductivity.
Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
Even Thingstad, Pierre Fromholz, Flavio Ronetti, Daniel Loss, Jelena Klinovaja
Topological magnetic insulators host chiral gapless edge modes. In the presence of strong interaction effects, the spin of these modes may fractionalize. Studying a 2D array of coupled insulating spin-1/2 chains, we show how spatially modulated magnetic fields and Dzyaloshinskii-Moriya interactions can be exploited to realize chiral spin liquids or integer and fractional spin quantum Hall effect phases. These are characterized by a gapped bulk spectrum and gapless chiral edge modes with fractional spin. The spin fractionalization is manifested in the quantized spin conductance, which can be used to probe the fractional spin quantum Hall effect. We analyze the system via bosonization and perturbative renormalization group techniques that allow us to identify the most relevant terms induced by the spin-spin interactions that open gaps and render the system topological under well-specified resonance conditions. We show explicitly that the emerging phase is a genuine chiral spin liquid. We suggest that the phases can be realized experimentally in synthetic spin chains and ultracold atom systems.
Thermal transport across a Josephson junction in a dissipative environment
Tsuyoshi Yamamoto, Leonid I. Glazman, Manuel Houzet
At zero temperature, a Josephson junction coupled to an ohmic environment displays a quantum phase transition between superconducting and insulating phases, depending whether the resistance of the environment is below or above the resistance quantum. At finite temperature, this so-called Schmid transition turns into a crossover. We determine the conditions under which the temperature dependence of the thermal conductance, which characterizes heat flow from a hot to cold resistor across the Josephson junction, displays universal scaling characteristic of the Schmid transition. We also discuss conditions for heat rectification to happen in the circuit. Our work can serve as a guide for identifying signatures of the Schmid transition in heat transport experiments.
Note on Angular Momentum of Phonons in Chiral Crystals
Akihito Kato, Jun-ichiro Kishine
Phonon angular momentum in chiral materials has been widely studied in spintronics and condensed matter physics. In chiral crystals, this is not the conserved quantity in contrast to the pseudo-angular momentum. To highlight this point and to understand the behavior of the angular momentum, we reexamine phonon dispersion theory based on the irreducible representation of helix and show the distinction of these angular momentum is originated from chirality.
(Note)(phonon)(angular momentum)
Difference between angular momentum and pseudo-angular momentum
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.
(Note)(magnon)(angular momentum)
Intrinsic Magnon Orbital Hall Effect in Honeycomb Antiferromagnets
Gyungchoon Go, Daehyeon An, Hyun-Woo Lee, Se Kwon Kim
We theoretically investigate the transport of magnon orbitals in a honeycomb antiferromagnet. We find that the magnon orbital Berry curvature is finite even without spin-orbit coupling and thus the resultant magnon orbital Hall effect is an intrinsic property of the honeycomb antiferromagnet rooted only in the exchange interaction and the lattice structure. Due to the intrinsic nature of the magnon orbital Hall effect, the magnon orbital Nernst conductivity is estimated to be orders of magnitude larger than the predicted values of the magnon spin Nernst conductivity that requires finite spin-orbit coupling. For the experimental detection of the predicted magnon orbital Hall effect, we invoke the magnetoelectric effect that couples the magnon orbital and the electric polarization, which allows us to detect the magnon orbital accumulation through the local voltage measurement. Our results pave a way for a deeper understanding of the topological transport of the magnon orbitals and also its utilization for low-power magnon-based orbitronics, namely magnon orbitronics.
(magnon)(Hall effect)(orbital)
Orbital angular momentum and current-induced motion of a Skyrmion-textured domain wall in a ferromagnetic nanotube
Seungho Lee, Se Kwon Kim
We theoretically study the current-induced dynamics of a domain wall in a ferromagnetic nanotube by developing a theory for the orbital angular momentum of a domain wall and the current-induced torque on it. Specifically, a domain wall with nontrivial magnetization winding along the circumference is shown to possess finite orbital angular momentum, which is proportional to the product of its Skyrmion charge and position, and the current is shown to exert a torque changing the orbital angular momentum of the domain wall and thereby drives it. The current-induced torque is interpreted as the transfer of orbital angular momentum from electrons to the domain wall, which occurs due to the emergent magnetic field associated with the Skyrmion charge. Our results reveal a hitherto unrecognized utility of the orbital degree of freedom of magnetic solitons.
(orbital)
Orbital Magnetic Moment of Magnons
Robin R. Neumann, Alexander Mook, Jürgen Henk, Ingrid Mertig
In experiments and applications usually the spin magnetic moment of magnons is considered. In this Paper we identify an additional degree of freedom of magnons: an \emph{orbital} magnetic moment brought about by spin-orbit coupling.Our microscopic theory uncovers that spin magnetization and orbital magnetization are independent quantities. They are not necessarily collinear; thus, even when the total spin moment is compensated due to antiferromagnetism, orbital magnetization may be nonzero. This scenario of orbital weak ferromagnetism is realized in paradigmatic kagome antiferromagnets with Dzyaloshinskii-Moriya interaction. We demonstrate that magnets exhibiting a magnonic orbital moment are omnipresent and propose transport experiments for probing it.
(magnon)(orbital)
Orbital Angular Momentum of Magnons in Collinear Magnets
Randy S. Fishman, Jason S. Gardner, Satoshi Okamoto
We study the orbital angular momentum of magnons for collinear ferromagnet (FM) and antiferromagnetic (AF) systems with nontrivial networks of exchange interactions. The orbital angular momentum of magnons for AF and FM zig-zag and honeycomb lattices becomes nonzero when the lattice contains two inequivalent sites and is largest at the avoided-crossing points or extremum of the frequency bands. Hence, 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 arrangement of spins.
(magnon)(orbital)
Twisted magnon beams carrying orbital angular momentum
Chenglong Jia, Decheng Ma, Alexander F. Schäffer & Jamal Berakdar
Low-energy eigenmode excitations of ferromagnets are spin waves or magnons that can be triggered and guided in magnonic circuits without Ohmic losses and hence are attractive for communicating and processing information. Here we present new types of spin waves that carry a definite and electrically controllable orbital angular momentum (OAM) constituting twisted magnon beams. We show how twisted beams emerge in magnonic waveguides and how to topologically quantify and steer them. A key finding is that the topological charge associated with OAM of a particular beam is tunable externally and protected against magnetic damping. Coupling to an applied electric field via the Aharanov-Casher effect allows for varying the topological charge. This renders possible OAM-based robust, low-energy consuming multiplex magnonic computing, analogously to using photonic OAM in optical communications, and high OAM-based entanglement studies, but here at shorter wavelengths, lower energy consumption, and ready integration in magnonic circuits.
(magnon)(orbital)
Angular Momentum of Phonons and Einstein-de Haas Effect
Lifa Zhang, Qian Niu
We study angular momentum of phonons in a magnetic crystal. In the presence of a spin-phonon interaction, we obtain a nonzero angular momentum of phonons, which is an odd function of magnetization. At zero temperature, phonon has a zero-point angular momentum besides a zero-point energy. With increasing temperature, the total phonon angular momentum diminishes and approaches to zero in the classical limit. The nonzero phonon angular momentum can have a significant impact on the Einstein-de Haas effect. To obtain the change of angular momentum of electrons, the change of phonon angular momentum needs to be subtracted from the opposite change of lattice angular momentum. Furthermore, the finding of phonon angular momentum gives a potential method to study the spin-phonon interaction. Possible experiments on phonon angular momentum are also discussed.
(phonon)(EdH)
Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach
Harsh Varshney, Rohit Mukherjee, Arijit Kundu, Amit Agarwal
We present a systematic study of the nonlinear thermal Hall responses in bosonic systems using the quantum kinetic theory framework. We demonstrate the existence of an intrinsic nonlinear boson thermal current, arising from the quantum metric which is a wavefunction dependent band geometric quantity. In contrast to the nonlinear Drude and nonlinear anomalous Hall contributions, the intrinsic nonlinear thermal conductivity is independent of the scattering timescale. We demonstrate the dominance of this intrinsic thermal Hall response in topological magnons in a two-dimensional ferromagnetic honeycomb lattice without Dzyaloshinskii-Moriya interaction. Our findings highlight the significance of band geometry induced nonlinear thermal transport and motivate experimental probe of the intrinsic nonlinear thermal Hall response with implications for quantum magnonics.
Transport theory in non-Hermitian systems
Qing Yan, Hailong Li, Qing-Feng Sun, X. C. Xie
Non-Hermitian systems have garnered significant attention due to the emergence of novel topology of complex spectra and skin modes. However, investigating transport phenomena in such systems faces obstacles stemming from the non-unitary nature of time evolution. Here, we establish the continuity equation for a general non-Hermitian Hamiltonian in the Schrödinger picture. It attributes the universal non-conservativity to the anti-commutation relationship between particle number and non-Hermitian terms. Our work derives a comprehensive current formula for non-Hermitian systems using Green's function, applicable to both time-dependent and steady-state responses. To demonstrate the validity of our approach, we calculate the local current in models with one-dimensional and two-dimensional settings, incorporating scattering potentials. The spatial distribution of local current highlights the widespread non-Hermitian phenomena, including skin modes, non-reciprocal quantum dots, and corner states. Our findings offer valuable insights for advancing theoretical and experimental research in the transport of non-Hermitian systems.
Quantum many-body dynamics of the Einstein-de Haas effect
J.H. Mentink, M.I. Katsnelson, M. Lemeshko
In 1915, Einstein and de Haas and Barnett demonstrated that changing the magnetization of a magnetic material results in mechanical rotation, and vice versa. At the microscopic level, this effect governs the transfer between electron spin and orbital angular momentum, and lattice degrees of freedom, understanding which is key for molecular magnets, nano-magneto-mechanics, spintronics, and ultrafast magnetism. Until now, the timescales of electron-to-lattice angular momentum transfer remain unclear, since modeling this process on a microscopic level requires addition of an infinite amount of quantum angular momenta. We show that this problem can be solved by reformulating it in terms of the recently discovered angulon quasiparticles, which results in a rotationally invariant quantum many-body theory. In particular, we demonstrate that non-perturbative effects take place even if the electron--phonon coupling is weak and give rise to angular momentum transfer on femtosecond timescales.
(EdH)
Magnonic Einstein–de Haas Effect: Ultrafast Rotation of Magnonic Microspheres
A. Kani, F. Quijandría, and J. Twamley
Phys. Rev. Lett. 129, 257201 (2022): Open Access
Magnons, collective spin excitations in magnetic crystals, have attracted much interest due to their ability to couple strongly to microwaves and other quantum systems. In compact magnetic crystals, we show that there are magnonic modes that can support orbital angular momentum and that these modes can be driven by linearly polarized microwave fields. Because of conservation of angular momentum, exciting such magnon modes induces a mechanical torque on the crystal. We study a levitated magnetic crystal, a yttrium iron garnet (YIG) microsphere, where such orbital angular momentum magnon modes are driven by microwaves held in a microwave high-Q microwave cavity. We find that the YIG sphere experiences a mechanical torque and can be spun up to ultralarge angular speeds exceeding 10 GHz.
(magnon)(EdH)
Einstein-de Haas Effect of Topological Magnons
Jun Li, Trinanjan Datta, Dao-Xin Yao
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.
(magnon)(EdH)
Schwinger mechanism of magnon-antimagnon pair production on magnetic field inhomogeneities and the bosonic Klein effect
T. C. Adorno, S. P. Gavrilov, D. M. Gitman
Effective field theory of low-energy exitations-magnons that describes antiferromagnets is mapped into scalar electrodynamics of a charged scalar field interacting with an external electromagnetic potential. In the presence of a constant inhomogeneous external magnetic field the latter problem is technically reduced to the problem of charged-particle creation from the vacuum by an electric potential step (x-step). Magnetic moment plays here the role of the electric charge, and magnons and antimagnons differ from each other in the sign of the magnetic moment. In the framework of such a consideration, it is important to take into account the vacuum instability (the Schwinger effect) under the magnon-antimagnon production on magnetic field inhomogeneities (an analog of pair creation from the vacuum by electric-like fields). We demonstrate how to use the strong field QED with x-steps developed by the authors (SPG and DMG) to study the magnon-antimagnon pair production on magnetic field inhomogeneities. Characteristics of the vacuum instability obtained for some magnetic steps that allows exact solving the Klein-Gordon equation are presented. In particular, we consider examples of magnetic steps with very sharp field derivatives that correspond to a regularization of the Klein step. In the case of smooth-gradient steps, we describe an universal behavior of the flux density of created magnon pairs. We also note that since the low-energy magnons are bosons with small effective mass, then for the first time maybe the opportunity will arise to observe the Schwinger effect in the case of the Bose statistics, in particular, the bosonic Klein effect in laboratory conditions. Moreover, it turns out that in the case of the Bose statistics appears a new mechanism for amplifying the effect of the pair creation, which we call statistically-assisted Schwinger effect.
Introduction to nuclear spin waves in ferro- and antiferromagnets
Sergio M. Rezende
Journal of Applied Physics 132, 091101 (2022): Open Access
Collective nuclear spin excitations, called nuclear spin waves or magnons, are enabled in strongly magnetic materials by the hyperfine coupling of the nuclear and electronic spins in an atom and the exchange interaction between electronic spins of neighboring atoms. Nuclear spin waves attracted the interest of theoretical and experimental researchers worldwide about four to five decades ago and then waned. Very recently, two experimental reports of nuclear spintronic effects in the canted antiferromagnet MnCO3 have shown that spin currents can be generated using nuclear spin states, bridging two quite separate worlds, one of nuclear spin excitations and the other of spintronics. In this Tutorial, we briefly review the basic concepts and properties of nuclear spin waves in ferro- and antiferromagnetic (AF) materials and present a few significant experimental results obtained some time ago with the uniaxial anisotropy AF MnF2 and the cubic anisotropy AF RbMnF3 and compare them with theory. We also briefly present the recent experimental observations of the nuclear spin pumping effect and the nuclear spin Seebeck effect in the canted antiferromagnet MnCO3. Other possible AF candidates for studies of nuclear spintronic effects are discussed.
(Review)(magnon)(nuclear spin)
Dissipative Spin-wave Diode and Nonreciprocal Magnonic Amplifier
Ji Zou, Stefano Bosco, Even Thingstad, Jelena Klinovaja, Daniel Loss
We propose an experimentally feasible dissipative spin-wave diode comprising two magnetic layers coupled via a non-magnetic spacer. We theoretically demonstrate that the spacer mediates not only coherent interactions but also dissipative coupling. Interestingly, an appropriately engineered dissipation engenders a nonreciprocal device response, facilitating the realization of a spin-wave diode. This diode permits wave propagation in one direction alone, given that the coherent Dzyaloshinskii- Moriya (DM) interaction is balanced with the dissipative coupling. The polarity of the diode is determined by the sign of the DM interaction. Furthermore, we show that when the magnetic layers undergo incoherent pumping, the device operates as a unidirectional spin-wave amplifier. The amplifier gain is augmented by cascading multiple magnetic bilayers. By extending our model to a one-dimensional ring structure, we establish a connection between the physics of spin-wave amplification and non-Hermitian topology. Our proposal opens up a new avenue for harnessing inherent dissipation in spintronic applications.
(magnon)(QME)(Born-Markov approximation)
Unidirectional propagation of zero-momentum magnons
Ondřej Wojewoda, Jakub Holobrádek, Dominik Pavelka, Ekaterina Pribytova, Jakub Krčma, Jan Klíma, Jan Michalička, Tomáš Lednický, Andrii V. Chumak, Michal Urbánek
We report on experimental observation of unidirectional propagation of zero-momentum magnons in synthetic antiferromagnet consisting of strained CoFeB/Ru/CoFeB trilayer. Inherent non-reciprocity of spin waves in synthetic antiferromagnets with uniaxial anisotropy results in smooth and monotonous dispersion relation around Gamma point, where the direction of the phase velocity is reversed, while the group velocity direction is conserved. The experimental observation of this phenomenon by intensity-, phase-, and time-resolved Brillouin light scattering microscopy is corroborated by analytical models and micromagnetic simulations.
A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
Francesco Campaioli, Jared H. Cole, Harini Hapuarachchi
Quantum master equations are an invaluable tool to model the dynamics of a plethora of microscopic systems, ranging from quantum optics and quantum information processing, to energy and charge transport, electronic and nuclear spin resonance, photochemistry, and more. This tutorial offers a concise and pedagogical introduction to quantum master equations, accessible to a broad, cross-disciplinary audience. The reader is guided through the basics of quantum dynamics with hands-on examples that build up in complexity. The tutorial covers essential methods like the Lindblad master equation, Redfield relaxation, and Floquet theory, as well as techniques like Suzuki-Trotter expansion and numerical approaches for sparse solvers. These methods are illustrated with code snippets implemented in python and other languages, which can be used as a starting point for generalisation and more sophisticated implementations.
(Review)(Lindblad)(QME)
Keldysh Field Theory for Driven Open Quantum Systems
L. M. Sieberer, M. Buchhold, S. Diehl
Recent experimental developments in diverse areas - ranging from cold atomic gases over light-driven semiconductors to microcavity arrays - move systems into the focus, which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in condensed matter. This concerns both their non-thermal flux equilibrium states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
(Review) (Lindblad)(QME)(Keldysh)
(Uchino-san: Effective Hamiltonian thorugh path integral)
Field Theory of Many-Body Lindbladian Dynamics
Foster Thompson, Alex Kamenev
We review and further develop the Keldysh functional integral technique for the study of Lindbladian evolution of many-body driven-dissipative quantum systems. A systematic and pedagogical account of the dynamics of generic bosonic and fermionic Lindbladians is presented. Our particular emphasis is on unique properties of the stationary distribution function, determined by the Lyapunov equation. This framework is applied to study examples of Lindbladian dynamics in the context of band theory, disorder, collisionless collective modes, and mean-field theory.
(Review)(Lindblad)(QME)(Keldysh)
Master equation of the Lindblad form based on a microscopic Hamiltonian through stochastic limit approximation
湯浅一哉
（抜粋：一部改訂）スピン緩和現象,デコヒーレンスといった話題を初めとし,量子論における散逸現象の研究が盛んに行われている.その難しさ (そして,その面白さ)は,非可逆な現象を時間反転対称な量子論でいかに記述するかという点にあると言えよう.現在標準的となっているのは,注目している系と相互作用する無限自由度の ｢環境系｣をも含めた ｢仝体系｣の Hamiltonianを出発点として量子論を展開し,環境系についての平均操作を経て,注目系の非可逆ダイナミックスを導く理論である.CaldeiraとLeggettは,環境系として無限個の調和振動子の集まりを採用したモデルを用いて量子Brown運動を定式化し,量子散逸現象の研究に大きな影響をもたらした.また,それ以前から,量子光学の分野において大きな成功 を収めている.
一方で,環境系の詳細に立ち入ることはしない現象論的立場も存在する.一般に密度行列演算子が線形でMarkov的な時間発展をするならば,そのマスター方程式はLindblad型であることが必要十分条件として示される.そこで,この形のマスター方程式を理論の出発点にしようというのである.VonNeumann方程式には見られない "散逸項"の存在により,散逸現象を記述することができる.また,CaldeiraとLeggettが,高温近似,Markov近似の下に導出したマスター方程式はLindblad型になっておらず,その帰結として密度行列演算子の正値性が保証されないことが知られているが,この立場では初めからその困難に悩まされることはない.
ただ,この Lindblad型のマスター方程式を出発点とする理論では,H,L_i,A_iとして何を採用するかということが問題となる.それらの選択が物理モデルを決めることになるが,Lindbladの数学理論はその指針までは与えない.
本稿では,仝体系のHamiltonianから出発する微視的立場から基礎付けることで,それらの物理的構造を見ることにしよう.
（解説）(Lindblad)(QME)
Exceptional points for parameter estimation in open quantum systems: Analysis of the Bloch equations
Morag Am-Shallem, Ronnie Kosloff, Nimrod Moiseyev
We suggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: The dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator L. The eigenvalues of L are complex, reflecting unitary as well as dissipative dynamics. For certain values of parameters defining L, non-hermitian degeneracies emerge, i.e. exceptional points (EP). The dynamical signature of these EPs corresponds to a unique time evolution. This unique feature can be employed experimentally to locate the EPs and thereby to determine the intrinsic system parameters with a high accuracy. This way we turn the disadvantage of the dissipation into an advantage. We demonstrate this method in the open system dynamics of a two-level system described by the Bloch equation, which has become the paradigm of diverse fields in physics, from NMR to quantum information and elementary particles.
（EP）(Lindblad)(Non-Hermitian)(Nuclear spin)
Master equation of the Lindblad form based on a microscopic Hamiltonian through stochastic limit approximation : For rapidly decaying systems
湯浅一哉, 木村元, 今福健太郎
（抜粋：一部改訂）スピン緩和現象, デコヒーレンスといった現象を説明するためには, 散逸現象を量子論に基づいて記述する必要がある. しかしながら, 量子論はもともと閉じた系が適用対象であり, また, 時間反転対称性をもっていることから, それが可能か否かは自明ではなく, 興味深いテーマである. 現在標準的となっている方法のひとつは, 注目している (散逸) 系と相互作用する無限自由度系 「環境系」 をも含めた 「全体系」 を閉じた系として量子論的に取り扱い, 興味のない環境系に対する平均操作を通じて, 注目系の非可逆ダイナミクスを導く方法である. CaldeiraとLeggettは経路積分を用いて量子 Brown 運動を定式化することに成功し, また, 近年のテクノロジーの進歩は, 量子光学におけるこの方法の成功を明らかにした.
Accardi et al. の確率極限近似 (stochastic limit approximation)は, 全体系から散逸ダイナミクスを引き出す有力な手法である.例えば, 電磁場 $H_{B}$ 中の原子 $H_{S}$ を考えよ. 量子光学においてしばしば興味のある状況である. その場合, 電磁相互作用 $\lambda V$ は十分弱く $(\lambda<<1)$ , 摂動計算は十分に良い近似を与えるであろう. 確率極限近似は, 同時に時間の粗視化 $t\mapsto\tau=\lambda^{2}t$ を行い, 弱結合極限 (weak coupling limit) $\lambdaarrow 0$($\tau$ 固定) によって摂動の最低次の寄与を抽出することで, 最小限ではあるが十分に興味深い散逸ダイナミクスを導く方法である
しかしながら, Hamiltonian (1)に確率極限近似を適用して導かれるダイナミクスは, 少々状況が限定されている. 一般に, 緩和定数 $\gamma$ に対する相互作用の最低次の寄与は $\lambda^{2}$ に比例し, 注目系
$H_{S}$ の特徴的振動数 $\Omega$ に比べて $\gamma\ll\Omega$. すなわち, 弱い散逸 ( $\mathrm{W}\mathrm{D}$ :Weak Damping) が導かれるのである. 量子光学はこの状況にあたる. これに比べて緩和が速い $\gamma\sim\Omega$ という状況 ( $\mathrm{R}\mathrm{D}$ :RapidDecay) を導こうと思ったら, 別の扱いが必要なのである. また,$\mathrm{R}\mathrm{D}$ の取り扱いは, WD に比べて少々注意を要することが指摘されている $[2,12]$ . $\mathrm{W}\mathrm{D}$ においては通常Lindblad型マスター方程式が導かれている一方で,$\mathrm{R}\mathrm{D}$ の状況において導出されるマスター方程式は, しばしばLindblad 型でないのである. そのため,$\mathrm{R}\mathrm{D}$ のマスター方程式はしばしば, 確率の正値性が保証されないという困難を伴うことになる. CaldeiraとLeggett のマスター方程式はその一
例である.
本稿では, 確率極限近似を全体系 Hamiltonian に適用する枠組みを与える. 注目系の振動数 $\Omega$ は $O(\lambda^{2})$ のオーダーであり, $\gamma\sim\Omega$ という $\mathrm{R}\mathrm{D}$ の状況が導かれることになる. そして, ここで与える方法で得られるマスター方程式が Lindblad 型であることを見よう.
（解説）(Lindblad)(QME)
Universal Hall conductance scaling in non-Hermitian Chern insulators
Solofo Groenendijk, Thomas L. Schmidt, Tobias Meng
We investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a characteristic non-analytical contribution to the Hall conductance. Near its onset, this contribution exhibits a universal power-law with a power 3/2 as a function of Dirac mass, chemical potential and gain strength. Our results pave the way for the study of non-Hermitian topology in electronic transport experiments.
(Lindblad)(QME)
超対称量子力学とその拡張
山田吉英
（抜粋：一部改訂）超対称性の概念は素粒子物理学の研究の中から生まれてきたものである.超対称性とはポーズ粒子とフェルミ粒子の間の対称性を意味しており，それは自怒界に存在する 4つの力を統ーするのに必要不可欠な概念であると考えられている.素粒子物理学は基本的には場の理論の枠組みで論じちれるため，超対称性の概念もまた場の理論の枠組みにおいて定式化されている.しかしながら場の理論における超対称性の帰結〈とりわけ考えているモデルが超対称性の自発的破れを示すか否か〉を分析することは難しい問題であり，そのためトイモデルとして超対称量子力学というものが提唱されたのである.
かように超対称量子力学というものは元来，超対称場の理議の理解を助けるためのモデルに過ぎなかったのであるが，ひとたび定式化がなされると，そこに様々な興味深い性質があることが認識されていった.そして間もなく，これらの性賓が本質的には Darboux変換や因子分解法という，既に知られた手法の再定式化であることが明らかにされた.
Darboux変換とは，基底状態が既知のハミルトニアンから，新しいハミルトニアンを生成する変換である.このような変換で作られたハミルトニアンは，元のハミルトニアンと同ーの(ただし第 1励起状態から始まる)スペクトルを持つ.一方，因子分解法とは，ハミルトニアンを 2通りに因子分解することにより シュレーディンガ一方程式の国有値問題を代数的に解く手法である.これらの変換と解法とを，超対称量子力学は非常に見通しのよい形で内包している.
そして現在，超対称量子力学は一つの研究分野を形成しており，多くの応用や拡張理論を生んでいる.もちろん様々な流儀はあるのだが，あえて単純化して一言で言えば，超対称量子力学とは等スペクトル系の理論である.すなわち，スペクトルの等しい2つの系が超対称量子力学によって構成されるのである.この意味で超対称性とは“系を超えた対称性"ということができる.
超対称量子力学においては，絡合子 (intertwiner)とよばれる譲算子が本質的な役割を果たす.絡合子が 2つのハミルトニアンを絡み合わせるとき，その 2つの系は等スペクトルになり，それらの組を超対称系と称するのである.
歴史的に絡合子という演算子は，ハミルトニアンの因子として導入されている.したがってそれは運動量について 1次の演算子であった.しかしひとたび絡合子と 2つのハミルトニアンの関係が樹立されてしまえば，もはやハミルトニアンの国子分解にこだわる必要はない.こうして運動量について高次の絡合子へと道が関かれる.このような高次の絡合子による等スペクトル系を多重超対称系と称する.このような多重超対称等スペクトル系は，その一部として高次の Darboux変換 (Crum変換)を含んでいるが，それには婦着されない系も存在する.
また絡合子による等スペクトル系構成を 3次元に拡張するためには，多重超対称系への一般化が不可欠であることが明らかになった.
本論文は超対称量子力学とその多重超対称系への拡張，また 3次元空間への拡張について述べたものである.第1節は超対称量子力学の基本事項のレビューであるが，他のレビュー論文のようにハミルトニアンの因子分解に基礎を主くのではなく，より本質と思われる絡合関係式を基礎におき議論の整理を試みた.第2節は因子分解法の再定式化である形状不変性についてのレビューである.量子力学の初学者であってもすぐに使えるよう，解法の手続きを明確化するよう努めた.
(解説)(超対称量子力学)(SUSY)
Supersymmetric quantum mechanics of one-dimensional systems
C V Sukumar
J. Phys. A: Math. Gen. 18 2917 (1985)
It is shown that every one-dimensional quantum mechanical Hamiltonian H1 can have a partner H2 such that H1 and H2 taken together may be viewed as the components of a supersymmetric Hamiltonian. The term 'supersymmetric Hamiltonian' is taken to mean a Hamiltonian defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of H1 and H2 are explored. It is shown how the supersymmetric pairing may be utilised to eliminate the ground state of H1, or add a state below the ground state of H1 or maintain the spectrum of H1. It is also explicitly demonstrated that the supersymmetric pairing may be used to generate a class of anharmonic potentials with exactly specified spectra. The complete spectrum of an anharmonic potential so generated consists of all the eigenstates of the simple harmonic oscillator and, in addition, a ground state at a specified energy E which lies arbitrarily below the E=1/2 ground state of the harmonic oscillator.
（Review)(解説)(超対称量子力学)(SUSY)
Supersymmetric Quantum Mechanics
David J. Fernandez C
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first and second order for one-dimensional arbitrary systems, and we will illustrate the method through the trigonometric Poschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.
（Review)(解説)(超対称量子力学)(SUSY)
Supersymmetry and Quantum Mechanics
Fred Cooper, Avinash Khare, Uday Sukhatme
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p.
（Review)(解説)(超対称量子力学)(SUSY)
Magnon Landau levels and emergent supersymmetry in strained antiferromagnets
Mary Madelynn Nayga, Stephan Rachel, Matthias Vojta
Inhomogeneous strain applied to lattice systems can induce artificial gauge fields for particles moving on this lattice. Here we demonstrate how to engineer a novel state of matter, namely an antiferromagnet with a Landau-level excitation spectrum of magnons. We consider a honeycomb-lattice Heisenberg model and show that triaxial strain leads to equally spaced pseudo-Landau levels at the upper end of the magnon spectrum, with degeneracies characteristic of emergent supersymmetry. We also present a particular strain protocol which induces perfectly quantized magnon Landau levels over the whole bandwidth. We discuss experimental realizations and generalizations.
非断熱位相操作を用いた量子波制御
萱沼洋輔
（抜粋）量子系を操って様々な機能を発現させようとするとき、われわれに操作できるのは無限に重いマクロな自由度としての「外場」であり、波動関数はシュレーディンガ一方程式を通じて間接的に駆動される。これを外場による量子駆動問題と名づける。時間をあらわに含む量子駆動問題は基底状態や熱平衡状態の性質を問う従来の問題とは全く異なる新しいタイプの問題である。このことは、最も単純な量子系である 2準位系の定常状態はトリビアルに求められるのに、時間にあらわに依存するパラメタを含む時開発展問題の一般解は求められない、という事実からも明らかであろう。ましてや、相互作用する多体系の量子駆動問題などはほとんど手付かずの状態である。この講義では、単純な「解ける」量子駆動問題としての Landau.Zener遷移の復習からはじめて、その発展として非断熱選移と位相干渉の関わるいくつかの間題について紹介し、応用例のーつとして位相干渉効果を用いた新しい qubit操作の提案を行う。
（解説）(Landau–Zener)