Many-body theory of spin-current driven instabilities in magnetic insulators

Abstract

We consider a magnetic insulator in contact with a normal metal. We derive a self-consistent Keldysh effective action for the magnon gas that contains the effects of magnon-magnon interactions and contact with the metal to lowest order. Self-consistent expressions for the dispersion relation, temperature and chemical potential for magnons are derived. Based on this effective action, we study instabilities of the magnon gas that arise due to spin-current flowing across the interface between the normal metal and the magnetic insulator. We find that the stability phase diagram is modified by an interference between magnon-magnon interactions and interfacial magnon-electron coupling. These effects persist at low temperatures and for thin magnetic insulators.

All‐Electrical Magnon Transport Experiments in Magnetically Ordered Insulators

“…Clearly, a description of the dynamics in the MOI in this nonequilibrium regime is challenging as chaotic dynamics may be encountered, but it will be insightful to see if such an effective zero damping state allows the investigation of magnon Bose-Einstein condensates and related phenomena. [29,[193][194][195][196][197][198][199][200][201][202]254] The field of antiferromagnetic magnonics has received exceedingly more interest in the last years. [94,255] As the natural frequency of magnons in antiferromagnets is THz, NM/AFI heterostructures allow realization of SHNOs operating at THz frequencies, enabling DC-to-THz conversion.…”

“…This damping compensation effect via a DC charge current may allow all-electrical experimental studies of magnon transport in the limit of spin superfluidity and magnon BoseÀEinstein condensates, [23,27,28,[190][191][192] as discussed in recent theoretical publications. [29,[193][194][195][196][197][198][199][200][201][202] For example, the study by Takei et al [197] provides analytical expressions for the evolution of the magnon transport close to the point of damping compensation. Another aspect not covered in this brief discussion is contribution from localized magnon modes, which in general exhibit lower threshold values for achieving damping compensation and may also affect the magnon transport.…”

Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons

“…We note that Eq. ( 69) is much more complex that what is typically used in spintronics literature [33,36,[38][39][40][41]. Most importantly, it shows that MBPT or diagrammatic Monte Carlo simulations [86,87] for interacting electron-magnon system must deal with nonlinear [84] electron-boson interactions.…”

“…This is precisely the situation frequently encountered in transport phenomena within spintronics. The nonequilibrium MBPT [20,21] for such problems is virtually always conducted using HP transformation, but truncated, as exemplified by theoretical and computational modeling of inelastic electron tunneling spectroscopy in magnetic tunnel junctions [33]; spin-transfer [34][35][36] and spin-orbit torques [37]; ultrafast demagnetization [38]; and conversion of magnonic spin currents into electronic spin current or vice versa at magnetic-insulator/normal-metal interfaces [39,40]. Similarly, truncated HP transformation is chosen mapping from localized spin operators to bosonic operators for problems of quantum magnonics focused on nonequilibrium dynamics of localized spins within magnetic insulators which interact with each other [11][12][13]41] or with external electromagnetic fields [42].…”

Spin transport in an electrically-driven magnon gas near Bose-Einstein condensation: Hartree-Fock-Keldysh theory

“…In the context of exciton-polariton systems, the Keldysh path integral formalism has proved useful for systematically analyzing the effects of the external pump and dissipation in the self-consistent mean-field description of the coherent state and of the fluctuations beyond the mean-field limit. 16 This powerful theoretical machinery is beginning to be applied to the nonequilibrium magnon BEC phenomenon 17 and could be useful in rigorously addressing the properties of a magnon gas tuned close to the BEC transition in a driven-dissipative environment. This approach should not only elucidate the combined effects of dissipation and nonequilibrium drive on the BEC instability criteria but also on the finite temperature crossover behaviors and spin transport properties of near-critical magnon gases.…”