Parity-time symmetry breaking in magnetic systems

Abstract

The understanding of out-of-equilibrium physics, especially dynamic instabilities and dynamic phase transitions, is one of the major challenges of contemporary science spanning the broadest wealth of research areas that range from quantum optics to living organisms. Focusing on non-equilibrium dynamics of an open dissipative spin system, we introduce a non-Hermitian Hamiltonian approach, in which non-Hermiticity reflects dissipation and deviation from equilibrium. The imaginary part of the proposed spin Hamiltonian describes the effects of Gilbert damping and applied Slonczewski spin-transfer torque. In the classical limit, our approach reproduces Landau-Lifshitz-Gilbert-Slonczewski dynamics of a large macrospin. We reveal the spin-transfer torque driven parity-time symmetry breaking phase transition corresponding to a transition from precessional to exponentially damped spin dynamics. Micromagnetic simulations for nanoscale ferromagnetic disks demonstrate the predicted effect. Our findings can pave the way to a general quantitative description of out-of-equilibrium phase transitions driven by spontaneous parity-time symmetry breaking.

Antiferromagnetism Emerging in a Ferromagnet with Gain

“…Loss and gain are ubiquitous in nature. Tantalizing physics under their balance has attracted enormous interest and found many great applications in the context of parity-time (PT ) symmetry and exceptional point (EP) [11] in a broad field of quantum mechanics [12], optics [13][14][15][16], acoustics [17,18], optomechanics [19,20], electronics [21][22][23][24][25], and very recently in spintronics [26][27][28][29][30] and cavity spintronics [31,32]. In Ref.…”

Experimental Realization of Floquet PT -Symmetric Systems

“…In the opposite limit, coined the broken PT -phase, the spectrum consists (partially or completely) of pairs of complex conjugate eigenvalues while the eigenfunctions cease to be eigenfunctions of the PT operator. The transition point γ = γ PT shows all the characteristic features of an exceptional point (EP) singularity where both eigenfunctions and eigenvalues coalesce.Although originally the interest on PT -symmetric systems was driven by a mathematical curiosity [1], during the last five years the field has blossomed and many applications in areas of physics, ranging from optics [2-18], matter waves [19,20] and magnonics [21,22] [4, 9, 10, 12-14, 17, 18, 24-26]. Importantly, the existence of the PT phase transition and specifically of the EP singularity played a prominent role in many of these studies, and subsequent technological applications.…”

“…Although originally the interest on PT -symmetric systems was driven by a mathematical curiosity [1], during the last five years the field has blossomed and many applications in areas of physics, ranging from optics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], matter waves [19,20] and magnonics [21,22] to acoustics [23][24][25] and electronics [26][27][28], have been proposed and experimentally demonstrated [4, 9, 10, 12-14, 17, 18, 24-26]. Importantly, the existence of the PT phase transition and specifically of the EP singularity played a prominent role in many of these studies, and subsequent technological applications.…”

Exceptional points in classical spin dynamics

“…To derive non-reciprocal time evolution of classical spin, we consider the eigenspectrum of the Hamiltonian (5) in two-dimensional parameter space of mutually orthogonal magnetic fields, (h x , h y ), at fixed β. (1) is PT -symmetric [20,19]. The interval of this line between the EPs corresponds to the regime of broken PT symmetry, with the eigenvalues forming complex conjugate pairs, while on the part of the line outside of this interval the eigenvalues are purely real.…”