Josephson-like magnetic tunnel junction -- transition from classical to quantum regime

TL;DR

This paper presents a theoretical framework showing that a Josephson-like MTJ can host macroscopic quantum spin dynamics by mapping low-dissipation easy-plane MTJ behavior to Josephson phase dynamics. By deriving a Lagrangian and a Hamiltonian, the authors identify three qubit regimes—transmon, flux, and charge—governed by the hierarchies of $E_1$, $E_2$, and $E_H^{\parallel}$, and discuss how spin currents can tune effective damping to control coherence times. They provide parameter estimates, geometry constraints, and temperature bounds, concluding that transmon and flux MTJ qubits are the most practical with potential microsecond-scale coherence, while charge qubits face significant fabrication challenges. The findings support a CMOS-compatible, all-spintronic route to scalable quantum information processing, with dissipation engineering via spin currents as a key feature. In sum, the work lays the theoretical foundation for MTJ-based spin qubits and their integration into solid-state quantum architectures.

Abstract

We theoretically propose and analyze a Josephson-like magnetic tunnel junction (MTJ) structure that exhibits quantum spin dynamics analogous to those in superconducting Josephson junctions. By exploiting the isomorphism between the equations of motion for low-dissipation MTJs with easy-plane anisotropy and the Josephson phase dynamics, we construct a theoretical framework for realizing spintronic qubits. Within this framework, we identify the physical parameters -- such as anisotropy constants, Gilbert damping, spin current amplitude, and geometric factors -- that govern the transition from classical to quantum behavior. We show that different types of spintronic qubits, including analogs of charge, flux, and transmon superconducting qubits, can be implemented depending on the hierarchy of energy scales. A Hamiltonian formalism is developed for each regime, enabling an analytical treatment of the two-level quantum dynamics and estimation of coherence times. In particular, we demonstrate that the spin current can be used not only to excite but also to stabilize the qubit states through dissipation control. These findings provide a route toward integrating spintronic qubits into CMOS-compatible architectures and lay the groundwork for a fully spintronic platform for quantum computation.

Figures (6)

• Figure 1: (a) Schematic representation of the MTJ structure. $H$ is the external magnetic field, $M$ is the magnetization of the free layer, and $\varphi$ and $\theta$ are the azimuthal and polar angles, respectively. (b) Potential energy of the magnetic layer as a function of the azimuthal angle at a fixed external magnetic field $H = 100$ Oe and $\theta \approx \pi/2$.
• Figure 2: a) Diagram of the maximal value of the oscillations amplitude of the polar angle during the switching process in coordinates $\tau-J$. b) and c) are examples of the dynamic process for two different points of the diagram; red point corresponds to the $J = 9\cdot 10^5$ A/cm$^2$, $\tau = 40$ ps and green point corresponds to the $J = 3\cdot 10^5$ A/cm$^2$, $\tau = 10$ ps. Inset in (a) shows the saturated magnetization case corresponds to the $J = 8\cdot 10^6$ A/cm$^2$, $\tau = 100$ ps.
• Figure 3: Diagram of the realization qubit regime in coordinates temperature -- aspect ratio $\beta = a/b$. The blue area in the diagram corresponds to the realization of the qubit regime; $T_{J}$ is characteristic temperature for realization of the superconducting Josephson qubit.
• Figure 4: Schematic illustration of quantized energy levels: blue dotted curve corresponds to a quantum harmonic oscillator (QHO), while the green solid curve represents the anharmonic potential and nonequidistant energy levels of a transmon qubit.
• Figure 5: Schematical potential landscape and energy levels of the two well potential; the dotted lines demonstrate the hybridization of the quantum state due to tunneling.