The effect of dephasing and spin-lattice relaxation during the switching processes in quantum antiferromagnets

TL;DR

This work analyzes how dephasing and spin-lattice relaxation affect ultrafast switching of the Néel order in quantum antiferromagnets. It employs time-dependent Schwinger boson mean-field theory augmented with Lindblad dissipation to separate the roles of dephasing and relaxation and to study open-system dynamics. The results show that dephasing drives a slow, power-law decay of magnetization post-switch, while spin-lattice relaxation induces an exponential relaxation to a stable, reoriented state, with exchange-enhanced switching enabling switching at relatively low external fields. These findings point to a viable pathway for robust, ultrafast THz-scale antiferromagnetic spintronics and data storage, though singular dissipative-mode effects warrant further investigation with more general dissipation models.

Abstract

The control of antiferromagnetic order can pave the way to large storage capacity as well as fast manipulation of stored data. Here achieving a steady-state of sublattice magnetization after switching is crucial to prevent loss of stored data. The present theoretical approach aims to obtain instantaneous stable states of the order after reorienting the Néel vector in open quantum antiferromagnets using time-dependent Schwinger boson mean-field theory. The Lindblad formalism is employed to couple the system to the environment. The quantum theoretical approach comprises differences in the effects of dephasing, originating from destructive interference of different wave vectors, and spin-lattice relaxation. We show that the spin-lattice relaxation results in an exponentially fast convergence to the steady-state after full ultrafast switching.

Figures (9)

• Figure 1: The illustration of the system that is weakly coupled to an environment, e.g., lattice vibrations and hence spin-phonon interactions are taken into account.
• Figure 2: (a) The temporal evolution of spin expectation values under the effect of dephasing without relaxation. The switching field is present in the time interval $0< t< 10 \, J^{-1}$, as shown by the vertical gray dashed line marking the time until the field is applied, and its strength is $h=0.08 \,J$. The anisotropy parameter is $\chi=0.9$ and temperature is set to zero. (b) The illustration of exchange-enhanced switching from $t=0$ till switching. The initial state is shown by the arrows in the first circles on the left, the final state in the last circles on the right. The orange and blue arrows in the circles show the directions of the antiferromagnetic sublattice magnetizations. Applied staggered magnetic fields are shown with red arrows. The spins cant slightly after the magnetic field is applied, and at the same time they form a resulting strong effective field (black arrow) due to the exchange interaction. Consequently, the spins rotate (green curved arrows show the direction of rotation ) around the resulting effective field, i.e, the switching occurs.
• Figure 3: Illustration of an open quantum antiferromagnet. The red springs, connected to magnetization arrows, represent coupling of the spins to the environment, e.g. lattice vibrations and the gray layer represents the bath.
• Figure 4: (a) The dynamics of the mean occupation of the Schwinger bosons, as well as the resulting sublattice magnetization. (b) The time evolution of the spin expectation values under the effect of relaxation for the rate $\eta=0.05 \,J$. The applied external field is $h=0.09 \,J$ and the anisotropy parameter is $\chi=0.9$.
• Figure 5: (a) The dynamics of the sublattice magnetization of an antiferromagnet coupled to the environment for different relaxation rates at $\chi=0.9$. The static staggered magnetic field is present in the time interval $0<t<10 \,J^{-1}$ with the value $h=0.094 \, J$. The zoom is included to show the decay of oscillations more clearly at different decay rates. The panel (b) shows the damping of the oscillations of the magnetization in (a). We define $\Delta m=m_0-|m_\mathrm{max}(t_i)|$ where $m_0$ is the initial magnetization at $t=0$ and $m_{\text{max}}(t_i)$ is the value of the magnetization when the oscillations reach a peak at time $t_i$. The fitting functions are: $\Delta m_\text{fit,1}=C/t^{\alpha_\text{fit,1}}$ with $\alpha_\text{fit,1}\approx 0.345$ and $\Delta m_\text{fit,2}=C/\ln({\alpha_\text{fit,2}t})$ with $\alpha_\text{fit,2}\approx 0.142 \,J$ ; $\Delta m_\text{fit,3}=Ce^{-\eta_\text{fit}t}$ with $\eta_\text{fit}\approx0.022 \,J$ for $\eta=0.02$ data, $\eta_\text{fit}\approx0.042 \,J$ for $\eta=0.04$, $\eta_\text{fit}\approx0.061 \,J$ for $\eta=0.06$ and $\eta_\text{fit}\approx0.082 \,J$ for $\eta=0.08$ case. The fitting for $\eta=0$ is done in the interval $75 \,J^{-1}< t <200 \,J^{-1}$. The nonlinear part of the data in $\eta=0.06 \,J$ and $\eta=0.08 \,J$ are neglected during the fitting, because very small values appear due to the numerical inaccuracies only.