Storage of Classical Information in Quantum Spins

Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and backaction of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both reading and recording classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where a spin-polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom.

Figure 1

Schematic evolution of the energy spectrum and degeneracies versus $E$ for: (a) integer spin $S=2$ and (b) half-integer spin $S=5/2$. Magnetization curves of the Fe (c) and Mn (d) adatoms probed with a spin-polarized tip with ${\mathcal{P}}_T=0.74$ for three applied biases: $V=0$ (thick solid line), $V=-10\mathrm{meV}$ (dashed line), and $V=+10\mathrm{meV}$ (dotted-dashed line). Here $T=0.5\mathrm{K}$, $T_J/T_0=0.5$, $v_{\eta }=1$, and ${\rho }_T={\rho }_S$.

Figure 2

(a) Substrate-mediated elastic spin relaxation rate ${\Gamma }^{\mathrm{el}}$ in units of ${\gamma }_0\equiv {\gamma }_{S,S}^{JJ}(1\mathrm{meV})$ for an ideal half-integer spin system with $D=-5|E|=-1\mathrm{meV}$ and $T=0.4\mathrm{K}$. (b) Total relaxation rate (${\Gamma }^{\mathrm{inel}}+{\Gamma }^{\mathrm{el}}$) for $S=5/2$ at three different temperatures. Here ${\mathcal{P}}_T=-1$, $v_S=1$, $v_T=0.7$, $T_J/T_0=0.5$, and ${\rho }_S^2{T}_J^2=0.01$.