Abstract
We solve the Schrödinger equation for various quantum regimes describing a tunneling macrospin coupled to a torsional oscillator. The energy spectrum and freezing of spin tunneling are studied. Magnetic susceptibility, noise spectrum, and decoherence due to entanglement of spin and mechanical modes are computed. We show that the presence of a tunneling spin can be detected via splitting of the mechanical mode at the resonance. Our results apply to experiments with magnetic molecules coupled to nanoresonators.
- Received 21 May 2011
DOI:https://doi.org/10.1103/PhysRevX.1.011005
This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Popular Summary
It is well known that south and north magnetic poles of a small magnet can interchange due to thermal noise. This effect is called superparamagnetism and is a phenomenon of classical (as opposed to quantum) physics. In the quantum world, magnets of smallest sizes, for example, magnetic molecules or nanomagnets, show superparamagnetism of a different origin: Their magnetic poles would interchange periodically as the result of quantum tunneling, even when the temperature is at absolute zero. In this theoretical paper we study what happens to a quantum magnet, in particular, to its magnetic poles, when it is placed in an external magnetic field and on a quantum nanocantilever that rotates in an oscillatory fashion about an axis aligned parallel to the magnetic field. The magnetism of the quantum magnet comes from aligned spins of the electrons in it, and the resulting total spin behaves as a quantum rotator in the aligning magnetic field. The composite system acts therefore like two quantum gyroscopes coupled together: one being the mechanical rotational oscillator that carries the nanomagnet and the other being the total spin of the nanomagnet.
The fundamental description of such a quantum system is a Schrödinger equation tailored for it. Solving the Schrödinger equation leads us to a lot of insights, not least into how the flipping of the magnet’s poles (or its total spin) is influenced by the size and the frequency of rotation of the mechanical oscillator. It turns out that only when the mechanical rotational oscillator is sufficiently heavy does the nanomagnet display superparamagnetism. In other words, when the rotational oscillator is light, magnetic-pole flipping becomes frozen. Moreover, and interestingly, if the rotational frequency is matched in a particular way with the difference in the energies of the north-pole-north, south-pole-south and the north-pole-south, south-pole-north states, the magnetic-pole flipping is predicted to appear together with a splitting of a certain mechanical mode of the rotational oscillator. The splitting can be detected experimentally.
This theoretical work should add fuel to the currently active research on molecular quantum spintronics.
