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arXiv:cond-mat/9810261 · Europhysics Letters (EPL)

Quantum coherence in Fe 8 molecular nanomagnets

Enrique del Barco, N. Vernier, J. M. Hernández, Javier Tejada, Eugene M. Chudnovsky, Elı́es Molins, Guy Bellessa

Published Sep 15, 1999• 84 citations
arXivHTMLPDF

Abstract

We report observation of coherent quantum oscillations in spin-10 Fe 8 molecular clusters. The powder of magnetically oriented Fe 8 crystallites was placed inside a resonator, in a dc magnetic field perpendicular to the magnetization axis. The field dependence of the ac-susceptibility was measured up to 5 T, at 680 MHz, down to 25 mK. Two peaks in the imaginary part of the susceptibility have been detected, whose positions coincide, without any fitting parameters, with the predicted two peaks corresponding to the quantum splitting of the ground state in the magnetic field parallel and perpendicular to the hard magnetization axis.

DOI
10.1209/epl/i1999-00450-8

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We report observation of coherent quantum oscillations in spin-10 Fe 8 molecular clusters. The powder of magnetically oriented Fe 8 crystallites was placed inside a resonator, in a dc magnetic field perpendicular to the magnetization axis. The field dependence of the ac-susceptibility was measured up to 5 T, at 680 MHz, down to 25 mK. Two peaks in the imaginary part of the susceptibility have been detected, whose positions coincide, without any fitting parameters, with the predicted two peaks corresponding to the quantum splitting of the ground state in the magnetic field parallel and perpendicular to the hard magnetization axis.
We study the dynamics of molecular nanomagnets through a fully quantum mechanical model describing high-spin and high-anisotropy magnetic molecules subjected to a time-dependent magnetic field along the quantization axis, which continuously inverts the population of spin states. Crystals of molecular nanomagnets placed inside a resonant cavity interact with a quantized electromagnetic field. Relaxation of excited states takes place by means of spin-photon interaction, allowing stimulated emission of radiation and creating a maser effect.
We propose two potential realizations for quantum bits based on nanometre-scale magnetic particles of large spin S and high-anisotropy molecular clusters. In case (1) the bit-value basis states |0⟩ and |1⟩ are the ground and first excited spin states S z = S and S -1, separated by an energy gap given by the ferromagnetic resonance frequency. In case (2), when there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, |0⟩, and antisymmetric, |1⟩, combinations of the twofold degenerate ground state S z = ± S . In each case the temperature of operation must be low compared to the energy gap, Δ, between the states |0⟩ and |1⟩. The gap Δ in case (2) can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware.
Tunnel splitting oscillations in the molecular magnet Fe8 are best interpreted in terms of interfering spin paths. However, this picture is incomplete and one must also consider discontinuous paths to explain the observations. This is one example of how the Fe8 system has motivated workers to better understand spin coherent state path integrals and the semiclassical limit for spin. As a second example, we discuss the recently derived Bohr-Sommerfeld rule for spin. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Magnetic sensors are typically much more sensitive to oscillating (AC) magnetic fields than static (DC) fields, due to the presence of more noise at lower frequency, typically scaling with a 1/f1/f1/f dependence. For quantum magnetometers, this characteristic noise is reflected in the ensemble dephasing time T2∗T_2^*T2∗​, the relevant sensing time for a DC field, being much lower than the spin coherence time T2T_2T2​, which determines the sensitivity to AC fields. Here, we demonstrate measurement of DC magnetic fields using a physically rotating ensemble of nitrogen-vacancy centres at a precision limited by the electron spin coherence time, T2T_2T2​. We rotate the host diamond with a period comparable to T2T_2T2​, such that the angle between the NV axis and the magnetic field to be detected changes as a function of time, upconverting the static magnetic field to an oscillating field in the physically rotating frame. Using spin-echo interferometry, we observe an order of magnitude improvement in DC magnetometer response compared to a conventional Ramsey experiments. Enhancements to our scheme could realise DC sensitivities equivalent to demonstrated AC magnetic field sensitivities with NV centres.
Molecular nanomagnets are zero-dimensional spin systems that exhibit quantum-mechanical behavior at low temperatures. Exploiting quantum-information theoretic measures, we quantify here the size of linear superpositions that can be generated within the ground multiplet of high- and low-spin nanomagnets. Amongst the former class of systems, we mainly focus on Mn12{}_{12}12​ and Fe8{}_{8}8​. General criteria for maximizing such measures are also outlined, and illustrated with reference to spin clusters of different geometries. The actual character (micro or macroscopic) of linear superpositions in low-spin systems is inherently ill-defined. Here, this issue is addressed with specific reference to the Cr7{}_{7}7​Ni and V15{}_{15}15​ molecules, characterized by an S=1/2S=1/2S=1/2 ground state. In both cases, the measures we obtain are larger than those of a single s=1/2s=1/2s=1/2 spin but not proportionate to the number and value of the constituent spins.
Quantum dynamics time evolution of a molecular magnet Fe 8 interacting with an electron nuclear spin is studied by solving the time-dependent Schrödinger equations. It is found that the variation of Fe 8 magnetization and the nuclear spin crucially depends on the interaction strength. The time evolution of the entanglement between the injecting electron and Fe 8 is evaluated. It is observed that the entanglement oscillates in time and is tightly related to the spin variation of the injecting electron. From these characteristics, the technique for the reversing and read-out of Fe 8 spin states is suggested.