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arXiv:cond-mat/0405501

Comment on 'Quantum Coherence between High Spin Superposition States of Single Molecule Magnet Ni4'

Wolfgang Wernsdorfer

Published May 21, 2004• 0 citations
arXivHTMLPDF

Abstract

In a recent paper, cond-mat/0405331 (Ref. 1), del Barco et al. reported experimental studies on a Ni4 molecular system. They used an experimental method (combining microwave spectroscopy with high sensitivity magnetic measurements) that we have introduced before, cond-mat/0404410 (see also Ref. 2 and 3). Among other things, our technique allows us to monitor spin-state populations in the presence of microwave magnetic fields. Absorption line-widths give rough 'upper bounds' on the decoherence rate similar to 'standard' high frequency electron paramagnetic resonance (HF-EPR) techniques. In the case of quasi continuous radiation our technique does NOT give directly the spin-lattice relaxation time T1. For measurements like those of del Barco et al., it simply gives access to the phonon-bottleneck time, a parameter that is many orders of magnitude longer than the spin-lattice relaxation time. Any conclusion concerning quantum coherence is preliminary.

DOI
10.48550/arxiv.cond-mat/0405501

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Quantum Superposition of High Spin States in the Single Molecule Magnet Ni4

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Quantum tunneling of the magnetization in a single molecule magnet has been studied in experiments that combine microwave spectroscopy with high sensitivity magnetic measurements. By monitoring spin-state populations in the presence of microwave radiation, the energy splittings between low lying superpositions of high-spin states of single molecule magnet Ni4 (S=4) have been measured. Absorption linewidths give an upper bound on the rate of decoherence. Pulsed microwave experiments provide a measure of energy relaxation time, which is found to increase with frequency.

arXiv:cond-mat/0405331•Physical Review Letters•Oct 4, 2004•77 citations

Reply to Comment on "Quantum Coherence between High Spin Superposition States of Single Molecule Magnet Ni$_4$"

Enrique del Barco, Andrew D. Kent

Here we respond briefly to a comment on our work in arXiv:cond-mat/0405501.

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In a recent paper, cond-mat/0405331 (Ref. 1), del Barco et al. reported experimental studies on a Ni4 molecular system. They used an experimental method (combining microwave spectroscopy with high sensitivity magnetic measurements) that we have introduced before, cond-mat/0404410 (see also Ref. 2 and 3). Among other things, our technique allows us to monitor spin-state populations in the presence of microwave magnetic fields. Absorption line-widths give rough 'upper bounds' on the decoherence rate similar to 'standard' high frequency electron paramagnetic resonance (HF-EPR) techniques. In the case of quasi continuous radiation our technique does NOT give directly the spin-lattice relaxation time T1. For measurements like those of del Barco et al., it simply gives access to the phonon-bottleneck time, a parameter that is many orders of magnitude longer than the spin-lattice relaxation time. Any conclusion concerning quantum coherence is preliminary.
Quantum tunneling of the magnetization in a single molecule magnet has been studied in experiments that combine microwave spectroscopy with high sensitivity magnetic measurements. By monitoring spin-state populations in the presence of microwave radiation, the energy splittings between low lying superpositions of high-spin states of single molecule magnet Ni4 (S=4) have been measured. Absorption linewidths give an upper bound on the rate of decoherence. Pulsed microwave experiments provide a measure of energy relaxation time, which is found to increase with frequency.
Reply to Comment on "Quantum Coherence between High Spin Superposition States of Single Molecule Magnet Ni4_44​"
We herein probe the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagetic Resonance measurements at X-band (9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10^-1 , 10^-2 and 10^-3 % doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, Tm, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields Tm is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a Tm in the range 1 – 11 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10^-3 %, and under dynamic decoupling conditions, the ratio of Tm versus the time it takes t0 implement a quantum gate, TG, reaches the order of 104, in the example of a single qubit π-rotation, which corresponds to a gate fidelity of 99.99 %, reaching thus the lower limit for implementations in Quantum Information Technologies.
Molecular magnets are ideal systems to probe the realm that borders quantum and classical physics, as well as to study decoherence phenomena in nanoscale systems. The control of the quantum behavior of these materials and their structural characteristics requires synthesis of new complexes with desirable properties which will allow probing of the fundamental aspects of nanoscale physics and quantum information processing. Of particular interest among the magnetic molecular materials are single-molecule magnets (SMMs) and antiferromagnetic (AFM) molecular wheels in which the spin state of the molecule is known to behave quantum mechanically at low temperatures. In previous experiments the dynamics of the magnetic moment of the molecules is governed by incoherent quantum tunneling. Short decoherence times are mainly due to interactions between molecular magnets within the crystal and interactions of the electronic spin with the nuclear spin of neighboring ions within the molecule. This decoherence problem has imposed a limit to the understanding of the molecular spin dynamics and the sources of decoherence in condensed matter systems. Particularly, intermolecular dipolar interactions within the crystal, which shorten the coherence times in concentrated samples, have stymied progress in this direction. Several recent works have reported a direct measurement of the decoherence time in molecular magnets. This has been done by eliminating the dephasing created by dipolar interactions between neighboring molecules. This has been achieved by a) a dilution of the molecules in a liquid solution to decrease the dipolar interaction by separating the molecules, and b) by polarizing the spin bath by applying a high magnetic field at low temperatures. Unfortunately, both approaches restrict the experimental studies of quantum dynamics. For example, the dilution of molecular magnets in liquid solution causes a dispersion of the molecular spin orientation and anisotropy axes, while the large fields required to polarize the spin bath overcome the anisotropy of the molecular spin. In this thesis I have explored two methods to overcome dipolar interactions in molecular magnets: a) studying the dynamics of molecular magnets in single crystals where the separation between magnetic molecules is obtained by chemical doping or where the high crystalline quality allows observations intrinsic to the quantum mechanical nature of the tunneling of the spin, and b) studying the electronic transport through an individual magnetic molecule which has been carefully placed in a single-electron transistor device. I have used EPR microstrip resonators to measure Fe17Ga molecular wheels within single crystals of Fe18 AFM wheels, as well as demonstrating, for the first time in a Single Molecule Magnet, the complete suppression of a Quantum Tunneling of the Magnetization transition forbidden by molecular symmetry.
Quantum relaxometry is one of the most successful applications of nitrogen-vacancy (NV) centers in diamond and, more broadly, solid-state spin qubits, enabling ultrasensitive detection of magnetic noise and paramagnetic species via measurements of the spin-lattice relaxation time T1T_1T1​. Conventional pulsed protocols, however, probe T1T_1T1​ efficiently only over a limited temporal range, which restricts the scope and throughput of the technique. Here we introduce a continuous-wave quantum relaxometry protocol that operates in the frequency domain. By measuring the frequency response of the optically detected magnetic resonance signal under low-frequency microwave amplitude modulation, we extract T1T_1T1​ from the characteristic response time of the spin system. The method enables efficient T1T_1T1​ measurements spanning more than three orders of magnitude -- directly demonstrated from 60 μμμs to 200 ms in our experiments -- across a broad temperature range and under substantial ensemble inhomogeneity. We further show that this protocol enables quantitative relaxometry-based sensing in nanodiamonds, achieving a substantial speed-up over the pulsed methods and offering a practical approach to optimizing nanodiamond size for enhanced sensitivity.
The frequency-field and orientation dependences of the electron paramagnetic resonance (EPR) spectra are measured for impurity Tm 3+ ions in yttrium orthosilicate (Y 2 SiO 5 ) single crystals by stationary EPR spectroscopy in the frequency range of 50–100 GHz at 4.2 K. The position of the impurity ion in the crystal lattice and its magnetic characteristics are determined. The temperature dependences of the spin–lattice and phase relaxation times are measured by pulse EPR methods in the temperature range of 5–15 K and the high efficiency of the direct single-phonon mechanism of spin–lattice relaxation is established. This greatly shortens the spin–lattice relaxation time at low temperatures and makes impurity Tm 3+ ions in Y 2 SiO 5 a promising basis for the implementation of high-speed quantum memory based on rare-earth ions in dielectric crystals.