Dynamics and thermalization of the nuclear spin bath in the single-molecule magnetMn12−ac: Test for the theory of spin tunneling

Abstract

The description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest, and is relevant for many solid-state qubit designs. Most of the attention is usually given to the dynamics of the "central spin" (i.e., the qubit), while little is known about the spin bath itself. Here we present a detailed study of the dynamics of the nuclear spin bath in the Mn12-ac single-molecule magnet, probed by NMR experiments down to very low temperatures (T ≃ 20 mK). The results are critically analyzed in the framework of the Prokof'ev-Stamp theory of nuclear-spin mediated quantum tunneling. We find that the longitudinal relaxation rate of the 55 Mn nuclei in Mn12-ac becomes roughly T -independent below T ≃ 0.8 K, and can be strongly suppressed with a longitudinal magnetic field. This is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin, and we attribute the tunneling fluctuations to the minority of fast-relaxing molecules present in the sample. The transverse nuclear relaxation is also T -independent for T < 0.8 K, and can be explained qualitatively and quantitatively by the dipolar coupling between like nuclei in neighboring molecules. This intercluster nuclear spin diffusion mechanism is an essential ingredient for the global relaxation of the nuclear spin bath. We also show that the isotopic substitution of 1 H by 2 H leads to a slower nuclear longitudinal relaxation, consistent with the decreased tunneling probability of the molecular spin. Finally, we demonstrate that, even at the lowest temperatures -where only T -independent quantum tunneling fluctuations are present -the nuclear spins remain in thermal equilibrium with the lattice phonons, and we investigate the timescale for their thermal equilibration. After a review of the theory of macroscopic spin tunneling in the presence of a spin bath, we argue that most of our experimental results are consistent with that theory, but the thermalization of the nuclear spins is not. This calls for an extension of the spin bath theory to include the effect of spin-phonon couplings in the nuclear-spin mediated tunneling process.

Quantum Nanomagnets and Nuclear Spins: An Overview

“…the influence of quantum tunneling of the nanomagnets on the nuclear spin dynamics, was observed short thereafter for 1 H [43] and 57 Fe in Fe 8 [4], and 55 Mn in Mn 12 [25,27] [Fig. 3(c)].…”

“…that it should be strongly suppressed by a longitudinal external field. Indeed, it has been observed that the nuclear T 1 in Mn 12 at very low temperatures becomes almost two orders of magnitude slower with the application of a small longitudinal field [25,27], as compared to the zero-field case [ Fig. 3(d)].…”

“…This observation seems to imply that the nuclear spins in Mn 12 -ac find a way to thermalize to the phonon bath even at very low-T , and even without large transverse fields. The definitive experimental proof of the thermal equilibrium in the nuclear spins of Mn 12 -ac was then found by directly measuring the 55 Mn nuclear spin temperature by NMR techniques [25,27]. This is a crucial observation because the nuclear spins have essentially no direct link to the phonon bath, therefore their thermal equilibration must proceed via the coupling to the electron spins and their subsequent spin-lattice relaxation process.…”

“…(11)], and is actually very close to the observed nuclear-spin mediated tunneling rate. The precise value appears to be a matter of sample size, cooling power and thermal contact to the refrigerator, and it's quite plausible that τ −1 th ≃ Γ N in the limit of small sample and perfect contact to the thermal bath [25].…”

“…The picture has been completed by experiments looking at the "other side of the coin", i.e. studying directly the dynamics of the nuclear spins by NMR experiments [17,11,14,25,27,4], and finding that such dynamics is indeed profoundly entangled with the quantum fluctuations of the giant spin. At the present stage, much of the efforts in the field are directed towards using quantum nanomagnets as spin qubits for quantum information purposes, by pushing the giant spins into a regime where the tunneling can be made coherent [29].…”