Quantum Interference Oscillations of the Superparamagnetic Blocking in an ${\mathrm{Fe}}_{8}$ Molecular Nanomagnet

Quantum Interference Oscillations of the Superparamagnetic Blocking in an ${Fe}_{8}$ Molecular Nanomagnet

E. Burzurí, F. Luis, O. Montero, B. Barbara, R. Ballou, and S. Maegawa

Phys. Rev. Lett. 111, 057201 – Published 31 July 2013

Abstract

We show that the dynamic magnetic susceptibility and the superparamagnetic blocking temperature of an ${Fe}_{8}$ single molecule magnet oscillate as a function of the magnetic field $H_{x}$ applied along its hard magnetic axis. These oscillations are associated with quantum interferences, tuned by $H_{x}$ , between different spin tunneling paths linking two excited magnetic states. The oscillation period is determined by the quantum mixing between the ground $S = 10$ and excited multiplets. These experiments enable us to quantify such mixing. We find that the weight of excited multiplets in the magnetic ground state of ${Fe}_{8}$ amounts to approximately 11.6%.

Received 16 November 2012

DOI:https://doi.org/10.1103/PhysRevLett.111.057201

Authors & Affiliations

E. Burzurí, F. Luis^*, and O. Montero

Instituto de Ciencia de Materiales de Aragón (ICMA), C.S.I.C.-Universidad de Zaragoza, E-50009 Zaragoza, Spain

B. Barbara and R. Ballou

Institut Néel, CNRS and Université Joseph Fourier, BP166, 38042 Grenoble Cedex 9, France

S. Maegawa

Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan

^*fluis@unizar.es

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Vol. 111, Iss. 5 — 2 August 2013

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Figure 1
(a) Molecular structure of the [ $(C_{6} H_{15} N_{3})_{6} {Fe}_{8} O_{2} (OH)_{12}$ ] molecular magnet, briefly referred to as ${Fe}_{8}$ . (b) Two equivalent tunneling paths linking states with $S_{z} = + m$ and $S_{z} = - m$ . A magnetic field along the hard axis (denoted by $x$ ) shifts the relative phases of these trajectories, thus leading to constructive and destructive interferences. (c) Dependence of the quantum tunnel splittings ${Δ でるた}_{m}$ on $H_{x}$ calculated with Eq. (1) for states $\pm m$ , with $m = 10$ (bottom curve) to $m = 1$ (top curve).Reuse & Permissions
Figure 2
ac susceptibility of an ${Fe}_{8}$ single crystal measured at several frequencies. (a) temperature dependence of the real (solid symbols) and imaginary (open symbols) components. (b) frequency dependence of the imaginary component. Lines are least-square fits with Cole-Cole function ${χ かい}^{''} (ω おめが, T) = Δ でるた χ かい (ω おめが τ たう)^{β べーた} \sin (β べーた π ぱい / 2) / [1 + (ω おめが τ たう)^{2 β べーた} + 2 (ω おめが τ たう)^{β べーた} \cos (β べーた π ぱい / 2)]$ , where $Δ でるた χ かい ≃ {χ かい}_{T}$ , the equilibrium susceptibility, and $β べーた ≃ 0.92$ . (c) Arrhenius plot of the relaxation time $τ たう$ extracted from these fits. The solid line is a least-squares linear fit of data measured below 2.6 K. (d) Effective activation energy $U$ for the magnetic relaxation process, obtained from the slope of the Arrhenius plot. The horizontal lines show magnetic energy levels derived from the giant spin Hamiltonian (1).Reuse & Permissions
Figure 3
Left: ${χ かい}^{'}$ and ${χ かい}^{''}$ susceptibility components of ${Fe}_{8}$ measured at $ω おめが / 2 π ぱい = 333 Hz$ and for three different $H_{x}$ values. Right: blocking temperature $T_{b}$ as a function of $H_{x}$ for the same frequency. Dotted and solid lines are theoretical predictions following from, respectively, the giant spin model [Eq. (1)] and the two-spin model [Eq. (2)], which includes $S$ -mixing effects, for $ϕ = 4 \deg$ . The inset compares blocking temperatures measured with $\vec{H}$ along the hard ( $x$ ) and medium ( $y$ ) axes.Reuse & Permissions
Figure 4
(a) ${χ かい}^{'}$ of ${Fe}_{8}$ vs $H_{x}$ measured at $T = 2.6 K$ and $ω おめが / 2 π ぱい = 333 Hz$ . (b) transverse field dependence of the magnetic relaxation time $τ たう$ determined at different temperatures. (c) temperature dependence of the quantum oscillation periods estimated from Landau-Zener relaxation measurements (⋆) [11], ${χ かい}^{'}$ vs $H_{x}$ at $T = 2.6 K$ (●), and ${χ かい}^{'}$ vs $T$ at different $H_{x}$ (*). Dotted and solid lines are theoretical predictions, for $ϕ = 4 \deg$ ., that follow from the giant spin model [Eq. (1)] and the two-spin model [Eq. (2)], respectively.Reuse & Permissions
Figure 5
Scheme of exchange pathways connecting ${Fe}^{3 +}$ ions in the ${Fe}_{8}$ core. Approximate values of the exchange constants are [29] $J_{1} / k_{B} = - 36 K$ , $J_{2} / k_{B} = - 201 K$ , $J_{3} / k_{B} = - 26 K$ , and $J_{4} / k_{B} = - 59 K$ .Reuse & Permissions

Physical Review Letters

Quantum Interference Oscillations of the Superparamagnetic Blocking in an Fe8 Molecular Nanomagnet

E. Burzurí, F. Luis, O. Montero, B. Barbara, R. Ballou, and S. Maegawa

Phys. Rev. Lett. 111, 057201 – Published 31 July 2013

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Quantum Interference Oscillations of the Superparamagnetic Blocking in an ${Fe}_{8}$ Molecular Nanomagnet