Session P13: Focus Session: Low-Dimensional and Molecular Magnetism - Single-Molecule Magnets - Dynamics, structure and interactions

Quantum Tunneling of Magnetization in Trigonal Single-Molecule Magnets

We perform a numerical analysis of the quantum tunneling of magnetization (QTM) that occurs in a spin $S$ = 6 single-molecule magnet (SMM) with idealized $C_{3}$ symmetry. The deconstructive points in the QTM are located by following the Berry-phase interference (BPI) oscillations. We find that the $\hat {O}_4^3 $ ($=\frac{1}{2}[\hat {S}_z ,\hat {S}_+^3 +\hat {S}_-^3 ])$ operator unfreezes odd-$k$ QTM resonances and generates three-fold patterns of BPI minima in all resonances, including $k$~=~0! This behavior cannot be reproduced with operators that possess even rotational symmetry about the quantization axis. We find also that the $k$ = 0 BPI minima shift away from zero longitudinal field. The wider implications of these results will be discussed in terms of the QTM behavior observed in other SMMs.   

Exploration of the Berry phase interference in a single-molecule magnets of trigonal symmetry

The quantum behavior of single-molecule magnets (SMM) is mainly governed by their molecular composition and crystallographic symmetries, thus playing an essential role in the tunneling dynamics. We present low temperature magnetometry measurements on a trigonal symmetric, low nuclearity Mn3 SMM. The experiments are designed to explore the behavior of the tunnel splittings within the transverse field magnitude/direction phase space, by applying a transverse field (0-1~T) along different directions within the hard anisotropy plane of the molecules. The expected quantum interference pattern can be understood as an outcome of a competition between different intramolecular magnetic interactions. A multi-spin description using non-collinear zero-field splitting tensors and intra molecular dipolar interactions between the manganese ions is employed to explain the symmetry patterns.   

Investigation of the Barriers of Blocking of Magnetization In Strongly Anisotropic SMM By Ab Initio Methods

A large amount of data concerning the blocking barriers of reversal of magnetization in various complexes with strongly anisotropic metal ions (Ln$^{III}$, Co$^{II})$ became recently available. Understanding the mechanisms of formation of these barriers is of primary importance for an efficient design of Ln-based single-molecule magnet (SMM) and represents a challenging task for the theory. Here an ab initio based approach for the investigation of blocking barriers will be presented. The methodology will be applied for the construction of the blocking barriers and the understanding of the variation of SMM properties in the series of mixed 3d-4f trinuclear complexes Co-Ln-Co, Ln=Gd, Tb, Dy. In particular, the reasons for a more pronounced SMM behavior manifested by the gadolinium complex will be elucidated. Another example is a recently synthesized Dy$_{3}$ complex, for which the origin of magnetization steps in the hysteresis loops will be explained. \\[4pt] [1] T. Yamaguchi, J.-P. Costes, Y. Kishima, M. Kojima, Y. Sunatsuki, N. Br\'{e}fuel, J.-P. Tuchagues, L. Vendier, W. Wernsdorfer \textit{Inorg. Chem}. \textbf{2010}, $49$, 9125--9135.   

Decoherence: Intrinsic, Extrinsic, and Environmental

Environmental decoherence times have been difficult to predict in solid-state systems. In spin systems, environmental decoherence is predicted to arise from nuclear spins, spin-phonon interactions, and long-range dipolar interactions [1]. Recent experiments have confirmed these predictions quantitatively in crystals of Fe$_8$ molecules [2]. Coherent spin dynamics was observed over macroscopic volumes, with a decoherence $Q$-factor $Q_{\phi} = 1.5 \times 10^6$ (the upper predicted limit in this system being $Q_{\phi} = 6 \times 10^7$). Decoherence from dipolar interactions is particularly complex, and depends on the shape and the quantum state of the system. No extrinsic ``noise'' decoherence was observed. The generalization to quantum dot and superconducting qubit systems is also discussed. We then discuss searches for ``intrinsic'' decoherence [3,4], coming from non-linear corrections to quantum mechanics. Particular attention is paid to condensed matter tests of such intrinsic decoherence, in hybrid spin/optomechanical systems, and to ways of distinguishing intrinsic decoherence from environmental and extrinsic decoherence sources. \\[4pt] [1] Morello, A. Stamp, P. C. E. \& Tupitsyn, Phys. Rev. Lett. {\bf 97}, 207206 (2006).\\[0pt] [2] S. Takahashi et al., Nature {\bf 476}, 76 (2011).\\[0pt] [3] Stamp, P. C. E., Stud. Hist. Phil. Mod. Phys. {\bf 37}, 467 (2006). \\[0pt] [4] Stamp, P.C.E., Phil. Trans. Roy. Soc. A (to be published)   

The Effect of Uniaxial Pressure on the Spin Hamiltonian of Mn12-Ac Single-Molecule Magnet

We study the effect of uniaxial pressure on the magnetic hysteresis loops of the single-molecule magnet Mn12-Ac. We find that the application of pressure along the easy axis increases the fields at which quantum tunneling of magnetization occurs. Density functional theory (DFT) calculations yield the pressure dependence of the energy barrier for spin reversal that is consistent with the experimental results. The observations, when constrained by the DFT calculations, indicate that the pressure induces changes in both the second-order anisotropy constant $D$ and the fourth-order anisotropy constant $A$.   

Mitigation of decoherence in crystals of a Ho$_{x}$Y$_{1{\-}x}$W$_{10}$ ($x$ = 0.001 to 0.25) single-molecule magnet

Mononuclear lanthanide-based single-molecule magnets (SMMs) have attracted considerable recent attention due to their potential application in quantum information processing devices [Nat. Nanotechnol. \textbf{2}, 312 (2007)]. In these systems, the magnetization is associated with a single rare-earth ion, which facilitates mitigation of spin decoherence due to nuclear hyperfine and electron dipolar interactions via isotope purification and dilution. Their large magnetic moments enable coherent manipulation at low driving fields. We report multi-frequency electron paramagnetic resonance (EPR) studies on a Ho polyoxometalate (POM). Simulations indicate appreciable transverse spin-orbit anisotropy, resulting in a gap in the spectrum of several GHz between pairs of levels having the same nuclear projection (effectively a tunneling gap between excited electron-nuclear spin states). Measurements at 9~GHz reveal electron-spin-echoes at low temperatures. Remarkably, a $T_{2}$ time of several hundred nanoseconds is found for concentrated samples, with much longer values found in diluted samples containing deuterated solvent. We show that these long coherence times are related to the tunneling gap, which results in an insensitivity of the spin dynamics to dipolar field fluctuations.   

Single-molecule magnets ``without'' intermolecular interactions

Intermolecular magnetic interactions (dipole-dipole and exchange) affect strongly the magnetic relaxation of crystals of single-molecule magnets (SMMs), especially at low temperature, where quantum tunneling of the magnetization (QTM) dominates. This leads to complex many-body problems [l]. Measurements on magnetically diluted samples are desirable to clearly sort out the behaviour of magnetically-isolated SMMs and to reveal, by comparison, the effect of intermolecular interactions. Here, we diluted a Fe4 SMM into a diamagnetic crystal lattice, affording arrays of independent and iso-oriented magnetic units. We found that the resonant tunnel transitions are much sharper, the tunneling efficiency changes significantly, and two-body QTM transitions disappear. These changes have been rationalized on the basis of a dipolar shuffling mechanism and of transverse dipolar fields, whose effect has been analyzed using a multispin model. Our findings directly prove the impact of intermolecular magnetic couplings on the SMM behaviour and disclose the magnetic response of truly-isolated giant spins in a diamagnetic crystalline environment.\\[4pt] [1] W. Wernsdorfer, at al, PRL 82, 3903 (1999); PRL 89, 197201 (2002); Nature 416, 406 (2002); IS Tupitsyn, PCE Stamp, NV Prokof'ev, PRB 69, 132406 (2004).   

How Weak Dipole Interactions Can Enhance of the Collective Coupling of an Ensemble of Single-molecule Magnets to a Microwave Cavity

When $N$ identical spins are on resonance with a resonant mode of an electromagnetic cavity, the coupling strength (Vacuum Rabi splitting) is enhanced by $\sqrt{N}$ [1]. Add some inhomogeneity so that the spins' resonant frequencies are distributed around the cavity frequency with width $\sigma_\omega$, and this enhancement will remain as long as $\sigma_\omega < \sqrt{N} g_1$, where $g_1$ is the coupling strength of a single, isolated spin to the cavity [2]. Recent experiments have shown that $\sim 10^{16}$ spins in a crystal of the single-molecule magnet Fe$_8$ nevertheless exhibit the enhanced collective coupling to a cavity, despite substantial inhomogeneous broadening. I present numerical calculations that show that weak dipole interactions between the spins can enhance the coupling of the spins to the cavity, allowing collective coupling even when the inhomogeneous broadening is large (i.e.~when $\sigma_\omega > \sqrt{N} g_1$). \\[4pt] [1] M. Tavis and F. W. Cummings, Phys. Rev. {\bf 170}, 379 (1968).\break [2] R. Houdre, R. P. Stanley and M. Ilegems, Phys. Rev. A {\bf 53}, 2711 (1996).   

Quantum deflagration in Mn$_{12}$-acetate in the presence of a transverse field

Mn$_{12}$-acetate single crystal have been shown to exhibit abrupt reversal of the magnetic moment through propagation of a narrow front at subsonic velocities, termed magnetic deflagration [1]. Experiments where avalanches in Mn$_{12}$-acetate are triggered at a fixed applied field have shown that the velocity of the front has maxima at resonant fields (kH$_{o}$, H$_{o}$ = 0.45 T, k$>$1), due to thermally assisted tunneling of magnetization [2]. Application of a transverse field increases the tunnel splitting, which increases the magnetic relaxation and allows us to explore the deflagration for the first time at small longitudinal fields (k=0 and 1). Using time resolved measurements of local magnetization by an array of micron sized Hall sensors at temperature of 350 mK, we present the measurements on both spontaneously ignited and triggered deflagration for a large transverse field ($>$ 3 T) allowing us to explore directly the effect of a significant tunneling splitting on both the ignition and the velocity of the front. [1] Y. Suzuki, et. al PRL 95, 147201 (2005) \newline [2] A. Hernandez-Minguez, et. al, PRL 95, 217205 (2005)   

Demagnetizing effect in local magnetic measurements

It is well-known that magnetic measurements need to be corrected for the presence of demagnetizing fields that depend on both $\chi$ and the sample shape. Calculated demagnetization factors are generally available in tabular form for standard shapes, such as ellipsoids, spheres, and parallelopipeds, thereby providing corrections for measurements of the magnetization of the entire sample. However, appropriate corrections are not available for measurements obtained by local probes, such as micron-size Hall sensors. In this talk we present calculations of the local demagnetizing field profile and show how these results can be applied to interpret local magnetization measurements in Mn$_{12}$-ac.   

Simulation of AC Susceptibility and Electronic Structure of Mn-containing Molecular Magnets

The family of Mn$_{12}$-Acetate molecular magnets has been recently enhanced by the synthesis of new members with S = 20/2 and S = 19/2 ground states. These closely related systems display similar but not identical AC susceptibility paterns which we have modelled in terms of their real ($\chi^{\prime}$) and imaginary ($\chi^{\prime \prime}$) components. The fits of AC data, as a function of frequency, show subtle differences between the parameters that control the spin dynamics in the S = 20/2 and S = 19/2 systems. To further understand the dynamic parameters we have performed electronic structure calculations based on spin density functional theory (SDFT) on both systems. Results from SDFT calculations, which describe the ground state and magnetic structures, have been correlated to the AC data to gain insight about the subtle differences in their magnetization dynamics.   

Exact and quasi exact numerical methods for giant magnetic molecules

The determination of the energy spectra of large magnetic molecules is a demanding numerical problem. In this contribution we demonstrate that theory has advanced very much in recent years. We first show that it is possible to diagonalize the Heisenberg Hamiltonian by employing the spin-rotational symmetry SU(2) in combination with arbitrary point-group symmetries [1]. This goes far beyond earlier approaches and enables us to evaluate thermodynamic observables such as the magnetization and spectroscopic data for molecules as large as the famous ferric wheel Fe$_{10}$ with a Hilbert space dimension of more than 60 Millions. Then we explain how the finite-temperature Lanczos method can be applied to magnetic molecules in order to determine thermodynamic functions for Hilbert spaces as large as up to 1 Billion [2]. The new method enables us to discuss the magnetic properties of the highly frustrated Keplerate molecule \{$\textrm{W}_{72}\textrm{V}_{30}$\} which behaves like a finite size Kagome lattice antiferromagnet. \\[4pt] [1] R. Schnalle and J. Schnack, Int. Rev. Phys. Chem. 29 (2010) 403; R. Schnalle, J. Schnack, Phys. Rev. B 79 (2009) 104419. \\[0pt] [2] J. Schnack, O. Wendland, Eur. Phys. J. B 78 (2010) 535-541.   

Low temperature magnetic properties of antiferromagnetic rings V6 and V7 studied by NMR

The recent progress in synthesizing odd-member antiferromagnetic (AF) ring molecules gives us the opportunity to investigate spin frustration effects on magnetic properties in systems with small number of magnetic ions. Na$_{7}$[(VO)$_{7}$Na$_{7}$(H$_{2}$O)$_{7}(\beta $-CD)$_{14})_{2}$]59D$_{2}$O (in short, V7) is known to be one of the odd-member AF rings, in which seven V$^{4+}$ (S=1/2) ions make an almost coplanar ring shape. Magnetic susceptibility measured at T=1.8 -300K follows a Curie-Weiss law with a Weiss temperature of -0.5K. This indicates an AF interaction between V$^{4+}$ spins is of order of 0.5K. In order to investigate ground state magnetic properties of the spin frustrated V7 ring, we have carried out proton NMR measurements at low temperatures down to 0.05K using a dilution refrigerator. We also carried out proton NMR in another non-frustrated ring system (V6) which is comprised by six V$^{4+}$ ions for a comparison. NMR spectrum line width in V7 increases with decreasing temperature down to 0.05K. On the other hand, for V6, line width shows a peak around 0.2K and decreases below the temperature. These results clearly indicate that these systems have a different magnetic ground state and the ground state of V6 is a spin singlet state but V7 has a magnetic ground state.