Session Q32: Focus Session: Molecular Magnets II

Strongly Correlated Electrons in the $\mathbf{\left[Ni(hmp)(ROH)X\right]_4}$ Single Molecule Magnet: A DFT+U Study

The single molecule magnet $\mathrm{\left[Ni(hmp)(MeOH)Cl\right]_4}$ is studied using both density functional theory and the DFT+U method, and the results are compared. By incorporating a Hubbard-U like term for both of the nickel and oxygen atoms, the experimental ground state is successfully recovered, and the exchange coupling constants derived from the DFT+U calculation fit the experimental results very well. The results show that the nickel 3d electrons and oxygen 2p electrons in this molecule are strongly correlated, and thus the inclusion of on-site Coulomb energies is crucial to obtain correct results. This work is supported by DOE DE-FG02-02ER45995 (H.-P. Cheng and C. Cao), NSF/DMR/ITR-0218957 (H.-P. Cheng and C. Cao), NSF DMR0239481 (S. Hill), and NSF DMR0506946 (S. Hill). The authors want to thank NERSC, CNMS/ORNL and the University of Florida High Performance Computing Center for providing computational resources and support that have contributed to the research results reported within this paper.   

Spin excitations in the molecule Mn$_{19}$ with a record ground-state spin $S$ = 83/2

In the magnetic molecule Mn$_{19}$, 12 Mn(III) and 7 Mn(II) ions are ferromagnetically coupled such as to yield a $S$ = 83/2 ground state. We recorded Q-band EPR and inelastic neutron scattering (INS) spectra on powder samples of Mn$_{19}$. The EPR data is well interpreted by the model of an isolated $S$ = 83/2 spin with uniaxial magnetic anisotropy, $H$ = \textit{DS}$_{z}^{2}$ + \textit{g$\mu $}$_{B}$\textbf{S}$\cdot $\textbf{B}. We find $D$ = 0.004 cm$^{{\-}1}$, hence Mn$_{19}$ is not a single-molecule magnet. The INS spectra show a broad feature I at ca. 0.25 meV, which exhibits an uncommon temperature dependence, and two peaks II and III at ca. 3.0 and 5.7 meV. The analysis of the INS data is complicated by the huge Hilbert space of Mn$_{19}$ of 6.8 10$^{13}$ states. Peaks II and III are assigned to discrete ferromagnetic spin waves. Understanding feature I is more difficult because it consists of many transitions which combine such as to yield a complex temperature dependence. Hence, its behavior cannot be described in a single-spin picture, but requires an inherent many-body description.   

Looking for higher anisotropy barriers in single-molecule magnets

We report single-crystal high-frequency electron paramagnetic resonance (HFEPR) studies of a series of recently discovered $\mbox{Mn}_{\mbox{6}}^{\mbox{III}} $ single-molecule magnets (SMMs) with large barriers to magnetization reversal. All of the complexes consist of $\mbox{Mn}_{\mbox{3}}^{\mbox{III}} $ triangles with a ferromagnetic interaction between them. Recent studies have shown that the exchange interactions within the triangular $\mbox{Mn}_{\mbox{3}}^{\mbox{III}} $ units can be switched from antiferromagnetic to ferromagnetic,$^{1}$ resulting in a switching of the spin from $S$ = 4 to 12 for many of the Mn$_{6}$ complexes. This strategy to ``increase $S$'' has resulted in the highest magnetic energy barrier and blocking temperature for any known SMM to date. Extensive frequency, temperature and field-orientation dependent HFEPR measurements were performed to determine the magnetic anisotropy parameters for each complex. These studies have contributed to important new insights concerning strategies for designing SMMs with high blocking temperatures, particularly for complexes containing manganese in its +3 oxidation state. $^{1}$ T. C. Stamatatos et al., J. Am. Chem. Soc. 129, 12505-12511, 2007.   

Theory of tunneling spectroscopy in a $Mn_{12}$ single-electron transistor by DFT methods

We present a theory of single-electron tunneling transport through a $Mn_{12}$ molecular magnet in the Coulomb blockade regime. We employ spin density functional theory to calculate the low-energy spin multiplet states for neutral and charged (anion and cation) $Mn_{12}$, split by spin-orbit interaction. Tunneling matrix elements between these states are the basic ingredients of a master equation formalism that gives the tunneling conductance as a function of the bias and gate voltage. We compare the results of this formalism with the ones obtained using a phenomenological giant-spin Hamiltonian and highlight the importance of the orbital degree of freedom included in our SDFT approach.   

First-principles study of a monolayer of single-molecule magnets Mn$_{12}$ on a gold surface

Over the past decade, single-molecule magnets have drawn considerable attention due to observed magnetic quantum tunneling and interference and a possibility of using them in devices. There have been significant experimental efforts to build and characterize thin films or monolayers of single-molecule magnets on surfaces or single-molecule magnets bridged between electrodes. In parallel, theoretical models have been proposed to understand the properties of single-molecule magnets coupled to a metal substrate. However, there do not exist atomic-scale simulations on this complex system. We simulate, within density-functional theory, prototype Mn$_{12}$ molecules adsorbed via a thiol group onto a gold surface. We investigate how strongly a Mn$_{12}$ molecule is coupled to the metal surface and how much charge and spin moments are transferred between a Mn$_{12}$ molecule monolayer and the metal surface. In particular, we compare the electronic and magnetic properties of the Mn$_{12}$ monolayer on a gold surface with those of an isolated Mn$_{12}$ in the presence of spin-orbit interaction. Our results may shed light into tailoring of the magnetic properties of nanomagnets as a result of electronic transfer from a proximal metallic surface.   

Ignition of magnetic deflagration in Mn$_{12}$ acetate

We study the conditions for the ignition of two types of magnetic avalanches in the molecular magnet Mn$_{12}$-acetate corresponding to the major species and a fast-relaxing minor species. The minor component, which has a lower anisotropy barrier, exists in these crystals at the level of $5-7$\%. The ignition temperatures are measured using small ($30 \times 30 \mu$m$^2$) Ge thermometers. In addition, the magnetization dynamics are measured using an array of Hall sensors of comparable size. Various aspects of the ignition will be discussed, including: the reduction of the ignition threshold due to quantum tunneling, the catalytic effect of the minor species, and the shift of the ignition point as a function of external magnetic field. The work at City College was supported by NSF grant DMR-00451605. E. Z. acknowledges the support of the Israel Ministry of Science, Culture and Sports. Support for G. C. was provided by NSF grant CHE-0414555.   

Quantum Interference in the Longitudinal Oscillations of the Total Spin of a Dimeric Molecular Nanomagnet

The synthetic flexibility of molecular magnets allows one to systematically produce samples with desirable properties such as those with entangled spin states for implementation in quantum logic gates. Here we report direct evidence of quantum oscillations of the \textit{total spin length} of a dimeric molecular nanomagnet through the observation of quantum interference associated with tunneling trajectories between states having different spin quantum numbers. As we outline, this is a consequence of the unique characteristics of a molecular Mn$_{12}$ wheel which behaves as a (weak) ferromagnetic exchange-coupled molecular dimer: each half of the molecule acts as a single-molecule magnet (SMM), while the weak coupling between the two halves gives rise to an additional internal spin degree of freedom within the molecule, namely that its total spin may fluctuate. This extra degree of freedom accounts for several magnetization tunneling resonances that cannot be explained within the usual giant spin approximation. More importantly, the observation of quantum interference provides unambiguous evidence for the quantum mechanical superposition involving entangled states of both halves of the wheel.   

EPR Studies of Magnetically Dilute Ga-Doped Single Crystals of Fe$_{18}$ Antiferromagnetic Molecular Wheels

Studies of the quantum dynamics of the electron spins in solid state systems has gained considerable interest recently due to their potential for use as quantum computing substrates. One class of materials, molecular magnets, are of particular importance, owing to the seemingly limitless array of spin configurations due to synthetic chemical flexibility. Efforts are currently devoted to minimizing decoherence times by diminishing dipolar effects. In this regard, we have carried out EPR measurements on small single crystals of 0.5{\%} Ga doped Fe18 molecular antiferromagnetic wheels at temperatures down to 300 mK using planar resonators patterned on GaAs wafers. This system constitutes a dilute sample of $S$ = 5/2 molecules dispersed within a sea of $S$ = 0 (at low temperature) molecules, which significantly reduces dipolar interactions and might provide a means of observing Rabi oscillations in crystals of molecular magnets. Detailed angular dependence studies reveal significant anisotropy with $D$ = 500 mK and $E$ = 20 mK. The presence of second order anisotropy (E) is very unusual for such a high symmetry system and its interpretation will be discussed. Pulsed-EPR measurements and doping concentration dependence will also be discussed.   

Spin-Jahn-Teller effect in the antiferromagnetic molecular wheel CsFe8

In an antiferromagnetic (AF) molecular wheel magnetic metal ions are clamped together by organic ligands such as to form rings. Due to AF Heisenberg interactions in the wheel, the molecule's ground state at zero magnetic field is nonmagnetic with total spin $S$ = 0. The higher lying states belong to $S$ = 1, 2, ... In a magnetic field these states are Zeeman split, leading to a series of level-crossings (LCs) at characteristic fields at which the ground state changes from $S$ = 0, $M$ = 0 to $S$ = 1, $M$ = -1, and so on. Hence, via the field, the magnetic ground state of the molecule can be tuned through a degeneracy at the LC. Field-dependent measurements of the magnetic torque and $^{1}$H-NMR on CsFe8 single crystals were performed, which show clear indications of a phase transition at the LCs at low temperatures [PRL 96, 027206 (2006); PRL 99, 087201 (2007)]. These phase transitions are explained by a field-induced spin-Jahn-Teller effect (JTE) due to a magneto-elastic coupling between the spins of the wheel and the lattice: For fields close to a LC, a spontaneous structural distortion of the CsFe8 wheel occurs such as to lift the degeneracy in the magnetic energy spectrum, hence the spin-JTE.   

Magneto-infrared investigations of [Mo$^{V}_{12}$O$_{30}$($\mu_2$-OH)$_{10}$ H$_2$\{Ni$^{II}$(H$_2$O)$_3$\}$_4$]

We measured the magneto-infrared spectrum of [Mo$^{V}_{12}$O$_{30}$($\mu_2$-OH)$_{10}$H$_2$\-\{Ni$^{II}$(H$_2$O)$_3$\}$_4$] in order to test the suggestion that molecular structure(and thus interactions between spins) may be changing with applied magnetic field. Although this low-noise magneto-infrared work was done in a superconducting magnet (which limits the field range to only 18 T), these experiments do provide direct evidence for small field-induced local distortions of the lattice. The field-induced change in the localized H$_2$O wagging mode on the O attached to the Ni sites is particularly evident. This result is consistent with previous magneto-optics work indicating a small change in the Ni$^{2+}$ crystal field environment at 30 T. We also consider whether the magneto-infrared results and the consequent small implied changes in local structure with magnetic field are enough to account for the observed magnetization data, and we discuss complementary mechanisms based on more extended spin Hamiltonians that may also account for large changes in $J$ and $D$ in molecule-based magnets.   

Dzyaloshinskii-Moriya interactions and multiferroic behavior in high-symmetry single molecule magnets

We study analytically the effects of the antisymmetric exchange, or Dzyaloshinskii-Moriya interactions in high-symmetry single molecule magnets with 2-4 magnetic ions per cluster. When the Moriya rules allow it, such as when an ionic bond does not contain a center of inversion, these interactions can lead to interesting observable effects, including the presence of an electric polarization driven by an applied magnetic field, and associated multiferroic behaviors. We will present our results for tetramers with the common S$_4$ molecular group symmetry, and for other ultrasmall single molecule magnets.   

Spin echo experiments on dilute ensembles of single molecule magnets

Single molecule magnets (SMMs) have been suggested as candidates for qubits in quantum processors. However, the coherence time ($T_2$) of high-spin molecules has not been determined. In SMM single crystals the strong dipolar interactions between molecules (separated by only 1~nm) is expected to drastically reduce the coherence time. In order to determine the coherence times in SMMs, we work with dilute ensembles of molecules. In particular, dilute frozen solutions of the SMM Ni$_4$ have been studied using a high frequency D-band (130~GHz) EPR setup [1]. Despite the random orientation of the molecules, well defined EPR absorption peaks are observed, due to the strong variation of the splittings between the different spin-states on magnetic field. Temperature dependent studies ($> 4$~K) and comparison with simulations enable identification of the spin transitions and determination of the Hamiltonian parameters, found to be close to those of Ni$_4$ single crystals. The absence of echo in pulsed experiments sets an upper bound of about 50~ns on the spin coherence time in Ni$_4$ at 130~GHz and T = 5.5~K. [1] G. de Loubens {\it et al.}, arXiv:0709.2146   

Transition Metal Dimers and Physical Limits on Magnetic Anisotropy

Recent advances in nanoscience have raised interest in the minimum bit size required for classical information storage, i.e. for bistability with suppressed quantum tunnelling and energy barriers that exceed ambient temperatures. In the case of magnetic information storage much attention has centred on molecular magnets with bits consisting of ~ 100 atoms, magnetic uniaxial anisotropy energy barriers ~ 50 K, and very slow relaxation at low temperatures. In our recent article (Nature Materials 6, 648 - 651 (2007)), we draw attention to the remarkable magnetic properties of some transition metal dimers which have energy barriers approaching ~ 500 K with only two atoms. The spin dynamics of these ultra small nanomagnets is strongly affected by a Berry phase which arises from quasi-degeneracies at the electronic Highest Occupied Molecular Orbital (HOMO) energy. In a giant spin-approximation, this Berry phase makes the effective reversal barrier thicker.   

Magnetic anisotropies of late transition metal atomic clusters

We analyze the impact of the magnetic anisotropy on the geometric structure and magnetic ordering of small atomic clusters of palladium, iridium, platinum and gold. We have employed a non-collinear implementation of Density Functional Theory where the spin-orbit interaction has been included self-consistently. The size of the clusters range from two to five, six or seven atoms, depending on the element. Our results highlight the relevance of the spin orbit interaction in the magnetic properties of small atomic clusters made of fourth- and fifth-row elements [1]. \newline [1] L. Fern\'andez-Seivane and J. Ferrer, Phys. Rev. Lett. {\bf 99}, 183401 (2007)   

Dirac Equation for Electrodynamic Model Particle

We set up the Maxwell's equations and subsequently the classical wave equations for the electromagnetic waves which together with their generating source, an oscillatory charge of zero rest mass, make up a particle travelling at velocity $v$ as with the charge in the fields of an external scalar and vector potentials. The direct solutions in constant external field are Doppler-displaced plane waves propagating at the velocity of light $c$; at the de Broglie wavelength scale and expressed in terms of the dynamically equivalent and appropriate geometric mean wave variables, these render as functons identical to the space-time functions of the Dirac spinor, and these are identical to the de Broglie phase waves given previously from explicit superposition. For two spin-half particles of a common set of space-time functions constrained with antisymmetric spin functions as follows the Pauli principle for same charges and as separately indirectly induced based on experiment for opposite charges, the complete wave functions are identical to a Dirac spinor. The back-substitution of the so explicitly determined complete wave functions in the corresponding classical wave equations of the two particles, subjected further to reductions appropriate for the stationary- state particle motion and to rotation invariance when in three dimensions, give a Dirac equation set; the procedure and conclusion are directly extendible to arbitrarily varying potentials by use of the Furious theorem and to three dimensions (full paper: QTS5).