Marshall Luban

Iowa State University, Ames, Iowa, United States

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Publications (138)370.11 Total impact

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    ABSTRACT: We consider the dynamics and thermodynamics of a pair of magnetic dipoles interacting via their magnetic fields. We consider only the "spin" degrees of freedom; the dipoles are fixed in space. With this restriction it is possible to provide the general solution of the equations of motion in analytical form. Thermodynamic quantities, such as the specific heat and the zero field susceptibility are calculated by combining low temperature asymptotic series and a complete high temperature expansion. The thermal expectation value of the autocorrelation function is determined for the low temperature regime including terms linear in $T$. Furthermore, we compare our analytical results with numerical calculations based on Monte Carlo simulations.
    Journal of Physics A Mathematical and Theoretical 10/2014; 48(18). DOI:10.1088/1751-8113/48/18/185002 · 1.58 Impact Factor
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    ABSTRACT: We present a refined model of the ${{\mathrm{Fe}}_{9}}$ tridiminished icosahedron magnetic molecule system. This molecule was originally modeled as being composed of two (${{\mathrm{Fe}}_{3}}$ and ${{\mathrm{Fe}}_{6}}$) clusters, with the ${\mathrm{Fe}}^{3+}$ ions within each cluster being coupled via exchange interactions, but with no coupling between the clusters. The present inelastic neutron scattering (INS) measurements were used to probe the low-lying energy spectrum of ${{\mathrm{Fe}}_{9}}$, and these results demonstrate that the previously published model of two uncoupled clusters is incomplete. To achieve agreement between the experiment and theory, we have augmented the model with relatively small exchange coupling between the clusters. A combination of Lanczos matrix diagonalization and quantum Monte Carlo simulations have been used to achieve good agreement between the experimental data and the improved model of the full ${{\mathrm{Fe}}_{9}}$ system despite the complexity of this model (with Hilbert space dimension $>{10}^{7}$).
    Physical Review B 06/2014; 89(21). DOI:10.1103/PhysRevB.89.214415 · 3.74 Impact Factor
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    ABSTRACT: POM and circumstance: Nanometer-sized polyoxometalates (POMs) bring a new direction to anion-templated supramolecular chemistry. The Keggin- (left) and Dawson-type (right) polyoxoanions direct the assembly of giant metallomacrocycles through an array of weak hydrogen-bonding interactions. The concerted action of multiple hydrogen bonds keeps the templating guests embedded within the hosts, even in the solution state.
    Angewandte Chemie International Edition 09/2013; 52(40). DOI:10.1002/anie.201304887 · 11.26 Impact Factor
  • Heinz-Jürgen Schmidt · Marshall Luban
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    ABSTRACT: We investigate the stationary states and low temperature order of interacting classical Heisenberg spins occupying the vertices of diverse polyhedra. For highly symmetric cases group-theoretical methods can be used to enumerate a number of stationary states. Quantitative results are presented for the cuboctahedron, icosidodecahedron, icosahedron, and dodecahedron. The behavior inferred for the classical Heisenberg model points the way for an effective quantum treatment of newly synthesized, large magnetic molecules with polyhedral arrays of paramagnetic ions.
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    ABSTRACT: The magnetic properties and spin dynamics of the spin frustrated polyoxometalate {W72V30}, where 30 V^{4+} ions (s = 1/2) occupy the sites of an icosidodecahedron, have been investigated by low temperature magnetization, magnetic susceptibility, proton and vanadium nuclear magnetic resonance, and theoretical studies. The field-dependent magnetization at 0.5 K increases monotonically up to 50 T without any sign of staircase behavior. This low-temperature behavior cannot be explained by a Heisenberg model based on a single value of the nearest-neighbor exchange coupling. We analyze this behavior upon assuming a rather broad distribution of nearest-neighbor exchange interactions. Slow spin dynamics of {W72V30} at low temperatures is observed from the magnetic field and temperature dependence of nuclear spin-lattice relaxation rate 1/T_1 measurements.
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    ABSTRACT: A polyoxometalate-based {Mn(III)(3)Mn(IV)} single-molecule magnet exhibits a large axial anisotropy (D = -0.86 cm(-1)) resulting from a near-parallel alignment of Jahn-Teller axes. Its rigorous three-fold symmetry (i.e. rhombicity E→ 0) and increased intercluster separation via co-crystallization effectively hamper quantum tunnelling of the magnetization.
    Dalton Transactions 04/2012; 41(33):9867-70. DOI:10.1039/c2dt30451a · 4.20 Impact Factor
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    ABSTRACT: The magnetic molecules Pr13 and W72V30 have been studied by DC and AC magnetic susceptibilities and NMR. These molecules exhibit geometrical frustration resulting from antiferromagnetic intramolecular coupling of nearest neighbor paramagnetic ions. In Pr13, 12 Pr^III ions (S=1) interact along edge sites of an icosahedron centered about an additional Pr^III ion. For W72V30, 30 V^IV ions (S=1/2) interact along corner sharing sites of a near perfect icosidodecahedron, a spherical representation of a 2-D Kagome Lattice. Characterizing the DC magnetic response requires a distribution of exchange constants for both molecules at low temperatures. Results are compared to similar frustrated systems which feature a variety of magnetic phenomena - metamagnetic phase transitions, magnetic hysteresis without anisotropy, spin glass behavior, and superparamagnetism.
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    ABSTRACT: Ligand modification transforms a polyoxometalate-anchored cubane-type [Mn(III)(3)Mn(IV)O(4)] core into a centrosymmetric [Mn(III)(6)Mn(IV)O(8)] di-cubane cluster, and restores the slow magnetization relaxation characteristics typical for [Mn(4)O(4)] cubane-based single-molecule magnets.
    Chemical Communications 11/2011; 48(9):1218-20. DOI:10.1039/c1cc15520b · 6.83 Impact Factor
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    ABSTRACT: We investigate the dynamical behavior of finite rings of classical spin vectors interacting via nearest-neighbor isotropic exchange in an external magnetic field. Our approach is to utilize the solutions of a continuum version of the discrete spin equations of motion (EOM) which we derive by assuming continuous modulations of spin wave solutions of the EOM for discrete spins. This continuum EOM reduces to the Landau-Lifshitz equation in a particular limiting regime. The usefulness of the continuum EOM is demonstrated by the fact that the time-evolved numerical solutions of the discrete spin EOM closely track the corresponding time-evolved solutions of the continuum equation. It is of special interest that our continuum EOM possesses soliton solutions, and we find that these characteristics are also exhibited by the corresponding solutions of the discrete EOM. The robustness of solitons is demonstrated by considering cases where initial states are truncated versions of soliton states and by numerical simulations of the discrete EOM equations when the spins are coupled to a heat bath at finite temperatures.
    Journal of Physics Condensed Matter 09/2011; 23(38):386003. DOI:10.1088/0953-8984/23/38/386003 · 2.35 Impact Factor
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    ABSTRACT: Compound (IV) crystallizes in the triclinic space group P with Z = 2 (single crystal XRD).
    ChemInform 08/2011; 42(35):no-no. DOI:10.1002/chin.201135022
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    ABSTRACT: The magnetism of the polyoxometalate cluster {Mo75V20}, containing a sawtooth ring of 10 corner-sharing triangles located on the equator of the barrel-shaped molecule, has remained debatable since it is masked by contributions from impurities as well as temperature-independent paramagnetism. In this article we demonstrate the usefulness of ESR measurements since the temperature dependence of the ESR intensity can discriminate between impurity and molecular contributions. We determine the exchange parameters and therefore also the low-lying spectrum of {Mo75V20}, especially the low-lying singlet states which so far have been probed solely by specific heat measurements.
    Physical review. B, Condensed matter 07/2011; 85(2). DOI:10.1103/PhysRevB.85.024413 · 3.66 Impact Factor
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    ABSTRACT: Hexametallic chromium(III) chains can act as fluoride donor ligands to lanthanide ions giving {(Cr(6))Ln(x)}(n) complexes; preliminary spectroscopic studies are reported.
    Chemical Communications 06/2011; 47(22):6251-3. DOI:10.1039/c1cc11516b · 6.83 Impact Factor
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    ABSTRACT: In Schale geworfen: Ein 4.3 nm großes Kern-Schale-Aggregat aus 16 Polyoxowolframat-Baueinheiten (W/Mn-Metallgerüst siehe Bild) definiert die aktuelle Obergrenze für strukturelle Komplexität bei molekularen Metalloxidclustern. Entscheidend für diese Struktur ist ein Rückgrat aus MnOW-Doppelbrücken; eine Retroanalyse ihrer Bildung lässt auf die wichtige Rolle von Templateffekten und kinetischer Kontrolle bei der selbstorganisierten Bildung des {MnIII40WVI224}-Polyanions schließen.
    Angewandte Chemie 05/2011; 123(22). DOI:10.1002/ange.201008225
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    ABSTRACT: In a nutshell: A 4.3 nm core-shell aggregate of 16 polyoxotungstate building units (see picture of the W/Mn skeleton) delineates the upper limit for structural complexity in molecular metal oxide cluster chemistry to date. This structure is defined by a backbone network of dual Mn-O=W bridges; a retroanalysis of their formation suggests the importance of templation and kinetic control in the self-assembly of the {MnIII40W VI224} polyanion.
    Angewandte Chemie International Edition 05/2011; 50(22):5212-6. DOI:10.1002/anie.201008225 · 11.26 Impact Factor
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    ABSTRACT: The differential magnetic susceptibility for a series of Cr12Ln4 (Ln=Y,Eu,Gd,Tb,Dy,Ho,Yb) magnetic molecules was measured in static (up to 16 T) and pulsed (up to 45 T) magnetic fields using a rf tunnel-diode resonator (TDR). At low temperatures, the behavior of these finite spin systems is governed by discrete energy spectra of the individual molecules. In magnetic field, low-energy quantum levels Zeeman-split, crossing at field values where magnetization exhibits a step corresponding to switching between different spin states. In high fields, we detect multiple level crossings which allow for a detailed mapping of the energy diagram. We then perform quantum Monte Carlo (QMC) using a Heisenberg Hamiltonian with three adjustable exchange constants whose values are chosen so as to optimize agreement with the experimental energy spectrum. The variations in results for the studied molecules are correlated to the magnetic properties of the lanthanide ions.
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    Xikui Fang · Marshall Luban
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    ABSTRACT: The assembly of a tetradeca-manganese magnetic cluster [Mn(14)W(48)O(192)H(20)](26-), containing two high spin Mn(7) cores and supported exclusively by isopolytungstate ligands, demonstrates the promising perspective of using "defect" isopolyanions as ligands/synthons to construct large aggregated structures and model the surface deposition of molecular magnets.
    Chemical Communications 02/2011; 47(11):3066-8. DOI:10.1039/c0cc04403b · 6.83 Impact Factor
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    ABSTRACT: Inelastic neutron scattering (INS) in variable magnetic field and high-field magnetization measurements in the millikelvin temperature range were performed to gain insight into the low-energy magnetic excitation spectrum and the field-induced level crossings in the molecular spin cluster {Cr(8)}-cubane. These complementary techniques provide consistent estimates of the lowest level-crossing field. The overall features of the experimental data are explained using an isotropic Heisenberg model, based on three distinct exchange interactions linking the eight Cr(III) paramagnetic centers (spins s = 3/2), that is supplemented with a relatively large molecular magnetic anisotropy term for the lowest S = 1 multiplet. It is noted that the existence of the anisotropy is clearly evident from the magnetic field dependence of the excitations in the INS measurements, while the magnetization measurements are not sensitive to its effects.
    Journal of Physics Condensed Matter 11/2010; 22(46):466001. DOI:10.1088/0953-8984/22/46/466001 · 2.35 Impact Factor
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    ABSTRACT: We show that intramolecular exchange disorder recently found in the geometrically frustrated magnetic molecules {Mo(72)Fe(30)} and {Mo(72)Cr(30)} leads, in a classical Heisenberg model description, to spin freezing and slow magnetization dynamics reminiscent of spin glass behaviour. Also we suggest that our low temperature and low magnetic field nuclear magnetic resonance (NMR) measurements on {Mo(72)Fe(30)}, showing rapid and strong broadening of the proton line width on cooling below 600 mK, are evidence for a crossover from paramagnetic behaviour to a frozen spin configuration. Similar broadening is observed in {Mo(72)Cr(30)}. This observed effect is consistent with our theory of spin freezing and slow magnetization dynamics in these systems due to exchange disorder.
    Journal of Physics Condensed Matter 06/2010; 22(21):216007. DOI:10.1088/0953-8984/22/21/216007 · 2.35 Impact Factor
  • Larry Engelhardt · Marshall Luban
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    ABSTRACT: The Heisenberg model provides a simple but powerful theoretical platform for modelling magnetic molecules. In this article, we demonstrate that--despite its simplicity--an isotropic Heisenberg model successfully provides a comprehensive description of the magnetic properties of the {Fe₈}-cubane and the {Cr₁₂Cu₂} magnetic molecules. However, in order to achieve this success, it is necessary to employ a variety of sophisticated experimental and theoretical techniques. These include the use of pulsed-field measurements to observe a high-field (41 T) ground-state level crossing in the {Fe₈}-cubane system, and tunnel-diode oscillator measurements, which we use to observe excited-state level crossings in the {Cr₁₂Cu₂} ring. For these two systems, the theoretical modelling was carried out using matrix diagonalization and quantum Monte Carlo calculations, respectively.
    Dalton Transactions 05/2010; 39(20):4687-92. DOI:10.1039/C000356E · 4.20 Impact Factor
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    ABSTRACT: Many magnetic molecules form crystals in which intermolecular interactions can be ignored and at suitably low temperatures the description of these finite -- spin systems can be reduced to the analysis of a discrete spectrum of quantum energy levels within an individual molecule. By applying external magnetic field one can access information about low-lying energy levels that cross due to Zeeman splitting. Conventional experimental techniques are only sensitive to the ground state level crossings. Tunnel-diode resonator is a radio-frequency technique to measure the differential magnetic susceptibility in the millikelvin range and in high static external field. Having 1 ppb sensitivity, it can probe the magnetic energy spectrum in both the ground state and low-lying excited states. As a successful example, the TDR technique has recently been used to investigate the magnetic molecules Cr12Cu2 and Cr10Cu2. When compared with theoretical quantum Monte Carlo (QMC) simulations, we find the TDR results to be in extraordinary agreement with the predicted energy spectrum. This shows that the TDR technique is a unique and powerful spectroscopic tool for studies of magnetic molecules.

Publication Stats

2k Citations
370.11 Total Impact Points


  • 1985–2014
    • Iowa State University
      • • Department of Physics and Astronomy
      • • Ames Laboratory
      Ames, Iowa, United States
  • 2005–2009
    • Bielefeld University
      • Faculty of Chemistry
      Bielefeld, North Rhine-Westphalia, Germany
  • 2008
    • Kookmin University
      Sŏul, Seoul, South Korea
  • 2004
    • Nagoya University
      • Department of Chemistry
      Nagoya, Aichi, Japan
  • 2001
    • Weizmann Institute of Science
      • Department of Chemical Physics
      Tel Aviv, Tel Aviv, Israel
  • 1982
    • Washington University in St. Louis
      • Department of Physics
      Saint Louis, MO, United States