Spin electric effects in molecular antiferromagnets

Molecular nanomagnets show clear signatures of coherent behavior and have a wide variety of effective low-energy spin Hamiltonians suitable for encoding qubits and implementing spin-based quantum information processing. At the nanoscale, the preferred mechanism for control of quantum systems is through application of electric fields, which are strong, can be locally applied, and rapidly switched. In this work, we provide the theoretical tools for the search for single molecule magnets suitable for electric control. By group-theoretical symmetry analysis we find that the spin-electric coupling in triangular molecules is governed by the modification of the exchange interaction, and is possible even in the absence of spin-orbit coupling. In pentagonal molecules the spin-electric coupling can exist only in the presence of spin-orbit interaction. This kind of coupling is allowed for both $s=1/2$ and $s=3/2$ spins at the magnetic centers. Within the Hubbard model, we find a relation between the spin-electric coupling and the properties of the chemical bonds in a molecule, suggesting that the best candidates for strong spin-electric coupling are molecules with nearly degenerate bond orbitals. We also investigate the possible experimental signatures of spin-electric coupling in nuclear magnetic resonance and electron spin resonance spectroscopy, as well as in the thermodynamic measurements of magnetization, electric polarization, and specific heat of the molecules.Comment: 31 pages, 24 figure

Spin anisotropy effects in dimer single molecule magnets

We present a model of equal spin $s_1$ dimer single molecule magnets. The spins within each dimer interact via the Heisenberg and the most general set of four quadratic anisotropic spin interactions with respective strengths $J$ and $\{J_j\}$, and with the magnetic induction ${\bf B}$. We solve the model exactly for $s_1=1/2, 1, 5/2$, and for antiferromagnetic Heisenberg couplings ($J<0$), present ${\bf M}({\bf B})$ curves at low $T$ for these cases. Low-$T$ $C_V({\bf B})$ curves for $s_1=1/2$ and electron paramagnetic susceptibility $\chi({\bf B},\omega)$ for $s_1=1$ are also provided. For weak anisotropy interactions, we employ a perturbative treatment, and show that the Hartree and extended Hartree approximations lead to reliable analytic results at low $T$ and large $B$ for these quantities and for the inelastic neutron scattering cross-section $S({\bf B}, {\bf q},\omega)$. Our results are discussed with regard to existing ${\bf M}({\bf B})$ experiments on $s_1=5/2$ Fe$_2$ dimer single molecule magnets, and suggest that one of them contains a substantial amount of single-ion anisotropy, without any sizeable global spin anisotropy. We urge further experiments of the above types on single crystals of Fe$_2$ and on some $s_=9/2$ [Mn$_4$]$_2$ dimers, in order to elucidate the precise values of the various microscopic interactions.Comment: 30 pages, 25 figures, submitted to Phys. Rev.

Single-ion and exchange anisotropy effects and multiferroic behavior in high-symmetry tetramer single molecule magnets

We study single-ion and exchange anisotropy effects in equal-spin $s_1$ tetramer single molecule magnets exhibiting $T_d$, $D_{4h}$, $D_{2d}$, $C_{4h}$, $C_{4v}$, or $S_4$ ionic point group symmetry. We first write the group-invariant quadratic single-ion and symmetric anisotropic exchange Hamiltonians in the appropriate local coordinates. We then rewrite these local Hamiltonians in the molecular or laboratory representation, along with the Dzyaloshinskii-Moriay (DM) and isotropic Heisenberg, biquadratic, and three-center quartic Hamiltonians. Using our exact, compact forms for the single-ion spin matrix elements, we evaluate the eigenstate energies analytically to first order in the microscopic anisotropy interactions, corresponding to the strong exchange limit, and provide tables of simple formulas for the energies of the lowest four eigenstate manifolds of ferromagnetic (FM) and anitiferromagnetic (AFM) tetramers with arbitrary $s_1$. For AFM tetramers, we illustrate the first-order level-crossing inductions for $s_1=1/2,1,3/2$, and obtain a preliminary estimate of the microscopic parameters in a Ni$_4$ from a fit to magnetization data. Accurate analytic expressions for the thermodynamics, electron paramagnetic resonance absorption and inelastic neutron scattering cross-section are given, allowing for a determination of three of the microscopic anisotropy interactions from the second excited state manifold of FM tetramers. We also predict that tetramers with symmetries $S_4$ and $D_{2d}$ should exhibit both DM interactions and multiferroic states, and illustrate our predictions for $s_1=1/2, 1$.Comment: 30 pages, 14 figures, submitted to Phys. Rev.

Pressure Dependence of the Magnetic Anisotropy in the "Single-Molecule Magnet" [Mn4O3Br(OAc)3(dbm)3]

The anisotropy splitting in the ground state of the single-molecule magnet [Mn4O3Br(OAc)3(dbm)3] is studied by inelastic neutron scattering as a function of hydrostatic pressure. This allows a tuning of the anisotropy and thus the energy barrier for slow magnetisation relaxation at low temperatures. The value of the negative axial anisotropy parameter $D_{\rm cluster}$ changes from -0.0627(1) meV at ambient to -0.0603(3) meV at 12 kbar pressure, and in the same pressure range the height of the energy barrier between up and down spins is reduced from 1.260(5) meV to 1.213(9) meV. Since the $\rm Mn-Br$ bond is significantly softer and thus more compressible than the $\rm Mn-O$ bonds, pressure induces a tilt of the single ion Mn$^{3+}$ anisotropy axes, resulting in the net reduction of the axial cluster anisotropy.Comment: 4 pages, 3 figure

Spin-Triplet Excitons in the S=1/2S=1/2 Gapped Antiferromagnet BaCuSi2_2O6_6: Electron Paramagnetic Resonance Studies

BaCuSi$_2$O$_6$, a $S=1/2$ quantum antiferromagnet with a double-layer structure of Cu$^{2+}$ ions in a distorted planar-rectangular coordination and with a dimerized spin singlet ground state, is studied by means of the electron paramagnetic resonance technique. It is argued that multiple absorptions observed at low temperatures are intimately related to a thermally-activated spin-triplet exciton superstructure. Analysis of the angular dependence of exciton modes in BaCuSi$_2$O$_6$ allows us to accurately estimate anisotropy parameters. In addition, the temperature dependence of EPR intensity and linewidth is discussed.Comment: Submitted to Phys. Rev.

Bounding and approximating parabolas for the spectrum of Heisenberg spin systems

We prove that for a wide class of quantum spin systems with isotropic Heisenberg coupling the energy eigenvalues which belong to a total spin quantum number S have upper and lower bounds depending at most quadratically on S. The only assumption adopted is that the mean coupling strength of any spin w.r.t. its neighbours is constant for all N spins. The coefficients of the bounding parabolas are given in terms of special eigenvalues of the N times N coupling matrix which are usually easily evaluated. In addition we show that the bounding parabolas, if properly shifted, provide very good approximations of the true boundaries of the spectrum. We present numerical examples of frustrated rings, a cube, and an icosahedron.Comment: 8 pages, 3 figures. Submitted to Europhysics Letter

Thermal anomalies and fluid geochemistry framework in occurrence of the 2000-2001 Nizza Monferrate seismic sequence (northern Italy): Episodic changes in the fault zone heat flow or chemical mixing phenomena?

International audienceThe paper discusses the correlation between the heating of shallow groundwater over a 10 × 20 km wide area close to the town of Nizza Monferrato (Piemonte Region, Northern Italy) and the concomitant local seismic sequences during the period August 2000 ? July 2001. The first seismic sequence started on 21 August 2000 with a Ml = 5.2 earthquake. Within few hours, the local authorities received calls alerting that the groundwater temperature rose from 10 to 30°C in many shallow wells. Our geochemical experimental data and the geological-seismotectonic framework do not allow the hypothesis of simple fluid mixing between the thermal reservoir of Acqui Terme and the Nizza-Monferrato shallow groundwater to explain the observed thermal anomalies. On the other hand, we invoke more complex processes such as frictional heating, mechano-chemistry, fault-valve mechanism, adiabatic decompression and hydrogeologically driven heat flow i.e., thermal effects due to variations of basin-scale permeability field. All these processes are able to transmit heat to the surface and to generate a transient incremental heat flow better than the mass transfer occurring typically when fluids from different reservoirs mix

Spin dynamics in the low-dimensional magnet TiOCl

We present detailed ESR investigations on single crystals of the low-dimensional quantum magnet TiOCl. The anisotropy of the g-factor indicates a stable orbital configuration below room temperature, and allows to estimate the energy of the first excited state as 0.3(1) eV ruling out a possible degeneracy of the orbital ground state. Moreover, we discuss the possible spin relaxation mechanisms in TiOCl and analyze the angular and temperature dependence of the linewidth up to 250 K in terms of anisotropic exchange interactions. Towards higher temperatures an exponential increase of the linewidth is observed, indicating an additional relaxation mechanism.Comment: 10 pages, 8 figures; accepted for publication in Phys. Rev.

Field-induced level crossings in spin clusters: Thermodynamics and magneto-elastic instability

Quantum spin clusters with dominant antiferromagnetic Heisenberg exchange interactions typically exhibit a sequence of field-induced level crossings in the ground state as function of magnetic field. For fields near a level crossing, the cluster can be approximated by a two-level Hamiltonian at low temperatures. Perturbations, such as magnetic anisotropy or spin-phonon coupling, sensitively affect the behavior at the level-crossing points. The general two-level Hamiltonian of the spin system is derived in first-order perturbation theory, and the thermodynamic functions magnetization, magnetic torque, and magnetic specific heat are calculated. Then a magneto-elastic coupling is introduced and the effective two-level Hamilitonian for the spin-lattice system derived in the adiabatic approximation of the phonons. At the level crossings the system becomes unconditionally unstable against lattice distortions due to the effects of magnetic anisotropy. The resultant magneto-elastic instabilities at the level crossings are discussed, as well as the magnetic behavior.Comment: 13 pages, 8 figures, REVTEX

Exchange-coupling constants, spin density map, and Q dependence of the inelastic neutron scattering intensity in single-molecule magnets

The Q dependence of the inelastic neutron scattering (INS) intensity of transitions within the ground-state spin multiplet of single-molecule magnets (SMMs) is considered. For these transitions, the Q dependence is related to the spin density map in the ground state, which in turn is governed by the Heisenberg exchange interactions in the cluster. This provides the possibility to infer the exchange-coupling constants from the Q dependence of the INS transitions within the spin ground state. The potential of this strategy is explored for the M = +-10 -> +- 9 transition within the S = 10 multiplet of the molecule Mn12 as an example. The Q dependence is calculated for powder as well as single-crystal Mn12 samples for various exchange-coupling situations discussed in the literature. The results are compared to literature data on a powder sample of Mn12 and to measurements on an oriented array of about 500 single-crystals of Mn12. The calculated Q dependence exhibits significant variation with the exchange-coupling constants, in particular for a single-crystal sample, but the experimental findings did not permit an unambiguous determination. However, although challenging, suitable experiments are within the reach of today's instruments.Comment: 11 pages, 6 figures, REVTEX4, to appear in PR