Session U16: Focus Session: Magnetic Molecules and Antiferromagnetic Chains

Transverse Field and Random-Field Ising Ferromagnetism in Mn$_{12}$-acetates

Single molecule magnets (SMMs) single crystals can exhibit long range ferromagnetic order associated with intermolecular interactions, principally magnetic dipole interactions. With their high spin (S $\sim$ 10) and strong Ising-like magnetic anisotropy, they are model materials to the study of physics associated with Transverse-Field Ising Ferromagnet Model (TFIFM). We have measured magnetic susceptibility of single crystals of the prototype SMM, Mn$_{12}$-acetate, and of a new high-symmetry variant, Mn$_{12}$-ac-MeOH. At zero transverse field the inverse susceptibility of both SMMs is found to accurately follow a Curie-Weiss law with an intercept at a non-zero temperature T$_{cw}$ $\sim$ 0.9 K, indicating a transition to a ferromagnetic phase due to dipolar interactions. With increasing transverse field, the susceptibility and the Curie-Weiss temperature decreases due to increase in spin fluctuations but the nature of the decrease is very different in the two materials. We find that in Mn$_{12}$-ac-MeOH, the suppression of ferromagnetism by the transverse field is consistent with TFIFM, while the suppression of ferromagnetism by the transverse field is considerably more rapid in Mn$_{12}$-acetate. Previous studies show that due to solvent disorder Mn$_{12}$-acetate has an intrinsic distribution of discrete tilts of the molecular magnetic easy axis from the global easy axis of the crystal. Thus with the application of transverse field, the molecules with tilted easy axis experience an additional field along their easy axis and give rise to a distribution of random-fields that further destroys the long-range order, suggesting that this prototypical molecular magnet is a realization of Random-Field Ising Ferromagnet (RFIFM).\\[4pt] [1] \textit{Phys. Rev. B} \textbf{85,} 013441 (2012).\\[0pt] [2] \textit{Phys. Rev. B} \textbf{82,} 014406 (2010).\\[0pt] [3] \textit{Phys. Rev. B} \textbf{82,} 174405(2010)   

Geometric-phase interference in a Mn$_{12}$ single-molecule magnet with four-fold rotational symmetry

We study the magnetic relaxation rate $\Gamma$ of the single-molecule magnet Mn$_{12}$-tBuAc as a function of magnetic field component $H_T$ transverse to the molecule's easy axis. When the spin is near a magnetic quantum tunneling resonance, we find that $\Gamma$ increases abruptly at certain values of $H_T$. These increases are observed just beyond values of $H_T$ at which a geometric-phase interference effect suppresses tunneling between two excited energy levels. The effect is washed out by rotating $H_T$ away from the spin's hard axis, thereby suppressing the interference effect. Detailed numerical calculations of $\Gamma$ using the known spin Hamiltonian accurately reproduce the observed behavior. These results are the first experimental evidence for geometric-phase interference in a single-molecule magnet with true four-fold symmetry. Furthermore, the results demonstrate that geometric-phase-interference effects can play a role in the thermally assisted tunneling regime.   

Synthesis and spectroscopic characterization of the single molecule magnet Mn$_{12}$-acetate

The single molecule magnet [Mn$_{12}$O$_{12}$(CH$_{3}$COO)$_{16}$(H$_{2}$O)$_{4}$]$\cdot$2CH$_{3}$COOH$\cdot$4H$_{2}$O (abbreviated as Mn$_{12}$-acetate) system is currently of great interest because it exhibits a number of fascinating properties, such as quantum tunneling of magnetization and unusual relaxation behavior. High-quality single crystals of Mn$_{12}$-acetate were grown and characterized by X-ray diffraction and magnetization measurements. Room temperature micro-Raman (inelastic light) scattering results on these crystals show phonon spectra consistent with earlier measurements. The frequencies of several Mn-O phonon modes exhibit anomalous behavior as a function of temperature. Studies of the Raman active phonons as functions of magnetic field and pressure are being conducted to better understand the role of different phonons in magnetic quantum tunneling in this system.   

B and C doped Cuboctohedral Mn$_{13}$ Clusters with Giant Magnetic Moments

Using first-principles calculations based on gradient corrected density functional theory we show that an otherwise distorted icosahedric Mn$_{13}$ ferrimagnetic cluster, when doped with six B or C atoms, transforms into a ferromagnetic cuboctahedral cluster with a magnetic moment that is an order of magnitude larger than that of the pure Mn$_{13}$ cluster. The origin of this magnetic transition is attributed to the change in the Mn-Mn interatomic distance resulting from the structural transformation. These doped clusters remain ferromagnetic with giant moments even after removing a B or C atom. However, similar doping with N atom does not lead to ferromagnetic ordering and Mn$_{13}$N$_{6}$ remains ferrimagnetic with a magnetic moment of only 3 $\mu_{\mathrm{B}}$, just as in its parent Mn$_{13}$ cluster.   

Geometry and magnetic structure variation in manganese-oxide clusters determined by a self-consistent, LCAO method

\textit{Ab initio} simulations are used to study the variation in geometry and magnetic structure in Mn$_{x}$O$_{y}$ ($x=$3,4; $y=$1,2) clusters. The groundstate wavefunctions for clusters with different magnetic coupling (ferromagnetic, ferrimagnetic and antiferromagnetic) are modeled with linear combinations of atomic orbitals (LCAOs). Self-consistent energies for different spin isomers are calculated by constraining the magnetic moments of Mn atoms constituting each basis AO. The ferrimagnetic and antiferromagnetic ground-state structures of Mn$_{x}$O$_{y}$ are 0.16--1.20 eV lower in energy than their ferromagnetic isomers. The presence of oxygen thus stabilizes low-spin isomers relative to the preferred high-spin ordering of bare Mn$_{3}$ and Mn$_{4}$. Each cluster has a preferred overall magnetic moment, and no evidence is seen of competing states with different spin multiplicities. However, non-degenerate isomags (clusters that possess the same spin multiplicity but different arrangements of local moments) do contribute to peak broadening observed in negative-ion photoelectron spectra. Proper accounting for all possible isomags is shown to be critical for accurate comparison with experimental spectra.   

Exploring Magnetic Interactions of an Mo$_3$O$_{13}$ Trimer Containing Compound: La$_5$Mo$_6$O$_{21}$

When searching for exotic magnetic ground states, it is often useful to seek out materials with certain geometric networks such as: triangular, kagome, and even square lattices with uniform magnetic exchange. Recently, the formation of a condensed valence bond state was proposed to explain the physical properties of LiZn$_2$Mo$_3$O$_8$. This low-temperature ground state emanates from the interactions of one unpaired electron residing on the Mo$_3$O$_{13}$ magnetic subunits. Thus, compounds containing related Mo$_3$O$_{13}$ subunits may prove to be a fertile playground for the study of magnetic interactions between these molecule-like clusters. Earlier structural reports of La$_5$Mo$_6$O$_{21}$ showed that this compound was built from these subunits, as well as, 1-D ``double lambda'' perovskite-like MoO$_6$ octahedra. The Mo atoms residing on the Mo$_3$O$_{13}$ trimers and the double lambda units have oxidation states of 4+ and 5+, respectively. Consequently, the magnetic response and entropy loss ca. 10 K are likely due to the magnetic interactions between the double lambda units and not the Mo$_3$O$_{13}$ trimers. In this presentation, the analysis of the total neutron scattering of La$_5$Mo$_6$O$_{21}$ will be used to draw correlations between the structure and the properties.   

Magnetic Response of Mn(III)F(salen) at Low Temperatures

Due to a report suggesting Mn(III)F(salen), salen $=$ H$_{14}$C$_{16}$N$_{2}$O$_{2}$, is a $S=$ 2 Haldane system with $J/k_{B}=$ 50 K and no long-range order down to 2 K,\footnote{T. Birk \textit{et al}., Inorg. Chem. \textbf{50} (2011) 5312.} we have studied its magnetic response. Torque magnetometry, down to 20 mK and up to 18 T, revealed a feature at 3.8 T when $T$ \textless\ 400 mK. ESR ($\sim $ 200 GHz) studies, using single crystals at 4 K and in 5 T, have not detected any signal. The low-field, high-$T$ susceptibility is unchanged for $P$ \textless\ 1.0 GPa. Using a randomly-oriented, powder-like, deuterated (12 of 14 H replaced by D) sample, neutron scattering data, acquired with the CNCS at SNS, are not consistent with a uniform system consisting of $S=$ 2 Heisenberg antiferromagnetic chains. The INS data show strong, dispersionless excitations, suggesting the possibility of isolated magnetic clusters.   

Anisotropic thermal expansion and magnetostructural coupling in CuSb$_{2}$O$_{6}$

Low-dimensional (Quasi-1D or 2D) spin \emph{S}= $1\over 2$ solid-state systems exhibit intriguing electronic and magnetic properties that deserve fundamental attention.\footnote{M. Hase et al., Phys. Rev. Lett. \textbf{70}, 3651 (1993).} Besides, they have long been the subject of intense investigation since the discovery of high-$T_c$ superconductivity in cuprates. Here we present results on anisotropic thermal expansion (TE) and magnetic properties in single crystalline CuSb$_{2}$O$_{6}$ in the temperature range $5 < T < 350$ K. We observe spin-flop transitions for magnetic field applied in $a(b)$ axis, but not in $c$. Our TE data reveals a magnetoelastic coupling in the vicinity of paramagnetic to antiferromagnetic phase transition around $T_{N}$. Also, the temperature dependence of 1D short range magnetic correlations in CuSb$_{2}$O$_{6}$ above $T_{N}$ is reflected in the changes in sample length measured using high resolution dilatometer. Using the scaling of thermal expansion data with the heat capacity data around $T_{N}$,the pressure derivative of $T_{N}$ is obtained as $dT_{N}/dP$= -0.11(1) K/GPa.   

Heat conduction in the one-dimensional AF spin chain compound CuSb$_2$O$_6$

We report thermal conductivity ($\kappa$) measurements on single crystals of the $S=1/2$ antiferromagnetic spin-chain compound CuSb$_2$O$_6$ over the temperature range $5{\rm K}\leq {\rm T}\leq 300 {\rm K}$. A much larger spin contribution to $\kappa$ is evident along the spin chains ([110] direction) than along [100] and [010]. The possible roles of spin-phonon scattering and twinning will be discussed along with $\kappa$ measurements in applied magnetic field.   

Multiple magnetic transitions of the pseudo-1D antiferromagnet CoNiTAC

Magnetic susceptibility and crystal growing methods are reported for the pseudo-one-dimensional antiferromagnet $\left[\left(CH_{3}\right)_{3}NH\right]Co_{1-x}Ni_{x}Cl_{3}\cdot2H_{2}O$ (abbreviated CoNiTAC). For high quality single crystals in the Ni mole fraction range $0.1 < x < 0.6$, two magnetic transitions with transition temperatures separated on the order of 0.1 K were observed. This indicates the possibility of a transition due to a change in the canting angle.   

Anomalous transport and thermalization in Heisenberg spin chains

In spite of long history 1D spin systems still offer challenging open questions, mostly regarding finite-temperature spin and heat transport as well as the relevance for recent experiments on spin-chain materials. In the talk some recent findings regarding properties of anisotropic spin-1/2 Heisenberg chains, both integrable and nonintegrable, will be presented. Within the Ising-type regime we show that the integrable XXZ model unveils the coexistence of anomalous and normal diffusion resolving in this way conflicting conclusions on Mott insulators. In the gapless regime numerical results in the hydrodynamic regime, consistent with the normal spin diffusion for a nonintegrable model, reveal vanishing current decay rate in the integrable case. The behavior is closely related to the thermalization phenomena in spin-chain systems so that diagonal matrix elements for integrable models show evident deviations from the eigenstate thermal hypothesis. In a weakly perturbed integrable system the finite-size scaling reveals that the crossover between anomalous and normal regime is given by a scale related to the scattering length. The theory of thermal conductivity in spin chains and the relation to recent experiments will be also discussed.   

Quench dynamics of the Heisenberg chain

We study the time evolution of the one dimensional Heisenberg chain after a quench from strongly (anti-)ferromagnetic coupling to the isotropic point ($\Delta=1$). We generalize the Yudson integral representation for arbitrary states to the Heisenberg model and use it to study time-evolution of observables and correlation functions.   

Quenching Dynamics of Anisotropic Heisenberg Model through a Critical Point

We study the quenching dynamics of the anisotropic Heisenberg model (XXZ model) with the Yudson contour representation, which is a general method of obtaining the dynamics of integrable models. It replaces the summation over all Bethe eigenstates by integrals over continuous momentum on carefully chosen contours. We begin by applying it to the few-particle case of XXZ model, and then focus on a quenching through the critical point: how a antiferromagnetic phase evolve with time into a spin fluid phase.