Microscopic theory of cooperative spin crossover: Interaction of molecular modes with phonons

In this article, we present a new microscopic theoretical approach to the description of spin crossover in molecular crystals. The spin crossover crystals under consideration are composed of molecular fragments formed by the spin-crossover metal ion and its nearest ligand surrounding and exhibiting well defined localized (molecular) vibrations. As distinguished from the previous models of this phenomenon, the developed approach takes into account the interaction of spin-crossover ions not only with the phonons but also a strong coupling of the electronic shells with molecular modes. This leads to an effective coupling of the local modes with phonons which is shown to be responsible for the cooperative spin transition accompanied by the structural reorganization. The transition is characterized by the two order parameters representing the mean values of the products of electronic diagonal matrices and the coordinates of the local modes for the high- and low-spin states of the spin crossover complex. Finally, we demonstrate that the approach provides a reasonable explanation of the observed spin transition in the [Fe(ptz)6](BF4)2 crystal. The theory well reproduces the observed abrupt low-spin → high-spin transition and the temperature dependence of the high-spin fraction in a wide temperature range as well as the pronounced hysteresis loop. At the same time within the limiting approximations adopted in the developed model, the evaluated high-spin fraction vs. T shows that the cooperative spin-lattice transition proves to be incomplete in the sense that the high-spin fraction does not reach its maximum value at high temperature.

Nonequilibrium hysteresis and spin relaxation in the mixed-anisotropy dipolar-coupled spin-glass LiHo0.5Er0.5F4

We present a study of the model spin-glass LiHo0.5Er0.5F4 using simultaneous ac susceptibility, magnetization, and magnetocaloric effect measurements along with small angle neutron scattering (SANS) at sub-Kelvin temperatures. All measured bulk quantities reveal hysteretic behavior when the field is applied along the crystallographic c axis. Furthermore, avalanchelike relaxation is observed in a static field after ramping from the zero-field-cooled state up to 200–300 Oe. SANS measurements are employed to track the microscopic spin reconfiguration throughout both the hysteresis loop and the related relaxation. Comparing the SANS data to inhomogeneous mean-field calculations performed on a box of one million unit cells provides a real-space picture of the spin configuration. We discover that the avalanche is being driven by released Zeeman energy, which heats the sample and creates positive feedback, continuing the avalanche. The combination of SANS and mean-field simulations reveal that the conventional distribution of cluster sizes is replaced by one with a depletion of intermediate cluster sizes for much of the hysteresis loop.

Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, AbelianU(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev’s toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

Two-Dimensional Supramolecular Electron Spin Arrays

A bottom-up approach is introduced to fabricate two-dimensional self-assembled layers of molecular spin-systems containing Mn and Fe ions arranged in a chessboard lattice. We demonstrate that the Mn and Fe spin states can be reversibly operated by their selective response to coordination/decoordination of volatile ligands like ammonia (NH3).

Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

High-Spin Molecules: Synthesis, X-ray Characterization, and Magnetic Behavior of Two New Cyano-Bridged Ni II 9 Mo V 6 and Ni II 9 W V 6 Clusters with a S = 12 Ground State

The preparations, X-ray structures, and magnetic characterizations are presented for two new pentadecanuclear cluster compounds:  [NiII{NiII(MeOH)3}8(μ-CN)30{MV(CN)3}6]·xMeOH·yH2O (MV = MoV (1) with x = 17, y = 1; MV = WV (2) with x = 15, y = 0). Both compounds crystallize in the monoclinic space group C2/c, with cell dimensions of a = 28.4957(18) Å, b = 19.2583(10) Å, c = 32.4279(17) Å, β = 113.155(6)°, and Z = 4 for 1 and a = 28.5278(16) Å, b = 19.2008(18) Å, c = 32.4072(17) Å, β = 113.727(6)°, and Z = 4 for 2. The structures of 1 and 2 consist of neutral cluster complexes comprising 15 metal ions, 9 NiII and 6 MV, all linked by μ-cyano ligands. Magnetic susceptibilities and magnetization measurements of compounds 1 and 2 in the crystalline and dissolved state indicate that these clusters have a S = 12 ground state, originating from intracluster ferromagnetic exchange interactions between the μ-cyano-bridged metal ions of the type NiII−NC−MV. Indeed, these data show clearly that the cluster molecules stay intact in solution. Ac magnetic susceptibility measurements reveal that the cluster compounds exhibit magnetic susceptibility relaxation phenomena at low temperatures since, with nonzero dc fields, χ‘ ‘M has a nonzero value that is frequency dependent. However, there appears no out-of-phase (χ‘ ‘M) signal in zero dc field down to 1.8 K, which excludes the expected signature for a single molecule magnet. This finding is confirmed with the small uniaxial magnetic anisotropy value for D of 0.015 cm-1, deduced from the high-field, high-frequency EPR measurement, which distinctly reveals a positive sign in D. Obviously, the overall magnetic anisotropy of the compounds is too low, and this may be a consequence of a small single ion magnetic anisotropy combined with the highly symmetric arrangement of the metal ions in the cluster molecule.