Giant Keplerate molecule Fe30 - the first octopole magnet

The multipole expansion technique is applied to one of the largest magnetic molecules, Fe30. The molecule's dipole, toroid and quadrupole magnetic moments are equal to zero (in the absence of magnetic field) so the multipole expansion starts from the octopole moment. Probably the Fe30 molecule is the most symmetrical magnetic body synthesized so far. The magnetization process is considered theoretically in different geometries. Some components of the octopole moment experience a jump while the magnetization rises linearly up to its saturation value. An elementary octopole moment consisting of four magnetic dipoles is proposed as a hint for designing of an experiment for measurement of octopole magnetic moment components.Comment: 7 pages, 9 figure

Supersymmetric spin-phonon coupling prevents odd integer spins from quantum tunneling

Irländer K, Schmidt H-J, Schnack J. Supersymmetric spin-phonon coupling prevents odd integer spins from quantum tunneling. The European Physical Journal B . 2021;94(3): 68.Quantum tunneling of the magnetization is a phenomenon that impedes the use of small anisotropic spin systems for storage purposes even at the lowest temperatures. Phonons, usually considered for temperature dependent relaxation of magnetization over the anisotropy barrier, also contribute to magnetization tunneling for integer spin quantum numbers. Here we demonstrate that certain spin-phonon Hamiltonians are unexpectedly robust against the opening of a tunneling gap, even for strong spin-phonon coupling. The key to understanding this phenomenon is provided by an underlying supersymmetry that involves both spin and phonon degrees of freedom

Stochastic thermodynamics of a finite quantum system coupled to a heat bath

Schmidt H-J, Schnack J, Gemmer J. Stochastic thermodynamics of a finite quantum system coupled to a heat bath. Zeitschrift für Naturforschung A. 2021;76(8):731-745.We consider a situation where an N-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation, we derive general Jarzynski-type equations and conclude that heat and entropy is flowing from the hot bath to the cold NLS and, vice versa, from the hot NLS to the cold bath. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. Our approach is illustrated by an analytical example

Periodic thermodynamics of the Rabi model with circular polarization for arbitrary spin quantum numbers

Schmidt H-J, Schnack J, Holthaus M. Periodic thermodynamics of the Rabi model with circular polarization for arbitrary spin quantum numbers. PHYSICAL REVIEW E. 2019;100(4): 42141.We consider a spin s subjected to both a static and an orthogonally applied oscillating, circularly polarized magnetic field while being coupled to a heat bath and analytically determine the quasistationary distribution of its Floquet-state occupation probabilities for arbitrarily strong driving. This distribution is shown to be Boltzmannian with a quasitemperature which is different from the temperature of the bath and independent of the spin quantum number. We discover a remarkable formal analogy between the quasithermal magnetism of the nonequilibrium steady state of a driven ideal paramagnetic material and the usual thermal paramagnetism. Nonetheless, the response of such a material to the combined fields is predicted to show several unexpected features, even allowing one to turn a paramagnet into a diamagnet under strong driving. Thus, we argue that experimental measurements of this response may provide key paradigms for the emerging field of periodic thermodynamics

Floquet theory of the analytical solution of a periodically driven two-level system

Schmidt H-J, Schnack J, Holthaus M. Floquet theory of the analytical solution of a periodically driven two-level system. APPLICABLE ANALYSIS. 2019:1-18.We investigate the analytical solution of a two-level system subject to a monochromatical, linearly polarized external field that was first published in 2007. In particular, we derive an explicit expression for the quasienergy. Moreover, we calculate the time evolution of a typical two-level system over a full period by evaluating series solutions of the confluent Heun equation. This is possible without invoking the connection problem of this equation since the complete time evolution of the system under consideration can be reduced to that of the first quarter-period. As a physical application we consider the work performed on a two-level system

Observation of phase synchronization and alignment during free induction decay of quantum spins with Heisenberg interactions

Vorndamme P, Schmidt H-JB, Schröder C, Schnack J. Observation of phase synchronization and alignment during free induction decay of quantum spins with Heisenberg interactions. New Journal of Physics. 2021.Equilibration of observables in closed quantum systems that are described by a unitary time evolution is a meanwhile well-established phenomenon apart from a few equally well-established exceptions. Here we report the surprising theoretical observation that integrable as well as non-integrable spin rings with nearest-neighbor or long-range isotropic Heisenberg interaction not only equilibrate but moreover also synchronize the directions of the expectation values of the individual spins. We highlight that this differs from spontaneous synchronization in quantum dissipative systems. Here, we observe mutual synchronization of local spin directions in closed systems under unitary time evolution. In our numerical simulations, we investigate the free induction decay (FID) of an ensemble of up to $N = 25$ quantum spins with $s = 1/2$ each by solving the time-dependent Schr\"odinger equation numerically exactly. Our findings are related to, but not fully explained by conservation laws of the system. Even if we cannot provide a full understanding of the phenomenon, it is very robust against for instance random fluctuations of the Heisenberg couplings and inhomogeneous magnetic fields. The observed synchronization is independent of whether the interaction is ferro- or antiferromagnetic. Synchronization is not observed with strong enough symmetry-breaking interactions such as the dipolar interaction. We also compare our results to closed-system classical spin dynamics which does not exhibit phase synchronization due to the lack of entanglement and since the fixed magnitude of individual classical spins effectively acts like additional $N$ conservation laws

Accuracy of the typicality approach using Chebyshev polynomials

Schlüter H, Gayk F, Schmidt H-J, Honecker A, Schnack J. Accuracy of the typicality approach using Chebyshev polynomials. Zeitschrift für Naturforschung A, Journal of Physical Sciences . 2021;76(9):823-834.Trace estimators allow us to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finitetemperature Lanczos method (FTLM) which relies on a Krylov space expansion of the exponential describing the Boltzmann weights. Here we report investigations of an alternative approach which employs Chebyshev polynomials. This method turns out to be also very accurate in general, but shows systematic inaccuracies at low temperatures that can be traced back to an improper behavior of the approximated density of states with and without smoothing kernel. Applications to archetypical quantum spin systems are discussed as examples

Odd and Even Numbered Ferric Wheels

The structurally related odd and even numbered wheels [FeIII11ZnII4(tea)10(teaH)1(OMe)Cl8] (1) and [FeIII12ZnII4(tea)12Cl8] (2) can be synthesized under ambient conditions by reacting FeIII and ZnII salts with triethanolamine (teaH3), the change in nuclearity being dictated by the solvents employed. Antiferromagnetic exchange between nearest neighbours, J = -10.0 cm-1 for 1 and J = -12.0 cm-1 for 2, leads to a frustrated S = 1/2 ground state in the former and an S = 0 ground state in the latter

Magnetic exchange, anisotropy and excitonic fluctuations in a [NiII7] Anderson wheel

The solvothermal reaction of Ni(ClO4)2·6H2O with hmpH and picH in a basic MeOH solution affords [Ni7(hmp)7.55(pic)4.45](ClO4)2·6MeOH (1·6MeOH) directly upon cooling the mother liquor. The metallic skeleton of 1 describes a [NiII7] centred hexagon, commonly referred to as an Anderson wheel. Magnetic meaurements reveal ferromagnetic exchange between the central Ni ion and the ring Ni ions, and antiferromagnetic exchange between neighbouring ring Ni ions. They also confirm the presence of easy-plane anisotropy for the central Ni ion, and easy-axis anisotropy for the ring Ni ions, in agreement with DFT calculations and neutron scattering. For the analysis of the latter we apply an excitonic formalism using a Green\u27s function response theory