arXiv subjects

J. Schnack

Publications and source records attributed to J. Schnack.

At least 37 records · Page 2Linked to original sources

arXiv2020

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

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.

cond-mat.str-el↗

arXiv2020

Magnon crystallization in the kagome lattice antiferromagnet

We present numerical evidence for the crystallization of magnons below the saturation field at non-zero temperatures for the highly frustrated spin-half kagome Heisenberg antiferromagnet. This phenomenon can be traced back to the existence of independent localized magnons or equivalently flat-band multi-magnon states. We present a loop-gas description of these localized magnons and a phase diagram of this transition, thus providing information for which magnetic fields and temperatures magnon crystallization can be observed experimentally. The emergence of a finite-temperature continuous transition to a magnon-crystal is expected to be generic for spin models in dimension $D>1$ where flat-band multi-magnon ground states break translational symmetry.

cond-mat.str-el↗

arXiv2020

Spin-phonon interaction induces tunnel splitting in single-molecule magnets

Quantum tunneling of the magnetization is a major obstacle to the use of single-molecule magnets (SMMs) as basic constituents of next-generation storage devices. In this context, phonons are often only considered (perturbatively) as disturbances that promote the spin system to traverse the anisotropy barrier. Here, we demonstrate the ability of phonons to induce a tunnel splitting of the ground doublet which then reduces the required bistability due to Landau-Zener tunneling of the magnetization. Harmful are those phonons that modify the spin Hamiltonian so that its rotational symmetry about the field axis is destroyed. In our calculations we treat spins and phonons on the same footing by performing quantum calculations of a Hamiltonian where the single-anisotropy tensors are coupled to harmonic oscillators.

cond-mat.str-el↗

arXiv2020

Finite-size scaling of typicality-based estimates

According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation, or trace estimator, provides a powerful approach to, e.g., thermodynamic quantities for systems with large Hilbert-space sizes, which usually cannot be treated exactly, analytically or numerically. Here, we discuss the finite-size scaling of the accuracy of such trace estimators from two perspectives. First, we study the full probability distribution of random-vector expectation values and, second, the full temperature dependence of the standard deviation. With the help of numerical examples, we find pronounced Gaussian probability distributions and the expected decrease of the standard deviation with system size, at least above certain system-specific temperatures. Below and in particular for temperatures smaller than the excitation gap, simple rules are not available.

cond-mat.stat-mech↗

arXiv2020

Decoherence of a singlet-triplet superposition state under dipolar interactions of an uncorrelated environment

Recently it was shown that by means of an STM it is experimentally possible to stimulate clock transitions between the singlet and the non-magnetic triplet state of a Heisenberg-coupled spin dimer (Bae et al., Science Advances 4, eaau4159). This leads to more strongly protected clock transitions while ordinary ones only provide first-order protection against magnetic noise. However, large decoherence times of clock like states normally refer to ensembles of spins which do not dephase. In the cited experiment only one single dimer is manipulated and not an ensemble. For this reason we simulate how a single dimer behaves in an environment of other spins which couple to the dimer via dipolar interactions. We perform unitary time evolutions in the complete Hilbert space including dimer and a reasonably large environment. We will see that for a weak environment this approach confirms long decoherence times for the clock like state, but with stronger couplings this statement does not hold. As a reference we compare the behavior of the dimer with other, non-clock like, superposition states. Furthermore, we show that the internal dynamics of the bath plays an important role for the decoherence time of the system. In a regime where the system is weakly coupled to the bath, stronger interactions among environmental spins worsen the decoherence time up to a certain degree, while if system and bath are strongly coupled, stronger interactions in the environment improve decoherence times.

cond-mat.str-el↗

arXiv2020

Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates

We study trace estimators for equilibrium thermodynamic observables that rely on the idea of typicality and derivatives thereof such as the finite-temperature Lanczos method (FTLM). As numerical examples quantum spin systems are studied. Our initial aim was to identify pathological examples or circumstances, such as strong frustration or unusual densities of states, where these methods could fail. Instead we failed with the attempt. All investigated systems allow such approximations, only at temperatures of the order of the lowest energy gap the convergence is somewhat slower in the number of random vectors over which observables are averaged.

cond-mat.str-el↗

arXiv2019

The delta-chain with ferro- and antiferromagnetic interactions in applied magnetic field

We study the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions in an external magnetic field which generalizes the field-free case studied previously. This model plays an important role for the recently synthesized compound Fe$_{10}$Gd$_{10}$ which is nearly quantum critical. The classical version of the model is solved exactly and explicit analytical results for the low-temperature thermodynamics are obtained. The spin-$s$ quantum model is studied using exact diagonalization and finite-temperature Lanzos techniques. Particular attention is focused on the magnetization and the susceptibility. The magnetization of the classical model in the ferromagnetic part of the phase diagram defines the universal scaling function which is valid for the quantum model. The dependence of the susceptibility on the spin quantum number $s$ at the critical point between the ferro- and ferrimagnetic phases is studied and the relation to Fe$_{10}$Gd$_{10}$ is discussed.

cond-mat.str-el↗

arXiv2019

Thermal DMRG for highly frustrated quantum spin chains: a user perspective

Thermal DMRG is investigated with emphasis of employability in molecular magnetism studies. To this end magnetic observables at finite temperature are evaluated for two one-dimensional quantum spin systems: a Heisenberg chain with nearest-neighbor antiferromagnetic interaction and a frustrated sawtooth (delta) chain. It is found that thermal DMRG indeed accurately approximates magnetic observables for the chain as well as for the sawtooth chain, but in the latter case only for sufficiently high temperatures. We speculate that the reason is due to the peculiar structure of the low-energy spectrum of the sawtooth chain induced by frustration.

cond-mat.str-el↗

arXiv2019

Combined use of translational and spin-rotational invariance for spin systems

Exact diagonalization and other numerical studies of quantum spin systems are notoriously limited by the exponential growth of the Hilbert space dimension with system size. A common and well-known practice to reduce this increasing computational effort is to take advantage of the translational symmetry $C_N$ in periodic systems. This represents a rather simple yet elegant application of the group theoretical symmetry projection operator technique. For isotropic exchange interactions, the spin-rotational symmetry SU(2) can be used, where the Hamiltonian matrix is block-structured according to the total spin- and magnetization quantum numbers. Rewriting the Heisenberg Hamiltonian in terms of irreducible tensor operators allows for an efficient and highly parallelizable implementation to calculate its matrix elements recursively in the spin-coupling basis. When combining both $C_N$ and SU(2), mathematically, the symmetry projection technique leads to ready-to-use formulas. However, the evaluation of these formulas is very demanding in both computation time and memory consumption, problems which are said to outweigh the benefits of the symmetry reduced matrix shape. We show a way to minimize the computational effort for selected systems and present the largest numerically accessible cases.

cond-mat.str-el↗

arXiv2019

Evidence of Low-Energy Singlet Excited States in the Spin-1/2 Polyhedral Clusters {Mo$_{72}$V$_{30}$} and {W$_{72}$V$_{30}$} with Strongly Frustrated Kagomé Networks

Magnetization, specific heat, and electron spin resonance (ESR) measurements are carried out to clarify the low-energy excitations for the S = 1/2 polyhedral clusters {Mo$_{72}$V$_{30}$} and {W$_{72}$V$_{30}$}. The clusters provide unique model systems of Kagomé network on a quasi-sphere. The linear field variation of magnetization at low temperatures indicates that the ground state is singlet for both clusters. The temperature and the magnetic field dependence of specific heat shows a distinct difference between two clusters with differing structural symmetries. In {W$_{72}$V$_{30}$} with I$_h$ symmetry, the existence of the several tens of low-energy singlet excited states below the lowest triplet excited state is revealed. The specific heat of the slightly distorted {Mo$_{72}$V$_{30}$} with D$_{5h}$ symmetry leads to a drastic decrease of the singlet contribution, which is consistent with the partial lifting of the frustration and the decrease of degenerated low-energy states. The singlet excitation existence is confirmed further by the temperature dependence of the ESR spectra. Comprehensive experimental studies have demonstrated unique low-energy excitations of the spherical Kagomé networks and their sensitivity to the cluster symmetry.

cond-mat.str-el↗

arXiv2018

Thermodynamics of delta-chain with ferro- and antiferromagnetic interactions

Motivated by a novel cyclic compound $Fe_{10}Gd_{10}$ with record ground state spin in which the arrangement of magnetic ions with $s=\frac{5}{2}$ and $s=\frac{7}{2}$ corresponds to a saw-tooth chain we investigate the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions. We study both classical and quantum versions of the model. The classical model is exactly solved and quantum effects are studied using full diagonalization and a finite temperature Lanczos technique for finite delta-chains as well as modified spin wave theory. It is shown that the main features of the magnetic susceptibility of the quantum spin delta chain are correctly described by the classical spin model, while quantum effects significantly change the low-temperature behavior of the specific heat. The relation of the obtained results to the $Fe_{10}Gd_{10}$ system is discussed.

cond-mat.str-el↗

arXiv2018

Magnetization curves of deposited finite spin chains

The characterization and manipulation of deposited magnetic clusters or molecules on surfaces is a prerequisite for their future utilization. In recent years techniques like spin-flip inelastic electron tunneling spectroscopy using a scanning tunneling microscope proved to be very precise in determining e.g. exchange constants in deposited finite spin chains in the meV range. In this article we tackle the problem numerically by investigating the transition from where a pure spin Hamiltonian is sufficient to the point where the interaction with the surface significantly alters the magnetic properties. To this end we study the static, i.e. equilibrium impurity magnetization of antiferromagnetic chains for varying couplings to a conduction electron band of a metal substrate. We show under which circumstances the screening of a part of the system enables one to deduce molecular parameters of the remainder from level crossings in an applied field.

cond-mat.str-el↗

arXiv2018

Magnetism of the N=42 kagome lattice antiferromagnet

For the paradigmatic frustrated spin-half Heisenberg antiferromagnet on the kagome lattice we performed large-scale numerical investigation of thermodynamic functions by means of the finite-temperature Lanczos method for system sizes of up to N=42. We present the dependence of magnetization as well as specific heat on temperature and external field and show in particular that a finite-size scaling of specific heat supports the appearance of a low-temperature shoulder below the major maximum. This seems to be the result of a counterintuitive motion of the density of singlet states towards higher energies. Other interesting features that we discuss are the asymmetric melting of the 1/3 magnetization plateau as well the field dependence of the specific heat that exhibits characteristic features caused by the existence of a flat one-magnon band. By comparison with the unfrustrated square-lattice antiferromagnet the tremendous role of frustration in a wide temperature range is illustrated.

cond-mat.str-el↗

arXiv2018

Rotational magnetocaloric effect of anisotropic giant spin systems

The magnetocaloric effect, that consists of adiabatic temperature changes in a varying external magnetic field, appears not only when the amplitude is changed, but in cases of anisotropic magnetic materials also when the direction is varied. In this article we investigate the magnetocaloric effect theoretically for the archetypical single molecule magnets Fe8 and Mn12 that are rotated with respect to a magnetic field. We complement our calculations for equilibrium situations with investigations of the influence of non-equilibrium thermodynamic cycles.

cond-mat.str-el↗

arXiv2017

Young's moduli of carbon materials investigated by various classical molecular dynamics schemes

Classical carbon potentials together with classical molecular dynamics are employed to calculate structures and physical properties of such carbon-based materials where quantum mechanical methods fail either due to the excessive size, irregular structure or long-time dynamics. Examples are given by recently synthesized free-standing carbon nanomembranes (CNM) with molecular thickness and macroscopic lateral size as well as by amorphous carbon. Although such potentials, as for instance implemented in LAMMPS, yield reasonably accurate bond lengths and angles for several carbon materials such as graphene, it is not clear how accurate they are in terms of mechanical properties such as Young's moduli. We performed large-scale classical molecular dynamics investigations of three carbon-based materials using the various potentials implemented in LAMMPS as well as the highly sophisticated EDIP potential of Nigel Marks. We demonstrate how the Young's moduli vary with classical potentials and compare to experimental results. Since classical descriptions of carbon are bound to be approximations it is not astonishing that different realizations yield differing results. One should therefore carefully check for which observables a certain potential is suited. We hope to contribute to such a clarification.

cond-mat.mtrl-sci↗

arXiv2016

Investigation of thermalization in giant-spin models by different Lindblad schemes

The theoretical understanding of time-dependence in magnetic quantum systems is of great importance in particular for cases where a unitary time evolution is accompanied by relaxation processes. A key example is given by the dynamics of single-molecule magnets where quantum tunneling of the magnetization competes with thermal relaxation over the anisotropy barrier. In this article we investigate how good a Lindblad approach describes the relaxation in giant spin models and how the result depends on the employed operator that transmits the action of the thermal bath.

cond-mat.str-el↗

arXiv2016

Alternating-spin S=3/2 and sigma=1/2 Heisenberg chain with three-body exchange interactions

The promotion of collinear classical spin configurations as well as the enhanced tendency towards nearest-neighbor clustering of the quantum spins are typical features of the frustrating isotropic three-body exchange interactions in Heisenberg spin systems. Based on numerical density-matrix renormalization group calculations, we demonstrate that these extra interactions in the Heisenberg chain constructed from alternating S=3/2 and sigma=1/2 site spins can generate numerous specific quantum spin states, including some partially-polarized ferrimagnetic states as well as a doubly-degenerate non-magnetic gapped phase. In the non-magnetic region of the phase diagram, the model describes a crossover between the spin-1 and spin-2 Haldane-type states.

cond-mat.str-el↗

arXiv2015

Influence of intermolecular interactions on magnetic observables

Very often it is an implied paradigm of molecular magnetism that magnetic molecules in a crystal interact so weakly that measurements of dc magnetic observables reflect ensemble properties of single molecules. But the number of cases where the assumption of virtually non-interacting molecules does not hold grows steadily. A deviation from the non-interacting case can especially clearly be seen in clusters with antiferromagnetic couplings, where steps of the low-temperature magnetization curve are smeared out with increasing intermolecular interaction. In this investigation we demonstrate with examples in one-, two, and three space dimensions how intermolecular interactions influence typical magnetic observables such as magnetization, susceptibility and specific heat.

cond-mat.str-el↗