arXiv subjects

J. Schnack

Publications and source records attributed to J. Schnack.

At least 91 records · Page 5Linked to original sources

arXiv2005

Frustration effects in magnetic molecules

By means of exact diagonalization we study the ground-state and the low-temperature physics of the Heisenberg antiferromagnet on the cuboctahedron and the icosidodecahedron. Both are frustrated magnetic polytopes and correspond to the arrangement of magnetic atoms in the magnetic molecules Cu12La8 and Mo72Fe30. The interplay of strong quantum fluctuations and frustration influences the ground state spin correlations drastically and leads to an interesting magnetization process at low temperatures. Furthermore the frustration yields low-lying non-magnetic excitations resulting in an extra low-temperature peak in the specific heat.

cond-mat.str-el↗

arXiv2004

Competing Spin Phases in Geometrically Frustrated Magnetic Molecules

We have found a class of zero-dimensional geometrically frustrated Heisenberg spin systems exhibiting anomalous behavior in an external magnetic field B similar to that occuring in geometrically frustrated planar antiferromagnetic lattices. Our calculations for both the classical and quantum isotropic Heisenberg models show the emergence of a pronounced minimum in the differential susceptibility dM/dB at B_sat/3 as the temperature T is raised from 0K for structures based on corner-sharing triangles, specifically the octahedron, cuboctahedron, and icosidodecahedron. Low temperature measurements of magnetization M versus B for the giant Keplerate magnetic molecule Mo72Fe30 (Fe(3+) ions with spin s=5/2 on the 30 vertices of an icosidodecahedron) are consistent with our calculational results. The minimum in dM/dB is due to the fact that for low temperatures when B is approx. B_sat/3 there exist two competing families of spin configurations of which one behaves magnetically 'stiff' leading to a reduction of the susceptibility.

cond-mat.mtrl-sci↗

arXiv2004

Magnetic characterization of the frustrated three-leg ladder compound [(CuCl2tachH)3Cl]Cl2

We report the magnetic features of a new one-dimensional stack of antiferromagnetically coupled equilateral copper(II) triangles. High-field magnetization measurements show that the interaction between the copper triangles is of the same order of magnitude as the intra-triangle exchange although only coupled via hydrogen bonds. The infinite chain turns out to be an interesting example of a frustrated cylindrical three-leg ladder with competing intra- and inter-triangle interactions. We demonstrate that the ground state is a spin singlet which is gaped from the triplet excitation.

cond-mat.mtrl-sci↗

arXiv2004

Exact diagonalization studies of doped Heisenberg spin rings

Motivated by magnetization studies of the "telephon number compound" Sr_14Cu_24O_41 we investigate doped Heisenberg spin rings by means of complete numerical diagonalization of a Heisenberg Hamiltonian that depends parametrically on hole positions. A comparison with experimental magnetization data reveals rather accurate information about the screened electrostatic interaction between the charged holes on the ring which appears to be astonishingly strong.

cond-mat.str-el↗

arXiv2004

Exchange interactions and magnetic anisotropy in the "Ni_4" magnetic molecule

Magnetic properties of a tetrahedral "Ni_4" molecule are discussed in terms of the Heisenberg model, with magnetic anisotropy terms included, and on the basis of first-principle calculations within the density functional theory. It is shown that the isotropic Heisenberg model does not provide an adequate description of magnetization at low temperatures; an inclusion of single-site anisotropy terms does not help to improve the situation either. We suppose that the magnetostriction of the molecule and hence the dependence of interatomic coupling parameters on the magnetization might be important for an adequate description of magnetic properties. The first-principle calculations confirm the system's general preference for antiferromagnetic coupling, as well as the failure of the isotropic Heisenberg model. A conjugated-gradient search for the relaxed structure of the "Ni_4" molecule in ferromagnetic and antiferromagnetic configurations did not show any clear tendency to diversification of interatomic distances. These calculations however have not yet included the spin-orbit coupling, which can be essential for analyzing the effects of magnetostriction.

cond-mat.mtrl-sci↗

arXiv2003

Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices

For a class of frustrated spin lattices including e.g. the 1D sawtooth chain, the 2D kagomé and checkerboard, as well as the 3D pyrochlore lattices we construct exact product eigenstates consisting of several independent, localized one-magnon states in a ferromagnetic background. Important geometrical elements of the relevant lattices are triangles being attached to polygons or lines. Then the magnons can be trapped on these polygons/lines. If the concentration of localized magnons is small they can be distributed randomly over the lattice. Increasing the number of localized magnons their distribution over the lattice becomes more and more regular and finally the magnons condensate in a crystal-like state. The physical relevance of these eigenstates emerges in high magnetic fields where they become groundstates of the system. As a result a macroscopic magnetization jump appears in the zero-temperature magnetization curve just below the saturation field. The height of the jump decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

cond-mat.str-el↗

arXiv2003

Improved upper and lower energy bounds for antiferromagnetic Heisenberg spin systems

Large spin systems as given by magnetic macromolecules or two-dimensional spin arrays rule out an exact diagonalization of the Hamiltonian. Nevertheless, it is possible to derive upper and lower bounds of the minimal energies, i.e. the smallest energies for a given total spin S. The energy bounds are derived under additional assumptions on the topology of the coupling between the spins. The upper bound follows from "n-cyclicity", which roughly means that the graph of interactions can be wrapped round a ring with n vertices. The lower bound improves earlier results and follows from "n-homogeneity", i.e. from the assumption that the set of spins can be decomposed into n subsets where the interactions inside and between spins of different subsets fulfill certain homogeneity conditions. Many Heisenberg spin systems comply with both concepts such that both bounds are available. By investigating small systems which can be numerically diagonalized we find that the upper bounds are considerably closer to the true minimal energies than the lower ones.

cond-mat.stat-mech↗

arXiv2003

Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings

We suggest a general rule for the shift quantum numbers k of the relative ground states of antiferromagnetic Heisenberg spin rings. This rule generalizes well-known results of Marshall, Peierls, Lieb, Schultz, and Mattis for even rings. Our rule is confirmed by numerical investigations and rigorous proofs for special cases, including systems with a Haldane gap. Implications for the total spin quantum number S of relative ground states are discussed as well as generalizations to the XXZ model.

cond-mat.stat-mech↗

arXiv2003

Nose-Hoover sampling of quantum entangled distribution functions

While thermostated time evolutions stand on firm grounds and are widely used in classical molecular dynamics (MD) simulations, similar methods for quantum MD schemes are still lacking. In the special case of a quantum particle in a harmonic potential, it has been shown that the framework of coherent states permits to set up equations of motion for an isothermal quantum dynamics. In the present article, these results are generalized to indistinguishable quantum particles. We investigate the consequences of the (anti-)symmetry of the many-particle wavefunction which leads to quantum entangled distribution functions. The resulting isothermal equations of motion for bosons and fermions contain new terms which cause Bose-attraction and Pauli-blocking. Questions of ergodicity are discussed for different coupling schemes.

cond-mat.stat-mech↗

arXiv2002

Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices

For a class of frustrated spin lattices including the kagome lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the kagome lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

cond-mat.str-el↗

arXiv2001

Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann

O. Waldmann has shown that some spin systems, which fulfill the condition of a weakly homogeneous coupling matrix, have a spectrum whose minimal or maximal energies are rather poorly approximated by a quadratic dependence on the total spin quantum number. We comment on this observation and provide the new argument that, under certain conditions, the approximating parabolas appear as natural bounds of the spectrum generated by spin coherent states.

cond-mat.stat-mech↗

arXiv2001

Quantum rotational band model for the Heisenberg molecular magnet Mo72Fe30

We derive the low temperature properties of the molecular magnet Mo72Fe30, where 30 Fe(3+) paramagnetic ions occupy the sites of an icosidodecahedron and interact via isotropic nearest-neighbour antiferromagnetic Heisenberg exchange. The key idea of our model (J.S. & M.L.) is that the low-lying excitations form a sequence of rotational bands, i.e., for each such band the excitation energies depend quadratically on the total spin quantum number. For temperatures below 50 mK we predict that the magnetisation is described by a staircase with 75 equidistant steps as the magnetic field is increased up to a critical value and saturated for higher fields. For higher temperatures thermal broadening effects wash out the staircase and yield a linear ramp below the critical field, and this has been confirmed by our measurements (R.M.). We demonstrate that the lowest two rotational bands are separated by an energy gap of 0.7 meV, and this could be tested by EPR and inelastic neutron scattering measurements. We also predict the occurrence of resonances at temperatures below 0.1 K in the proton NMR spin-lattice relaxation rate associated with level crossings. As rotational bands characterize the spectra of many magnetic molecules our method opens a new road towards a description of their low-temperature behaviour which is not otherwise accessible.

cond-mat.mtrl-sci↗

arXiv2001

Independent magnon states on magnetic polytopes

For many spin systems with constant isotropic antiferromagnetic next-neighbour Heisenberg coupling the minimal energies E_{min}(S) form a rotational band, i.e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Lande interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase.

cond-mat.mtrl-sci↗

arXiv2001

Heisenberg exchange parameters of molecular magnets from the high-temperature susceptibility expansion

We provide exact analytical expressions for the magnetic susceptibility function in the high temperature expansion for finite Heisenberg spin systems with an arbitrary coupling matrix, arbitrary single-spin quantum number, and arbitrary number of spins. The results can be used to determine unknown exchange parameters from zero-field magnetic susceptibility measurements without diagonalizing the system Hamiltonian. We demonstrate the possibility of reconstructing the exchange parameters from simulated data for two specific model systems. We examine the accuracy and stability of the proposed method.

cond-mat.stat-mech↗

arXiv2001

Partition functions and symmetric polynomials

We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been considered are essentially of combinatorical origin and known for a long time as theorems on symmetric polynomials. For example, a recurrence relation for partition functions appearing in the textbook of P. Landsberg is nothing else but Newton's identity in disguised form. Conversely, a certain theorem on symmetric polynomials translates into a new and unexpected relation between fermionic and bosonic partition functions, which can be used to express the former by means of the latter and vice versa.

cond-mat.stat-mech↗

arXiv2001

Nose-Hoover dynamics for coherent states

The popular method of Nose and Hoover to create canonically distributed positions and momenta in classical molecular dynamics simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum harmonic oscillator, the equations of motion in terms of coherent states can easily be modified in an analogous manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble. Possible applications to more complex systems, especially interacting Fermion systems, are proposed.

cond-mat.stat-mech↗

arXiv2001

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.

cond-mat.stat-mech↗

arXiv2000

Rotational modes in molecular magnets with antiferromagnetic Heisenberg exchange

In an effort to understand the low temperature behavior of recently synthesized molecular magnets we present numerical evidence for the existence of a rotational band in systems of quantum spins interacting with nearest-neighbor antiferromagnetic Heisenberg exchange. While this result has previously been noted for ring arrays with an even number of spin sites, we find that it also applies for rings with an odd number of sites as well as for all of the polytope configurations we have investigated (tetrahedron, cube, octahedron, icosahedron, triangular prism, and axially truncated icosahedron). It is demonstrated how the rotational band levels can in many cases be accurately predicted using the underlying sublattice structure of the spin array. We illustrate how the characteristics of the rotational band can provide valuable estimates for the low temperature magnetic susceptibility.

cond-mat.mtrl-sci↗