arXiv subjects

Marshall Luban

Publications and source records attributed to Marshall Luban.

At least 19 recordsLinked to original sources

arXiv2014

Dynamics and thermodynamics of a pair of interacting magnetic dipoles

We consider the dynamics and thermodynamics of a pair of magnetic dipoles interacting via their magnetic fields. We consider only the "spin" degrees of freedom; the dipoles are fixed in space. With this restriction it is possible to provide the general solution of the equations of motion in analytical form. Thermodynamic quantities, such as the specific heat and the zero field susceptibility are calculated by combining low temperature asymptotic series and a complete high temperature expansion. The thermal expectation value of the autocorrelation function is determined for the low temperature regime including terms linear in $T$. Furthermore, we compare our analytical results with numerical calculations based on Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2011

Determination of exchange energies in the sawtooth spin ring {Mo75V20} by ESR

The magnetism of the polyoxometalate cluster {Mo75V20}, containing a sawtooth ring of 10 corner-sharing triangles located on the equator of the barrel-shaped molecule, has remained debatable since it is masked by contributions from impurities as well as temperature-independent paramagnetism. In this article we demonstrate the usefulness of ESR measurements since the temperature dependence of the ESR intensity can discriminate between impurity and molecular contributions. We determine the exchange parameters and therefore also the low-lying spectrum of {Mo75V20}, especially the low-lying singlet states which so far have been probed solely by specific heat measurements.

cond-mat.str-el↗

arXiv2009

Theory of severe slowdown in the relaxation of rings and clusters with antiferromagnetic interactions

We show that in the severe slowing down temperature regime the relaxation of antiferromagnetic rings and similar magnetic nanoclusters is governed by the quasi-continuum portion of their quadrupolar fluctuation spectrum and not by the lowest excitation lines. This is at the heart of the intriguing near-universal power-law temperature dependence of the electronic correlation frequency $ω_c$ with an exponent close to 4. The onset of this behavior is defined by an energy scale which is fixed by the lowest spin gap $Δ_0$. This explains why experimental curves of $ω_c$ for different cluster sizes and spins nearly coincide when $T$ is rescaled by $Δ_0$.

cond-mat.other↗

arXiv2008

Multiple nearest-neighbor exchange model for the frustrated magnetic molecules Mo72Fe30 and Mo72Cr30

Our measurements of the differential susceptibility dM/dH of the frustrated magnetic molecules Mo72Fe30 and Mo72Cr30 reveal a pronounced dependence on magnetic field (H) and temperature (T) in the low H - low T regime, contrary to the predictions of existing models. Excellent agreement with experiment is achieved upon formulating a nearest-neighbor classical Heisenberg model where the 60 nearest-neighbor exchange interactions in each molecule, rather than being identical as has been assumed heretofore, are described by a two-parameter probability distribution of values of the exchange constant. We suggest that the probability distribution provides a convenient phenomenological platform for summarizing the combined effects of multiple microscopic mechanisms that disrupt the idealized picture of a Heisenberg model based on a single value of the nearest-neighbor exchange constant.

physics.atm-clus↗

arXiv2008

Modulated spin waves and robust quasi-solitons in classical Heisenberg rings

We investigate the dynamical behavior of finite rings of classical spin vectors interacting via nearest-neighbor isotropic exchange in an external magnetic field. Our approach is to utilize the solutions of a continuum version of the discrete spin equations of motion (EOM) which we derive by assuming continuous modulations of spin wave solutions of the EOM for discrete spins. This continuous EOM reduces to the Landau-Lifshitz equation in a particular limiting regime. The usefulness of the continuum EOM is demonstrated by the fact that the time-evolved numerical solutions of the discrete spin EOM closely track the corresponding time-evolved solutions of the continuum equation. Of special interest, our continuum EOM possesses soliton solutions, and we find that these characteristics are also exhibited by the corresponding solutions of the discrete EOM. The robustness of solitons is demonstrated by considering cases where initial states are truncated versions of soliton states and by numerical simulations of the discrete EOM equations when the spins are coupled to a heat bath at finite temperatures.

cond-mat.other↗

arXiv2005

Low temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

Accurate results are obtained for the low temperature magnetization versus magnetic field of Heisenberg spin rings consisting of an even number N of intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor antiferromagnetic (AF) exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular the values of the level-crossing fields, provides accurate results for the lowest energy eigenvalue E(N,S,s) for each value of the total spin quantum number S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For s <= 5/2, data are presented for all even N <= 20, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for s > 1 the dependence of E(N,S,s) on s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 <= s <= 7/2. Considering ring sizes in the interval 8 <= N <= 50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1/N^a, where a = 0.76 for s = 3/2 and a = 0.84 for s = 5/2. Finally, we demonstrate the usefulness of our present results for E(N,S,s) by examining the Fe12 ring-type magnetic molecule, leading to a new, more accurate estimate of the exchange constant for this system than has been obtained heretofore.

cond-mat.stat-mech↗

arXiv2005

Master Equations for pulsed magnetic fields: Application to magnetic molecules

We extend spin-lattice relaxation theory to incorporate the use of pulsed magnetic fields for probing the hysteresis effects and magnetization steps and plateaus exhibited, at low temperatures, by the dynamical magnetization of magnetic molecules. The main assumption made is that the lattice degrees of freedom equilibrate in times much shorter than both the experimental time scale (determined by the sweep rate) and the typical spin-lattice relaxation time. We first consider the isotropic case (a magnetic molecule with a ground state of spin $S$ well separated from the excited levels and also the general isotropic Heisenberg Hamiltonian where all energy levels are relevant) and then we include small off-diagonal terms in the spin Hamiltonian to take into account the Landau-Zener-Stückelberg (LZS) effect. In the first case, and for an $S=1/2$ magnetic molecule we arrive at the generalized Bloch equation recently used for the magnetic molecule \{V$_6$\} in Phys. Rev. Lett. 94, 147204 (2005). An analogous equation is derived for the magnetization, at low temperatures, of antiferromagnetic ring systems. The LZS effect is discussed for magnetic molecules with a low spin ground state, for which we arrive at a very convenient set of equations that take into account the combined effects of LZS and thermal transitions. In particular, these equations explain the deviation from exact magnetization reversal at $B\approx 0$ observed in \{V$_6$\}. They also account for the small magnetization plateaus (``magnetic Foehn effect''), following the LZS steps, that have been observed in several magnetic molecules. Finally, we discuss the role of the Phonon Bottleneck effect at low temperatures and specifically we indicate how this can give rise to a pronounced Foehn effect.

cond-mat.mes-hall↗

arXiv2005

Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron

The observation of hysteresis effects in single molecule magnets like Mn$_{12}$-acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In this Letter we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically, where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearest-neighbor Heisenberg interaction giving rise to geometric frustration. At T=0 this system undergoes a first order metamagnetic phase transition at a critical field $\Bcrit$ between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution.

cond-mat.mtrl-sci↗

arXiv2004

Analytic solution of the microcausality problem in Discretized Light Cone Quantization

It is shown that that violation of causality in two-dimensional light-front field theories quantized in a finite ``volume'' $L$ with periodic or antiperiodic boundary conditions is marginal and vanishes smoothly in the continuum limit. For this purpose, we derive an exact integral representation for the complete infinite series expansion of the two-point functions of a free massive scalar and fermi field for an arbitrary finite value of $L$ and show that in the $L \to \infty$ limit we retrieve the correct continuum results.

hep-th↗

arXiv2004

An Exact Solution to the Time-dependent Schrodinger Equation for a Model One-dimensional Potential

Analytical solutions to the time-dependent Shrödinger equation in one dimension are developed for time-independent potentials, one consisting of an infinite wall and a repulsive delta function. An exact solution is obtained by means of a convolution of time-independent solutions spanning the given Hilbert space with appropriately chosen spectral functions. Square-integrability and the boundary conditions are satisfied. The probability for the particle to be found inside the potential well is calculated and shown to exhibit non-exponential decay decreasing at large times as $t^{-3}$. The result is generalized for all square-integrable solutions to this problem.

quant-ph↗

arXiv2002

Classical ground states of symmetrical Heisenberg spin systems

We investigate the ground states of classical Heisenberg spin systems which have point group symmetry. Examples are the regular polygons (spin rings) and the seven quasi-regular polyhedra including the five Platonic solids. For these examples, ground states with special properties, e.g. coplanarity or symmetry, can be completely enumerated using group-theoretical methods. For systems having coplanar (anti-) ground states with vanishing total spin we also calculate the smallest and largest energies of all states having a given total spin S. We find that these extremal energies depend quadratically on S and prove that, under certain assumptions, this happens only for systems with coplanar S=0 ground states. For general systems the corresponding parabolas represent lower and upper bounds for the energy values. This provides strong support and clarifies the conditions for the so-called rotational band structure hypothesis which has been numerically established for many quantum spin systems.

cond-mat↗

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

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

Zero-field Time Correlation Functions of Four Classical Heisenberg Spins on a Ring

A model relevant for the study of certain molecular magnets is the ring of N=4 classical spins with equal near-neighbor isotropic Heisenberg exchange interactions. Assuming classical Heisenberg spin dynamics, we solve explicitly for the time evolution of each of the spins. Exact triple integral representations are derived for the auto, near-neighbor, and next-nearest-neighbor time correlation functions for any temperature. At infinite temperature, the correlation functions are reduced to quadrature. We then evaluate the Fourier transforms of these functions in closed form, which are double integrals. At low temperatures, the Fourier transform functions explicitly demonstrate the presence of magnons. Our exact results for the infinite temperature correlation functions in the long-time asymptotic limit differ qualitatively from those obtained assuming diffusive spin dynamics. Whether such explicitly non-hydrodynamic behavior would be maintained for large-N rings is discussed.

cond-mat.mes-hall↗

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

Continuous families of isospectral Heisenberg spin systems and the limits of inference from measurements

We investigate classes of quantum Heisenberg spin systems which have different coupling constants but the same energy spectrum and hence the same thermodynamical properties. To this end we define various types of isospectrality and establish conditions for their occurence. The triangle and the tetrahedron whose vertices are occupied by spins 1/2 are investigated in some detail. The problem is also of practical interest since isospectrality presents an obstacle to the experimental determination of the coupling constants of small interacting spin systems such as magnetic molecules.

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↗

arXiv1999

Transition from quantum to classical Heisenberg trimers: Thermodynamics and time correlation functions

We focus on the transition from quantum to classical behavior in thermodynamic functions and time correlation functions of a system consisting of three identical quantum spins s that interact via isotropic Heisenberg exchange. The partition function and the zero-field magnetic susceptibility are readily shown to adopt their classical forms with increasing s. The behavior of the spin autocorrelation function (ACF) is more subtle. Unlike the classical Heisenberg trimer where the ACF approaches a unique non-zero limit for long times, for the quantum trimer the ACF is periodic in time. We present exact values of the time average over one period of the quantum trimer for s less or equal 7 and for infinite temperature. These averages differ from the long-time limit, (9/40)\ln3+(7/30), of the corresponding classical trimer by terms of order 1/(s*s). However, upon applying the Levin u-sequence acceleration method to our quantum results we can reproduce the classical value to six significant figures.

cond-mat.stat-mech↗