arXiv subjects

D. A. Garanin

Publications and source records attributed to D. A. Garanin.

At least 37 records · Page 2Linked to original sources

arXiv2016

Ordered vs Disordered States of the Random-Field Model in Three Dimensions

We report numerical investigation of the glassy behavior of random-field exchange models in three dimensions. Correlation of energy with the magnetization for different numbers of spin components has been studied. There is a profound difference between the models with two and three spin components with respect to the stability of the magnetized state due to the different kinds of singularities: vortex loops and hedgehogs, respectively. Memory effects pertinent to such states have been investigated. Insight into the mechanism of the large-scale disordering is provided by numerically implementing the Imry-Ma argument in which the spins follow the random field averaged over correlated volumes. Thermal stability of the magnetized states is investigated by the Monte Carlo method.

cond-mat.stat-mech↗

arXiv2016

Thermal fluctuations of the Josephson current in a ring of superconducting grains

Thermal fluctuations of the Josephson current $I$ induced by the magnetic flux through a ring of $N$ superconducting grains are studied. When a half-fluxon is threading the ring, $I$ exhibits incoherent transitions between the two degenerate states due to thermal phase slips. We propose a new numerical method to deal with both equilibrium and dynamic properties of Josephson systems. Computed transition rate has the form $Γ= A(N)\exp[-B(N)/T]$, where $B(N)$ agrees with the analytical result derived for the energy barrier associated with phase slips. In the non-degenerate case (e.g., at a quarter-fluxon) the equilibrium value of $I$ decreases with $T$ due to harmonic excitations and then gets destroyed by phase slips.

cond-mat.supr-con↗

arXiv2016

Persistent current in a 2D Josephson junction array wrapped around a cylinder

We study persistent currents in a Josephson junction array wrapped around a cylinder. The $T=0$ quantum statistical mechanics of the array is equivalent to the statistical mechanics of a classical $xy$ spin system in 2+1 dimensions at the effective temperature $T^{*}=\sqrt{2JU}$, with $J$ being the Josephson energy of the junction and $U$ being the charging energy of the superconducting island. It is investigated analytically and numerically on lattices containing over one million sites. For weak disorder and $T^{*}\ll J$ the dependence of the persistent current on disorder and $T^{*}$ computed numerically agrees quantitatively with the analytical result derived within the spin-wave approximation. The high-$T^{*}$ and/or strong-disorder behavior is dominated by instantons corresponding to the vortex loops in 2+1 dimensions. The current becomes destroyed completely at the quantum phase transition into the Cooper-pair insulating phase.

cond-mat.supr-con↗

arXiv2015

Quantum decay of the persistent current in a Josephson junction ring

We study the persistent current in a ring consisting of N >> 1 Josephson junctions threaded by the magnetic flux. When the dynamics of the ring is dominated by the capacitances of the superconducting islands the system is equivalent to the xy spin system in 1+1 dimensions at the effective temperature T*=(2JU)^(1/2), with J being the Josephson energy of the junction and U being the charging energy of the superconducting island. The numerical problem is challenging due to the absence of thermodynamic limit and slow dynamics of the Kosterlitz-Thouless transition. It is investigated on lattices containing up to one million sites. At T << J the quantum phase slips are frozen. The low-T* dependence of the persistent current computed numerically agrees quantitatively with the analytical formula provided by the spin-wave approximation. The high- T* behavior depends strongly on the magnetic flux and on the number of superconducting islands N. Depending on the flux, the persistent current gets destroyed by the phase slips and/or by the superconductor-insulator transition on increasing T*.

cond-mat.supr-con↗

arXiv2015

Angular momentum in spin-phonon processes

Quantum theory of spin relaxation in the elastic environment is revised with account of the concept of a phonon spin recently introduced by Zhang and Niu (PRL 2014). Similar to the case of the electromagnetic field, the division of the angular momentum associated with elastic deformations into the orbital part and the part due to phonon spins proves to be useful for the analysis of the balance of the angular momentum. Such analysis sheds important light on microscopic processes leading to the Einstein - de Haas effect.

cond-mat.mes-hall↗

arXiv2014

Damping of a nanocantilever by paramagnetic spins

We compute damping of mechanical oscillations of a cantilever that contains flipping paramagnetic spins. This kind of damping is mandated by the dynamics of the total angular momentum, spin + mechanical. Rigorous expression for the damping rate is derived in terms of measurable parameters. The effect of spins on the quality factor of the cantilever can be significant in cantilevers of small length that have large concentration of paramagnetic spins of atomic and/or nuclear origin.

cond-mat.mes-hall↗

arXiv2013

Random Field XY Model in Three Dimensions

We study random-field xy spin model at T=0 numerically on lattices of up to 1000 x 1000 x 1000 spins with the accent on the weak random field. Our numerical method is physically equivalent to slow cooling in which the system is gradually losing the energy and relaxing to an energy minimum. The system shows glass properties, the resulting spin states depending strongly on the initial conditions. Random initial condition for the spins leads to the vortex glass (VG) state with short-range spin-spin correlations defined by the average distance between vortex lines. Collinear and some other vortex-free initial conditions result in the vortex-free ferromagnetic (F) states that have a lower energy. The energy difference between the F and VG states correlates with vorticity of the VG state. Correlation functions in the F states agree with the Larkin-Imry-Ma theory at short distances. Hysteresis curves for weak random field are dominated by topologically stable spin walls raptured by vortex loops. We find no relaxation paths from the F, VG, or any other states to the hypothetical vortex-free state with zero magnetization.

cond-mat.dis-nn↗

arXiv2013

Random Field XY Model in Three Dimensions: The Role of Vortices

We study vortex states in a 3d random-field XY model of up to one billion lattice spins. Starting with random spin orientations, the sample freezes into the vortex-glass state with a stretched-exponential decay of spin correlations, having short correlation length and a low susceptibility, compared to vortex-free states. In a field opposite to the initial magnetization, peculiar topological objects -- walls of spins still opposite to the field -- emerge along the hysteresis curve. On increasing the field strength, the walls develop cracks bounded by vortex loops. The loops then grow in size and eat the walls away. Applications to magnets and superconductors are discussed.

cond-mat.stat-mech↗

arXiv2013

Turbulent fronts of quantum detonation in molecular magnets

Dipolar-controlled quantum deflagration going over into quantum detonation in the elongated Mn_12 Ac molecular magnet in a strong transverse field has been considered within the full 3d model. It is shown that within the dipolar window around tunneling resonances the deflagration front is non-flat. With increasing bias, dipolar instability makes the front turbulent, while its speed reaches sonic values, that is a signature of detonation.

cond-mat.mes-hall↗

arXiv2012

Theory of deflagration and fronts of tunneling in molecular magnets

Decay of metastable states in molecular magnets (MM) leads to energy release that results in temperature increase that, in turn, positively affects the decay rate. This is the mechanism of recently discovered magnetic deflagration that is similar to regular chemical burning and can propagate in a form of burning fronts in long MM crystals. Near spin-tunneling resonances the decay rate is also affected by the dipolar field (self-consistent with the switching magnetization) that can block or unblock tunneling. There are non-thermal fronts of tunneling in which the magnetization adjusts in such a way that the system is on resonance within the front core, so that the tunneling front can propagate. In general, both dipolar field and temperature control fronts of quantum deflagration. The front speed can reach sonic values if a strong transverse field is applied to boost tunneling.

cond-mat.mes-hall↗

arXiv2012

Reversal of magnetization of a single-domain magnetic particle by the ac field of time-dependent frequency

We report numerical and analytical studies of the reversal of the magnetic moment of a single-domain magnetic particle by a circularly polarized ac field of time-dependent frequency. For the time-linear frequency sweep, the phase diagrams are computed that illustrate the dependence of the reversal on the frequency sweep rate v, the amplitude of the ac field h, the magnetic anisotropy field d, and the damping parameter alpha. It is shown that the most efficient magnetization reversal requires a non-linear time dependence of the frequency, omega(t), for which an exact analytical formula is derived with account of damping. The necessary condition of the reversal is h > alpha d. Implementation of a small-scale magnetization reversal is proposed in which a nanomagnet is electromagnetically coupled to two weak superconducting links controlled by the voltage. Dynamics of such a system is analyzed with account of the back effect of the magnet on the superconducting links.

cond-mat.mes-hall↗

arXiv2012

Collapse of Skyrmions in 2d Ferro- and Antiferromagnets

Collapse of a skyrmion due to the discreteness of a crystal lattice in isotropic two-dimensional ferro- and antiferromagnets has been studied analytically and by numerical solution of equations of motion for up to 2000 x 2000 classical spins on a square lattice coupled via Heisenberg exchange interaction. Excellent agreement between analytical and numerical results has been achieved. The lifetime of the skyrmion scales with its initial size, lambda_0, as(lambda_0/a)^5 in ferromagnets and as (lambda_0/a)^2.15 in antiferromagnets, with a being the lattice parameter. This makes antiferromagnetic skyrmions significantly shorter lived than ferromagnetic skyrmions.

cond-mat.str-el↗

arXiv2012

Quantum deflagration and supersonic fronts of tunneling in molecular magnets

Theory of magnetic deflagration taking into account dipolar-controlled spin tunneling has been applied to the realistic model of molecular magnet Mn_12 Ac. At small transverse field, the front speed v has tunneling maxima on the bias field B_z reflecting those of the molecular spin's relaxation rate calculated from the density-matrix equation. At high transverse field, spin tunneling directly out of the metastable ground state leads to front speeds that can exceed the speed of sound. Both for the weak and strong transverse field, the spatial profile of the deflagration front near tunneling resonances shows a front of tunneling that triggers a burning front behind it.

cond-mat.stat-mech↗

arXiv2012

Dipolar-controlled spin tunneling and relaxation in molecular magnets

Spin tunneling in molecular magnets controlled by dipole-dipole interactions (DDI) in the disordered state has been considered numerically on the basis of the microscopic model using the quantum mean-field approximation. In the actual case of a strong DDI spin coherence is completely lost and there is a slow relaxation of magnetization, described by t^{3/4} at short times. Fast precessing nuclear spins, included in the model microscopically, only moderately speed up the relaxation.

cond-mat.stat-mech↗

arXiv2011

Conservation of Angular Momentum in a Flux Qubit

Oscillations of superconducting current between clockwise and counterclockwise directions in a flux qubit do not conserve the angular momentum of the qubit. To compensate for this effect the solid containing the qubit must oscillate in unison with the current. This requires entanglement of quantum states of the qubit with quantum states of a macroscopic body. The question then arises whether slow decoherence of quantum oscillations of the current is consistent with fast decoherence of quantum states of a macroscopic solid. This problem is analyzed within an exactly solvable quantum model of a qubit embedded in an absolutely rigid solid and for the elastic model that conserves the total angular momentum. We show that while the quantum state of a flux qubit is, in general, a mixture of a large number of rotational states, slow decoherence is permitted if the system is macroscopically large. Practical implications of entanglement of qubit states with mechanical rotations are discussed.

cond-mat.supr-con↗

arXiv2011

Quantum Tunneling of the Magnetic Moment in a Free Particle

We study tunneling of the magnetic moment in a particle that has full rotational freedom. Exact energy levels are obtained and the ground-state magnetic moment is computed for a symmetric rotor. The effect of the mechanical freedom on spin tunneling manifests itself in a strong dependence of the magnetic moment on the moments of inertia of the rotor. Energy of the particle exhibits quantum phase transitions between states with different values of the magnetic moment. Particles of various shapes are investigated and quantum phase diagram is obtained.

cond-mat.mes-hall↗

arXiv2011

Quantum entanglement of a tunneling spin with mechanical modes of a torsional resonator

We solve Schrödinger equation describing a tunneling macrospin coupled to a torsional oscillator. Energy spectrum is studied for various quantum regimes. Magnetic susceptibility and noise spectrum are computed. We show that entanglement of the spin with mechanical modes of a subnanometer oscillator results in the decoherence of spin tunneling. For larger oscillators the presence of a tunneling spin can be detected through splitting of the mechanical mode at the resonance. Our results apply to experiments with magnetic molecules coupled to nanoresonators.

cond-mat.mes-hall↗

arXiv2010

Dipolar ordering in crystals of Mn12 Ac

Ordering in realistic elongated box-shape crystals of the molecular magnet Mn_12 Ac is investigated with the site-resolved mean-field approximation that does not assume a uniform ordering. It is shown that ferromagnetic ordering should not occur in crystals with the aspect ratio up to 12. Instead, for the aspect ratio about 6, the inner and outer regions of the crystal order in different directions, uniformly along its length. Finding ordering temperature by extrapolating the inverse susceptibility curve does not provide a correct T_C.

cond-mat.stat-mech↗