arXiv subjects

D. A. Garanin

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

At least 109 records · Page 6Linked to original sources

arXiv2000

Cumulant expansion for systems with large spins

A method is proposed for obtaining a systematic expansion of thermodynamic functions of spin systems with large spin S in powers of 1/S. It uses the cumulant technique and a coherent-state representation of the partition function Z. The expansion of Z in terms of cumulants yields an effective classical Hamiltonian with temperature-dependent quantum corrections. For the Heisenberg quantum Hamiltonian, they have a non-Heisenberg form. The effective Hamiltonian can be solved by methods familiar for classical systems.

cond-mat.stat-mech↗

arXiv2000

The new integral relaxation time for thermal activation of spins

The integral relaxation time for the difference of populations of the two potential wells for double-well classical spin systems is introduced. For the uniaxial symmetry, it is given by a quadrature. Unlike the previously introduced integral relaxation time for the magnetization, the former at low temperatures describes the rate of crossing the barrier under all conditions, including the strongly biased case. In the high-barrier case, the new integral relaxation time approaches the inverse of the lowest eigenvalue of the Fokker-Planck equation. It can be more conveniently found by numerical methods than the latter.

cond-mat.stat-mech↗

arXiv1999

Tunneling of a large spin via hyperfine interactions

We consider a large spin \bf S in the magnetic field parallel to the uniaxial crystal field, interacting with N >> 1 nuclear spins \bf I_i via Hamiltonian \cal H = -DS_z^2 - H_zS_z+ A{\bf S}\cdot \sum_{i=1}^N {\bf I}_i with A << D, at temperature T. Tunneling splittings and the selection rules for the resonant values of H_z are obtained perturbatively. The quantum coherence exists at T << ASI while at T >= ASI the coherence is destroyed and the relaxation of \bf S is described by a stretched dependence which can be close to log t under certain conditions. Relevance to Mn-12 acetate is discussed.

cond-mat.stat-mech↗

arXiv1999

Finite-size versus Surface effects in nanoparticles

We study the finite-size and surface effects on the thermal and spatial behaviors of the magnetisation of a small magnetic particle. We consider two systems: 1) A box-shaped isotropic particle of simple cubic structure with either periodic or free boundary conditions. This case is treated analytically using the isotropic model of D-component spin vectors in the limit $D\to \infty$, including the magnetic field. 2) A more realistic particle ($γ$-Fe$_{2}$O$_{3}$) of ellipsoidal (or spherical) shape with open boundaries. The magnetic state in this particle is described by the anisotropic classical Dirac-Heisenberg model including exchange and dipolar interactions, and bulk and surface anisotropy. This case is dealt with by the classical Monte Carlo technique. It is shown that in both systems finite-size effects yield a positive contribution to the magnetisation while surface effects render a larger and negative contribution, leading to a net decrease of the magnetisation of the small particle with respect to the bulk system. In the system 2) the difference between the two contributions is enhanced by surface anisotropy. The latter also leads to non saturation of the magnetisation at low temperatures, showing that the magnetic order in the core of the particle is perturbed by the magnetic disorder on the surface. This is confirmed by the profile of the magnetisation.

cond-mat.mtrl-sci↗

arXiv1999

Integral Relaxation Time of Single-Domain Ferromagnetic Particles

The integral relaxation time τ_{int} of thermoactivating noninteracting single-domain ferromagnetic particles is calculated analytically in the geometry with a magnetic field H applied parallel to the easy axis. It is shown that the drastic deviation of τ_{int}^{-1} from the lowest eigenvalue of the Fokker-Planck equation Λ_1 at low temperatures, starting from some critical value of H, is the consequence of the depletion of the upper potential well. In these conditions the integral relaxation time consists of two competing contributions corresponding to the overbarrier and intrawell relaxation processes.

cond-mat.stat-mech↗

arXiv1999

Uniform susceptibility of classical antiferromagnets in one and two dimensions in a magnetic field

We simulated the field-dependent magnetization m(H,T) and the uniform susceptibility χ(H,T) of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of χ(H,T) at small T,H: \lim_{T \to 0}\lim_{H \to 0} χ(H,T)=1/(2J_0)(1-1/D) and \lim_{H \to 0}\lim_{T \to 0} χ(H,T)=1/(2J_0), where D=3 is the number of spin components, J_0=zJ, and z is the number of nearest neighbors. A good agreement is achieved in a wide range of temperatures T and magnetic fields H with the first-order 1/D expansion results [D. A. Garanin, J. Stat. Phys. 83, 907 (1996)]

cond-mat.stat-mech↗

arXiv1999

Quantum-Classical Escape-Rate Transition of a Biaxial Spin System with a Longitudinal Field: a Perturbative Approach

The quantum-classical transition of the escape rate of the spin model \cal H= -DS_z^2 - H_zS_z + B S_x^2 is investigated by a perturbative approach with respect to B [D. A. Garanin, J. Phys A {\bf 24}, L61 (1991)]. The transition is first order for B<B_c(H_z), the boundary line going to zero as B_c/D ~ 1 - H_z/(2SD) in the strongly biased limit. The range of the first-order transition is thus larger than for the model \cal H = -DS_z^2 - H_zS_z - H_x S_x studied earlier, where in the strongly biased case H_{xc}/(2SD) ~ [1-H_z/(2SD)]^{3/2}. The temperature of the quantum-classical transition, T_0, behaves linearly in the strongly biased case for both models: T_0 ~ 2SD - H_z.

cond-mat.stat-mech↗

arXiv1999

Classical Spin Liquid: Exact Solution for the Infinite-Component Antiferromagnetic Model on the Kagomé Lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the kagomé lattice are studied for the exactly solvable infinite-component spin-vector model, D \to \infty. In this limit, the critical coupling of fluctuations dies out and the critical behavior simplifies, but the effect of would be Goldstone modes preventing ordering at any nonzero temperature is properly accounted for. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r < ξ_c \propto \exp(T^*/T), correlations in the kagomé-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as <{\bf S}_0 {\bf S}_r> \propto 1/r^2 in the range a_0 << r << ξ_c \propto T^{-1/2}, where a_0 is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are in fairly good quantitative agreement with the MC simulations for the classical Heisenberg model, D=3. The neutron scattering cross section has its maxima beyond the first Brillouin zone; at T\to 0 it becomes nonanalytic but does not diverge at any q.

cond-mat.stat-mech↗

arXiv1998

Fokker-Planck and Landau-Lifshitz-Bloch Equations for Classical Ferromagnets

A macroscopic equation of motion for the magnetization of a ferromagnet at elevated temperatures should contain both transverse and longitudinal relaxation terms and interpolate between Landau-Lifshitz equation at low temperatures and the Bloch equation at high temperatures. It is shown that for the classical model where spin-bath interactions are described by stochastic Langevin fields and spin-spin interactions are treated within the mean-field approximation (MFA), such a ``Landau-Lifshitz-Bloch'' (LLB) equation can be derived exactly from the Fokker-Planck equation, if the external conditions change slowly enough. For weakly anisotropic ferromagnets within the MFA the LLB equation can be written in a macroscopic form based on the free-energy functional interpolating between the Landau free energy near T_C and the ``micromagnetic'' free energy, which neglects changes of the magnetization magnitude |{\bf M}|, at low temperatures.

cond-mat.stat-mech↗

arXiv1998

Ordering in magnetic films with surface anisotropy

Effects of the surface exchange anisotropy on ordering of ferromagnetic films are studied for the exactly solvable classical spin-vector model with D \to \infty components. For small surface anisotropy η'_s << 1 (defined relative to the exchange interaction), the shift of T_c in a film consisting of N >> 1 layers behaves as T_c^{\rm bulk} - T_c(N) ~ (1/N)\ln(1/η'_s) in three dimensions. The finite-size-scaling limit T_c^{\rm bulk} - T_c(N) \propto 1/(η'^{1/2}N^2), which is realized for the model with a bulk anisotropy η' << 1 in the range Nη'^{1/2} >~ 1, never appears for the model with the pure surface anisotropy. Here for N\exp(-1/η'_s) >~ 1 in three dimensions, film orders at a temperature above T_c^{\rm bulk} (the surface phase transition). In the semi-infinite geometry, the surface phase transition occurs for whatever small values of η'_s (i.e., the special phase transition corresponds to T_c^{\rm bulk}) in dimensions three and lower.

cond-mat.stat-mech↗

arXiv1998

Curie Temperature of Anisotropic Ferromagnetic Films

Dimensional crossover of ordering in ferromagnetic films with both periodic and free boundary conditions is studied for the exactly solvable uniaxial model of classical D-component spin vectors in the limit D \to \infty. Analytical and numerical solution of the exact equations describing this model shows that for lattice dimensionalities d>4, finite-size corrections to the bulk values of T_c are characterized by the mean-field exponents and anisotropy-dependent amplitudes. For d =< 4, the mean-field behavior is only realized in the region κ_c N >> 1, where κ_c is the dimensionlesss inverse transverse (with respect to the easy axis) bulk correlation length at T_c and N is the number of layers in the film. In the region κ_c N << 1 and the dimensionality range 3 < d =< 4, finite-size corrections are described by the universality class of the isotropic D=\infty model. For d =< 3, magnetic ordering vanishes in the isotropic limit, κ_c \to 0, since the film behaves as an object of dimensionality d'=d-1 =< 2 and long-wavelength fluctuations destroy the order. Here the suppression of T_c of a film can be substantial, depending on the competition between the weakening anisotropy and the increasing film thickness. For thick films, T_c becomes small only for very small anisotropy.

cond-mat.stat-mech↗

arXiv1998

Quantum-Classical Transition of the Escape Rate of a Uniaxial Spin System in an Arbitrarily Directed Field

The escape rate Γof the large-spin model described by the Hamiltonian H = -DS_z^2 - H_zS_z - H_xS_x is investigated with the help of the mapping onto a particle moving in a double-well potential U(x). The transition-state method yields $Γ$ in the moderate-damping case as a Boltzmann average of the quantum transition probabilities. We have shown that the transition from the classical to quantum regimes with lowering temperature is of the first order (dΓ/dT discontinuous at the transition temperature T_0) for h_x below the phase boundary line h_x=h_{xc}(h_z), where h_{x,z}\equiv H_{x,z}/(2SD), and of the second order above this line. In the unbiased case (H_z=0) the result is h_{xc}(0)=1/4, i.e., one fourth of the metastability boundary h_{xm}=1, at which the barrier disappears. In the strongly biased limit δ\equiv 1-h_z << 1, one has h_{xc} \cong (2/3)^{3/4}(\sqrt{3}-\sqrt{2})δ^{3/2}\cong 0.2345 δ^{3/2}, which is about one half of the boundary value h_{xm} \cong (2δ/3)^{3/2} \cong 0.5443 δ^{3/2}.The latter case is relevant for experiments on small magnetic particles, where the barrier should be lowered to achieve measurable quantum escape rates.

cond-mat.stat-mech↗

arXiv1998

Semi-Infinite Anisotropic Spherical Model: Correlations at T >= T_c

The ordinary surface magnetic phase transition is studied for the exactly solvable anisotropic spherical model (ASM), which is the limit D \to \infty of the D-component uniaxially anisotropic classical vector model. The bulk limit of the ASM is similar to that of the spherical model, apart from the role of the anisotropy stabilizing ordering for low lattice dimensionalities, d =< 2, at finite temperatures. The correlation functions and the energy density profile in the semi-infinite ASM are calculated analytically and numerically for T >= T_c and 1 =< d =< \infty. Since the lattice dimensionalities d=1,2,3, and 4 are special, a continuous spatial dimensionality d'=d-1 has been introduced for dimensions parallel to the surface. However, preserving a discrete layer structure perpendicular to the surface avoids unphysical surface singularities and allows numerical solitions that reveal significant short-range features near the surface. The results obtained generalize the isotropic-criticality results for 2 < d < 4 of Bray and Moore [Phys. Rev. Lett. 38, 735 (1977); J. Phys. A: Math. Gen. 10, 1927 (1977)].

cond-mat.stat-mech↗

arXiv1998

Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is developed.The observed slow dynamics of the system is described by master equations for the populations of spin levels.The latter are obtained by the adiabatic elimination of fast degrees of freedom from the density matrix equation with the help of the perturbation theory developed earlier for the tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There exists a temperature range (thermally activated tunneling) where the escape rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias field due to tunneling at the top of the barrier. At lower temperatures this regime crosses over to the non-Arrhenius law (thermally assisted tunneling). The transition between the two regimes can be first or second order, depending on the transverse field, which can be tested in experiments. In both regimes the resonant maxima of the rate occur when spin levels in the two potential wells match at certain field values. In the thermally activated regime at low dissipation each resonance has a multitower self-similar structure with progressively narrowing peaks mounting on top of each other.

cond-mat.stat-mech↗

arXiv1998

Quantum Thermoactivation of Nanoscale Magnets

The integral relaxation time describing the thermoactivated escape of a uniaxial quantum spin system interacting with a boson bath is calculated analytically in the whole temperature range. For temperatures T much less than the barrier height ΔU, the level quantization near the top of the barrier and the strong frequency dependence of the one-boson transition probability can lead to the regularly spaced deep minima of the thermoactivation rate as a function of the magnetic field applied along the z axis.

cond-mat.stat-mech↗

arXiv1998

First- and Second-Order Transitions between Quantum and Classical Regimes for the Escape Rate of a Spin System

We have found a novel feature of the bistable large-spin model described by the Hamiltonian H = -DS_z^2 - H_xS_x.The crossover from thermal to quantum regime for the escape rate can be either first (H_x<SD/2) or second (SD/2<H_x<2SD) order, that is, sharp or smooth, depending on the strength of the transverse field. This prediction can be tested experimentally in molecular magnets like Mn_12Ac.

cond-mat.stat-mech↗

arXiv1998

Spherical Model for Anisotropic Ferromagnetic Films

The corrections to the Curie temperature T_c of a ferromagnetic film consisting of N layers are calculated for N \gg 1 for the model of D-component classical spin vectors in the limit D \to \infty, which is exactly soluble and close to the spherical model. The present approach accounts, however, for the magnetic anisotropy playing the crucial role in the crossover from 3 to 2 dimensions in magnetic films. In the spatially inhomogeneous case with free boundary conditions the D=\infty model is nonequivalent to the standard spherical one and always leads to the diminishing of T_c(N) relative to the bulk.

cond-mat.stat-mech↗

arXiv1998

Self-Consistent Gaussian Approximation for Classical Spin Systems: Thermodynamics

The self-consistent Gaussian approximation (SCGA) for classical spin systems described by a completely anisotropic D-component vector model is proposed, which takes into account fluctuations of the molecular field and thus is a next step beyond the molecular field approximation. The SCGA is sensitive to the lattice dimension and structure and to the form of spin interactions and yields rather accurate values of the field-dependent magnetization m(H,T) and other thermodynamic functions in the whole plane (H,T) excluding the vicinity of the critical point (0,T_c), where the SCGA breaks down, showing a first-order phase transition. The values of T_c themselves can be determined in the SCGA with an accuracy better than 1% for actual 3-dimensional structures. At low and high temperatures the SCGA recovers the leading terms of the spin-wave theory, the low- and high-temperature series expansions, respectively. The accuracy of the SCGA increases with the increase of the spin dimension D, and in the limit D \to \infty the exact solution for the spherical model is recovered.

cond-mat.stat-mech↗