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

Abstract

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 $\Gamma$ 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.

17 PR pages, 16 figures; published version

References in corpus (5)

• Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others
• First- and Second-Order Transitions between Quantum and Classical Regimes for the Escape Rate of a Spin System
• Decay of Metastable States: Sharp Transition from Quantum to Classical Behavior
• Quantum Thermoactivation of Nanoscale Magnets
• Skyrme Sphalerons of an O(3)-sigma Model and the Calculation of Transition Rates at Finite Temperature

Cited by in corpus (43)

• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Quantum metrology in Lipkin-Meshkov-Glick critical systems
• Crossover between Thermally Assisted and Pure Quantum Tunneling in Molecular Magnet Mn12-Acetate
• Resonant Tunneling in Truly Axial Symmetry Mn12 Single-Molecule Magnets: Sharp Crossover between Thermally Assisted and Pure Quantum Tunneling
• Dislocation-induced spin tunneling in Mn-12 acetate
• Quantum-Classical Escape-Rate Transition of a Biaxial Spin System with a Longitudinal Field: a Perturbative Approach
• 55Mn NMR in Mn12 acetate: Hyperfine interaction and magnetic relaxation of cluster
• Phase transition between quantum and classical regimes for the escape rate of a biaxial spin system
• The Lipkin-Meshkov-Glick model with Markovian dissipation -- A description of a collective spin on a metallic surface
• Quasi-spin Model for Macroscopic Quantum Tunnelling between Two Coupled Bose-Einstein Condensates
• Open system quantum annealing in mean field models with exponential degeneracy
• Universal Critical Behaviors in Non-Hermitian Phase Transitions
• Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model
• Tunneling with dissipation and decoherence for a large spin
• Quantum statistical metastability for a finite spin
• Non-Kramers Freezing and Unfreezing of Tunneling in the Biaxial Spin Model
• Finite-size criticality in fully connected spin models on superconducting quantum hardware
• Self-organized patterns of macroscopic quantum tunneling in molecular magnets
• Two-mode Bose gas: Beyond classical squeezing
• Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model
• Quantum-classical phase transition of escape rate in biaxial spin system with an arbitrarily directed magnetic field
• Escape-Rate Crossover between Quantum and Classical Regimes in Molecular Magnets: A Diagonalization Approach
• First- and second-order transitions of the escape rate in ferrimagnetic or antiferromagnetic particles
• Wehrl entropy production rate across a dynamical quantum phase transition
• Macroscopic quantum effects generated by the acoustic wave in a molecular magnet
• Escape rate of a biaxial nanospin system in a magnetic field : first- and second-order transition between quantum and classical regimes
• Deflagration with quantum and dipolar effects in a model of a molecular magnet
• Semi-classical Analysis of Spin Systems near Critical Energies
• Magnetization quantum tunneling at excited levels for a biaxial spin system in an arbitrarily directed magnetic field
• Phase interference of spin tunneling in an arbitrarily directed magnetic field
• Crossover from thermal hopping to quantum tunneling in Mn_{12}Ac
• Periodic Instanton and Phase Transition in Quantum Tunneling of Spin Systems
• Phase transition between quantum and classical regimes for the escape rate of dimeric molecular nanomagnets in a staggered magnetic field
• Squeezing in driven bimodal Bose-Einstein Condensates: Erratic driving versus noise
• Goldilocks Probes for Noisy Interferometry via Quantum Annealing to Criticality
• Spin relaxation in phase space
• Quantum-classical transition of the escape rate of uniaxial antiferromagnetic particles in an arbitrarily directed field
• Spin tunneling of trigonal and hexagonal ferromagnets in an arbitrarily directed magnetic field
• Spin-phase interference, coherent superposition, and quantum tunneling at excited levels in nano-antiferromagnets
• Phase transitions in quantum tunneling and quasi-exact solvability for a family of parametric double-well potentials
• Quantum-classical transition of the escape rate of a biaxial ferromagnetic spin with an external magnetic field
• Quantum-classical phase transition of the escape rate of two-sublattice antiferromagnetic large spins