Eugene M. Chudnovsky

Magnetic qubits as hardware for quantum computers

We propose two potential realizations for quantum bits based on nanometre-scale magnetic particles of large spin S and high-anisotropy molecular clusters. In case (1) the bit-value basis states |0 and |1 are the ground and first excited spin states Sz = S and S-1, separated by an energy gap given by the ferromagnetic resonance frequency. In case (2), when there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, |0, and antisymmetric, |1, combinations of the twofold degenerate ground state Sz = ±S. In each case the temperature of operation must be low compared to the energy gap, Δ, between the states |0 and |1. The gap Δ in case (2) can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware.

Magnetic properties of amorphous ferromagnets (invited)

Some magnetic properties of amorphous ferromagnets are well described within the random‐anisotropy real‐space model. This model assumes that the neighboring spins are ferromagnetically coupled with each other, and that there is a local magnetic anisotropy whose axes are correlated over a small length Ra due to short‐range structural order. The system is characterized by a small parameter λ∼R2aK/A which depends on temperature and on the concentration of magnetic atoms via the local anisotropy K and exchange constant A. In zero magnetic field the local magnetization smoothly rotates over the solid with a characteristic length Rf =Ra/λ2. The zero‐field susceptibility is very sensitive to the exchange, the anisotropy, and the amorphous structure: χ∝A3K−4R−6a. The magnetization law in approaching saturation (M→M0) is universal (M0−M)∝1/(H)1/2 for H<2A/M0R2a. These and other predictions of the model seem to be in a good agreement with many recent experimental results.

Thermally activated resonant magnetization tunneling in molecular magnets: Mn 12 Ac and others

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn

Macroscopic quantum tunneling in antiferromagnets

{}_{12}\mathrm{Ac}

QUANTUM TUNNELING OF MAGNETIZATION IN SOLIDS

(S=10)

Quantum Hysteresis in Molecular Magnets

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 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.

Dependence of the magnetization law on structural disorder in amorphous ferromagnets

Abstract Starting from the Neel state of a uniaxial antiferromagnetic particle, we show that, due to the tunneling of the Neel vector between easy directions, the ground state of a sufficiently small particle is a quantum superposition of two equivalent Neel states. A certain orientation of the Neel vector becomes frozen as the volume of the particle grows, or the dissipation due to the interaction of the Neel vector with microscopic degrees of freedom increases. For the weak dissipation, which is mostly the case, the crossover from classical to quantum regime occurs at temperature T∗∼(ϵaϵe) 1 2 TN, where ϵa and ϵ e are anisotropy and exchange constants, TN is the Neel temperature.

Phenomenological theory of amorphous magnets with small random anisotropy

We argue that superconductor/ferromagnet multilayers of nanoscale period should exhibit strong pinning of vortices by the magnetic domain structure in magnetic fields below the coercive field when ferromagnetic layers exhibit strong perpendicular magnetic anisotropy. The estimated maximum magnetic pinning energy for single vortex in such a system is about 100 times larger than the pinning energy by columnar defects. This pinning energy may provide critical currents as high as 106−107 A/cm2 at high temperatures (but not very close to Tc) at least in magnetic fields below 0.1 T.

FIRST- AND SECOND-ORDER TRANSITIONS BETWEEN QUANTUM AND CLASSICAL REGIMES FOR THE ESCAPE RATE OF A SPIN SYSTEM

Magnetic solids should, under certain circumstances, show macroscopic quantum behavior, in which coherence exists between completely distinct magnetization states, each involving a very large number of spins (~1012 spins). This article reviews the recent work in this field, concentrating particularly on macroscopic quantum tunneling (MQT) of magnetization. The two main phenomena discussed are (a) the tunneling of magnetization in singledomain particles or grains (in which some 103−104 spins rotate together through an energy barrier), and (b) the tunneling of domain walls in films or in bulk magnets; where walls containing ~ 1010 spins may tunnel off a pinning potential, or from one pinning centre to another. Some attention is also given to the quantum nucleation of magnetization reversal in a bulk magnet, and to the quantum motion of other magnetic solitons (such as vortices). After a thorough analysis of the basic grain and wall tunneling phenomena, we continue on to a discussion of the various dissipative or “decoherence” mechanisms, which destroy the phase correlations involved in tunneling. The coupling of grain magnetization to phonons, photons, and electrons is shown to have little consequence for weaklyconducting or insulating grains. Domain walls couple to these and also to magnons and impurities or defects; the 3rd order coupling to magnons can have serious effects, but if one uses pure insulators at low temperatures, these can also be ignored. As a result, theory indicates that MQT should be visible in both grains and bulk magnets at low temperatures (at least below ~1 K). The present experimental evidence for such behavior is inconclusive, partly because few experiments have been done. We discuss these experiments, and make some suggestions for future work. It is hoped this review will stimulate such work, not only because of the fundamental interest in macroscopic quantum phenomena, but also because of the considerable scope for technological innovation.