THE precise manner in which quantum-mechanical behaviour at the microscopic level underlies classical behaviour at the macroscopic level remains unclear, despite seventy years of theoretical investigation. Experimentally, the crossover between these regimes can be explored by looking for signatures of quantum-mechanical behaviour—such as tunneling—in macroscopic systems1. Magnetic systems (such as small grains, spin glasses and thin films) are often investigated in this way2–12 because transitions between different magnetic states can be closely monitored. But transitions between states can be induced by thermal fluctuations, as well as by tunnelling, and definitive identification of macroscopic tunnelling events in these complex systems is therefore difficult13. Here we report the results of low-temperature experiments on a single crystal composed of super-paramagnetic manganese clusters (Mn12-ac), which clearly demonstrate the existence of quantum-mechanical tunnelling of the bulk magnetization. In an applied magnetic field, the magnetization shows hysteresis loops with a distinct 'staircase' structure: the steps occur at values of the applied field where the energies of different collective spin states of the manganese clusters coincide. At these special values of the field, relaxation from one spin state to another is enhanced above the thermally activated rate by the action of resonant quantum-mechanical tunnelling. These observations corroborate the results of similar experiments performed recently on a system of oriented crystallites made from a powdered sample4.

Macroscopic quantum tunnelling of magnetization in a single crystal of nanomagnets

For many years physicists thought small structures would be nearly ideal systems in which to explore and manipulate magnetic interactions. On a small enough length scale the interactions between individual atomic spins cause their magnetic moments to align in the ordered pattern of a single domain, without the complication of domain walls separating regions of varying orientation. For particle sizes at or below that of a single domain, many theoretical models of dynamical behavior predict simple, stable magnets with controllable classical properties. However, as with advances in semiconductor physics, the process of miniaturizing magnetic materials has unexpectedly revealed fascinating new classical and quantum mechanical phenomena. Even the simplest magnetic system, the isolated single‐domain particle, exhibits a wealth of exotic behavior that pushes us to the limits of our present understanding of the fundamentals of magnetism.

Complex dynamics of mesoscopic magnets

Magnetic properties of Co3O4 nanoparticles

This review is intended as an introduction to mesomagnetism, with an emphasis on what the defining length scales and their origins are. It includes a brief introduction to the mathematics of domains and domain walls before examining the domain patterns and their stability in 1D and 2D confined magnetic structures. This is followed by an investigation of the effects of size and temperature on confined magnetic structures. Then, the relationship between mesomagnetism and the developing field of spin electronics is discussed. In particular, the various types of magnetoresistance, with an emphasis on the theory and applications of giant magnetoresistance and tunnelling magnetoresistance, are studied. Single electronics are briefly examined before concluding with an outlook on future developments in mesomagnetism.

https://iopscience.iop.org/article/10.1088/0953-8984/14/49/201/pdf

The defining length scales of mesomagnetism: a review

Measurements of magnetic noise emanating from ferromagnets owing to domain motion were first carried out nearly 100 years ago, and have underpinned much science and technology. Antiferromagnets, which carry no net external magnetic dipole moment, yet have a periodic arrangement of the electron spins extending over macroscopic distances, should also display magnetic noise. However, this must be sampled at spatial wavelengths of the order of several interatomic spacings, rather than the macroscopic scales characteristic of ferromagnets. Here we present a direct measurement of the fluctuations in the nanometre-scale superstructure of spin- and charge-density waves associated with antiferromagnetism in elemental chromium. The technique used is X-ray photon correlation spectroscopy, where coherent X-ray diffraction produces a speckle pattern that serves as a 'fingerprint' of a particular magnetic domain configuration. The temporal evolution of the patterns corresponds to domain walls advancing and retreating over micrometre distances. This work demonstrates a useful measurement tool for antiferromagnetic domain wall engineering, but also reveals a fundamental finding about spin dynamics in the simplest antiferromagnet: although the domain wall motion is thermally activated at temperatures above 100 K, it is not so at lower temperatures, and indeed has a rate that saturates at a finite value - consistent with quantum fluctuations - on cooling below 40 K.

/pdf/direct-measurement-of-antiferromagnetic-domain-fluctuations-o16ansdd95.pdf

Direct measurement of antiferromagnetic domain fluctuations

Magnetic relaxation experiments constitute a unique method of determining the nature of fluctuations in dissipative magnetic systems. At high temperatures these fluctuations are thermal and strongly temperature dependent. At low temperatures, where quantum fluctuations dominate, magnetic relaxation becomes independent of temperature. Such behavior has been observed in many systems. In this review we emphasize the study of low temperature relaxation in ferromagnetic nanoparticles, layers, and multilayers (including ‘‘domain wall junctions’’), and large single crystals. The results of magnetic relaxation experiments are shown to agree with theoretical predictions of quantum tunneling of the magnetization. When dissipation becomes important, in large and complex systems, a time dependent WKB exponent needs to be introduced.

/pdf/quantum-tunneling-in-magnetic-systems-of-various-sizes-1gdapthez9.pdf

Quantum tunneling in magnetic systems of various sizes (invited)

The time delayed reversal of the magnetization of magnetic system with distributions of energy barriers, is in general strongly dependent on temperature at high temperature. At low temperature it becomes independent of the temperature. This result is interpreted in terms of a crossover between a thermal regime, in which the irreversible rotation of the magnetization is thermally activated, and a quantum regime in which it proceeds by quantum tunnelling. In this paper we show some results obtained in nanoparticles, layers and multilayers. In particular an analogy with Josephson junction will be made for the case of the sandwiches (domain wall junction). The role of dissipation will be discussed.

J. E. Wegrowe

Papers

Quantum tunneling in magnetic systems of various sizes (invited)

Quantum tunnelling in magnetic particles, layers and multilayers