Entangled quantum state of magnetic dipoles

Free magnetic moments usually manifest themselves in Curie laws, where weak external magnetic fields produce magnetizations that vary as the reciprocal of the temperature (1/T). For a variety of materials that do not display static magnetism, including doped semiconductors and certain rare-earth intermetallics, the 1/T law is replaced by a power law T(-alpha) with alpha < 1. Here we show that a much simpler material system-namely, the insulating magnetic salt LiHo(x)Y(1-x)F(4)-can also display such a power law. Moreover, by comparing the results of numerical simulations of this system with susceptibility and specific-heat data, we show that both energy-level splitting and quantum entanglement are crucial to describing its behaviour. The second of these quantum mechanical effects-entanglement, where the wavefunction of a system with several degrees of freedom cannot be written as a product of wavefunctions for each degree of freedom-becomes visible for remarkably small tunnelling terms, and is activated well before tunnelling has visible effects on the spectrum. This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.     

A ferromagnet in a continuously tunable random field

Most physical and biological systems are disordered, even though the majority of theoretical models treat disorder as a weak perturbation. One particularly simple system is a ferromagnet approaching its Curie temperature, T(C), where all of the spins associated with partially filled atomic shells acquire parallel orientation. With the addition of disorder by way of chemical substitution, the Curie point is suppressed, but no qualitatively new phenomena appear in bulk measurements as long as the disorder is truly random on the atomic scale and not so large as to eliminate ferromagnetism entirely. Here we report the discovery that a simply measured magnetic response is singular above the Curie temperature of a model, disordered magnet, and that the associated singularity grows to an anomalous divergence at T(C). The origin of the singular response is the random internal field induced by an external magnetic field transverse to the favoured direction for magnetization. The fact that ferromagnets can be studied easily and with high precision using bulk susceptibility and a large variety of imaging tools will not only advance fundamental studies of the random field problem, but also suggests a mechanism for tuning the strength of domain wall pinning, the key to applications.     

Direct measurement of antiferromagnetic domain fluctuations

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.