Our group works in two rather separate areas of experimental condensed matter physics: magnetic materials and granular materials. In the area of magnetic materials, we have studied a range of systems including, colossal magnetoresistance manganites, magnetic nanoparticles, ferromagnetic semiconductors, and both natural and artificial geometrically frustrated magnetic systems. In the area of granular materials we have studied the dynamics of wet granular materials, the nature of local jamming and the granular drag force, and the flux of grains from a shaken container. A more detailed description of some of the research is given below, but please also see the papers listed on the publication page. Our research has been funded from a number of different sources including: the Army Research Office, DARPA, the National Science Foundation, NASA, the Petroleum Research Fund, and the Alfred P. Sloan Foundation.
Geometrically Frustrated Magnetism
The large degeneracy of states resulting from the geometrical frustration of competing interactions is an essential ingredient of important problems in fields as diverse as magnetism, protein folding, and neural networks. Geometrically frustrated magnetic materials are those in which the geometry of the magnetic sublattice prevents the simultaneous minimization of the energies of different spin-spin interactions. We have an ongoing research program in collaboration with Prof. Robert Cava at Princeton, studying the bulk magnetic and thermodynamic properties of such materials, with the goal of understanding the low temperature magnetic state in the presence of strong frustration.
One important type of behavior seen in geometrically frustrated magnetic materials is a spin liquid state, in which frustration prevents the onset of long range order, and the spins thus continue to fluctuate down to the lowest temperatures measured. We have studied the spin liquid ground state of gadolinium gallium garnet, in which the application of a magnetic field results in antiferromagnetic long range order. We have demonstrated that the spin liquid state is distinct from a spin glass, and that the phase boundary with the ordered state is directly analogous to the melting curve of 4He. In another spin liquid materials, terbium titanate, we have found evidence for very slow spin relaxation in the presence of a strong magnetic field, possibly analogous to domain relaxation in ferromagnets.
Another subject of recent study has been a "spin ice" material, dysprosium titanate, in which the low temperature statistical properties of the spins are analogous to those of protons in frozen water. We have found a cooperative spin-freezing transition leading to the spin ice ground state in this material. This transition is associated with a very narrow range of relaxation times and represents a new modality for spin-freezing. The dynamics are a result of competing quantum mechanical and thermal spin relaxation, and they provide a new window through which to study glass-like behavior and the consequences of frustration in the limit of low disorder.
Schematic of frustration in water ice and spin ice. a. In water ice, each hydrogren ion is close to one or the other of its two oxygen neighbors, and each oxygen must have two hydrogen ions closer to it. b. In spin ice, the spins point either directly toward or away from the centers of the tetrahedra, and each tetrahedron is constrained to have two spins pointing in and two pointing out.
Another project along the same lines is a study of artificial frustrated magnets based on arrays of single-domain ferromagnetic islands. Using lithographically fabricated arrays, it is possible to engineer frustrated systems to alter the strength of interactions, the geometry of the lattice, the type and number of defects, and other properties which impact the nature of frustration. These systems also allow us to probe the magnetic moments of individual elements in this correlated system so that we can study the local accommodation of frustration.
Atomic force microscope and magnetic force microscope images of a frustrated lattice of ferromagnetic dots forming “artificial spin ice”. a. An atomic force microscope image of a typical permalloy array with lattice spacing of 400 nm. The islands are 80 x 220 nanometers and are elongated so that the magnetic moment of each island is forced to be along the axis of the island b. A magnetic force microscope image taken from the same array. Note the single-domain character of the islands, as indicated by the division of each island into black and white halves which indicate the south and north poles respectively of the magnetic moments of the islands. The colored outlines indicate examples of how four islands can be configured at a vertex where they meet.
Ferromagnetic Semiconductors
The possibility of devices based on an electron's spin rather than its charge has lead to the growing field of "spintronics." In this field the injection of a spin-polarized current into a semiconductor could lead to novel electronic devices such as spin polarized LEDs, spin transistors, and integration of memory and computation on the same chip. Ferromagnetic semiconductors are currently the most viable method of injecting polarized carriers into semiconductors, and (Ga,Mn)As is of particular interest because it has the highest established Curie temperature, a small coercive field, and can be grown in conjunction with other III-V semiconductors using molecular beam epitaxy. In collaboration with Prof. Nitin Samarth's group at Penn State, we have focused on characterizing the magnetic and transport properties of (Ga,Mn)As in the hope of improving current theoretical understanding of this material.
We have examined the magnetic, electronic, and structural properties of molecular beam epitaxially grown (Ga,Mn)As epilayers. Annealing at low temperatures has been shown to significantly enhance the conductivity and the ferromagnetic transition temperature. We have studied this annealing process in detail, since it appears essential to preparing the optimal material. Our work and that of other groups suggests that the most important effect of annealing appears to be the diffusion of Mn interstitials to the surface of the epilayer. The necessity of a free surface inhibits the effects of annealing of buried layers (such as would be used in devices), but we have shown that the effects of annealing can be regained in buried layers by lithographically defining structures of width ~ 100 nanometer. In another area of study we have demonstrated that it is possible to exchange bias (Ga,Mn)As by the growth of antiferromagnetic MnO on the surface.
Wet granular materials The dynamics of granular materials have been the subject of considerable attention from the non-linear physics community over the past decade, but almost all of the attention has focused on dry materials in which there is no significant attractive force between the grains. We have explored the physics of wet granular materials, in which small amounts of liquid added to grains lead to intergrain cohesion and lubrication. Through quantitative studies of both the increased stability of wet granular media and the dynamics of avalanches among wet grains, we have demonstrated that microscopic amounts of interstitial liquid can result in macroscopic changes in the granular properties. We observe a wide range of novel behavior with increasing liquid content, including the development of clumps of correlated grains and a viscoplastic regime of behavior in which the entire granular sample behaves coherently and the surface spontaneously forms regular patterns.
Drag and Penetration Force and Local Jamming When a stress is applied to a granular material, the grains "jam" to oppose the stress by forming a rigid structure. We have explored local jamming resulting from stress applied by a discrete solid object moving slowly through a dense granular medium. We have measured the low velocity drag force associated with such motion, a relatively simple property which had not been the subject of previous systematic study. We have characterized the average drag force on various objects to study geometrical and frictional effects, and we have also studied large stick-slip fluctuations in the drag which reflect the long range nature of force propagation in dense granular materials. Studies of boundary effects on the penetration force have demonstrated that there is a clear length scale to the jamming of grains in front of a solid object moving through a granular material.
The depth dependence of the penetration force required to push a plate vertically downward into a granular material consisting of spherical glass beads (apparatus on right). The different color curves correspond to different fill heights of the vessel, increasing from left to right for the data shown. The three different indicated regimes of the penetration curves (linear/hydrostatic, wall supported, and bottom dominated) correspond to the different mechanisms dominating the penetration process.
Peter Schiffer ©2010
