Magnetodynamics 2007
Goals
This project develops instruments, techniques, and theory for the understanding of the highspeed response of commercially important magnetic materials. Techniques used include linear and nonlinear magnetooptics and pulsed inductive microwave magnetometry. Emphasis is on highfrequency (above 1 gigahertz), timeresolved measurements for the study of magnetization dynamics under largefield excitation. Research addresses the nature of coherence and damping in ferromagnetic systems and their effects on the fundamental limits of magnetic data storage. Research on spinelectronic systems and physics concentrates on theoretical analysis of spinmomentumtransfer oscillators. The project provides results of interest to the magnetic disk drive industry, developers of magnetic randomaccess memory, and the growing spinelectronics research community.
Customer Needs
Advances in magnetic information storage are vital to economic growth and U.S. competitiveness in the world market for computer products and electronic devices. Our primary customers are the magnetoelectronics industries involved in the fabrication of magnetic disk drives, magnetic sensors, and magnetic randomaccess memory(MRAM).
Datatransfer rates are increasing at 40 percent per year (30 percent from improved linear bit density, and 10 percent from greater disk rotational speed). The maximum datatransfer rate in nanometric devices is currently 200 megabytes per second, with datachannel performance of over 1 gigahertz (in the microwave region), with corresponding magnetic switching times of less than 1 nanosecond. At these rates, a pressing need exists for an understanding of magnetization dynamics, and measurement techniques are needed to quantify the switching speeds of commercial materials.
The current laboratory demonstration record for storage density is over 30 gigabits per square centimeter (200 gigabits per square inch). How much further can longitudinal media (with inplane magnetization) be pushed? Can perpendicular recording, patterned media with discrete data bits, or heatassisted magnetic recording extend magnetic recording beyond the superparamagnetic limit at which magnetization becomes thermally unstable? We are developing the necessary metrology to benchmark the temporal performance of new methods of magnetic data storage.
The spin momentum transfer effect — or “spin torque” — offers new opportunities and challenges for the data storage and spintronics industries. In the commercial disk drive industry, spin torque degrades the performance of currentperpendicular toplane readhead components by driving unstable dynamics in the readhead sensor element. However, spin torque may also be used to fabricate nanoscale onchip oscillators for telecommunications devices. We are developing theory to understand this effect that may be used to harness the spin momentum transfer effect for future magnetoelectronic applications.
Technical Strategy
Nanomagnetodynamics — Our aim is to identify future needs in the datastorage and other magnetoelectronic industries, develop new metrology tools, and do the experiments and modeling to provide data and theoretical underpinnings. We concentrate on two major problems in the magneticdatastorage industry: (1) datatransfer rate, the problem of gyromagnetic effects, and the need for large damping without resorting to high magnetic fields, and (2) storage density and the problem of thermally activated reversal of magnetization. This has led to the development of instrumentation and experiments using magnetooptics and microwave circuits. Microwave coplanar waveguides are used to deliver magneticfield pulses to materials under test. In response, a specimen’s magnetization switches, but not smoothly. Rather, the magnetization vector undergoes precession. Sometimes, the magnetization can precess nonuniformly, resulting in the generation of spin waves or, in the case of small devices, incoherent rotation. We use several methods to detect the state of magnetization as a function of time. These include the following:
 The magnetooptic Kerr effect (MOKE) makes use of the rotation of polarization of light upon reflection from a magnetized film. We have used MOKE with an optical microscope to measure equilibrium and nonequilibrium decay of magnetization in recording media.

Timeresolved magnetooptic microprobe and
pulsed inductive microwave magnetometer (PIMM)
con figured to simultaneously measure magnetization
dynamics. Comparison of the two techniques permits
quantitative determination of linewidth contribution due
to spatial inhomogeneity of the gyromagnetic frequency.

 The secondharmonic magnetooptic Kerr effect (SHMOKE) is especially sensitive to surface and interface magnetization. We have used SHMOKE for timeresolved vectorial measurements of magnetization dynamics and to demonstrate the coherent control of magnetization precession.
 In our pulsed inductive microwave magnetometer (PIMM), the changing magnetic state of a specimen is deduced from the change in inductance of a waveguide. This technique is fast, inexpensive, and easily transferable to industry. It may also be used as a timedomain permeameter to characterize magnetic materials. Since the development of the PIMM at NIST, similar systems have been built at several industrial research laboratories and universities.
While these instruments have immediate use for the characterization of magnetic datastorage materials, they are also powerful tools for the elucidation of magnetodynamic theory. The primary mathematical tools for the analysis of magnetic switching data are essentially phenomenological. As such, they have limited utility in aiding industry in its goal of controlling the highspeed switching properties of heads and media. We seek to provide firm theoretical foundations for the analysis of timeresolved data, with special emphasis on those theories that provide clear and unambiguous predictions that can be tested with our instruments.
Theory For Spin Torque Nanooscillators
Our goal is to develop analytical and computational methods for the modeling and design of nanometer scale ferromagnetic multilayer systems where the spinmomentumtransfer effect is applied. The recent discovery and rapid development of these types of systems represent major technological advances, with great promise for technological applications. Spin momentum transfer (SMT) generates microwave oscillations with narrow linewidths in thin magnetic multilayers. As such, these systems have the potential for nextgeneration signal processing and communications applications. Experimental work in this field has proceeded at an incredible rate, but theoretical understanding lags behind. Fundamental questions involving nonlinear effects on oscillator properties such as line width, power, and the frequency dependence on system parameters remain open. Our current research, in collaboration with the University of Colorado–Boulder, has demonstrated that careful mathematical modeling is very effective in describing the behavior of real systems. We have undertaken a broad investigation of SMT systems in order to fundamentally understand the SMT effect so that it may be exploited in important applications including wireless communications and fast, highdensity data storage.
Accomplishments
 Analytical Model for SpinTorque Nano Oscillators — We developed a nonlinear model of spinwave excitation using a point contact in a thin ferromagnetic film. Largeamplitude magnetic solitary waves were computed using the model, which helps explain the dependence of frequency on current in recent spintorque experiments. Numerical simulations of the fully nonlinear model predict excitation frequencies in excess of 0.2 terahertz for contact diameters smaller than 6 nanometers. These simulations also predict a saturation and redshift of the frequency at currents large enough to invert the magnetization under the point contact. The nonlinear frequency shift caused by increasing current was found by means of numerical perturbation techniques, which agree with direct numerical
Contour plots of the x component of magnetization
in a spintorque nanooscillator. Left: Vortex mode
with odd symmetry (frequency 17.1 gigahertz); the
black dashed circle in the center represents the point
contact boundary. Right: Radially symmetric mode
with even symmetry (frequency 18.9 gigahertz),
when the Oersted field is neglected.

simulations. The model was extended to include the Oersted magnetic field generated around the point contact due to the current flow. The presence of the Oersted field fundamentally changes the symmetry of the excited mode from even to odd symmetry for inversion about the center of the point contact.
 Magnetization Dynamics Excited by Sequence of LargeAmplitude Field Pulses — We used a timeresolved ferromagnetic resonance technique to investigate the nonlinear magnetization dynamics of a 10 nanometer thin Permalloy (NiFe) film in response to a sequence of largeamplitude field pulses. The magnetic field pulse sequence was set at a repetition rate equal to the magnetic system’s resonance frequency. Both inductive and optical techniques were used to observe the resultant magnetization dynamics. We compared data obtained by this technique with conventional PIMM. The results for damping and frequency response obtained by these two different methods coincide in the limit of a smallangle excitation. However, when applying largeamplitude field pulses, there was a substantial increase in the apparent damping. Analysis of vectorresolved SHMOKE data indicate that the increase in damping is correlated with a decrease in the spatial homogeneity of the magnetization dynamics. This suggests that unstable spinwave generation occurs in the limit of largeamplitude dynamics.
 Comparison of Microscopic and Spatially Averaged Magnetization Dynamics — We adapted a timeresolved magnetooptic microprobe for use with the PIMM apparatus, allowing us to simultaneously measure the dynamics at micrometer and millimeter length scales. The microprobe has a spatial resolution of one micrometer. Comparison of the data was used to determine whether the inhomogeneous contribution to damping is in the localized or collective (that is, twomagnonscattering) limit. These two limiting cases were theoretically delineated by the Materials Science and Engineering Laboratory. The theory establishes a minimum spacing between magnetic inhomogeneities for linewidth broadening to be considered localized in character, in analogy to inhomogeneous broadening effects for electron spin resonance and nuclear magnetic resonance. If the inhomogeneities are spaced any closer, the inhomogeneities contribute to collective excitations that are not localized at the site of the inhomogeneity. In other words, the inhomogeneities act as defects that scatter energy from the uniform mode into nearly degenerate magnon modes. Analysis of our data indicates that the inhomogeneities present in Permalloy are spaced below the limit for localization, leading us to conclude that the apparent inhomogeneous contribution to the ferromagnetic damping is actually the result of a twomagnon scattering process.
 Comparison of Ferromagnetic Resonance Measurements Using Different Methods — Microwave stripline (SL), vector network analyzer (VNA), and PIMM techniques were used to measure the ferromagnetic resonance (FMR) linewidth for a series of Permalloy films with thicknesses of 50 and 100 nanometers. The SLFMR measurements were made for fixed frequencies from 1.5 to 5.5 gigahertz. The VNAFMR and PIMM measurements were made for fixed inplane fields from 1.6 to 8 kiloamperes per meter (20 to 100 oersteds). The results provide a confirmation, lacking until now, that the linewidths measured by these three methods are consistent and compatible. The linewidths in field are a linear function of frequency. The corresponding linewidth in frequency shows a weak upward curvature at the lowest measurement frequencies and a levelingoff at high frequencies.
Course
Tom Silva developed and taught a graduate level course on magnetism and magnetic materials at the University of Colorado–Boulder in spring 2006. It was attended by physicists and engineers, some from private industry.
Award
U.S. Department of Commerce Silver Medal (Bill Rippard, Stephen Russek, and Tom Silva) and EEEL Distinguished Associate Award (Matt Pufall and Shehzaad Kaka) for the discovery of mutual phaselocking, external frequencylocking, and frequency modulation of spintransfer nanooscillators, 2006.
