# Homework #5

Due 5pm on Friday of Week 5

Write a one paragraph summary (3 or 4 sentences) about an experimental or theoretical solid state physics paper from 2010 or 2011 that contains one or more of the following:

• Measurement of current (or resistance) in a magnetic field
• Measurements of current (or resistance) in a nanoscale system
• An STM spectroscopy measurement
• Measurement of current (or resistance) near a phase transition (for example, normal metal to superconductor).

Include bibliographic information (journal name, volume number, page number) for the paper you choose. Please limit yourself to the following journals:

• Science
• Nature
• Proceedings of the National Academy of Sciences (PNAS)
• Nature Physics (you will need to request an interlibrary loan to access Nature Physics)
• Physical Review Letters
• Nano Letters

## Tunnel Magnetoresistance (8 pts)

The physics of Tunnel magnetoresistance (TMR) is of great technological importance. The 2007 Nobel prize in physics was awarded for work leading to TMR devices.

The figure above illustrates the spin up and spin down density of states (using the free electron model for a 3d material) in a strongly polarized ferromagnet.

a) Within the free electron approximation, find the density of uncompensated spins, n_up - n_down. Assume n_tot = 1/(0.3 nm)^3 and give a numerical answer.

b) Find a number for

c Now consider two pieces of this ferromagnet separated by a tunnel barrier. The polarization of the magnets are either parallel (p) or antiparallel (a). When electrons tunnel across the barrier their is no spin-flip mechanism. Show that the relative change in resistance between these two configuration is

## Limits of superconducting magnets (7 pts)

This question is based on Problem 3 from A&M Chpt 34

Consider a Pb wire at T = 2 K with radius r = 1 millimeter.

a) What is the largest supercurrent the wire can carry? i.e. When does the B field at the surface of the wire reach B_critical? Refer to the graph above.

b) Where does this current flow (near the surface, in the core or uniformly distributed)?

c) If you wind a solenoid out of this wire and cool it to 2 K, what is the highest field you could establish before destroying superconductivity?

• Note: Commercial SC magnets can reach 20 Tesla. This is possible because Type II SCs have much higher critical fields than Type I SCs. (see A&M p732-733)

## Copper Pair Binding Energy (10 pts)

Problem 4 from A&M Chpt 34

Do the whole problem, parts a), b) and c).