MIT OpenCourseWare http ocw mit edu 8 512 Theory of Solids II Spring 2009 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 1 8 512 Theory of Solids Problem Set 11 Due May 6 2009 1 Using the results of Problem 1 Set 10 a Calculate the low temperature T for a Heisenberg antiferromagnet Show that it is proportional to T 2 b For an antiferromagnet with an Ising anisotropy argue that e T What is the value of 2 Consider an antiferromagnet with exchange J on a cubic lattice with an anisotropy term DSz2 where D 0 We showed in class that the spin wave spectrum is w k w0 wA 2 w02 k 2 where w0 2zJS wA 2DS k 1 z 1 eik and is the set of vectors to the z nearest neighbors a Show that in an external eld Hz parallel to z the doubly degenerate spectrum is split as wHz k w k g B Hz 2 b Now consider an external eld in the transverse direction i e H Hy y What happens to the spin wave spectrum
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