<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi. This is my first visit to sci.physics.researh. Hope this is an\nappropriate place for the following post.\n\nI\'m trying to follow a paper about spin flip across domain walls.\nThe magnetization within the wall is M=(cosx,sinx,0) and I\'m trying to\nunderstand how the author arrived at the spin component of the\nHamiltonian (he offers no explanation, so I think it\'s pretty simple).\nHe has a constant (-.5*exchange energy) times the matrix\n\n[[sinx cosx\ncosx, sinx]]\n\nI looked at another paper, where it gives this term as a constant times\nmagnetization dotted with the Pauli spin matrices. However, when I\nperform the same operation with the above M, I don\'t get the same value\nas the first paper. The problem I think that I\'m having is that I\ndon\'t really understand the pauli matrices (my background in quantum is\nvirtually nonexistent). It is not clear to me what physically\ndistinguishes the x,y,z matrices, or indeed what makes these axes\nnon-arbitrary. All I know about the region is that electrons are\ninjected into the domain wall with spins parallel to the wall (pointed\nin the y direction, as they travel in the x direction) and that the\nmagnetization within the wall is as defined above. I don\'t understand\nhow this defines axes for the pauli matrices and thus how he arrives at\nthe matrix in the Hamiltonian at all. I\'ve read a couple books where\nthey say the matrices are defined so as to diagonalize S^2 and Sz, but\nI don\'t have any idea what that means.\n\nExplanations, clues, or pointers to relevant sources appreciated.\n\nThanks in advance.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi. This is my first visit to sci.physics.researh. Hope this is an
appropriate place for the following post.
I'm trying to follow a paper about spin flip across domain walls.
The magnetization within the wall is
and I'm trying to
understand how the author arrived at the spin component of the
Hamiltonian (he offers no explanation, so I think it's pretty simple).
He has a constant (-.5*exchange energy) times the matrix
[[sinx cosx
cosx, sinx]]
I looked at another paper, where it gives this term as a constant times
magnetization dotted with the Pauli spin matrices. However, when I
perform the same operation with the above M, I don't get the same value
as the first paper. The problem I think that I'm having is that I
don't really understand the pauli matrices (my background in quantum is
virtually nonexistent). It is not clear to me what physically
distinguishes the x,y,z matrices, or indeed what makes these axes
non-arbitrary. All I know about the region is that electrons are
injected into the domain wall with spins parallel to the wall (pointed
in the y direction, as they travel in the x direction) and that the
magnetization within the wall is as defined above. I don't understand
how this defines axes for the pauli matrices and thus how he arrives at
the matrix in the Hamiltonian at all. I've read a couple books where
they say the matrices are defined so as to diagonalize
and Sz, but
I don't have any idea what that means.
Explanations, clues, or pointers to relevant sources appreciated.
Thanks in advance.
