Wikiadmin: Wikiadmin moved page Problem: Scattering from an antiferromagnet to Problem:Scattering from an antiferromagnet

2020-09-20T15:44:19Z

Wikiadmin moved page Problem: Scattering from an antiferromagnet to Problem:Scattering from an antiferromagnet

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2020-02-18T22:15:12Z

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ucph>Tommy at 18:42, 4 September 2019

2019-09-04T18:42:34Z

New page

This problem is a simple illustration of magnetic diffraction,
as calculated in section [[Magnetic diffraction]].

We consider the two-dimensional square lattice with lattice constant \(d\) and antiferromagnetic interactions
between nearest neighbours.

In the previous problem, we showed that this system is antiferromagnetic
with alternating spin directions between nearest neighbours, as illustrated in [[Elastic_magnetic_scattering#label-fig:magnetic_structures|this figure (middle)]] from the [[Elastic magnetic scattering]] page.

=====Question 1=====
Argue that the square 4-atom cell with side length \(2 d\) is a valid magnetic unit cell for the system
and that the reciprocal lattice then becomes a square lattice with side length \(\pi/d\).

=====Question 2=====
We define as usual the reciprocal lattice coordinates, \((h,k)\), in terms of the nuclear
reciprocal lattice vectors, \(|{\bf a}^*| = |{\bf b}^*| = 2 \pi/d\). Show that the points of the 4-atom
magnetic reciprocal lattice can be reached by integer and half-integer values of \(h\) and \(k\).

=====Question 3=====
In the nuclear Brillouin zone, there are 4 different magnetic reciprocal lattice points:
\((0,0)\), \((0,1/2)\), \((1/2,0)\), and \((1/2, 1/2)\). Calculate the magnetic scattering structure factor
for these 4 reflections when the spins are all pointing out of the plane (the \(l\)-direction). Draw a map
of \(q\)-space, showing the allowed nuclear and magnetic reflections, respectively.

=====Question 4=====
Compare to the value of the ordering \(Q\)-vector, \({\bf Q} = (1/2 1/2)\), found in the previous problem.

Problem:Scattering from an antiferromagnet - Revision history

Wikiadmin: Wikiadmin moved page Problem: Scattering from an antiferromagnet to Problem:Scattering from an antiferromagnet

Wikiadmin: 1 revision imported

ucph>Tommy at 18:42, 4 September 2019