We are all frustrated magnets trying to find which way to turn

It is so difficult when you are told to walk a path that you don’t know in the dark. You have no idea of when to turn left or right or when to just keep going straight ahead. However, this is what it is like for us as Christians- “Give careful thought to the paths for your feet and be steadfast in all your ways. Do not turn to the right or the left; keep your foot from evil.” (Proverbs 4:26-27). There can be times when we insist on ourselves to turn left or right and we become frustrated when it doesn’t work out. God knows the master plan, He sees your route, your map and knows where and why there are hindrances but we are quite like spins in a frustrated magnet not knowing the bigger picture.

Most people will remember what a bar magnet is, maybe after putting it under a piece of paper and scattering iron filings on top to see the shape it makes to correspond with its magnetic field. If you remember this far, then you’ll know that a bar magnet has a North (N) and South (S) pole which may have been coloured in red and blue, respectively and same poles repel (e.g. North-North) whilst unlike poles attract (i.e. South-North).

Bar magnet(left) denoted as an arrow (right), where the arrow head represents a North pole and the arrow tail represents a South pole. These arrows are called spins (the magnetic moment of an atom).

If you are lost then just think of the Earth, since it actually is one big bar magnet with a North and South pole.

It turns out, even atoms behave like a bar magnet (some more than others) and this is given the name “magnetic moment” or equivalently “spin”. As you can see in the diagram to the left, the spin of an atom is often denoted by an arrow but it is the same as a bar magnet.

Antiferromagnetic triangular lattice. An antiferromagnet favours spins alternating up and down. So how will each pair of interactions be satisfied when inserting a third spin (up or down)? Looking clockwise and anticlockwise you will find there is always an unfavourable pair (e.g. up up or down down). This is Frustration. Image taken from: http://discovery.ucl.ac.uk/1471485/1/BrooksBartlett_thesis.pdf, p.62

Now, lets take the triangular structure on the right here. If spins must align up and down alternately in the system, what will be the orientation of the spin labelled with a question mark?

Do you find that it is a struggle to get all three arrows alternating up and down if you follow clockwise or anticlockwise around the triangle? This is FRUSTRATION- all pairwise interactions cannot be satisfied simultaneously.

More specifically, this is geometrical frustration because of the triangular structure. If four of these same spins were placed on a square lattice then there would not be any frustration… try it!

As said before, God sees your path, God has arranged your life. Just like the “?” spin on the triangular lattice, we may not see the problem, we may not understand why we are frustrated turning left or right, but God sees the bigger picture (the whole lattice).

Take heart in the two scriptures below- knowing that God is in control and only seeks our best. Do not become frustrated, at least we have more guidance and hope than these poor spins!

Whether you turn to the right or to the left, your ears will hear a voice behind you, saying, “This is the way; walk in it.” (Isaiah 30:21).

“The Lord will make you the head, not the tail. If you pay attention to the commands of the Lord your God that I give you this day and carefully follow them, you will always be at the top, never at the bottom. Do not turn aside from any of the commands I give you today, to the right or to the left, following other gods and serving them.” (Deuteronomy 28:13-14).

Frustrated magnet- Rare Earth Pyrochlore Oxide. Ground states have 2-in 2-out of each tetrahedra with 4 out of 6 satisfied interactions for each tetrahedra. Image taken from http://discovery.ucl.ac.uk/1471485/1/BrooksBartlett_thesis.pdf p.77

When given enough energy, these Rare Earth Pyrochlore Oxides can contain effective magnetic monopoles, where one spin on each tetrahedra has flipped so there is no longer 2-in 2-out, but 3-in 1-out and 3-out 1-in. This gives a net pole.

FYI: An example of a real frustrated magnet are rare earth pyrochlore oxides (part of the corner sharing tetrahedra structure is shown in the figure above). When temperatures are very low, and we are talking about approaching absolute zero, the spins are arranged like that in the left figure (2 spins pointing in and 2 spins pointing out of each tetrahedra). In this case there are 2 pairwise interactions which are not satisfied (where satisfaction comes from a head-tail or tail-head interaction). With a little bit of energy (e.g. heat), one spin on each tetrahedra can flip and show exotic behaviour in these systems. Effective magnetic monopoles (denoted by N and S in the figure on the right) emerge as each tetrahedra now has 3-in and 1-out or 3-out and 1-in spins. Since the lattice is larger than two tetrahedra, these effective monopoles can separate throughout the lattice behaving independently of one another! This is amazing as no one has ever witnessed a North pole independent of a South pole. (More info see sections on p.62 and 69 of: http://discovery.ucl.ac.uk/1471485/1/BrooksBartlett_thesis.pdf).

QED.