# Field-induced incommensurate spin structure of TbNiAl4

A very interesting field within solid state science these days is magnetocaloric materials (I could put a link here but you might as well just do a quick search). To some extent a lot of magnetic materials are magnetocaloric. Essentially, since application of a field increases the degree of order of the material (since it makes the magnetic atoms become more aligned), it reduces the entropy and therefore (for an isolated system) causes the temperature to go up, since energy can’t get in or out.

Say the material starts off isolated but at room temperature, then heats up on application of the field, then we let it get into contact with the air. It will lose heat to the air and reach air temperature. Then, if we turn off the field adiabatically (i.e., after again isolating the system) some of the ‘temperature’ energy will go into disordering the magnetic moments of the atoms. Since again energy is conserved, this means the temperature goes down. This cooled magnetic material can then be used to cool a load — say, a refrigerator full of beer.

Advantages of this over conventional gas refrigeration include the lack of moving parts — essentially, it can be done by turning off and on magnetic fields — and the lack of nasty gases that might escape. Potentially there are robustness benefits too. The only problem is as yet we don’t have materials whose performance is good enough at everyday temperatures. Magnetic cooling has been used — and for a long time — by scientists trying to do low temperature physics.

TbNiAl_{4} is interesting as it is an inverse magnetocaloric material. It cools down when we apply a field to it. This implies that the application of a field *increases* the entropy. So we wanted to know what was going on. This we found out, and it was published a little while ago in *Physical Review B*. (And also here.) The first key piece of information is in the magnetisation as a function of applied magnetic field. That looks like this:

So there are a couple of interesting things here. First, as the field is increased (solid line) we get a sudden jump at about 6T (Tesla); the material is switching from antiferromagnetic to ferromagnetic. But clearly not all the magnetic moment on the Tb is involved, because a Tb^{3+} ion has over 9μ_{B} (Bohr magnetons,the unit of atomic magnetism) and at 6T we are getting about 3μ_{B}. Once we get to about 9T the moment increases again. So some of the moment gets aligned at 6T, some needs more field.

Then, when we go down in field we have to go all the way down to about 3T before the moments ‘unalign’ — we get a different result going forwards compared to backwards. This is hysteresis and means a first order (sudden) phase transition. So what’s going on?

Well, the best probe of magnetic ordering is neutron diffraction, so we went to Wombat at ANSTO and did some experiments. We had a single crystal of TbNiAl_{4} so we used Wombat to map reciprocal space (the diffraction pattern — where the neutrons go after they scatter off the material) at a range of fields and temperatures. We get a three-dimensional map of the scattering, something like this:

And from this what we found was that at low field the material shows a commensurate antiferromagnetic order, that is,the pattern of atomic magnetic moments repeats over a distance that can be measured in terms of a simple number of repeats of the crystal unit cell, and the moments are arranged such that they cancel each other out and the overall moment (magnetisation) of the sample is small. But as the field passes 6T, it switches into a state where: (1) A component of each moment aligns with the field, giving the ferromagnetic response (2) Some of the moment retains the antiferromagnetic order but adds a small incommensurate component. This means that the repeat is not a simple number of unit cells, and also means the degrees of freedom of the system have changed. It takes more parameters to describe the ordering at the higher field. So as we increase field, we get a rapid increase in overall moment plus enter a more complicated state. There is an entropy change associated with this, and it is this that gives the inverse magnetocaloric effect. There is no ‘disorder’ as such.

This work was driven by Dr Wayne Hutchison at PEMS at UNSW, and I am very grateful to have been part of this collaboration.