Edmund Stoner would be proud (Courtesy: University of Leeds)
By Hamish Johnston
There’s a nice paper in Science today about using a gas of ultracold atoms to gain a better understanding of the behaviour of electrons in solids — another triumph for the “quantum simulator”.
Physicists in the US and Canada have used a chilled gas of lithium-6 to gain important insights into why iron, nickel and other metals are magnetic.
Of course people have known that iron is magnetic for a very long time — but it turns out that the eponymous ferromagnet has some very tricky physics lurking within it.
Iron is called an “itinerant” ferromagnet because its magnetism arises from the spins of its conduction electrons. This means that its magnetic moments can move around the metal as well as flip between up and down — you can see it’s getting complicated already.
Many years ago physicists realized that electrons with overlapping wave functions experienced a repulsive “exchange” interaction. This repulsion is weaker when the electron spins point in the same direction, and therefore a gas of free electrons can minimize its energy by pointing all its spins in the same direction.
Sounds like a great explanation for iron, but calculations (and later experiments) suggest this should only occur at electron densities much lower than that found in iron. And to make matters worse, the conduction electrons in iron exist in very complicated d-bands so can’t really be thought of as truly free.
The first physicist to really make sense of all this was Edmund Stoner, who in 1933 expressed the exchange interaction felt by a single electron in terms of a field representing all the other electrons. Working at the University of Leeds, he found that if this field was strong enough, the spins would align. But actually calculating the field for a material like iron remains a formidable challenge.
Enter the “quantum simulator”, in which Stoner’s theory can be put through its paces using ultracold atoms instead of electrons.
The team, which included Nobel Laureate Wolfgang Ketterle of MIT, studied a cloud of atoms at about 150 micro Kelvin. The experiment began with half the atoms in one quantum state and the rest in another — which simulates the spin up and spin down states of the electron. Using the “magic” of the Feshbach resonances, the team were able to dial up a repulsive exchange-like interaction between atoms.
What did they see? Three signatures of a ferromagnetic transition as predicted by Stoner: fewer collisions between atoms of opposite “spin” and an increase in the kinetic energy of the atoms both suggested the formation of magnetic domains; along with a reduction in the pressure of the gas.
However, what they weren’t able to do is take images of the gas showing domains of spin up and spin down atoms — apparently the atoms started to form molecules before large domains were apparent.
Of course Stoner’s model is very simple, and much more work is needed to understand the magnetic states of matter — but the quantum simulator has again proven itself to be an important tool for the condensed matter physicist.