Origin of the Invar effect in iron–nickel alloys

In 1897 Guillaume1 discovered that face-centred cubic alloys of iron and nickel with a nickel concentration of around 35 atomic per cent exhibit anomalously low (almost zero) thermal expansion over a wide temperature range. This effect, known as the Invar effect, has since been found in various ordered and random alloys and even in amorphous materials2. Other physical properties of Invar systems, such as atomic volume, elastic modulus, heat capacity, magnetization and Curie (or Néel) temperature, also show anomalous behaviour. Invar alloys are used in instrumentation, for example as hair springs in watches. It has long been realized that the effect is related to magnetism2,3; but a full understanding is still lacking. Here we present ab initio calculations of the volume dependences of magnetic and thermodynamic properties for the most typical Invar system, a random face-centred cubic iron–nickel alloy, in which we allow for non-collinear spin alignments—that is, spins that may be canted with respect to the average magnetization direction. We find that the magnetic structure is characterized, even at zero temperature, by a continuous transition from the ferromagnetic state at high volumes to a disordered non-collinear configuration at low volumes. There is an additional, comparable contribution to the net magnetization from the changes in the amplitudes of the local magnetic moments. The non-collinearity gives rise to an anomalous volume dependence of the binding energy, and explains other peculiarities of Invar systems.