We have investigated the magnetic and structural phase diagram of iron employing the full potential linear augmented plane-wave method within the generalized gradient approximation. Therefore, total-energy calculations have been performed together with investigations with varying $c/a$ ratio to check the phase stability. This study focuses on the structural and magnetic properties relevant to Invar and anti-Invar and structural phase transitions occurring in these materials. We show that the properties of antiferromagnetic fcc iron can be understood by collinear full potential calculations. In order to do this, the antiferromagnetic structure has been distorted by short-range ferromagnetic nearest-neighbor coupling. From this we can conclude that the classical low-spin behavior can be replaced by antiferromagnetic ordering. Additionally, the thermal properties of iron, especially the free-energy and thermal-expansion coefficient $\alpha \mathrm{}\left(T\right)\mathrm{}$ have been analyzed, which is important for the understanding of the anti-Invar effect. The free energy and $\alpha \mathrm{}\left(T\right)\mathrm{}$ were estimated from a Debye scheme for which ab initio results were given as input. Besides the more common cubic phases we have investigated hcp Fe at large volumes in view of its magnetic structure.

We have done molecular-dynamics simulations of ${\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x$ employing a semiempirical model. We present a phase diagram of the martensite-austenite transition temperatures as a function of the Ni concentration which is in good agreement with experimental observations. In addition to this we have calculated the phonon dispersion curves of Fe and Ni from the model. Results show that the vibrational properties of the metals are well reproduced by the embedded-atom-method potentials. Finally, we have derived the phonon dispersion relations of bcc ${\mathrm{Fe}}_{80}{\mathrm{Ni}}_{20}.$ We find rather low energies of the $\left[110\right]-{\mathrm{TA}}_1$ phonons with a strong temperature dependence which we attribute to instabilities of Ni in the bcc phase. We do not find any indications of a soft mode at the martensite-austenite transition in ${\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x.$

First-principles calculations are used in order to investigate phonon anomalies in nonmagnetic and magnetic Heusler alloys. Phonon dispersions for several systems in their cubic $L{2}_1$ structure were obtained along the [110] direction. We consider compounds that exhibit phonon instabilities and compare them with their stable counterparts. The analysis of the electronic structure allows us to identify the characteristic features leading to structural instabilities. The phonon dispersions of the unstable compounds show that, while the acoustic modes tend to soften, the optical modes disperse in a way which is significantly different from that of the stable structures. The optical modes that appear to disperse at anomalously low frequencies are Raman active, which is considered an indication of a stronger polarizability of the unstable systems. We show that phonon instability of the ${\mathrm{TA}}_2$ mode in Heusler alloys is driven by interaction (repulsion) with the low-energy optical vibrations. The optical modes show their unusual behavior due to covalent interactions which are additional bonding features incommensurate with the dominating metallicity in Heusler compounds.

Zero- and finite-temperature (T) first-principles calculations versus composition (c) show that magnetochemical effects lead to Invar anomalies in Fe-(Ni, Co, Pt) alloys. Chemical short- or long-range order and negative interatomic exchange interaction of electrons in antibonding majority-spin states force the face-centered-cubic lattice to compete simultaneously for a smaller volume (from antiferromagnetic tendencies) and a larger volume (from Stoner ferromagnetic tendencies). The resulting additional negative lattice anharmonicity is very large for Fe-(Ni, Co) while absent for Fe-Pt. Our results explain the T- and c-dependent behavior of Invar properties, including the lattice softening and thermal expansion of Fe-Ni. In addition, the occurrence of a noncollinear spin structure at $T=0\mathrm{}\hspace{0.5em}\mathrm{K}$ near Invar can be understood on the basis of our results.

The structural and magnetic properties of functional Ni-Mn-$Z$ ($Z=\text{Ga}$, In, Sn) Heusler alloys are studied by first-principles and Monte Carlo methods. The ab initio calculations give a basic understanding of the underlying physics which is associated with the strong competition of ferro- and antiferromagnetic interactions with increasing chemical disorder. The resulting $d$-electron orbital dependent magnetic ordering is the driving mechanism of magnetostructural instability which is accompanied by a drop of magnetization governing the size of the magnetocaloric effect. The thermodynamic properties are calculated by using the ab initio magnetic exchange coupling constants in finite-temperature Monte Carlo simulations, which are used to accurately reproduce the experimental entropy and adiabatic temperature changes across the magnetostructural transition.