Large Negative Magnetic Contribution to the Thermal Expansion in Iron-Platinum Alloys: Quantitative Theory of the Invar Effect

We show that the large negative magnetic contribution to the thermal expansion in disordered Fe-Pt alloys can be understood within the disordered local moment (DLM) approach. On the basis of first principles calculations we quantitatively describe the spontaneous volume magnetostriction for various Pt concentrations. It is found that the Invar effect in these alloys is entirely related to the state of thermal magnetic disorder modeled by the DLM states. We also show that the experimentally observed anomaly in the temperature dependence of the magnetization is due to a spontaneous reduction of the local magnetic moments rather than to ‘‘hidden excitations.”

Figure 1

Total energy versus volume curves for various DLM states of the ${\mathrm{F}\mathrm{e}}_{70-x}^{+}{\mathrm{F}\mathrm{e}}_x^{-}{\mathrm{P}\mathrm{t}}_{30}$ alloy. The four curves shown are plotted such that their minimum energy is set to zero. Volume and energy is given per atom.

Figure 2

Dependence of the equilibrium volume on the degree of magnetic disorder $x$ for three chemical compositions. PM stands for ‘‘paramagnetism” and denotes the respective DLM state with complete magnetic disorder.

Figure 3

Temperature dependence of the magnetic moments in ${\mathrm{F}\mathrm{e}}_{70}{\mathrm{P}\mathrm{t}}_{30}$. The average magnetization per atom is given by the triangles; the local moments on Fe and Pt are represented by the squares and circles, respectively. The arrows indicate the spontaneous changes of the Fe local moment $M_{\mathrm{l}\mathrm{o}\mathrm{c}}$ with respect to its value at $T=0$.

Figure 4

Fractional length change $\Delta L/L$ as a function of the reduced temperature for two Invar concentrations.