Magnetic susceptibility contributions and electronic density of states in ${(\mathrm{Ti},\mathrm{Zr})}_{100-x}{(\mathrm{Ni},\mathrm{Cu})}_x$ metallic glasses and crystalline compounds

Available experimental data on the magnetic susceptibility of melt-quenched amorphous TE-TL alloys ($\mathrm{TE}=\mathrm{Ti}$ or Zr; $\mathrm{TL}=\mathrm{Ni}$ or Cu) and the corresponding crystalline counterparts are reviewed. In order to analyze the composition dependence of the magnetic susceptibility in these systems, the individual contributions (element-resolved Langevin diamagnetic, Van Vleck and Pauli spin susceptibility, as well as the Landau susceptibility) were determined directly by theoretical calculations for these TE-TL alloys in a face-centered-cubic (fcc) structure. The total susceptibility, both experimental and calculated, was found to decrease with increasing TL content up to about $60–70\mathrm{at.}\%$. This variation was mainly ascribed to corresponding changes of the Van Vleck contribution and the spin susceptibility. The composition dependence of the latter term is in line with the previously established trend of variation of the density of states at the Fermi level $n\left(E_F\right)$ upon alloying. As in previous reports on electronic band-structure calculations, it turned out that to get agreement with experiments on $n\left(E_F\right)$ in amorphous Zr-Ni alloys, at least some partial chemical ordering should be taken into account. Available experimental data of crystalline stoichiometric Zr-Ni compounds beyond $70\mathrm{at.}\%$ Ni show a gradual increase of the Pauli susceptibility, indicating an approach toward the onset of ferromagnetic order observed previously experimentally around $90\mathrm{at.}\%$ Ni in amorphous Zr-Ni alloys. The susceptibility calculations for fcc Ti-Ni and Zr-Ni alloys indicate a strong increase of the spin susceptibility component above $70\mathrm{at.}\%$ Ni, and the calculated Stoner enhancement for ${\mathrm{Zr}}_{10}{\mathrm{Ni}}_{90}$ fulfills the condition of ferromagnetism in agreement with the experimental observation.

Figure 1

Composition dependence of the experimental room-temperature magnetic susceptibility ${\chi }_{\mathrm{expt}}$ for amorphous Ti-Ni, Ti-Cu, Zr-Ni, and Zr-Cu alloys (for data sources, see text). The straight lines represent linear fits to the data as described in the text with fit parameters given in Eqs. (1, 2).

Figure 2

Composition dependence of the experimental room-temperature magnetic susceptibility ${\chi }_{\mathrm{expt}}$ for crystalline stoichiometric ${\mathrm{Zr}}_n{\mathrm{Ni}}_m$ intermetallic compounds (◻, Ref. 21). The average experimental magnetic susceptibility for amorphous Zr-Ni alloys from Fig. 1 is also indicated by the solid line.

Figure 3

Calculated diamagnetic susceptibility ${\chi }_{\mathrm{dia}}$ for (a) fcc Ti-Cu and fcc Zr-Cu alloys as a function of the Cu content and (b) fcc Ti-Ni and fcc Zr-Ni alloys as a function of the Ni content.

Figure 4

Calculated Landau susceptibility ${\chi }_L$ for fcc Ti-Cu, Zr-Cu, Ti-Ni, and Zr-Ni alloys as a function of the TL content ($\mathrm{TL}=\mathrm{Ni}$ or Cu).

Figure 5

Calculated Van Vleck susceptibility ${\chi }_{\mathrm{VV}}$ for the four alloy systems as a function of the Cu or Ni content: (a) element-resolved ${\chi }_{\mathrm{VV}}$ for fcc Ti-Cu and fcc Zr-Cu alloys, (b) element-resolved ${\chi }_{\mathrm{VV}}$ for fcc Ti-Ni and fcc Zr-Ni alloys, and (c) comparison of the alloy Van Vleck susceptibility for the four systems. It should be noted that the ${\chi }_{\mathrm{VV}}$ values displayed in these graphs include also the spin-orbit coupling term ${\chi }_{\mathrm{OS}}$.

Figure 6

Element-resolved and total calculated electronic density of states $n\left(E_F\right)$ at the Fermi level for fcc (a) Ti-Cu and (b) Zr-Cu alloys as a function of the Cu content. The experimental values (thick solid lines) deduced from electronic specific heat and superconducting data on amorphous Ti-Cu and Zr-Cu alloys (Ref. 1) and some results (symbols 엯) of theoretical band-structure calculations on amorphous Ti-Cu (Ref. 55) and Zr-Cu (Refs. 42, 55, 56) alloys are also included.

Figure 7

Calculated element-resolved and total density of states $n\left(E_F\right)$ at the Fermi level for fcc (a) Ti-Ni and (b) Zr-Ni alloys as a function of the Ni content. The theoretical results for partially ordered alloys [(b), gray diamonds] as well as the experimental values (thick solid lines) deduced from electronic specific heat and superconducting data on amorphous Ti-Ni and Zr-Ni alloys (Ref. 1) and some results [symbols 엯 (Ref. 42), ◻ (Ref. 57), and ● (Ref. 58)] of theoretical band-structure calculations on amorphous Zr-Ni alloys are also included. (c) The element-projected and total density of states of Zr-Ni alloys in the fully disordered fcc structure (filled symbols) and for the partially ordered state with the ${\mathrm{Cu}}_3\mathrm{Au}$ structure (open symbols).

Figure 8

Element-resolved and total calculated exchange integral $I$ for fcc (a) Ti-Cu and (b) Zr-Cu alloys as a function of the Cu content. The $I$ value for pure fcc-Cu (◻) is taken from Ref. 51. The values introduced as circles (엯) represent approximations for $I$ by using Eq. (16).

Figure 9

Element-resolved and total calculated exchange integral $I$ for fcc (a) Ti-Ni and (b) Zr-Ni alloys as a function of the Ni content. The $I$ value for pure fcc-Ni (◻) is taken from Ref. 51. The values introduced as circles (엯) represent approximations for $I$ by using Eq. (16).

Figure 10

Effective Stoner enhancement parameter $S$ calculated for fcc Ti-Cu, Zr-Cu, Ti-Ni, and Zr-Ni alloys on the basis of Eq. (10) by using the calculated $n\left(E_F\right)$ and $I$ values.

Figure 11

Calculated element-resolved and total spin susceptibility ${\chi }_{\text{spin}}$ as well as total susceptibility ${\chi }_{\text{total}}$ for (a) fcc Ti-Cu alloys and (b) fcc Zr-Cu alloys as a function of the Cu content. The thick solid lines represent the average experimental susceptibility for the corresponding amorphous alloys from Fig. 1.

Figure 12

Calculated element-resolved and total spin susceptibility ${\chi }_{\text{spin}}$ as well as total susceptibility ${\chi }_{\text{total}}$ for (a) fcc Ti-Ni alloys and (b) fcc Zr-Ni alloys as a function of the Ni content. The thick solid lines represent the average experimental susceptibility for the corresponding amorphous alloys from Fig. 1.

Figure 13

Comparison of the enhanced spin susceptibilities of Zr-Ni alloys obtained by different methods: spin susceptibility obtained by correcting the experimental total susceptibility $\left({\chi }_{\text{spin}}\right)$ for the calculated orbital ones (thick solid line), spin susceptibility derived from the experimental $\mathrm{DOS}\left(E_F\right)$ using the Stoner enhancement obtained in present calculations (dashed solid line), spin susceptibility derived in the same way but using the $\mathrm{DOS}\left(E_F\right)$ calculated accounting for CSRO (Ref. 58) (filled circles), and spin susceptibility obtained in the present calculations for the chemically fully disordered state (open circles).