Influence of composition, many-body effects, spin-orbit coupling, and disorder on magnetism of Co-Pt solid-state systems

Systematic trends in the magnetism of Co-Pt solid-state systems are explored by studying the effects of composition, electron correlations, spin-orbit coupling (SOC), and long-range order. Ab initio fully relativistic calculations were performed for bulk Co, a substitutional Pt impurity in Co, ${\text{Co}}_3\text{Pt}$, CoPt, ${\text{CoPt}}_3$, and a substitutional Co impurity in Pt. Many-body effects beyond the local spin-density approximation (LSDA) were included via the dynamical mean-field theory (DMFT); a comparison with results based on the Brooks orbital-polarization (OP) scheme was also made. The disorder was treated within the coherent-potential approximation. We found that while the spin magnetic moments ${\mu }_{\text{spin}}$ at the Co atoms monotonously increase with increasing Pt concentration, the orbital magnetic moments ${\mu }_{\text{orb}}$ do not follow the trend of ${\mu }_{\text{spin}}$. Magnetic moments ${\mu }_{\text{spin}}$ and ${\mu }_{\text{orb}}$ at Pt atoms do not depend on Pt concentration monotonously. Most of these trends can be understood in terms of hybridization and site-dependent SOC. The OP scheme of Brooks corrects the deficiencies of a pure LSDA only if the Pt concentration is low. The $\text{LSDA}+\text{DMFT}$ scheme provides ${\mu }_{\text{orb}}/{\mu }_{\text{spin}}$ ratios for Co atoms which agree with experiment even for high Pt content. Introducing disorder leads to an enhancement of ${\mu }_{\text{spin}}$ at Co atoms and to a suppression of ${\mu }_{\text{spin}}$ at Pt atoms. The ${\mu }_{\text{orb}}$ at Co atoms does not exhibit any systematic dependence on the degree of order, while ${\mu }_{\text{orb}}$ at Pt atoms decreases with increasing disorder for all Pt concentrations.

Figure 1

(Color online) Spin (top) and orbital (bottom) magnetic moments at Co (left) and Pt atoms (right) for a series of ordered Co-Pt systems. FP results are shown as solid lines with circles. Results of ASA calculation are shown as chain lines with stars (atomic radii of Co and Pt are equal) and via broken lines with diamonds (atomic radii of Co and Pt differ). The labels on the horizontal axes show the Pt concentration in the system. Note that the Pt data for a 0% Pt concentration stand for a Pt impurity hosted in bulk Co and the Co data for a 100% Pt concentration stand for a Co impurity hosted in bulk Pt.

Figure 2

(Color online) Spin magnetic moments at Pt atoms in ordered Co-Pt systems (solid line with circles, scale on the left vertical axis) compared to the sum of spin magnetic moments of all Co atoms which are nearest neighbors of the Pt atom (chain line with diamonds, scale on the right vertical axis).

Figure 3

(Color online) Spin (top) and orbital (bottom) magnetic moments at Co (left) and Pt atoms (right) in ordered Co-Pt systems as calculated using pure LSDA (solid lines with circles), LSDA with OP included via the Brooks scheme (dotted line with asterisks), $\text{LSDA}+\text{DMFT}$ with $U$ on Co atoms only (broken lines with squares), and $\text{LSDA}+\text{DMFT}$ with $U$ both on Co and on Pt atoms (chain lines with diamonds). Note that for the Brooks OP scheme, only ${\mu }_{\text{orb}}$ is shown because the corresponding ${\mu }_{\text{spin}}$ practically coincides with the pure LSDA results.

Figure 4

(Color online) The orbital moments ${\mu }_{\text{orb}}$ at the Co atoms (left) and at the Pt atoms (right) in ordered Co-Pt systems calculated if SOC is included on a single atomic site only (dotted lines with asterisks), if SOC is included at all the atoms (short broken line with triangles), if SOC is included only at the Co atoms (chain line with crossed circles), and if SOC is included only at the Pt atoms (long broken line with hearts).

Figure 5

(Color online) Spin-polarized $d$ components of the local DOS at the Co (top) and Pt (bottom) atoms for selected ordered Co-Pt systems, resolved according to the magnetic quantum number $m$. Leftmost panels show data for elemental hcp Co and for a Pt impurity in Co, middle panels show data for CoPt, and rightmost panels show data for a Co impurity in Pt and for elemental fcc Pt. Data for $m=-2$ are shown as solid lines, for $m=+2$ as long chain lines, for $m=-1$ as broken lines, for $m=+1$ as short chain lines, and for $m=0$ as dots. The DOS is given in units of states/Ry.

Figure 6

(Color online) Magnetic moments ${\mu }_{\text{spin}}$ (top) and ${\mu }_{\text{orb}}$ (middle) and their ratio ${\mu }_{\text{orb}}/{\mu }_{\text{spin}}$ (bottom) for Co (left) and Pt atoms (right) in ${\text{Co}}_{1-x}{\text{Pt}}_x$ alloys in a fully ordered phase ($S=1.0$, solid lines with circles), in a semiordered phase ($S=0.6$, chain lines with triangles), and in a disordered phase ($S=0.0$, broken lines with crosses).

Figure 7

(Color online) Total (spin plus orbital) magnetic moments at Co atoms (lines with diamonds, labeling on the left vertical axis) and at Pt atoms (lines with circles, labeling on the right vertical axis) for ${\text{CoPt}}_3$ with varying degrees of long-range order. Solid lines with full markers stand for our theoretical results; chain lines with open markers stand for the experimental results (Ref. 16).