Electronic and magnetic properties of Co and Ni impurities in Cu wires: First-principles investigation of local moment formation in one dimension

The local moment formation in one-dimensional (1D) systems is investigated in the framework of a generalized gradient approximation to density-functional theory (DFT). The electronic and magnetic properties of Co and Ni impurities in finite Cu wires are determined as a function of experimentally relevant parameters such as wire length, impurity-host distance, impurity position within the wire, and total spin polarization $S_z$. Results are given for the interatomic equilibrium distances, relative stability of different total spin configurations, local magnetic moments in both Wigner-Seitz and Bader cells, electronic density of states at the impurity, and induced magnetic moments in the 1D metal including their coupling with the impurity. The calculations show that the optimal total spin polarization is one above the minimal value. In fact, for chains having an even number of Cu atoms, the ground-state total spin is $S_z=1$ for Ni-doped wires and $S_z=3/2$ for Co-doped wires. Both Co and Ni impurities preserve their magnetic degree of freedom and develop large local magnetic moments in all low-lying spin configurations $\left(S_z\le 5/2\right)$. These almost completely saturated impurity moments are largely dominated by the $d$-electron contributions. In the ground-state the magnetic coupling between the impurity and the induced moments at the host atoms is ferromagneticlike. Thus, the local exchange energy dominates over hybridization and spin-fluctuation effects, at least in the framework of the present approximation to DFT. The local density of electronic states (LDOS) at the impurity is found to have essentially $d$ character in the whole valence-band range. Large exchange splittings consistent with saturated $d$ moments are observed, which imply a full minority-spin polarization of the LDOS at the Fermi energy ${\epsilon }_F$. A remarkable correlation is revealed between the rotational symmetry and the degree of delocalization of the impurity states close to ${\epsilon }_F$. Trends as a function of the local atomic environment are discussed.

Figure 1

(Color online) Electronic, magnetic, and structural properties of symmetric ${\text{Cu}}_m{\text{NiCu}}_m$ wires as a function of $m$: (a) magnetic excitation energy $\Delta E_m=E\left(S_z\right)-E\left(S_z^0\right)$ with respect to the ground state having $S_z^0=1$. (b) Local magnetic moment at the Ni atom within the WS sphere (full lines) and within the Bader atomic cell (dotted lines). (c) Equilibrium interatomic distance $d_{\text{NiCu}}$ between the Ni impurity and its Cu nearest neighbors. Circles refer to $S_z=0$, crosses to $S_z=1$, and dots to $S_z=2$. The lines connecting the points are a guide to the eyes.

Figure 2

(Color online) Electronic, magnetic, and structural properties of symmetric ${\text{Cu}}_m{\text{CoCu}}_m$ wires as a function of $m$: (a) magnetic excitation energy $\Delta E_m=E\left(S_z\right)-E\left(S_z^0\right)$ with respect to the ground state having $S_z^0=3/2$. (b) Local magnetic moment at the Co atom within the WS sphere (full lines) and within the Bader atomic cell (dotted lines). (c) Equilibrium interatomic distance $d_{\text{CoCu}}$ between the Co impurity and its Cu nearest neighbors. Circles refer to $S_z=1/2$, crosses to $S_z=3/2$, and dots to $S_z=5/2$. The lines connecting the points are a guide to the eyes.

Figure 3

(Color online) Local magnetic moment ${\mu }_i$ in the Bader atomic cells of (a) ${\text{Cu}}_4{\text{NiCu}}_4$ and (b) ${\text{Cu}}_5{\text{NiCu}}_5$. Circles refer to $S_z=0$, crosses to $S_z=1$, and dots to $S_z=2$. Results for the ground state of the corresponding pure ${\text{Cu}}_{2m+1}$ wires are also shown ($S_z=1/2$, triangles). The lines connecting the points are a guide to the eyes.

Figure 4

(Color online) Local magnetic moment ${\mu }_i$ in the Bader atomic cells of (a) ${\text{Cu}}_4{\text{CoCu}}_4$ and (b) ${\text{Cu}}_5{\text{CoCu}}_5$. Circles refer to $S_z=1/2$, crosses to $S_z=3/2$, and dots to $S_z=5/2$. Results for the ground state of the corresponding pure ${\text{Cu}}_{2m+1}$ wires are also shown ($S_z=1/2$, triangles). The lines connecting the points are a guide to the eyes.

Figure 5

(Color online) Spin-polarized LDOS at the impurity atom in (a) ${\text{Cu}}_4{\text{NiCu}}_4$ and (b) ${\text{Cu}}_4{\text{CoCu}}_4$ wires as a function of the energy $\epsilon$ relative to the Fermi energy ${\epsilon }_F$. Results are given for the total LDOS (full curves) and for the $d$-electron LDOS (dotted curves). Positive (negative) values correspond to majority (minority) spin. The numbers label the minority-spin states $k$ which are illustrated in Table .

Figure 6

(Color online) Spin-polarized LDOS at the impurity atom in (a) ${\text{Cu}}_5{\text{NiCu}}_5$ and (b) ${\text{Cu}}_5{\text{CoCu}}_5$ wires as a function of the energy $\epsilon$ relative to the Fermi energy ${\epsilon }_F$. Results are given for the total LDOS (full curves) and for the $d$-electron LDOS (dotted curves). Positive (negative) values correspond to majority (minority) spin. The numbers label the minority-spin states $k$ which are illustrated in Table .

Figure 7

(Color online) Electronic and magnetic properties of symmetric ${\text{Cu}}_4{\text{NiCu}}_4$ wires as a function of the nearest neighbors distance $d$: (a) magnetic excitation energies $\Delta E_m$ relative to the ground state having $S_z=1$, (b) local magnetic moment on the Ni atom, in the Wigner Seitz sphere (full line) and the Bader atomic cell (dotted lines). Circles refer to $S_z=0$, crosses to $S_z=1$, and dots to $S_z=2$. The lines connecting the points are a guide to the eyes. The vertical dashed line indicates the equilibrium CuNi distance of the fully relaxed chain for $S_z=1$.

Figure 8

(Color online) Electronic and magnetic properties of symmetric ${\text{Cu}}_4{\text{CoCu}}_4$ wires as a function of the nearest neighbors distance $d$: (a) magnetic excitation energies $\Delta E_m$ relative to the ground state having $S_z=3/2$, (b) local magnetic moment on the Co atom, in the Wigner Seitz sphere (full line) and the Bader atomic cell (dotted lines). Circles refer to $S=1/2$, crosses to $S_z=3/2$ and dots to $S_z=5/2$. The lines connecting the points are a guide to the eyes. The vertical dashed line indicates the equilibrium CuCo distance of the fully relaxed chain for $S_z=3/2$.

Figure 9

(Color online) Electronic, magnetic, and structural properties of ${\text{Cu}}_m{\text{NiCu}}_{12-m}$ wires as a function of the Ni impurity position given by $m$: (a) magnetic excitation energy $\Delta E_m=E\left(S_z\right)-E\left(S_z=1\right)$ with respect to the ground state having $S_z=1$, (b) local magnetic moment at the Ni atom within the Wigner-Seitz sphere (full lines) and the Bader atomic cell (dotted lines), and (c) equilibrium interatomic distance $d_{\text{NiCu}}$ between the Ni impurity and its Cu nearest neighbors. Circles refer to $S_z=0$, crosses to $S_z=1$, and dots to $S_z=2$. The lines connecting the points are a guide to the eyes.

Figure 10

(Color online) Electronic, magnetic, and structural properties of ${\text{Cu}}_m{\text{CoCu}}_{12-m}$ wires as a function of the Co impurity position given by $m$: (a) magnetic excitation energy $\Delta E_m=E\left(S_z\right)-E\left(S_z=3/2\right)$ with respect to the ground state having $S_z=3/2$, (b) local magnetic moment at the Co atom within the Wigner-Seitz sphere (full lines) and the Bader atomic cell (dotted lines), and (c) equilibrium interatomic distance $d_{\text{CoCu}}$ between the Co impurity and its Cu nearest neighbors. Circles refer to $S_z=1/2$, crosses to $S_z=3/2$, and dots to $S_z=5/2$. The lines connecting the points are a guide to the eyes.