Hidden Mn magnetic-moment disorder and its influence on the physical properties of medium-entropy NiCoMn solid solution alloys

The ab initio Korringa-Kohn-Rostoker method combined with the coherent potential approximation (CPA) was employed to investigate the electronic, magnetic, and transport properties of medium-entropy face-centered-cubic (fcc) NiCoMn solid solution alloys. By comparing the CPA electronic structure with that from supercell calculations, we uncovered an unconventional CPA ground state, which correctly distinguishes two equally populated Mn CPA components—with large spin moments but opposite orientations. Using the spin spiral calculations, we further demonstrated that this ground state is most energetically favorable in the presence of spin noncollinearity, and no significant longitudinal spin fluctuation is observed, justifying the applicability of the Heisenberg model. The finite-temperature magnetism was further studied using different approximations based on the Heisenberg model, and we found the Mn moments to be fully disordered at low temperature due to a small net effective Weiss field on Mn. In addition, the magnetic effect on the electron scattering at finite temperatures was evaluated and compared with other scattering mechanisms. Since the magnetization-induced electron scattering is almost saturated in the ground state, (full) spin disorder only yields a small addition to the resistivity, whereas the thermal displacements increase it modestly. Finally, we elucidate the role of hydrostatic pressure on the magnetic and transport properties. These findings reflect the importance of the magnetic signatures on the physical properties of alloys, and they provide a window into magnetism-controlled electronic structure and energy dissipation.

Figure 1

Total energy (meV/site) as a function of $c_{{\text{Mn}}^{\uparrow }}/(c_{{\text{Mn}}^{\uparrow }}+c_{{\text{Mn}}^{\downarrow }})$. The zero energy corresponds to the energy of the AFM state. The black arrow labels the energy minimum at $c_{{\text{Mn}}^{\uparrow }}/(c_{{\text{Mn}}^{\uparrow }}+c_{{\text{Mn}}^{\downarrow }})=0.51$.

Figure 2

(a) Total DOS (states/eV/site) and (b)–(f) species-resolved partial DOS (states/eV/site) of NiCoMn random alloy using the supercell method (black lines) and the CPA method that produces two states: the DLM-Mn state (blue lines) and the AFM state (green lines). In the supercell method, the black lines correspond to the averaged DOS in each case while their colored smearing of the partial DOS gives the standard deviation of the partial DOS at each energy point. This is obtained from sampling the partial DOS of all atoms with the same species in the supercell. (d), (e) ${\mathrm{Mn}}^{\uparrow }$ and ${\mathrm{Mn}}^{\downarrow }$ distinguish Mn with up spins and down spins, respectively. (f) Averaged Mn partial DOS from supercell method (black lines) and from the AFM state in CPA (green lines). All DOS plots are rescaled per atom, and the Fermi level (dashed green line) is shifted to zero energy.

Figure 3

The intraspecies (a) and interspecies (b) exchange parameters $\left(J_{\alpha }\right)$ as a function of bond length (for a certain $\alpha \mathrm{th}$ nearest-neighboring shell) in random alloy NiCoMn in the following multiple states: FM state, AFM state, DLM state, and DLM-Mn state. In the DLM-Mn state and DLM state, only the interactions centered around a spin-up Mn atom are shown.

Figure 4

(a) Sketch of the spin spiral state, propagating along the $y$ direction for an artificial one-dimensional atomic chain (blue spheres). (b) Adiabatic magnon energy (upper panel), defined as $\frac{E\left(\mathbf{q}\right)-E\left(0\right)}{{\text{sin}}^2\left(\mathrm{\Omega }\right)}$, given in meV/site, and spin spiral energy (lower panel), defined as $E\left(\mathbf{q}\right)-E\left(0\right)$, given in meV/site, in NiCo solid solution alloy for different cone angles $\mathrm{\Omega }$ (given in degrees). The spin spiral vector $\mathbf{q}$ is along $\mathrm{\Gamma }\text{−}X[\zeta ,0,0],X\text{−}\mathrm{\Gamma }[\zeta ,\zeta ,0]$, and $\mathrm{\Gamma }\text{−}L[\zeta ,\zeta ,\zeta ]$ direction. (c) Species-dependent local moments $\left({\mu }_B\right)$ and averaged net moment $\left({\mu }_B\right)$ for different spin spiral vectors.

Figure 5

(a) Adiabatic magnon energy (upper panel) and spin spiral energy (lower panel) in NiCoMn (AFM state) for different cone angle $\mathrm{\Omega }$ (given in degrees). The spin spiral vector $\mathbf{q}$ is along the $\mathrm{\Gamma }\text{−}X[\zeta ,0,0],X\text{−}\mathrm{\Gamma }[\zeta ,\zeta ,0]$, and $\mathrm{\Gamma }\text{−}L[\zeta ,\zeta ,\zeta ]$ directions. (b) Species-dependent local moments and averaged net moment for different spin spiral vectors.

Figure 6

(a) Adiabatic magnon energy (upper panel) and spin spiral energy (lower panel) in NiCoMn (DLM-Mn state) for different cone angle $\mathrm{\Omega }$ (given in degrees). The spin spiral vector $\mathbf{q}$ is along $\mathrm{\Gamma }\text{−}X[\zeta ,0,0],X\text{−}\mathrm{\Gamma }[\zeta ,\zeta ,0]$, and $\mathrm{\Gamma }\text{−}L[\zeta ,\zeta ,\zeta ]$ direction. (b) Species-dependent local moments and averaged net moment for different spin spiral vectors. Two types of Mn species are distinguished using ${\mathrm{Mn}}^{\sigma }$, where $\sigma =\uparrow$ or $\downarrow$ denote the spin orientation.

Figure 7

(a) Simulated net magnetization $M\left(T\right)({\mu }_B$/site) as a function of reduced temperature $(T/T_c)$ using three different statistical approximations: classical mean-field approximation (MF), classical pair cluster approximation (PC), and classical Monte Carlo (MC). The temperature-dependent reduced species-resolved magnetization $\left(\langle e_z^{\mu }\rangle \right)$ in (b) classical mean-field approximation, (c) classical pair cluster approximation, and (d) classical Monte Carlo approximation. Magnetic free energy $(F_{\text{mag}}$, meV/site) and the magnetic interaction energy $(F_{\text{mag}}+T\times \text{ln}4\pi$, meV/site) of NiCoMn in DLM-Mn state are plotted in (c) using PC. The temperature-dependent magnetic susceptibility using $8\times 8\times 8,12\times 12\times 12$, and $16\times 16\times 16$ cubic cells are displayed in (d) using MC.

Figure 8

A zoom-in of a representative spin configuration at 20 K for the DLM-Mn state, taken from a large $12\times 12\times 12$ unit cell. Red arrows indicate Co spins, sliver arrows denote Ni spins, and blue and light blue arrows are local moments on ${\mathrm{Mn}}^{\uparrow }$ and ${\mathrm{Mn}}^{\downarrow }$.

Figure 9

Resistivity of NiCoMn alloy at finite temperatures, $\rho \left(T\right)$, given in units of $\mu \mathrm{\Omega }\text{cm}$. Electron scattering due to the static displacements $\left(u_0\right)$, thermal displacements $\left[u\right(T\left)\right]$, and spin disorder (SD) are considered either separately or with different combinations (see the main text for details). The chemical disorder (CD) is always included. The mean-field transition temperature $\left(T_c\right)$ is also labeled.

Figure 10

The resistivity enhancement $\left[\mathrm{\Delta }\rho \right(T),\mu \mathrm{\Omega }\text{cm}]$ due to the effect of thermal displacements $\left[u\right(T\left)\right]$, with (red dots) and without (black diamonds) taking into account the static displacements $\left(u_0\right)$.

Figure 11

(a) The residual resistivity $\left({\rho }_0,\mu \mathrm{\Omega }\text{cm}\right)$ at different lattice parameter. The hydrostatic pressures $(P$, kbar) at different lattice parameters are also labeled. (b) The lattice-parameter-dependent local moment on different species. The experimental lattice parameter is labeled using a dashed line. (c) Curie temperature $\left(T_c,K\right)$ and effective exchange field on species $\mu (J_0^{\mu }$, meV) as a function of lattice parameter.