Magnetism of Eu-doped GaN modulations by spinodal nanodecomposition

By the Monte Carlo method, magnetic properties have been investigated for Eu-doped GaN involving internal nanostructures induced by nanoscale spinodal decomposition, where these nanostructures are spontaneously or artificially formed. In the present simulations, hysteretic and nonhysteretic magnetization curves are observed in the systems with the large-sized and small-sized nanostructures, respectively. These nanostructures affect the blocking temperatures as well. Furthermore, they influence temperature-dependent energy barriers of spin flipping; therefore, the simulations suggest that the magnetization is thermally stable. However, we observe that the blocking temperatures are smaller than the experimental values, which may be due to atomic vacancies.

Figure 1

Atomic configuration of the homogeneous phase. The cube indicates a calculation cell, which is a $20\times 20\times 20$ fcc supercell with a single side of 93.4 Å. A periodic boundary condition was applied along the lateral axes. The supercell contains $32000$ particles (Eu, Ga, and N ions) on a zinc-blende-type matrix of which 10% are Eu ions, occupying the Ga sites. Every particle is a single Eu ion; Ga and N ions are omitted. Figures of atomic configurations were prepared using VESTA, visualization for electronic and structural analysis [29].

Figure 2

Atomic configuration of the Dairiseki (a) and Konbu phases (b) after $10000$ Monte Carlo annealing steps. In the Konbu phase simulation, the crystal grows from the bottom upwards along the vertical direction. A concentration of 10% Eu ions is used for both phases. In the Dairiseki phase, the supercell contains 12 clusters of 100 or more Eu ions among which the maximum cluster contains 254 Eu ions. In the Konbu phase, the supercell contains three clusters of 100 or more Eu ions among which the maximum cluster contains 1045 Eu ions.

Figure 3

Atomic configuration of the Dairiseki (a) and Konbu phases (b) after $1000000$ Monte Carlo annealing steps. A concentration of 10% Eu ions is used. In the Dairiseki phase, the supercell contains eight clusters of 100 or more Eu ions among which the maximum cluster contains 654 Eu ions. In the Konbu phase, the supercell contains four clusters of 100 or more Eu ions among which the maximum cluster contains 1862 Eu ions. A periodic boundary condition was applied along the lateral axes; therefore, single nanorods across the cell boundary appear as separated rods in the Konbu phase.

Figure 4

The magnetic pair interaction $J_{ij}$ between the Eu ions in the zinc-blende GaN matrix. Numerical values (%) denote the concentration of the Eu ion. The concentration of Eu ranges from 6% to 12% in steps of 1%. $J_{ij}$ was used at a concentration of 10% (red boxes) to perform the magnetization simulations. Inset: $J_{ij}$ with a concentration of 10% on a logarithm scale.

Figure 5

The cumulant $U_L\left(T\right)$ intersection plots in the homogeneous phase. $T_c$ was calculated from the intersection of the fourth-order cumulant for three supercell sizes ($14\times 14\times 14$), ($18\times 18\times 18$), and ($22\times 22\times 22$), which are indicated by red boxes, green circles, and blue triangles.

Figure 6

Magnetization as a function of temperature for homogeneous, Dairiseki (concentration = 10%, annealing step = $1000000$), and Konbu (concentration = 10%, annealing step = $1000000$) phases, demonstrating the blocking temperature. The magnetization is normalized so as to become 1 when all spins are parallel. The anisotropic constant K is 0.001, and the external field is 0.001.

Figure 7

Magnetization vs external field at high temperature. The magnetization is normalized so as to become 1 when all spins are parallel. The anisotropy constant K is 0.001, and temperature is 1.0. Red boxes, green circles, and blue triangles indicate the magnetization of the homogeneous, Dairiseki, and Konbu phases, respectively.

Figure 8

Magnetization vs external field at a low temperature. The anisotropy constant K is 0.001, and temperature is 0.01. Red boxes, green circles, and blue triangles indicate the magnetization of the homogeneous, Dairiseki, and Konbu phases, respectively.

Figure 9

Magnetization as a function of temperature for homogeneous, Dairiseki (concentration = 10%, annealing step = $10000$), and Konbu (concentration = 10%, annealing step = $10000$) phases, demonstrating the blocking temperature. The magnetization is normalized so as to become 1 when all spins are parallel. The anisotropic constant K is 0.001, and the external field is 0.001.

Figure 10

Magnetization vs external field near the blocking temperature. The anisotropy constant K is 0.001, and temperature is 0.1. Red boxes, green circles, and blue triangles indicate the magnetization of the homogeneous, Dairiseki, and Konbu phases, respectively. The nanostructures were generated with 1000 annealing steps.