Tuning of exchange constants and magnetic anisotropy for terahertz antiferromagnetic resonance frequencies in cation-doped NiO

Advances in communication technology have moved carrier frequencies to the terahertz (THz) regime where the conventional microwave technologies and materials cannot work as their physical properties no longer respond to such frequencies. Antiferromagnets are materials whose magnetic properties respond and interact with THz-frequency electromagnetic waves. Phenomenologically, the response frequency is readily determined by the exchange energy and the magnetic anisotropy. In this paper, we revisit the antiferromagnetic resonance frequency of NiO, an archetypical antiferromagnetic material, and study the effect of cation doping (such as Li, Na, Be, Mg, Mn, Fe, and Zn) on its resonance frequency by first-principles calculations. The cation-dependent tunings of the exchange constant and magnetic anisotropy are demonstrated, with the resonance frequency varying from a minimum of $0.77$ THz by Li doping to a maximum of $1.60$ THz by Fe doping, referenced to a value of $1.20$ THz obtained for pure NiO. Our findings encourage exploring of antiferromagnetic materials for future THz spintronic applications.

Figure 1

Magnetic configurations considered in this study for (a) pure NiO and $X$-doped NiO with (b) $X=\mathrm{Li}$, Na, Be, Mg, and Zn and (c) $X=\mathrm{Mn}$ and Fe. See the main text for details of each magnetic configuration. Circles indicate Ni with opposite magnetization directions (blue and red), O (gray), and dopant $X$ (yellow). The spin direction of Ni cations is given as a guide to the eye and not the actual magnetization direction in the unit cell. The lattice vectors are shown in black.

Figure 2

(Top) Exchange constants between the first-nearest neighbor Ni-Ni ($J_1$; blue) and Ni-$X$ ($J_1^{\prime }$; skyblue) and (bottom) those between the second-nearest neighbor Ni-Ni ($J_2$; red) and Ni-$X$ ($J_2^{\prime }$; orange) for pure and $X$-doped NiO systems. Horizontal dashed lines represent the results of pure NiO for a reference.

Figure 3

Local DOS for (g) pure NiO and (a)–(f) and (h) $X$-doped NiO ($X=\mathrm{Li}$, $\mathrm{Na}$, $\mathrm{Be}$, $\mathrm{Mg}$, $\mathrm{Mn}$, $\mathrm{Fe}$, and $\mathrm{Zn}$). The DOS is projected on O (green), Ni (red), and $X$ (blue) with total DOS (gray). Positive and negative values in the vertical axes indicate DOSs in spin-up and -down states, respectively; the zero in the horizontal axes indicates Fermi level of $X=\mathrm{Li}$ and Na in metallic systems and the valence edge for pure NiO and $X=\mathrm{Be}$, Mg, Mn, Fe, and Zn in insulator systems. The local DOSs of Ni and O are the sum of the corresponding atoms in the unit cell. Insets in (a),(b) focus around the Fermi level.

Figure 4

Superexchange interaction mechanism between $X$ and $\mathrm{Ni}$ sites ($J_2^{\prime }$) in (a) Mn-doped and (b) Fe-doped NiO systems. Energy diagram at $X$ and $\mathrm{Ni}$ sites shows only minority-spin states (red arrows) and fully occupied majority-spin states are omitted for simplicity (see main text for light-red arrows), while at O site, both majority- and minority-spin states are shown. Magnetizations at $X$ and $\mathrm{Ni}$ sites are shown by gray arrows above the energy diagram.

Figure 5

$E_{\mathrm{MCA}}$ (blue), $E_{\mathrm{MDIA}}$ (red), and $E_{\mathrm{MA}}$ ($=E_{\mathrm{MCA}}+E_{\mathrm{MDIA}}$) (green) for pure and $X$-doped NiO systems. A positive (negative) value indicates a magnetic easy axis in the $[111]$ ($[11\overline{2}]$) direction. The $E_{\mathrm{MCA}}$ (approximately $1\text{μ}\mathrm{eV}$) values are represented by blue numbers. The inset illustrates the $(111)$ plane, where magnetization direction $[11\overline{2}]$ and $[111]$ are defined.

Figure 6

Dependence of $E_{\mathrm{MDIA}}$ with local spin magnetic moment at $X$ site for $X$-doped NiO (color circles) and pure NiO (black circle).

Figure 7

Energy dependence of $E_{\mathrm{MCA}}$ (top) and DOS of dopant ($X$) and Ni sites (bottom) for (a) Fe-doped NiO and (b) Mn-doped NiO. In the DOS, the $d$ states of $X$ and Ni sites are projected onto $m=0$ (green), $m=\pm 1$ (orange), and $m=\pm 2$ (blue). The Ni is at the first-nearest site from $X$.

Figure 8

(a) $H_{\mathrm{E}}$, (b) $H_{\mathrm{A}}$, and (c) ${\omega }_r$ for pure and $X$-doped NiO systems. The horizontal dashed lines indicate the values of pure NiO as a guide to the eye. The experimental results are plotted in (c); Ref. [16] (red circles), Ref. [20] (green triangle), Ref. [47] (magenta square), and Ref. [48] (blue cross). For cation-doped NiO [16], systems with dopant compositions close to our calculations (${\mathrm{Li}}_{0.10}{\mathrm{Ni}}_{0.90}\mathrm{O}$, ${\mathrm{Mg}}_{0.08}{\mathrm{Ni}}_{0.92}\mathrm{O}$, and ${\mathrm{Mn}}_{0.08}{\mathrm{Ni}}_{0.92}\mathrm{O}$) are plotted. The results for Li-doped NiO with the distortion are also presented (labeled as distorted).

Figure 9

Local DOS for Li-doped NiO where the crystal structure is distorted. The $U_{\mathrm{eff}}=5.3\mathrm{eV}$ is used for the calculations. The notations are the same as in Fig. 3.