Antiferromagnetic spin fluctuations and proximity to a quantum critical point in ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$

Spin-density functional calculations are used to investigate the proximity to antiferromagnetism and the effects of partial Ti substitution in ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$. Ti is found to enter the lattice as ${\mathrm{Ti}}^{4+}$ with only a small relaxation of the neighboring O ions. The Ti disrupts the $\mathrm{Ru}-\mathrm{O}-\mathrm{Ru}$ chains, leading to an increase in the local density of states, and thereby favors moment formation on the neighboring Ru sites. Supercell calculations and frozen spin-wave calculations show a weak antiferromagnetic instability at the Fermi surface nesting vector implying nearness to a quantum critical point. Properties of ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ are discussed in relation to these results.

Figure 1

Spin-spiral magnetic energy on a per formula unit basis as a function of wave vector $\mathbf{q}$ along $[\zeta ,\zeta ,0](2\pi ∕a)$ for ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ and an eight-formula-unit supercell with one Ru replaced by Ti (see text). The cone pitch angle is $\Theta =\pi ∕2$, which corresponds to the lowest energy. There is an energy minimum and magnetization maximum at ${\mathbf{q}}_N\approx [0.3,0.3,0]2\pi ∕a$. The computational noise of approximately $0.1\mathrm{mRy}$ and $0.25\mathrm{mRy}$, for ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ and ${\mathrm{Sr}}_2{\mathrm{Ru}}_{7∕8}{\mathrm{Ti}}_{1∕8}{\mathrm{O}}_4$, respectively, is due to the discrete zone sampling (see text).

Figure 2

(Color online) Top view of the $\mathrm{Ru}\mathrm{O}$ plane in the $2\times 2\times 1$ (left) and $4\times 1\times 1$ (right) supercells. O is denoted by the small red spheres, Ru by the large blue spheres, and Ti by the large orange spheres.

Figure 3

(Color online) Projected DOS (see text) for the $2\times 2\times 1$ (top) and $4\times 1\times 1$ (bottom) supercells. The curves are the $d$-character projections onto the Ti, Ru next to Ti (denoted Ru 1), and the second neighbor Ru (Ru 2). Ru (undoped) is the same projection for pure ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$. $E_F$ is at 0.