Longitudinal Spin Excitations and Magnetic Anisotropy in Antiferromagnetically Ordered $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$

We report on a spin-polarized inelastic neutron-scattering study of spin waves in the antiferromagnetically ordered state of $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$. Three distinct excitation components are identified, with spins fluctuating along the $c$ axis, perpendicular to the ordering direction in the $ab$ plane and parallel to the ordering direction. While the first two “transverse” components can be described by a linear spin-wave theory with magnetic anisotropy and interlayer coupling, the third “longitudinal” component is generically incompatible with the local-moment picture. It points toward a contribution of itinerant electrons to the magnetism that is already in the parent compound of this family of Fe-based superconductors.

Popular Summary

Iron pnictides, a class of high-temperature superconductors discovered only in 2008, have presented many fundamental puzzles for physicists working on superconductors. One of the puzzles is the proximity of an antiferromagnetic phase to the superconducting phase in these materials, raising the tantalizing possibility of a fundamental connection between magnetism and superconductivity in these materials. What is the microscopic origin of their antiferromagnetism, then? Existing experiments point to two possibilities: Either the antiferromagnetism arises from spin moments of electrons localized on (iron) nuclei or it comes from the collective ordering of the spins of itinerant (mobile) electrons. However, no “smoking-gun” evidence has been found for either of these possibilities. In this experimental paper, we present such evidence for the itinerant-electron scenario in a nonsuperconducting, strongly antiferromagnetic parent compound of iron pnictides.

The two scenarios leave fundamentally different signatures in how the microscopic magnetic moments (or spins) ordered into the antiferromagnetic state fluctuate when excited. In the local-moment picture, the moments have a fixed size, so their fluctuations are dominated primarily by their precessions around the ordering direction. In the itinerant-electron picture, the sizes of the moments themselves can additionally fluctuate, giving rise to “longitudinal spin excitations.” Indeed, spin-polarized inelastic neutron scattering can selectively determine the direction of the excited spin fluctuations. Using a state-of-the-art implementation of this technique and a very large single-crystal sample, we have achieved an unprecedented precision in determining the spin fluctuations and are thus able to uncover an unequivocal signature of longitudinal spin excitations in our experimental spectrum, in other words, smoking-gun evidence for a sizable contribution of itinerant electrons to the antiferromagnetism.

As itinerant electrons are in no doubt important for the superconductivity in materials derived from the parent compound through doping, the finding that the same electrons also contribute to the magnetism in the parent compound puts on a firmer footing the notion of an intimate connection between the magnetism and the superconductivity.

Figure 1

(a) Fermi surface of $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$, reproduced from Ref. 40 using the band structure from Ref. 42. Arrows indicate nesting vectors. (b) Spin arrangement and fluctuation directions in the AF phase of $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$. Coordinate systems for neutron polarization are indicated for two examples ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$.

Figure 2

(a) Energy scans at (1 0 3). BG is determined by fitting the ${\mathrm{SF}}_y+{\mathrm{SF}}_z-{\mathrm{SF}}_x$ intensity, which does not contain any magnetic signal, to a linear function of $\omega$. (b) $\mathbf{Q}$ scans at $\omega =22\mathrm{meV}$ fitted to a single Gaussian peak. (c),(d) Extracted ${\sigma }_y$ and ${\sigma }_z$ at (1 0 3) and (1 0 1). Meanings of symbols in (a)–(d): Circles are raw data, squares are ${\mathrm{SF}}_y$ or ${\mathrm{SF}}_z$ minus BG, triangles are ${\mathrm{SF}}_x$ minus ${\mathrm{SF}}_y$ or ${\mathrm{SF}}_z$, and empty and filled symbols are measured with final neutron energies $E_f=30.5$ and 50 meV, respectively. (e) Comparison of ${\sigma }_y$ data obtained with $E_f=24$ and 30.5 meV. (f) Combined data from (c) and (d). The dashed line indicates ${\sigma }_y$ at (1 0 3) after multiplying by a factor of 0.4. Dotted lines indicate maxima of ${\sigma }_y$. Solid lines in (c)–(f) are guides to the eye.

Figure 3

(a) ${\sigma }_z$ and (b) ${\sigma }_y$ at AF zone boundaries (see Fig. S3 in Ref. 30 for the raw data). The meanings of symbols are the same as in Fig. 2. Solid lines are guides to the eye.

Figure 4

Intrinsic magnetic responses (see Fig. 1 for the definition) calculated from the interpolated data in Figs. 2, 3.

Figure 5

${\sigma }_y$ at (1 0 5) calculated from $M_c$ and $M_a$ in Fig. 4, in comparison with data reported by Qureshi et al. [27] after normalizing by the ${\sigma }_z$ values of the two experiments.