NMR study of magnetic structure and hyperfine interactions in the binary helimagnet FeP

We report a detailed study of the ground-state helical magnetic structure in monophosphide FeP by means of ${}^{31}\mathrm{P}$ NMR spectroscopy. We show that the zero-field NMR spectrum of the polycrystalline sample provides strong evidence of an anisotropic distribution of local magnetic fields at the P site with substantially lower anharmonicity than that found at the Fe site by Mössbauer spectroscopy. From field-sweep ${}^{31}\mathrm{P}$ NMR spectra we conclude that a continuous spin-reorientation transition occurs in an external magnetic field range of 4–7 T, which is also confirmed by specific-heat measurements. We observe two pairs of magnetically inequivalent phosphorus positions resulting in a pronounced four-peak structure of the single crystal ${}^{31}\mathrm{P}$ NMR spectra characteristic of an incommensurate helimagnetic ground state. We revealed a spatial redistribution of local fields at the P sites caused by Fe spin-reorientation transition in high fields and developed an effective approach to account for it. We demonstrate that all observed ${}^{31}\mathrm{P}$ spectra can be treated within a model of an isotropic helix of Fe magnetic moments in the ($ab$)-plane with a phase shift of ${36}^{\circ }$ and ${176}^{\circ }$ between Fe1-Fe3 (Fe2-Fe4) and Fe1-Fe2 (Fe3-Fe4) sites, respectively, in accordance with the neutron scattering data.

Figure 1

(a) The crystal structure of FeP with iron atoms octahedrally coordinated by phosphorus and (b) representation of its magnetic structure.

Figure 2

Image of the FeP single crystal. The rotation axis $b$ is indicated as well as the faces perpendicular to the crystallographic axes $a$ and $c$.

Figure 3

${}^{31}\mathrm{P}$ zero-field NMR spectrum measured in FeP at 4.2 K. Black circles are experimental data, green line is the approximation pattern with the anharmonicity parameter $m=0.19$ (“Jacobian” helix) or $k=0.03$ (simple helix) and Lorentzian individual line shape ($\delta =0.06\mathrm{MHz}$). Red line is the direct simulation from hyperfine interaction tensor with the same individual line shape, as discussed in Sec. 4.

Figure 4

The magnitude of the local dipole fields at phosphorus, depending on the orientation of the Fe magnetic moments relative to the crystal $a$-axis. Top panel: The absolute values of the field at different P sites. Bottom panel: The field components at the P5 position. All the fields are calculated in the crystal coordinate system assuming the magnitude of $1{\mu }_{\mathrm{B}}$ for all Fe magnetic moments.

Figure 5

${}^{31}\mathrm{P}$ NMR spectra of the FeP powder sample measured at 1.55 K at various fixed frequencies. The frequency and the calculated Larmor field values $B_{\mathrm{L}}$ are specified inside each plot box. For comparison, the ${}^{31}\mathrm{P}$ NMR spectrum measured at 80 MHz in the paramagnetic state at 155 K is depicted in the left bottom panel. Solid lines are the theoretical spectra calculated for each given frequency according to the phenomenological “superposition” model (see text).

Figure 6

The FeP powder sample specific heat data. Main graph: $C(T$) experimental data (blue dots) and the lattice contribution (red line, see text) at zero external field. Left inset: Magnetic part of zero-field specific heat temperature dependence. Right inset: Magnetic field dependence of specific heat at 2 K.

Figure 7

${}^{31}\mathrm{P}$ NMR spectrum of the FeP single crystalline sample measured at 5 K (red circles) combined with the NMR spectrum of the powder sample (blue circles) at 120 MHz. The calculated Larmor field value $B_{\mathrm{L}}$ is specified by a vertical solid line.

Figure 8

The ${}^{31}\mathrm{P}$ NMR spectra of the FeP single crystalline sample measured at 33 MHz (below reorientation field) when it was rotated around the $b$-axis (black squares). Red lines are the simulations by Eq. (16).

Figure 9

Angular dependencies of the ${}^{31}\mathrm{P}$ NMR spectra singularities positions for the FeP single crystalline sample measurements at 33 MHz. The dashed line indicates the Larmor field value (1.915 T), the dotted line indicates the field value of $\sqrt{B_{\mathrm{L}}^2-B_{\text{loc}}^2}$ at which the borders of cycloid subspectra merge (see text). Solid lines are $B\left(\alpha \right)$ approximations by Eq. (17).

Figure 10

The ${}^{31}\mathrm{P}$ NMR spectra of the FeP single crystalline sample measured at 140 MHz ($T=5\mathrm{K}$) when it was rotated around the $b$-axis (circles). For comparison, low field spectrum shifted by the Larmor fields difference is also depicted (left bottom panel, open red squares). Solid lines are the simulation curves (see text).

Figure 11

The angular dependencies of the peak-to-Larmor field separations for the four peaks in the ${}^{31}\mathrm{P}$ NMR spectra of the FeP single crystalline sample measured at 140 MHz ($T=5\mathrm{K}$) when it was rotated around the $b$-axis in steps of 15 degrees. Solid lines are $B\left(\alpha \right)$ approximations by Eq. (17).