Spherical neutron polarimetry of the magnetic structure in $\mathrm{Ho}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$: Interplay between magnetic phases and superconductivity

Spherical neutron polarimetry has been used to answer open questions about different magnetic phases in $\mathrm{Ho}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$, which are important in their interplay with superconductivity. We established that the incommensurate ${\mathbf{a}}^{*}$ structure of ${\mathbf{k}}_3=\left(0.58500\right)$ at $5.4\mathrm{K}$ in a zero magnetic field is a transverse-amplitude modulated wave with the magnetic moment along the $\mathbf{b}$ direction of the tetragonal structure. The depolarization of a neutron beam scattered from the ${\mathbf{k}}_2=\left(000.915\right)$ reflections reveals a multidomain state but does not allow an unambiguous determination of the spin configuration. Based on present knowledge of borocarbides and other rare-earth systems we give preference to a long-range incommensurate helical structure as the origin of the ${\mathbf{k}}_2=\left(000.915\right)$ reflections.

Figure 1

(Color online) Determined ICM ${\mathbf{a}}^{*}$ structure of $\mathrm{Ho}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$: amplitude-modulated magnetic moment ($\mathbf{b}$ direction) propagating in the $\mathbf{a}$ direction.

Figure 2

(Color online) $\omega$ scan through the (0 0 3) reflection at several temperatures. Arrows point to the $\omega$ values where the polarization analysis has been performed. We attribute the double-peak structure to two slightly twisted crystallites.

Figure 3

Two magnetic configurations possible for $\mathrm{Ho}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ with a wave propagating in the $\mathbf{c}$ direction. $\left(c_1\right)$ Helix model. $\left(c_2\right)$ Antiphase domain formation with moments in a [1 1 0], respectively, $[-1-10]$ direction. A schematic illustration of Sjöström[20] for two specific magnetic helical structures: (a) bunched circular helix, (b) modulated helix.

Figure 4

Neutron powder-diffraction pattern of $\mathrm{Ho}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ at $T=5.25\mathrm{K}$. The first row of the vertical markers denotes the chemical structure, the second row the CM ${\mathbf{k}}_1$, the third row the ICM ${\mathbf{k}}_2$, the fourth row the ICM ${\mathbf{k}}_3$, and the fifth row denotes the third harmonic of the ICM ${\mathbf{k}}_2$ structure. The regions from 66.5° to 68.5° and from 77.5° to 81.5° with Bragg peaks from the aluminum sample container were excluded from the refinement.

Figure 5

(Color online) Temperature dependence of three magnetic peaks corresponding to CM ${\mathbf{k}}_1$ and ICM ${\mathbf{k}}_2$ and ${\mathbf{k}}_3$ wave vectors for $\mathrm{Ho}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$. The onset of the CM ${\mathbf{k}}_1$ structure, e.g., (1 0 0) peak is correlated with a pronounced intensity increase of the pure nuclear reflections, e.g., (2 0 0). We ascribe this to a strong extinction effect caused by a pronounced change of domain structure. The solid lines are guides to the eye.