Magnetic-field-induced orientation of superconducting $\mathrm{Mg}{\mathrm{B}}_2$ crystallites determined by x-ray diffraction

X-ray diffraction studies of fine polycrystalline samples of $\mathrm{Mg}{\mathrm{B}}_2$ in the superconducting state reveal that crystals orient with their $c$ axis in a plane normal to the direction of the applied magnetic field. The $\mathrm{Mg}{\mathrm{B}}_2$ samples were thoroughly ground to obtain average grain size $5–10\mu \mathrm{m}$ in order to increase the population of free single crystal grains in the powder. By monitoring Bragg reflections in a plane normal to an applied magnetic field we find that the powder is textured with significantly stronger $(0,0,l)$ reflections in comparison to $(h,k,0)$, which remain essentially unchanged. The orientation of the crystals with the $ab$ plane parallel to the magnetic field at all temperatures below $T_c$ demonstrates that the sign of the torque under magnetic field does not alter, in disagreement with current theoretical predictions.

Figure 1

(Color online) (a) Sketch of the diffractometer-magnet configuration. The scattering vector is in the plane normal to the direction of the applied magnetic field. (b) Illustration of the effect of single-crystal grains reorientations under magnetic field on the $(0,0,l)$ and $(h,k,0)$ reflections as a function of the scattering angle $2\theta$. The two sets of reflections at zero field (random orientation) are represented by same shape and intensity peaks for simplicity. Preferred alignment of the $c$ axis along the magnetic field, reduces the intensity of the $(0,0,l)$ increasing that of the $(h,0,0)$. If the grains orient with the $ab$ plane parallel to the field $\mathbf{H}\perp \mathbf{c}$, the $(0,0,l)$ will become more intense and there will be only a slight effect on the intensity of the $(h,0,0)$.

Figure 2

(Color online) Intensity versus scattering angle $2\theta$ at $T=4.5\mathrm{K}$ of the (0,0,1) for types of $\mathrm{Mg}{\mathrm{B}}_2$ samples (a) fiber grown (b) loosely sintered pellet grown at various magnetic fields as indicated. The intensity of each point is integrated over $60\text{degrees}$ rotation of the sample angle $\varphi$. Whereas a significant increase in intensity is observed for finely ground powder (filled symbols), there is almost no change in intensity for samples consisting of coarse grains (open symbols). After lowering the magnetic field the powder was randomized spontaneously by mechanical vibrations of the compressor-cooled magnet with a typical time constant of a few minutes with small remnant alignment (Ref. 20).

Figure 3

(Color online) Intensity versus scattering angle $2\theta$ at $T=4.5\mathrm{K}$ of (1,0,0) and (1,1,0) in-plane Bragg reflections in magnetic field.

Figure 4

(Color online) Intensity versus scattering angle $2\theta$ at $T=50\mathrm{K}$ at 0 and $4\text{Tesla}$ of the (0,0,1) of a finely ground sample. The sample was then cooled in field to reproduce the results obtained for the zero-field cooled sample shown in Fig. 2b.

Figure 5

(Color online) Integrated intensity of (0,0,1) versus magnetic field at various temperatures, for the finely ground loosely sintered pellet grown sample. We suggest to identify $H_{c2}^{\Vert c}\approx 0.5\mathrm{T}$ as the point of deviation from the trend of the low field data, i.e., with development of the first minimum and to assign $H_{c2}^{\perp c}\approx 3\mathrm{T}$ with the point of deviation from the asymptotic behavior at high fields. Magnetization measurements of $H_{c2}^{\perp c}$ and $H_{c2}^{\Vert c}$ at $32.5\mathrm{K}$ on similar powders from Ref. 3 are shown with dashed lines.