Atomic reconstruction induced by uniaxial stress in MnP

In condensed matter physics, pressure is frequently used to modify the stability of both electronic states and atomic arrangements. Under isotropic pressure, the intermetallic compound MnP has recently attracted attention for the interplay between pressure-induced superconductivity and complicated magnetic order in the vicinity . By contrast, we use uniaxial stress, a directional type of pressure, to investigate the effect on the magnetism and crystal structure of this compound. An irreversible magnetisation response induced by uniaxial stress is discovered in MnP at uniaxial stress as low as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.04\ \text {GPa}$$\end{document}0.04GPa. Neutron diffraction experiments reveal that uniaxial stress forms crystal domains that satisfy pseudo-rotational symmetry unique to the MnP-type structure. The structure of the coexisting domains accounts for the stress-induced magnetism. We term this first discovered phenomenon atomic reconstruction (AR) induced by uniaxial stress. Furthermore, our calculation results provide guidelines on the search for AR candidates. AR allows crystal domain engineering to control anisotropic properties of materials, including dielectricity, elasticity, electrical conduction, magnetism and superconductivity. A wide-ranging exploration of potential AR candidates would ensure that crystal domain engineering yields unconventional methods to design functional multi-domain materials for a wide variety of purposes.


Supplementary information I. Surfaces of pristine sample and stress-released sample
As seen in Fig. S1, light white lines appeared along b-axis on the surface of stress-released sample. We believe that contrast between the dark green and light white lines indicates boundaries separating nonidentical crystal structure. We also conclude that inhomogeneous stress inside the cuboid sample induced a set of structural changes that in turn caused a stepwise increase in magnetic susceptibility along a-axis (see

II. Preliminary neutron diffraction experiment
A preliminary neutron diffraction experiment was performed using the Sika spectrometer installed at the ANSTO. Fig. S2 shows rocking curves for pristine sample and stress-released sample. The experimental results suggest that uniaxial stress along a-axis irreversibly induces crystal structure which seems to possess six-fold symmetry around b-axis of pristine sample.

III. Neutron diffraction intensities of nuclear and ferromagnetic reflection
As for observation of neutron diffraction intensity, peaks of magnetic reflection due to ferromagnetic order always overlap those of nuclear reflection. Therefore, we need to subtract intensities of nuclear reflection from total intensities observed in the ferromagnetic phase to get intensities of ferromagnetic reflection.
We obtained integrated intensities at 10 K (helimagnetic phase) and 100 K (ferromagnetic phase), Iobs(T = 10 K) and Iobs(T = 100 K), respectively, by processing the data taken in the SENJU diffractometer with the software STARGazer [1]. The observed integrated intensities of nuclear and ferromagnetic reflection, Iobs(nuclear) and Iobs(ferromagnetic), respectively, were obtained by the following equations: At 320 K (paramagnetic phase), intensities of nuclear reflection are attenuated by the effects of thermal vibrations known as the Debye-Waller factor. At 10 K, where MnP has the helical magnetic structure in zero magnetic field, not the conical one, only nuclear reflection exists at Bragg points (with integer indices), while magnetic reflection appears not at the Bragg points, but at the satellite points on both sides of them.
Therefore, we adopted the integrated intensities at 10 K (except the helimagnetic satellite reflection), not at 320 K, as Iobs(nuclear). The values of Iobs(nuclear) well corresponded to our calculation results.
As an example of the ferromagnetic and helimagnetic satellite reflection, Fig. S3 shows time-of-flight profiles including (-2 0 0) reflection for pristine sample at 10 K and 100 K. There exists finite Iobs(ferromagnetic) at (-2 0 0), where nonzero intensity of ferromagnetic reflection was expected according to our calculation.
As for calculation of neutron diffraction intensity, the fractional coordinates of MnP [2] was used to obtain calculated intensities of nuclear and ferromagnetic reflection. We adopted the value 1.33 µB as the magnetic moment of Mn along c-axis in the ferromagnetic state [3].

ⅠV. Neutron diffraction measurements for several stress-released samples
We performed time-of-flight neutron diffraction measurements at 10 K, 100 K and 320 K for stress-released samples with various released uniaxial stress along a-axis using the SENJU diffractometer installed at the MLF, J-PARC. Fig. S4 shows part of (H0L) planes of reciprocal lattice space in the paramagnetic phase

V. X-ray Laue backscattering patterns of pristine sample and stress-released sample
We observed X-ray Laue backscattering patterns of pristine sample and stress-released sample at room temperature. Fig. S5 shows the Laue patterns in the direction of a-axis. The diffraction peaks from stressreleased sample were comparable in half width to those from pristine sample, although the pattern of stressreleased sample was modified significantly. The experimental result indicates that formation of the stressinduced domains is different from plastic deformations; if it belonged to plastic deformations such as slip deformation, half widths of diffraction peaks from stress-released sample would expand in response to inhomogeneous bends of crystal lattice.