5.4 Conclusion
6.1.1 Reciprocal-space tomography of the zero-eld cycloidal
SANS measurements with the wide-angle rotation (DOM angle) of the sam-ple were carried out at the Paul Scherrer Institute using a 25 mg single crystal of GaV4S8. The experiments were performed by S. Bordács and J.S. White, and I analyzed the data for the reconstruction of the tomographic images.
The sample was mounted on the sample stick with its 1¯10
direction co-aligned with the axis of the stick. Thereby, the high-symmetry crystallo-graphic planes,(111),(110), 11¯2
and (001), were brought perpendicular to the incident neutron beam and imaged during a half revolution of the sample, as shown in Fig. 6.1. Indeed, upon the half revolution of the sample, the full volume of the scattered intensity can be recovered.
The neutron wavelength of λn = 6Å was selected with the detector dis-tance as well as the collimator length set to d=8 m. The sample was cooled down toT = 10K in zero eld. Thereafter, it was rotated in 1◦steps followed by the SANS data acquisition of 60 s. The same measurements were repeated at T = 20K, in the paramagnetic phase of GaV4S8, which were subtracted as a background from the low-temperature measurements.
𝒌𝒊𝒏
Neutron source [110]
[001] [111]
𝒌𝑜𝑢𝑡
(110) (001)
(111) Reciprocal-space
image
Sample [110]
Figure 6.1: SANS imaging upon the wide-angle rotation of the sample. The rotation of the sample around the
1¯10
axis allows for the SANS imaging of the full three dimensional structure of the q-states.
Figure 6.2 shows the background-corrected SANS intensity maps averaged over a 10◦ moving window. In most of the SANS images with an arbitrary orientation six Bragg-spots are visible. This is, however, not the signature of the phase-locked triple-q structure of a skyrmion lattice, since only cycloidal modulations emerge in zero eld [26]. Instead, the spots are associated to cycloidal modulations in dierent rhombohedral domains the sample. The full three-dimensional distribution of the magnetic propagation vectors was
0° 10° 20° 30° 40° 50° 60° 70° 80°
90° 100° 110° 120° 130° 140° 150° 160° 170°
180° 190° 200°
(001)
(110)
(112)
(111)
(112) (112)
(111) [110]
Figure 6.2: SANS images measured upon the wide-angle rotation of GaV4S8. The images show the SANS intensities averaged over a 10◦ moving window in consecutive rotation steps of 10◦ The corresponding rotation angles are indicated in the top left corner of each frame. The vertical rotation axis is parallel to the
1¯10
crystallographic axis, as indicated in the rst image.
Images where the neutron beam is approximately perpendicular to a high-symmetry planes of the cubic setting are highlighted by red frames.
reconstructed using the full set of SANS images. Figure 6.3 (a) displays a per-spective view of the tomographic image of the modulation wavevectors with scattered intensities exceeding a distinct threshold value. The reciprocal-space distribution of the q-vectors can be decomposed to four intersecting rings with a xed radius, lying within the four {111}-type planes, as shown in Figs. 6.3 (b) and (c).
Each ring represents the scattering of one of the four polar domains that form below TS, featuring magnetic propagation vectors, q, conned to the plane normal to the associated rhombohedral axis, as shown in Fig. 6.3 (c), in accordance with the zero-eld solution of the Landau-functional in Eq. 2.12.
The length of the modulation vectors is xed by the relative strength of the Dzyaloshinsky-Moriya interaction (DMI) and the symmetric exchange, i.e. |q| ∝D/J. The total scattering intensities are roughly the same within each ring, indicating a nearly equal population of the rhombohedral domains in the bulk sample. Remarkably, the cycloidal wavevectors are distributed evenly over the rings in each {111}-type plane, suggesting that the in-plane magnetic anisotropy is relatively weak in GaV4S8. This partial order lies in stark contrast with B20 helimagnets, where the cubic anisotropy selects specic wavevectors at all temperatures in zero eld [29, 79, 80]. The order seen in GaV4S8 is more reminiscent of liquid crystals, but instead of uctua-tions of molecular orientauctua-tions in real space, here the orientational disorder
qz [nm-1]
(a) (b) (c)
Figure 6.3: Panel (a): Three-dimensional distribution of the modulation wavevectors in GaV4S8 as recovered by SANS tomography. Panel (b): Graph-ical representation of the reciprocal-space structure as four intersecting rings.
Each ring corresponds to the manifold of the modulation wavevectors in a sin-gle rhombohedral domain, lying within the plane normal to the corresponding rhombohedral axis as visualized in panel (c).
is reected by a broad q distribution. While the role of pinning is clear from these data, we cannot conclude about the spatial variations of the wavevec-tors, namely if their broad distribution is related to the rhombohedral domain walls or their variation occurs on the sub-domain scale.
Figure 6.4 displays the SANS images recorded in the major crystal planes together with the 3d tomography images. The Bragg-condition holds for the modulation vectors lying approximately within the plane normal to the neu-tron beam, given by the intersection of the full 3d structure and the image plane. For instance, the ring seen in the scattered intensity in the rst SANS image in Panel (a) corresponds to modulation vectors in the unique [111]
domain [displayed in blue color in Panel (c)]. The six spots superimposed on the ring intensity originate from those q-vectors within the three other structural domains which lie close to the (111) plane. Similarly, in the (110) plane shown in Panel (d), the top and bottom peaks correspond to two do-mains wherein the polar axis spans 35.2◦ with the axis of the neutron beam, whereas the other four spots to the side correspond to the two domains with their rhombohedral axis orthogonal to the neutron beam. This assignment of dierent regions of the scattering pattern to the dierent polar domains allows for the domain-specic analysis of the magnetic correlations. In par-ticular, by tracking the anomalies in the SANS intensity or the modulus of theq-vectors at specic regions of the SANS pattern, the phase transitions in the dierent domains can be distinguished. This provides a complementary
[110]
[111]
(112) (111) [110]
[112]
[110]
[110]
(001) [110]
[001]
(110)
(a) (b) (c) (d)
Figure 6.4: SANS images in high symmetry crystal planes compared with the 3d tomography image and its graphical representation viewed from the direction of the neutron beam. Rings with the four dierent colors represent scattering from the four types of rhombohedral domains.
method to bulk magnetization measurements to separate the critical elds of the magnetic phase transitions with respect to the angle enclosed by the magnetic eld and the rhombohedral axis. This method will be employed in sections 7.2.2 and 8.3 to assign the critical elds determined by magnetiza-tion measurements to magnetic phase transimagnetiza-tions within each rhombohedral domain in GaV4Se8 and GaMo4S8, respectively.