Vortex Lattice Studies in ${\mathrm{CeCoIn}}_5$ with $H\perp c$

We present small angle neutron scattering studies of the vortex lattice (VL) in ${\mathrm{CeCoIn}}_5$ with magnetic fields applied parallel ($H$) to the antinodal [100] and nodal [110] directions. For $H\parallel [100]$, a single VL orientation is observed, while a 90° reorientation transition is found for $H\parallel [110]$. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, $\Gamma =2.0\pm 0.05$. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for $H\parallel [001]$. At high fields, above which the upper critical field ($H_{c2}$) becomes a first-order transition, an increased disordering of the VL is observed.

Figure 1

VL structure with $H\parallel [100]$ (antinodal direction). (a) Diffraction pattern obtained at 9.0 T and 50 mK showing a distorted hexagonal VL. Only Bragg peaks on the upper half of the detector were rocked through the Ewald sphere. The open circles show positions of Bragg peaks obtained by a reflection through $q=0$. (b) Field dependence of the VL opening angle $\beta$ defined in (a), at 50 and 350 mK, following either a field cool (FC) or field ramp (FR) procedure [31]. The dotted line represents $H_{c2}$ at 50 mK [8].

Figure 2

VL with $H\parallel [110]$ (nodal direction). Diffraction pattern obtained at 90 mK and at an applied field of 7.5 T (a) and 9.5 T (b), respectively. (c) Field dependence of the VL opening angles $\beta$, $\varphi$, and $\alpha$ at 90 mK. The yellow (light gray) area indicates the transition region between the two VL orientations. The inset shows a diffraction pattern as well as a schematic of the rotated two-domain HF phase. (d) VL phase diagram showing the extent of the LF and HF VL phases. $H_0$ and $H_{c2}$ are adapted from Ref. 8 and $Q$ phase from Ref. 15.

Figure 3

Field dependence of the VL form factor. (a) Form factor with $H\parallel [100]$. The dashed lines are guides to the eye and $H_{c2}$ is shown for $T=50\mathrm{mK}$. (b) Comparison of $|F(q){|}^2$ measured with field along [100] and [001] [27]. (c) Multiplying the form factor for $H\parallel [100]$ by $(2.55{)}^2=6.5$ causes $|F(q){|}^2$ for the two field orientations to fall on a single curve.

Figure 4

VL rocking curve widths corresponding to the data in Fig. 1b. The significant scatter in the data at low fields is due to the low scattered intensity and higher background at shorter $q$. The calculated experimental resolution is shown by the dashed line. The insert compares the rocking curves obtained at 10.5 T following a FC and FR. The lines are Gaussian fits to the data and ${\theta }_0$ denotes the center of the rocking curve.