Nature of the Magnetic Order in the Charge-Ordered Cuprate ${\mathrm{La}}_{1.48}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_4$

Using polarized neutron scattering we establish that the magnetic order in ${\mathrm{La}}_{1.48}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_4$ is either (i) one dimensionally modulated and collinear, consistent with the stripe model or (ii) two dimensionally modulated with a novel noncollinear structure. The measurements rule out a number of alternative models characterized by 2D electronic order or 1D helical spin order. The low-energy spin excitations are found to be primarily transversely polarized relative to the stripe ordered state, consistent with conventional spin waves.

Figure 1

Models for the magnetic order in La-based cuprates at $x=1/8$ doping. (a) One-$\mathbf{q}$ domain with charge stripes (lines of open circles) and collinear spin order [2]. (b) One-$\mathbf{q}$ domain with helical spin order. (c) Collinear two-$\mathbf{q}$ structure of a diagonally modulated commensurate AFM [14]. (d) Two-$\mathbf{q}$ order of charge and spins in a noncollinear structure.

Figure 2

(a) Reciprocal space of the square ${\mathrm{CuO}}_2$ lattice showing the three quartets of magnetic peaks investigated. The peaks are displaced from AFM wave vectors by $\pm {\mathbf{q}}_1=(\pm \delta ,0)$ and $\pm {\mathbf{q}}_2=(0,\pm \delta )$ with $\delta \simeq x=0.12$. Also shown are the axes to which the polarization $\mathbf{P}$ and magnetic scattering are referred. (b)–(c) Unpolarized elastic scans through the expected Bragg peak positions for a $\pi$ spiral [19].

Figure 3

SF and NSF elastic scattering at $(1/2,1/2)+{\mathbf{q}}_1$ with $\mathbf{P}\parallel z$. The two-peak line shape is due to the presence of two crystallites separated by $\sim 1°$. The solid line in (a) is a fit to two Gaussians. The lines in (b)–(d) were obtained from a fit to the same line shape as in (a) but with the overall intensity scale and background allowed to vary.

Figure 4

Processed polarized-neutron data taken at $T=10\mathrm{K}$, showing the in-plane component $M_y$ of the magnetic cross section at each of six IC peaks of type ${\mathbf{q}}_1$ (left) and ${\mathbf{q}}_2$ (right). $M_y$ was calculated both from the SF data ($M_y=I_{\mathrm{SF}}^x-I_{\mathrm{SF}}^y$) and from the NSF data ($M_y=I_{\mathrm{NSF}}^y-I_{\mathrm{NSF}}^x$). After checking for consistency, data thus obtained were combined. The solid lines represent the model calculation described in the text.