Magnetostriction and Magnetostructural Domains in Antiferromagnetic ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6$

We use high-resolution neutron Larmor diffraction and capacitative dilatometry to investigate spontaneous and forced magnetostriction in undoped, antiferromagnetic ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.0}$, the parent compound of a prominent family of high-temperature superconductors. Upon cooling below the Néel temperature $T_N=420\mathrm{K}$, Larmor diffraction reveals the formation of magnetostructural domains of characteristic size $\sim 240\mathrm{nm}$. In the antiferromagnetic state, dilatometry reveals a minute ($4\times {10}^{-6}$) orthorhombic distortion of the crystal lattice in external magnetic fields. We attribute these observations to exchange striction and spin-orbit coupling induced magnetostriction, respectively, and show that they have an important influence on the thermal and charge transport properties of undoped and lightly doped cuprates.

Figure 1

(a) Temperature dependence of the $(\begin{array}{ccc}\frac{1}{2}& \frac{1}{2}& 5\end{array})$ antiferromagnetic Bragg peak intensity measured by neutron diffraction from ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.0}$. The line is a guide to the eye. The red and green symbols indicate temperatures below and above $T_N=420\mathrm{K}$, respectively. (b) Neutron beam polarization $P$ measured at the $(\begin{array}{ccc}2& 0& 0\end{array})$ Bragg reflection for the Larmor phase $\varphi =5000\mathrm{rad}$ (see Fig. 2). The reduction of $P$ below $T_N$ indicates a reduction of the structural domain size. (c) Sketch of the Larmor diffraction method. The radio frequency coils ($C1–C4$) act on the neutron spins (blue) in the same way as an effective static magnetic field $H$ (green).

Figure 2

Neutron beam polarization $P$ versus Larmor phase $\varphi$ at $T=300$ and 500 K for the $(\begin{array}{ccc}2& 2& 0\end{array})$ and $(\begin{array}{ccc}2& 0& 0\end{array})$ nuclear Bragg peaks. $P(\varphi =0)$ is normalized to 1. Lines are the results of fits to Gaussian peak profiles (see text). Inset: $P(\varphi )$ at $T=40\mathrm{K}$ for the $(\begin{array}{ccc}\frac{1}{2}& \frac{1}{2}& 5\end{array})$ antiferromagnetic Bragg reflection (blue), compared to the $(\begin{array}{ccc}2& 2& 0\end{array})$ and $(\begin{array}{ccc}0& 0& 6\end{array})$ nuclear Bragg reflections (red and green, respectively).

Figure 3

Forced magnetostriction at $T=2\mathrm{K}$ measured by dilatometry parallel to the Cu–O–Cu bond direction $x$ in the ${\mathrm{CuO}}_2$ plane. The field-induced change of the sample length along $x$ with magnetic field $\mathbf{B}$ applied parallel to the $x$, $y$, and $z$ directions is plotted in red, green, and blue, respectively. Inset: illustration of spin-orbit coupling induced magnetostriction for a single magnetostructural domain with $\mathit{B}\parallel b$. Because of magnetostriction, the spin-flop transition induced by the field is associated with a realignment of the crystallographic unit cell (dashed line for $\mathit{B}=0$, solid line for $\mathit{B}\gtrsim 5\mathrm{T}$.) The orthorhombic distortion is exaggerated for clarity.