NMR Determination of the Low-Field Magnetic Structure of the Cu-Based Mineral Rouaite Cu$_2$(OH)$_3$NO$_3$

Abstract

Frustrated interactions in the Cu-based mineral rouaite with alternating antiferromagnetic and ferromagnetic spin chains, Cu$_2$(OH)$_3$NO$_3$, introduce non-trivial magnetic ground states and exotic excitations arising from them. We investigated the magnetic structure of Cu$_2$(OH)$_3$NO$_3$ by $^1$H- and $^2$H-NMR measurements on single crystals. The internal fields in the ordered state were microscopically measured using the H nuclear moments as a local probe. The directions of the ordered moments were determined by comparing the experimental results to model calculations. The obtained magnetic structure suggests the importance of Dzyaloshinskii-Moriya interactions in stabilizing the low-field magnetic structure. The present result advances the theoretical understanding of the low-field magnetic states and will enable exploration of the exotic magnetic states emerging in high magnetic fields.

Figures (9)

• Figure 1: Crystal structure of Cu$_2$(OH)$_3$NO$_3$: (a) projected on the $\bm{ab}$ plane and (b) viewed from a direction close to the $\bm{b}$ axis. The thin black lines represent the unit cell. Cu1 (Cu2) sites form FM (AFM) chains along the $\bm{b}$ direction through Cu--O--Cu superexchange paths. The chain direction coincides with the $2_1$ screw axis in the $P2_1$ space group. H1, H2, and H3 sites are connected to O sites to form OH$^-$ groups, and participate in an interlayer hydrogen-bonding network essential for stabilizing the structure but not expected to allow significant exchange interactions. These hydrogen bonds are to NO$_3^{-}$ ions (not shown) stacked above and below the 2-D magnetic network, leading to a long and tortuous magnetic exchange pathway along the $\bm{c}$ direction.
• Figure 2: (a), (c) $^2$H-NMR spectra at room temperature measured in fields applied at 56$^\circ$ from the (a) $\bm{a}$ and (c) $\bm{b}$ axes. The NMR peaks assigned to the H1 and H2/H3 sites are labeled by filled circles and open triangles, respectively. (b), (d) Angle dependence of peak positions measured upon rotation within the (b) $\bm{ac}^{\ast}$ and (d) $\bm{bc}^{\ast}$ planes. The circle and triangle symbols correspond to the NMR peaks assigned in (a) and (c). The field angle was measured from the $\bm{a}$ axis for (b) and from the $\bm{b}$ axis for (d). The field orientations for the NMR spectra shown in (a) and (c) are indicated by vertical dashed lines, together with the $\bm{a}$, $\bm{b}$ and $\bm{c}^{\ast}$ directions.
• Figure 3: $^2$H-NMR spectra at representative temperatures measured in fields along the (a) $\bm{a}$, (b) $\bm{b}$, and (c) $\bm{c}^{\ast}$ axes. The peak positions shift to lower frequencies for $\bm{H}\!\parallel\bm{a}$ and $\bm{H}\!\parallel\bm{b}$ and higher frequencies for $\bm{H}\!\parallel\bm{c}^{\ast}$ due to the increase in the magnetization at low temperatures. The direction of the shift is determined by the sign of the coupling constants between the nuclear and electronic magnetic moments. The H1 and H2/H3 sites are more clearly resolved at low temperatures where the magnetization is larger for $\bm{H}\!\parallel\bm{a}$ and $\bm{H}\!\parallel\bm{c}^{\ast}$, while all sites are overlapped for $\bm{H}\!\parallel\bm{b}$ due to the similar coupling constants along the $\bm{b}$ axis for all H sites.
• Figure 4: (a) Temperature dependence of Knight shift for the $\bm{a}$, $\bm{b}$, and $\bm{c}^{\ast}$ directions. The Knight shifts for the H1 and H2/H3 sites are represented by filled circles and open triangles for the $\bm{a}$ and $\bm{c}^{\ast}$ directions, respectively. For the $\bm{b}$ direction, the Knight shift is plotted with filled triangles as the three H sites are not resolved in the NMR spectra. (b) The Knight shift is plotted against the bulk magnetization at the corresponding temperatures. The dashed lines are the results of linear fitting. From the slopes of these lines, the hyperfine coupling constants are estimated. The finite intercept at $\chi=0$ is caused by the electric quadrupolar interactions for $^2$H nuclear spins.
• Figure 5: Field-sweep $^1$H-NMR spectra for fields along the (a) $\bm{a}$, (b) $\bm{b}$, and (c) $\bm{c}^{\ast}$ directions. For all the field directions, the sharp $^1$H-NMR spectra in the paramagnetic state disappear once below the main transition at $T_\text{N1}$ and are restored below $T_\text{N2}$. A spectrum at 5 K in $H\parallel a$ is expanded by a factor of ten and shown together by a black line. The transition temperatures depend on the field orientation. The incommensurate (IC) phase in the intermediate temperature range between $T_\text{N1}$ and $T_\text{N2}$ is indicated by vertical arrows. In the ground state below $T_\text{N2}$, many split peaks due to the internal fields were observed.