Spin-charge coupling in lightly doped ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$

We use neutron scattering to study the influence of a magnetic field on spin structures of ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$. On cooling from room temperature, ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ goes through a series of antiferromagnetic (AF) phase transitions with different noncollinear spin structures. While a $c$-axis aligned magnetic field does not alter the basic zero-field noncollinear spin structures, a field parallel to the ${\mathrm{CuO}}_2$ plane can transform the noncollinear structure to a collinear one (“spin-flop” transition), induce magnetic disorder along the $c$ axis, and cause hysteresis in the AF phase transitions. By comparing these results directly to the magnetoresistance (MR) measurements of ${\mathrm{Nd}}_{1.975}{\mathrm{Ce}}_{0.025}{\mathrm{CuO}}_4$, which has essentially the same AF structures as ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$, we find that a magnetic-field-induced spin-flop transition, AF phase hysteresis, and spin $c$-axis disorder all affect the transport properties of the material. Our results thus provide direct evidence for the existence of a strong spin-charge coupling in electron-doped copper oxides.

Figure 1

${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ spin structures in (a) type-I∕III and (b) type-II noncollinear states, where spins are indicated by the arrows. $X$, $Y$, and $Z$ represent the interactions between $\mathrm{Nd}\text{−}\mathrm{Nd}$, $\mathrm{Nd}\text{−}\mathrm{Cu}$, and $\mathrm{Cu}\text{−}\mathrm{Cu}$ spins, respectively, as defined by Sachidanandam et al. (Ref. 12). (c) The schematic phase diagram of ${\mathrm{CuO}}_2$ planes in different phases at zero-field (bottom row) and ${\mathbf{B}}_{SF}\Vert \left[\overline{1}10\right]$ (top row). Here only $\mathrm{Cu}$ spins are shown for clarity. The filled and unfilled circles represent $L=0$ and $1∕2$ layers of $\mathrm{Cu}$ atoms, respectively. $T_1$, $T_2$, and $T_3$ represent transition temperatures for the three different noncollinear phases at zero field (Ref. 11).

Figure 2

The temperature dependence of $R_c$, $R_{\left[100\right]}$, and $R_{\left[110\right]}$ at zero field, where the subscripts represent the current directions. The resistances in all three directions go up rapidly with decreasing temperature. The inset shows the regular four-points setup. Throughout the measurement, the $c$ axis of the crystal is always along the axis of rotation and the magnetic field rotates within the ${\mathrm{CuO}}_2$ $\left(ab\right)$ plane.

Figure 3

Typical neutron scattering results around $(1∕2,1∕2,1)$ and $(1∕2,1∕2,2)$ Bragg peaks in the (a),(b) $\mathbf{B}=0$ spin noncollinear and (c),(d) $\mathbf{B}=5\mathrm{T}$ spin collinear states. We probed the magnetic Bragg peaks at 15, 40, and $80\mathrm{K}$ in type-III, II, and I phases, respectively. All peaks are fit by Gaussians on sloped backgrounds as shown by the solid lines. (e) The temperature dependence of the integrated intensities at $(1∕2,1∕2,1)$ and $(1∕2,1∕2,2)$ positions at $\mathbf{B}=5\mathrm{T}$. The type-III to II and type-II to I collinear phase transitions are around 30 and $70\mathrm{K}$, respectively.

Figure 4

(a) The in-plane $[H,H,1]$ scans across $(1∕2,1∕2,1)$ in two different processes at $40\mathrm{K}$. The schematic diagrams of processes $\mathbf{a}$ and $\mathbf{b}$ are shown in the inset. (b) The long $[1∕2,1∕2,L]$ scan in process $\mathbf{a}$, where $L$ changes from 0.8 to $5.2\mathrm{rlu}$. Only three resolution-limited peaks are found around $L=1$, 3, and 5. (c) Same scans as (b), but through process $\mathbf{b}$. Note that the $L$-widths of these peaks become considerably broader. The temperature and field in (b) are identical as that of (c), i.e., $T=40\mathrm{K}$ and $\mathbf{B}=5\mathrm{T}$. However, the processes of applying field are different, as shown in the inset of (a). The peaks in (b) and (c) are fitted by Gaussians and Lorentzians, respectively.

Figure 5

Magnetic field hysteresis effects on AF spin structures of ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ in all three phases. (a) $(1∕2,1∕2,1)$ Bragg position in phase II and (b) and (c) $(1∕2,1∕2,2)$ position in phase I and III, respectively. The corresponding processes of field and temperature are shown in the inset of each figure.

Figure 6

The field dependence of (a) integrated intensities and (b) FWHMs at the $(1∕2,1∕2,1)$ position during two different processes shown in the inset of (a). The error bars in (a) are obtained by taking the square root of total summed intensity in $L$-scans.

Figure 7

The integrated intensities of $(1∕2,1∕2,1)$, which shows temperature hysteresis across the transition (a) between type-II and III phases, and (b) between type-I and II phases. The arrows in the figures indicate the direction of changing temperatures. The insets show the detailed processes of field-temperature hysteresis.

Figure 8

$\Delta R_c∕R_c\left(0\right)$ as a function of increasing magnetic field at different temperatures around (a) $30\mathrm{K}$ and (b) $70\mathrm{K}$. Note that these temperatures are close to $T_3$ and $T_2$, respectively. The applied magnetic field is in the ${\mathrm{CuO}}_2$ $ab$-plane along the $\left[\overline{1}10\right]$ direction. The arrows in (a) indicate the temperature dependence of ${\mathbf{B}}_{SF}$. The inset in (b) plots the maximum of $\Delta R_c∕R_c\left(0\right)$ as a function of increasing temperature. It shows $1∕T$ behavior. Note that the vertical axes are log scale in (a) and linear scale in (b).

Figure 9

Angular dependence of $R_{\left[110\right]}$ at (a) $T=20\mathrm{K}$ in type-III phase and (b) $T=35\mathrm{K}$ in type-II phase, where $\left[110\right]$ indicates the current direction. The horizontal axes represent the angle (in degrees) between the magnetic field and the $a$ or $b$ axis which cannot be distinguished for the tetragonal system. Note that data in (a) at $1\mathrm{T}$ show a nonobservable MR effect while there are clear MR effects at $1\mathrm{T}$ in (b).

Figure 10

(a) Angular dependence of $R_{\left[100\right]}$ at $20\mathrm{K}$ and $10\mathrm{T}$. While we still observe the fourfold feature, the MR effects do not have the expected $90°$ symmetry. Although the effect could be an intrinsic property of the material, we speculate that this is due to the small misalignment of the sample with respect to the applied field. (b) Hysteresis behavior of $R_{\left[100\right]}$ around the transition between the type-II and III phases at $5\mathrm{T}$. At each measured temperature, a constant has been subtracted from the resistance values in processes $\mathbf{a}$ and $\mathbf{b}$ for clarity. The solid and dotted lines represent increasing ($\mathbf{b}$) and decreasing ($\mathbf{a}$) temperatures, respectively, as shown in the inset.

Figure 11

(a) $R_2-R_1$ during increasing and decreasing temperature processes, as shown by the arrows. The positions 1 and 2 are defined in the inset of (a). With increasing field, the widths of hysteresis become larger. (b) $R_{inc}-R_{dec}$, the differences between increasing and decreasing temperature processes at positions 1 and 2 are plotted by lines and symbols, respectively.

Figure 12

Angular dependence of $R_{\left[100\right]}$ and $R_c$ at $34\mathrm{K}$ and $5\mathrm{T}$ through processes $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{d}$ similar to that defined in Fig. 7a, except in this case the final temperature was fixed at $34\mathrm{K}$. Process $\mathbf{a}$ does not cross the phase transition temperature, and therefore does not exhibit disorder. Processes $\mathbf{b}$ and $\mathbf{d}$ have spin disorder. While clear differences are seen in $R_c$, there are no observable differences in $R_{\left[100\right]}$ for these different processes.