Magnetization of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_{4+\delta }$ $(0⩽x⩽0.5)$: Spin-glass and memory effects

We have studied the magnetization of a series of spin-charge-ordered ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_{4+\delta }$ single crystals with $0⩽x⩽0.5$. For fields applied parallel to the $ab$ plane there is a large irreversibility below a temperature $T_{\mathrm{F}1}\sim 50\mathrm{K}$ and a smaller irreversibility that persists up to near the charge-ordering temperature. We observed memory effects in the thermoremnant magnetization across the entire doping range. We found that these materials retain a memory of the temperature at which an external field was removed and that there is a pronounced increase in the thermoremnant magnetization when the system is warmed through a spin reorientation transition.

Figure 1

(a) Tetragonal unit cell of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_4$. (b) Pattern of spin-charge ordering in the $\mathrm{Ni}{\mathrm{O}}_2$ planes in ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$. Arrows denote $S=1$ spins on the ${\mathrm{Ni}}^{2+}$ ions and open circles represent holes, here assumed centered on Ni sites. The dashed lines indicate the charge stripes. The O sites are not shown for clarity.

Figure 2

Field-cooled (FC) and zero-field-cooled (ZFC) dc magnetization of ${\mathrm{La}}_{1.725}{\mathrm{Sr}}_{0.275}\mathrm{Ni}{\mathrm{O}}_4$. The curves were measured with a field of $500\mathrm{Oe}$ applied parallel to the $ab$ plane. $T_{\mathrm{SO}}$ and $T_{\mathrm{CO}}$ are the magnetic- and charge-ordering temperatures, respectively. The temperatures $T_{\mathrm{F}1}$ and $T_{\mathrm{F}2}$ are explained in the text.

Figure 3

Field-cooled (FC) and zero-field-cooled (ZFC) magnetization of single crystals of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_{4+\delta }$ with $0⩽x⩽0.5$. A rotating sample mount was employed to obtain the data with $H\Vert c$ for the $x=0.333$ crystal.

Figure 4

Charge-ordering temperature of single crystals of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_{4+\delta }$ as a function of Sr doping $x$. The inset shows the charge-ordering temperatures plotted against the effective hole concentration $n_h=x+2\delta$; the error in $n_h$ is $\pm 0.02$ due to the uncertainty in the oxygen content. Literature data are taken from Refs. 8, 12, 13, 14, 17, 22.

Figure 5

(Color online) Time dependence of the remnant magnetization for a crystal of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_4$ with $x=0.333$. The signal was induced by application of a magnetic field of strength $500\mathrm{Oe}$ parallel to the $ab$ plane for $5\min$ at $T=2\mathrm{K}$. The time is measured after the field has been switched off. The curve is the best fit to a stretched exponential.

Figure 6

(Color online) The thermoremnant magnetization (TRM) of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_4$ induced by field cooling down to $T_0=10\mathrm{K}$ in a field of $500\mathrm{Oe}$ followed by cooling to $2\mathrm{K}$ in zero field and measuring while warming in zero field. The symbols distinguish measurements made with the field applied parallel to the $ab$ plane (solid symbols) and parallel to the $c$ axis (open symbols). Panel (a) shows data for $x=0.2$, and panel (b) shows the corresponding measurements for the $x=0.333$ and $x=0.5$ samples, showing the striking effects associated with the spin reorientation transition (indicated by $T_{\mathrm{SR}}$) in these two compositions. The rotating mount was used to obtain $H\Vert c$ data for the $x=0.333$ sample.

Figure 7

(Color online) The TRM of LSNO, $x=0.275$, for different values of $T_0$, where $T_0$ is the temperature at which the magnetic field was switched off in the protocol described in the text and in the caption to Fig. 6. (a) shows data for $T_0=10\mathrm{K}$, $30\mathrm{K}$, $50\mathrm{K}$, $70\mathrm{K}$, and $200\mathrm{K}$, and (b) shows data for $T_0=70\mathrm{K}$, $90\mathrm{K}$, $140\mathrm{K}$, and $200\mathrm{K}$.

Figure 8

(Color online) The TRM of LSNO, $x=0.333$, for different values of $T_0$, where $T_0$ is the temperature at which the magnetic field was switched off in the protocol described in the text and in the caption to Fig. 6.

Figure 9

(Color online) The TRM of samples of LSNO with $x=0$, $\delta =0.11$, and $x=0.37$. Here, $T_0=10\mathrm{K}$ is the temperature at which the magnetic field was switched off in the protocol described in the text and in the caption to Fig. 6. The spin reorientation temperature $T_{\mathrm{SR}}$ of the $x=0.37$ sample is indicated.

Figure 10

(Color online) The TRM signal for the LSNO sample with $x=0.2$ resulting from the following protocol. First, the sample was cooled from room temperature to $T_0=20\mathrm{K}$ in a field of $500\mathrm{Oe}$ applied parallel to the $ab$ plane, the field removed, and the sample cooled to $2\mathrm{K}$ in zero field. The TRM was then measured while warming from $2\mathrm{K}\text{to}30\mathrm{K}$, then while cooling from $30\mathrm{K}\text{to}20\mathrm{K}$, and finally while warming from $20\mathrm{K}\text{to}60\mathrm{K}$.