Weak ferromagnetic spin and charge stripe order in ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$

We present magnetization and specific heat data of a ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$ single crystal in high magnetic fields. From the charge and spin stripe ordering temperatures, as well as a magnetic low temperature transition, we have constructed the electronic phase diagram for fields up to $14\text{Tesla}$. While the charge stripe ordering temperature $T_{\mathrm{CO}}$ is independent of the magnetic field, there is a significant shift of the spin stripe ordering temperature $T_{\mathrm{SO}}$ of about $1.5\mathrm{K}∕\text{Tesla}$, if the magnetic fields are applied parallel to the $\mathrm{Ni}{\mathrm{O}}_2$-planes. The specific heat measurements indicate a large anomalous entropy change at $T_{\mathrm{CO}}$. In contrast, no significant entropy change is observed at the spin stripe transition. The high field magnetization experiments reveal the presence of in-plane weak ferromagnetic moments in the charge stripe ordered phase. From a phenomenological analysis, the magnetic correlation length of these moments is determined. We suggest that the weak ferromagnetism is due either to the presence of bond-centered charge stripes or to double exchange interactions across site-centered charge stripes.

Figure 1

(a) Static susceptibility $\chi =M∕B$ of ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$ in a magnetic field of $B=1\mathrm{T}$ (FC) perpendicular and parallel to the $ab$-plane. The inset enlarges the temperature regime around $T_{\mathrm{SO}}$ and $T_{\mathrm{CO}}$. The dotted line in the inset marks a linear extrapolation of ${\chi }_{\Vert }$ in order to highlight the changes at $T_{\mathrm{SO}}$ in the case of $B\Vert ab$. (b) Derivative of the static susceptibility. The charge stripe transition at $T_{\mathrm{CO}}$ [as confirmed from x-ray scattering (Ref. 35)], the spin stripe transition at $T_{\mathrm{SO}}$ [as confirmed from neutron diffraction (Refs. 9, 10)], and the spin glass/spin reorientation transition at $T_{\mathrm{CA}}$ (cf. Refs. 10, 14) are indicated by dashed lines (Ref. 33). The triangles show the temperature regime where a jump in $d{\chi }_{\Vert }∕dT$ indicates the spin ordering.

Figure 2

(Color online) Specific heat of ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$ for $B=0$ (left ordinate). Applying $B=14\mathrm{T}$ does not change the results within the size of the data points. The dotted line refers to a polynomal function which has been fit to the data well outside the anomaly. Black circles (right ordinate) represent the difference of the data $(B=0)$ and the dotted line.

Figure 3

(Color online) (a) Static susceptibility $\chi$ of ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$ for $B=1\mathrm{T}$ (open symbols) and $B=14\mathrm{T}$ (FC) (full symbols) parallel and perpendicular to the $ab$-planes. The inset shows an enlargement of the temperature regime around $T_{\mathrm{SO}}$ and $T_{\mathrm{CO}}$ (only the $y$ axis is enlarged). (b) Derivative of ${\chi }_{\Vert }$ in magnetic fields $B=1$, 5, and $14\mathrm{T}$ parallel to the $ab$-planes. Data at $B=5\mathrm{T}$ and $B=14\mathrm{T}$ are shifted by $5\times {10}^{-6}$ and $1\times {10}^{-5}\mathrm{emu}∕(\mathrm{mol}\bullet \mathrm{K})$, respectively. Triangles mark the jump at $T_{\mathrm{SO}}$ (full triangle corresponds to $T_{\mathrm{SO}}^{*}$, see text).

Figure 4

Magnetic phase diagram of ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$ for a magnetic field $B\Vert ab$. $T_{\mathrm{CO}}$, $T_{\mathrm{SO}}^{*}$, and $T_{\mathrm{CA}}$ mark the temperatures, where charge stripe order, long range spin stripe order and a spin reorientation occur, respectively. $T_{\mathrm{CO}}$ does also not change for $B\perp ab$.

Figure 5

Field dependence $(B\Vert ab)$ of the magnetisation of ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$ at $T=100\mathrm{K}$. The linear estimate $M_{\mathrm{lin}}$ highlights the slightly nonlinear field dependence of $M\left(B\right)$. Subtracting the linear part as extracted from $M(B\sim 13.5\mathrm{T})$ results the nonlinear contribution. For comparison, $M$ for $B\perp ab$ at $T=100\mathrm{K}$ is also plotted. The inset shows the field derivative of $M(B\Vert ab)$ which confirms the nonlinearity.

Figure 6

(Color online) (a) Field dependence $(B\Vert ab)$ of the magnetization of ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$ at various temperatures. $\left(\mathrm{b}\right)+\left(\mathrm{c}\right)$ Nonlinear part of $M\left(B\right)$. The linear part has been extracted from $M(B\sim 13.5\mathrm{T})$ at increasing field. At $T=4.2\mathrm{K}$ there is a field hysteresis. In the case of the $T=4.2\mathrm{K}$ data set we have subtracted the linear term found for increasing field from both parts of the magnetization hysteresis. The straight lines in (b) are fits to the data according to Eq. (2).

Figure 7

(Color online) Site- and bond-centered stripes. Dashed lines show the underlying square lattice. ${\mathrm{Ni}}^{2+}$-spins in spin stripes are indicated by arrows, oxygen sites by circles. Large (red) circles indicate high hole density. Grey bars show domain walls. Canting of Ni-spins with respect to the stripe direction is neglected. (a) Site-centered domain walls. All Ni moments are equivalent and compensated. (b) Bond-centered domain walls. Ni moments near domain walls and in the center of spin stripes, respectively, are inequivalent. A net magnetic moment is possible. The figure is similar to Fig. 1 in Ref. 44.

Figure 8

Schematic picture of the spin arrangement (black arrows) in the magnetic stripes of ${\mathrm{La}}_{5∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Ni}{\mathrm{O}}_4$, where the ${\mathrm{Ni}}_{2+}$-Spins are canted with respect to the perfect antiferromagnetic order (grey arrows) due to ferromagnetic interactions. Arrows represent ${\mathrm{Ni}}^{2+}$ $(S=1)$, ${\mathrm{Ni}}^{3+}$ and oxygen sites are neglected for clarity. (a) Charge stripe with a resulting weak ferromagnetic moment due to a small canting angle $\varphi$. (b) Canted spin and charge stripe order in zero magnetic field with alternating weak ferromagnetic moments in adjacent stripes and (c) for $B>0$ with a macroscopic weak ferromagnetic moment.

Figure 9

Schematic drawing of a ${\mathrm{Ni}}^{2+}{\mathrm{Ni}}^{3+}{\mathrm{Ni}}^{2+}$ configuration. In addition to the antiferromagnetic coupling between the ${\mathrm{Ni}}^{2+}$ ions the double exchange mechanism may infer a ferromagnetic interaction.