Figure 1

(a) The $c$-axis and $ab$-plane isothermal magnetostriction of a $({\mathrm{La}}_{0.4}{\mathrm{Pr}}_{0.6}{)}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_2{\mathrm{O}}_7$ single crystal at $T=4.3$ and 10 K ($H\parallel c$). A dotted curve represents the $c$-axis data at 4.2 K in the case of $H\parallel ab$. The small magnetoresistance effect of the strain gauge itself gives a slight increase in both $d{L}_c$ and $d{L}_{ab}$. (b) Field dependence of the isothermal magnetization of the same crystal at selected temperatures ($H\parallel c$). For comparison, the $ab$-plane magnetization data are given at 3.5 K ($H\parallel ab$). (c) $c$-axis magnetoresistances of the same crystal at selected temperatures in the cases of $H\parallel c$. For comparison, the ${\rho }_{ab}$ data at 4.2 K ($H\parallel ab$) are cited.Reuse & Permissions

Figure 2

(a) $c$-axis magnetostriction as a function of cooling field (1, 1.4, 1.45, 1.5, and 1.6 T). For comparison, the $a$-axis data are displayed in the inset of (a). First, warming the sample from 4.3 K up to 200 K in the absence of field and then cooling it from 200 K down to 4.3 K in the respective field during 30 min (FC), the applied field was removed. Finally, we start measuring the magnetostriction upon increasing the field up to 8 T. For each measurement, we repeated the same procedure. The arrows labeled 1 and 4 mark $d{L}_c(H)$, before and after the transition, respectively. Arrow 2 represents the net lattice deformation, while arrow 3 points to the apparent change caused by the rise of sample temperature. (b) The corresponding bath temperature versus applied field. The slight decrease in the bath temperature as a function of $H$ arises from the magnetoresistance effect of the cernox thermometer. The inset of (b) represents the critical field $H_c$ versus the cooling field, at 4.3 K.Reuse & Permissions

Figure 3

Field dependence of the $c$-axis and $a$-axis isothermal magnetostriction, $d{L}_c$ and $d{L}_{ab}$, at 4.3 K ($H\parallel c$). (a) First scan, (b) second scan, and (c) third scan. Here, first scan of the applied field denotes $0\to 8\to 0\mathrm{T}$. Second (third) scan: $\mathrm{\text{local heating}}\to 0\to 8(12)\to 0\mathrm{T}$. (For details, see the text).Reuse & Permissions

Figure 4

Cooling rate dependence of $dL(H)$ from 200 and 300 K down to 4.3 K. In the case of 200 K, rapid and slow cooling rates are set at 30 min and 12 h. At 300 K, rapid and slow cooling rates in 20 min and 15 h, respectively.Reuse & Permissions