Dzyaloshinsky-Moriya spin canting in the low-temperature tetragonal phase of ${\mathrm{La}}_{2-x-y}{\mathrm{Eu}}_y{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$

Magnetization measurements in magnetic fields up to $14\text{Tesla}$ have been used to study the magnetism of the Cu spins in ${\mathrm{La}}_{2-x-y}{\mathrm{Eu}}_y{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ $(x⩽0.17;y⩽0.2)$. This system exhibits weak ferromagnetism due to a combination of the Dzyaloshinsky-Moriya interaction and tilting of the $\mathrm{Cu}{\mathrm{O}}_6$ octahedra. In the low-temperature orthorhombic (LTO) phase, the magnetic structure is the same as in the LTO phase of pure ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$; however, the Eu-doped system also exhibits low-temperature transitions to structural phases with different octahedral tilt patterns. There has been a long-standing debate about whether the spin-canting of the LTO phase continues to exist in the low-temperature tetragonal (LTT) phase. In contrast to theoretical predictions, our results clearly show that Cu spin canting is present in the LTT phase (within the antiferromagnetic regime) as well as in an intermediate low-temperature less-orthorhombic (LTLO) phase. Moreover, in ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ the canted moment is about 50% larger than in pure ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$, which we attribute to the larger tilt angle of the octahedra in the Eu-doped compound. We also find clear evidence that the size of the canted moment does not change significantly at the structural transition itself. The most important change induced by the transition is a significant reduction of the magnetic coupling between the $\mathrm{Cu}{\mathrm{O}}_2$ planes. As a consequence, the spin-flip for magnetic field perpendicular to the $\mathrm{Cu}{\mathrm{O}}_2$ planes, which is the most characteristic fingerprint of the canted Cu spin structure in the LTO phase, disappears in the LTT phase. The shape of the magnetization curves changes from the well known spin-flip type to a weak-ferromagnet type. However, no spontaneous weak ferromagnetism is observed even at very low temperatures, which seems to indicate that the interlayer decoupling in our samples is not perfect. Nonetheless, a small fraction $(\lesssim 15\%)$ of the canted Cu spin moments can be remanently magnetized throughout the entire antiferromagnetically ordered LTT/LTLO phase, i.e., for $T\lesssim 135\mathrm{K}$ and $x<0.02$. It appears that the remanent canted moment is perpendicular to the $\mathrm{Cu}{\mathrm{O}}_2$ planes. A small number of experiments were performed with the magnetic field applied parallel to the $\mathrm{Cu}{\mathrm{O}}_2$ planes, where in pure ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ a spin-flop transition was observed. We find that in ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ the critical field of the spin-flop seems to decrease in the LTLO phase, which might indicate a competition between different in-plane anisotropies. To study the Cu spin magnetism in ${\mathrm{La}}_{2-x-y}{\mathrm{Eu}}_y{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$, a careful analysis of the Van Vleck paramagnetism of the ${\mathrm{Eu}}^{3+}$ ions was performed.

Figure 1

Structural and electronic phase diagrams of ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ and ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$. Left: Data for Néel temperature $T_N$ of $3\mathrm{D}$-AF phase (엯) and structural transition $\mathrm{LTO}\leftrightarrow \mathrm{LTLO}∕\mathrm{LTT}$ (◇) from this work and Refs. 12, 92, 6. Spin-glasslike (SG) phase for $x<0.02$ (▵) and for $x>0.02$ (◻) after Refs. 6, 10, 38. In particular, ▵ extracted from maximum in longitudinal relaxation rate in NQR and $\mu \mathrm{SR}$ experiments similar to ▴ in the case of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$. Spin-stripe phase (◻) after Ref. 6. Right: Data for $T_N$ (●) from this work and Ref. 92. Spin glass phase for $x<0.02$ (▴) after Refs. 60, 77, 78 and for $x>0.02$ (∎) after Ref. 60. (---) $T_c$ of superconducting (SC) phase after Ref. 93. (—) The structural transition $\mathrm{HTT}\leftrightarrow \mathrm{LTO}$ in both diagrams is based on data in Refs. 65, 94, 95, 96. In ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ short-range diagonal spin stripe order was recently found in the SG phase (Refs. 79, 97, 98).

Figure 2

Spin structure (a) in LTO phase with antiferromagnetically $(H=0)$ and weak ferromagnetically ($H>H_c$ parallel $c$-axis) coupled $\mathrm{Cu}{\mathrm{O}}_2$ planes. Octahedral tilts and spin canting exaggerated. (b) Spin structure in two adjacent $\mathrm{Cu}{\mathrm{O}}_2$ planes in the LTO, LTLO and LTT phase. Spins are canted out of the plane of the paper. Gray (white) oxygen atoms are displaced below (above) $\mathrm{Cu}{\mathrm{O}}_2$ plane. Size of circles grows with displacement. Dashed lines indicate the octahedral tilt axis. Black arrows: Cu spins follow azimuthal rotation of tilt axis, i.e., spins are always perpendicular to the tilt axis. DM spin canting in LTT phase maximum. White arrows: spins rotate in opposite direction. In the LTT phase spins are parallel to tilt axis. There is no DM spin canting. (b) After Viertiö and Bonesteel (Ref. 16).

Figure 3

Static magnetic susceptibility $(H=1\text{Tesla})$ of pure and RE-doped ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ with ${\mathrm{RE}}_y={\mathrm{Nd}}_{0.3}$ and ${\mathrm{Eu}}_{0.2}$.

Figure 4

Static magnetic susceptibility $(H=1\text{Tesla})$ of ${\mathrm{La}}_{1.65}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_{0.15}\mathrm{Cu}{\mathrm{O}}_4$. Left: comparison of polycrystal data with averaged single crystal data as well as the susceptibility of a ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}\mathrm{Cu}{\mathrm{O}}_4$ polycrystal. $T_{\mathrm{LT}}$ indicates the $\mathrm{LTO}\leftrightarrow \mathrm{LTT}$ transition, $T_c$ the SC transition in the pure compound. Right: susceptibility of the single crystal for all three directions.

Figure 5

Static susceptibility $(H=1\text{Tesla})$ of a ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ polycrystal. (a) Total susceptibility $\chi$, calculated Eu Van Vleck susceptibility ${\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$, as well as difference $\chi -{\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$. The dotted lines indicate the antiferromagnetic transition at $T_N$ and the structural transition at $T_{\mathrm{LT}}$. (b) Comparison of $\chi -{\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ with $\chi$ of pure ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$. Data in (b) corrected for ${\chi }_{\mathrm{dia}}=-0.99\times {10}^{-4}\mathrm{emu}∕\mathrm{mol}$ and ${\chi }_{\mathrm{VV}}\left(\mathrm{Cu}\right)=0.43\times {10}^{-4}\mathrm{emu}∕\mathrm{mol}$. (◻) susceptibility ${\chi }_{2\mathrm{DHAF}}$ of a S1/2-$2\mathrm{D}$-HAF for $J=1550\mathrm{K}$ (after Monte Carlo data in Ref. 55).

Figure 6

Static susceptibility $(H=1\text{Tesla})$ of ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ polycrystals for different Sr concentrations $0⩽x⩽0.02$ after subtraction of ${\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$. Except for $x=0(800°\mathrm{C}\mathrm{vac.})$ all samples were annealed at $625°\mathrm{C}$ in ${\mathrm{N}}_2$ gas. Curves are shifted for clarity by $1\times {10}^{-4}\mathrm{emu}∕\mathrm{mol}$.

Figure 7

Static susceptibility $(H=1\text{Tesla})$ of ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ for different Sr concentrations $0.018⩽x⩽0.17$ (a),(b) after subtraction of ${\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$. (c) After additional subtraction of linear fit. In (a) curves are shifted by $5\times {10}^{-5}\mathrm{emu}∕\mathrm{mol}$, in (b) by $2.5\times {10}^{-5}\mathrm{emu}∕\mathrm{mol}$, and in (c) by $5\times {10}^{-6}\mathrm{emu}∕\mathrm{mol}$.

Figure 8

Static susceptibility of ${\mathrm{La}}_{1.78}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_{0.02}\mathrm{Cu}{\mathrm{O}}_4$ after subtraction of ${\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ and linear fit for different magnetic fields up to $14\text{Tesla}$. Curves are shifted for clarity by $0.75\times {10}^{-6}\mathrm{emu}∕\mathrm{mol}$.

Figure 9

Static susceptibility of ${\mathrm{La}}_{2-x-y}{\mathrm{Eu}}_y{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ for fixed Sr concentration (a) $x=0.017$ and (b) $x=0.08$ for different Eu doping $y$. (c) Phase diagram for $x=0.017$, and (d) for $x=0.08$.

Figure 10

Static susceptibility of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ after subtraction of ${\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ and pure of ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ for different magnetic fields $H$. For comparison $1\text{Tesla}$ data shown in all plots. Data corrected for ${\chi }_{\mathrm{dia}}$ and ${\chi }_{\mathrm{VV}}\left(\mathrm{Cu}\right)$ (cf. Fig. 5). Dashed line: susceptibility of S1/2-$2\mathrm{D}$-HAF for $J=1550\mathrm{K}$ (after Ref. 55).

Figure 11

Magnetization $M\left(H\right)$ of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$. (a) $M\left(H\right)$ and $M-M_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ at $150\mathrm{K}$. $M_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ is the calculated Van Vleck-term. (b),(c) $M-M_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ at different temperatures from measurements with increasing and decreasing magnetic field, respectively. $M_{\mathrm{SF}}$ and $M_B$ indicate spin-flip and weak ferromagnetic contribution of DM moment, respectively.

Figure 12

Derivative of $M-M_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ from measurements with increasing (엯) and decreasing (●) magnetic field. (a) In the LTO and LTT phase. (b) At $T=150\mathrm{K}$ in comparison with pure ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$. Curves are shifted for clarity.

Figure 13

Static susceptibility $(H=1\text{Tesla})$ of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ for magnetic fields perpendicular $\left({\chi }^c\right)$ and parallel to the $\mathrm{Cu}{\mathrm{O}}_2$ planes $({\chi }^{a*},{\chi }^{b*})$. (a) Total signal from measurements with decreasing temperature. (—) anisotropic Eu Van Vleck susceptibility. (●) polycrystal average. (b) After subtraction of ${\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ for increasing (●) and decreasing (엯) temperature. (+) Average of the two $\mathit{ab}$-measurements with decreasing $T$. In the shaded temperature range a mixed phase of LTO, LTLO, and LTT may exist.

Figure 14

Static susceptibility ${\chi }^c$ of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ before and after subtraction of ${\chi }_{\mathrm{VV}}^c\left(\mathrm{Eu}\right)$ for different $H$. Left: for $H⩽6\text{Tesla}$. Right: for $H⩾6\text{Tesla}$. Measurements with VSM (엯) were performed with increasing $T$, for Faraday balance (●) with decreasing $T$.

Figure 15

Magnetization $M^c-M_{\mathrm{VV}}^c\left(\mathrm{Eu}\right)$ of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ for increasing (엯) and decreasing (●) field. Data shifted for clarity. Inset: unshifted data for increasing field. The dotted line approximately indicates the contribution of $M_{\mathrm{SF}}^c$, $M_B^c$, and $H{\chi }_0^c$.

Figure 16

Deviations $\Delta M\left(H\right)$ of the magnetization from linearity at $0–2\text{Tesla}$ in ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ single and polycrystal as well as in ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ polycrystal at $T=150\mathrm{K}$. For comparison we show also scaled polycrystal data.

Figure 17

Remanent moment $M_{\mathrm{REM}}=M(H=0)$ versus temperature of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ after application of $14\text{Tesla}$ at $T=4\mathrm{K}$ for $H$ parallel and perpendicular to the $\mathrm{Cu}{\mathrm{O}}_2$ planes for (a) single crystal, (b) oriented powder, and (c) polycrystal.

Figure 18

Remanent moment $M_{\mathrm{REM}}\Vert c$ of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ after application of $+14\text{Tesla}$ at $T=4\mathrm{K}$ as a function of a negative counter-field at $T=40\mathrm{K}$.

Figure 19

Static susceptibility of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ after subtraction of ${\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$. (a) For $H=1\text{Tesla}$ for all three crystal directions and increasing (●) as well as decreasing (엯) temperature. (+) Average of the two $\mathit{ab}$-measurements with decreasing $T$. (b) For $H$ up to $14\text{Tesla}$ parallel to the two $\mathit{ab}$-directions as a function of increasing $T$.

Figure 20

Spin-flop in ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$. (a) Magnetization $M^{a*}$ and $M^{b*}$ after subtraction of Eu magnetism for different temperatures in the LTO and LTLO phase. (b) Deviation of $M^{a*}$ and $M^{b*}$ from linearity. (c) Derivative $d[M^{b*}-M_{\mathrm{VV}}^{\mathit{ab}}\left(\mathrm{Eu}\right)]∕dH$ at different temperatures. Curves are shifted for clarity. (d) Spin-flop field $H_{c1}$ versus temperature.

Figure 21

Magnetization $M^c\left(H\right)$ of ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ after subtraction of Eu Van Vleck term $M_{\mathrm{VV}}^c\left(\mathrm{Eu}\right)$. Left: in the LTO phase. Right: in the LTT phase. (—) result of fit according to Eq. (1) as well as the various contributions $H{\chi }_0^c$, $M_{\mathrm{SF}}^c$, and $M_B^c$.

Figure 22

Antiferromagnetic $M_{\mathrm{DM}}^{\mathrm{AF}}$ and weak ferromagnetic $M_{\mathrm{DM}}^{\mathrm{WF}}$ parts of DM moment as well as their sum $M_{\mathrm{DM}}^{\mathrm{AF}}+M_{\mathrm{DM}}^{\mathrm{WF}}$ in the ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ single crystal as a function of temperature for (a) increasing and (b) decreasing field. In the shaded temperature range a mixed phase of LTO, LTLO, and LTT may exist in ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$. Solid lines are guides to the eye.

Figure 23

Spin-flip field $H_c$ and width of the transition $\Delta H_c$ of the ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ single crystal as a function of temperature for increasing (full symbols) and decreasing (open symbols) field. Solid lines are guides to the eye.

Figure 24

Spin-flip parameters: (a) Antiferromagnetically ordered part $M_{\mathrm{DM}}^{\mathrm{AF}}$ of the DM moment, (b) spin-flip field $H_c$, and (c) effective interlayer coupling $J_{\perp }^{*}\propto M_{\mathrm{DM}}^{\mathrm{AF}}\times H_c$ versus temperature in ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$ single and polycrystal and in the ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ polycrystal. In the shaded temperature range a mixed phase of LTO, LTLO, and LTT may exist in ${\mathrm{La}}_{1.8}{\mathrm{Eu}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$.

Figure 25

Comparison of $\chi$ at $1\text{Tesla}$ of ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ after subtraction of ${\chi }_{\mathrm{VV}}\left(\mathrm{Eu}\right)$ and pure ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ for different Sr concentrations $x⩽0.02$. Data also corrected for ${\chi }_{\mathrm{dia}}$ and ${\chi }_{\mathrm{VV}}\left(\mathrm{Cu}\right)$ (cf. Fig. 5). The arrows for $x=0$ and 0.017 indicate the contribution of the DM-Moments ${\chi }_{\mathrm{DM}}$ in the LTO and LTT phase. The dashed line approximately represents ${\chi }_{2\mathrm{DHAF}}$.

Figure 26

Magnetization $M\left(H\right)$ of ${\mathrm{La}}_{1.782}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_{0.018}\mathrm{Cu}{\mathrm{O}}_4$ at different temperatures after subtraction of the Eu Van Vleck term $M_{\mathrm{VV}}\left(\mathrm{Eu}\right)$. Inset: after subtraction of linear function fitted to each curve at high fields $(6.5–8\text{Tesla})$.

Figure 27

Remanent moment $M_{\mathrm{REM}}$ of ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ for different Sr concentrations $x⩽0.02$ as a function of temperature. Inset: comparison with pure ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ for $x\sim 0.01$.

Figure 28

Magnetic and structural phase diagram of ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$. Data for pure ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ are shown for comparison. For $x=0.02$ the cluster spin glass transition at $T_{\mathrm{CSG}}$ is indicated as well. Solid lines are guides to the eyes.