Noncollinear antiferromagnetism of coupled spins and pseudospins in the double perovskite ${\mathbf{La}}_2{\mathbf{CuIrO}}_6$

We report the structural, magnetic, and thermodynamic properties of the double perovskite compound ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ from x-ray, neutron diffraction, neutron depolarization, $\mathit{dc}$ magnetization, $\mathit{ac}$ susceptibility, specific heat, muon-spin-relaxation $\left(\mu \mathrm{SR}\right)$, electron-spin-resonance (ESR) and nuclear magnetic resonance (NMR) measurements. Below $\sim 113$ K, short-range spin-spin correlations occur within the ${\mathrm{Cu}}^{2+}$ sublattice. With decreasing temperature, the ${\mathrm{Ir}}^{4+}$ sublattice is progressively involved in the correlation process. Below $T=74$ K, the magnetic sublattices of Cu (spin $\mathit{s}=\frac{1}{2}$) and Ir (pseudospin $\mathit{j}=\frac{1}{2}$) in ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ are strongly coupled and exhibit an antiferromagnetic phase transition into a noncollinear magnetic structure accompanied by a small uncompensated transverse moment. A weak anomaly in $\mathit{ac}$ susceptibility as well as in the NMR and $\mu \mathrm{SR}$ spin lattice relaxation rates at 54 K is interpreted as a cooperative ordering of the transverse moments which is influenced by the strong spin-orbit coupled $5\mathit{d}$ ion ${\mathrm{Ir}}^{4+}$. We argue that the rich magnetic behavior observed in ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ is related to complex magnetic interactions between the strongly correlated spin-only $3\mathit{d}$ ions with the strongly spin-orbit coupled $5\mathit{d}$ transition ions where a combination of the spin-orbit coupling and the low symmetry of the crystal lattice plays a special role for the spin structure in the magnetically ordered state.

Figure 1

(a) Rietveld refinement fit with triclinic $\mathit{P}\overline{1}$ space group of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ powder XRD pattern. The red symbol presents the observed intensity, black line is the fitted pattern, blue line is the corresponding difference intensity, and the green vertical symbols are the allowed Bragg reflections. (b) Neutron diffraction pattern at 295 K with fitted patterns by both $\mathit{P}{2}_1/\mathit{n}$ and $\mathit{P}\overline{1}$ space groups. The two strongest reflections originate from the aluminum of the sample container (their corresponding marks are not shown). The inset presents a blown-up fragment of the diffraction pattern, where the advantage of the $\mathit{P}\overline{1}$ fit over the $\mathit{P}{2}_1/\mathit{n}$ fit is most clearly seen. (c) Octahedral tilt in three crystallographic directions and the distortion in two types of in-plane octahedral arrangements with $\left[\mathrm{Cu}1{\mathrm{O}}_6\text{−}\mathrm{Ir}1{\mathrm{O}}_6\right]$ and $\left[\mathrm{Cu}2{\mathrm{O}}_6\text{−}\mathrm{Ir}2{\mathrm{O}}_6\right]$ types, as generated from the XRD refinement. The spin configuration is one of the possible patterns compatible with our data obtained from the neutron diffraction refinement.

Figure 2

(a) Temperature dependent field-cooled (FC) and zero-field-cooled (ZFC) magnetization of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ at various applied $\mathit{dc}$ magnetic fields $\left({\mathit{H}}_{\mathrm{dc}}\right)$ of 20, 50, 100, 200 and 500 Oe. The respective data for ${\mathit{H}}_{\mathrm{dc}}=10$ kOe are presented in (b). Plot (c) shows the variation of the corresponding difference between the FC and ZFC magnetizations at 10 K with ${\mathit{H}}_{\mathrm{dc}}$.

Figure 3

(a) Temperature dependent real component of the $\mathit{ac}$ susceptibility $\left[{\chi }^{\prime }\left(\mathit{T}\right)\right]$ of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ with $\mathit{ac}$ field of ${\mathit{H}}_{\mathrm{ac}}=17$ Oe and frequency, 110, 500, and 1000 Hz. (b) $\mathit{dc}$ biasing effect of ${\chi }^{\prime }\left(\mathit{T}\right)$ with a fixed $\mathit{ac}$ field. The corresponding inset show a zoomed-in view around $T_2$.

Figure 4

$M\text{−}H$ curves of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ at 2 K. The upper inset displays the corresponding zoomed in view at the low field region. The temperature dependence of the magnetization value at 5 T is presented in the lower inset.

Figure 5

(a) The deduced ferromagnetic magnetization component in ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ for different magnetic fields between 20 and 500 Oe [30]. (b) The magnetic susceptibility for $H_{\mathrm{dc}}=20\mathrm{Oe}$ around the two transitions. The red line is a fit to a Curie-Weiss [C-W] law (for details see text). (c) Temperature dependent reciprocal $\mathit{dc}$ susceptibility with straight line as the Curie-Weiss fit. Here $\mathrm{\Delta }{\chi }_{\mathrm{dc}}={\chi }_{\mathrm{dc}}-{\chi }_0$, where ${\chi }_0$ is a temperature independent contribution to ${\chi }_{\mathrm{dc}}$.

Figure 6

(a) Neutron powder diffraction patterns of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ as a function of the scattering angle $\left(2\theta \right)$ for different temperatures. The black solid line is the best Rietveld fit to the triclinic $\mathit{P}\overline{1}$ space group of the 90 K reference dataset measured above $T_1$. Calculated structural peak positions are shown with vertical lines below the plot. The two strongest reflections arise from the aluminum of the sample container (their corresponding marks are shifted downwards). The inset shows a blown-up fragment of the diffraction pattern at low scattering angles, where temperature-dependent magnetic Bragg peaks can be seen around $2\theta =18.0^{\circ }$ and $25.8^{\circ }$. They can be assigned to the commensurate $\left(\frac{1}{2}0\frac{1}{2}\right)$ and $\left(\frac{1}{2}\pm 1\frac{1}{2}\right)$ reflections whose calculated positions are shown below with two vertical lines. (b) The difference of the low- and high-temperature data sets, from which the respective difference of the structural models has been subtracted to eliminate the effect of thermal expansion. Two additional magnetic Bragg peaks marked by arrows can be seen. Positions of the forbidden magnetic reflections as described in the text are shown below the curve with dashed lines.

Figure 7

(a) Temperature dependent specific heat $\left[C_P\left(T\right)\right]$ of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ at zero applied magnetic field (black symbol) and the respective one of ${\mathrm{La}}_2{\mathrm{ZnIrO}}_6$ for $T>40$ K (red line). The latter was scaled by a factor of 1.017 (see text) in order to estimate the phononic contribution of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$. Inset shows the effect of external magnetic field on ${\mathrm{C}}_P(\mathit{T})$. (b) Zero-field magnetic specific heat of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ plotted as $C_{\mathrm{mag}}/T$ vs $T$ (left scale) and the deduced temperature dependent magnetic entropy $\left[S_{\mathrm{mag}}\left(T\right)\right]$ (right scale).

Figure 8

Selected ESR spectra of ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ at different temperatures at a fixed frequency of $\nu =32.22$ GHz [(a) as measured spectra; (b) after correction by the analyzer software]. The spectra are shifted vertically for clarity.

Figure 9

Temperature dependence of the integrated intensity $\mathit{I}\sim \mathit{A}\mathrm{\Delta }\mathit{H}$ (a), linewidth (b) and resonance field (c) determined from the ESR spectra at $\nu =32.22$ GHz in Fig. 8 using the fit function (3). In (a) the temperature dependence of the ${}^{139}\mathrm{La}$ NMR linewidth (open circles) and the calculated dependence of the order parameter (solid line) are shown for comparison (see section “NMR measurements”).

Figure 10

Frequency $\nu$ vs ${\mathit{H}}_0$ dependence of the ESR signal at $T=6\mathrm{K}$ (symbols) and a fit to the function $h\nu =\mathrm{\Delta }+g{\mu }_{\mathrm{B}}{\mathit{H}}_0$ (solid line). Representative ESR signals (absorption part) are shown in the insets.

Figure 11

(a) Temperature dependence of the ESR energy gap $\mathrm{\Delta }$ and (b) the $\mathit{g}$ factor obtained from the $\nu \left({\mathit{H}}_0\right)$ dependencies. Dashed red lines are guides for the eye. Horizontal dashed line in (b) panel denotes the spin-only $\mathit{g}$ factor of 2. The temperature dependence of the coercive field ${\mathit{H}}_{\mathrm{C}}$ is plotted as an open triangle in (a).

Figure 12

Temperature dependence of the transmitted neutron polarization intensity for ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$.

Figure 13

Experimental ${}^{139}\mathrm{La}$ NMR field sweep spectrum at $\mathit{T}=150\mathrm{K}$. The red dashed line shows the result of modeling as detailed in the text.

Figure 14

Temperature evolution of the ${}^{139}\mathrm{La}$ field-swept NMR spectra.

Figure 15

Temperature dependence of the linewidth (symbols). The red solid line is the bulk static magnetization measured at the field 5 T; the blue line is a fit to the phenomenological function ${\left[1-{(T/T_{\mathrm{N}})}^{{\alpha }^{\prime }}\right]}^{{\beta }^{\prime }}$, as described in the text.

Figure 16

Temperature dependence of the ${}^{139}\mathrm{La}$ longitudinal $T_{\mathrm{l}}^{-1}$ (filled stars) and transversal $T_{\mathrm{t}}^{-1}$ (circles) relaxation rates. Inset: stretching exponent $\mathit{p}$ as a function of temperature. Solid lines are guides for the eyes.

Figure 17

Zero field $\mu \mathrm{SR}$ spectra (muon spin polarization versus time) at representative temperatures. The lines represent the theoretical description as detailed in the text.

Figure 18

(a) Temperature dependence of the muon spin precession frequency in ${\mathrm{La}}_2{\mathrm{CuIrO}}_6$ (main panel) and of the magnetic volume fraction (inset). Lines indicate the fit with different phenomenological models. (b) Temperature dependence of the muon spin lattice relaxation rate ${\lambda }_{\mathrm{L}}$(main panel) and of the normalized static line width ${\lambda }_{\mathrm{T}}/{\mathit{f}}_{\mu }$ (inset).