Magnetic properties of ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ and ${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$: Magnetic hysteresis with coercive fields of up to 55 T

We report extraordinarily large magnetic hysteresis loops in the iridates ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_5$ and ${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$. We find coercive magnetic fields of up to 55 T with switched magnetic moments $\approx 1{\mu }_{\mathrm{B}}$ per formula unit in ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ and coercive fields of up to 52 T with switched moments $\approx 3{\mu }_{\mathrm{B}}$ per formula unit in ${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$. We propose that the magnetic hysteresis involves the field-induced evolution of quasi-one-dimensional chains in a frustrated triangular configuration. The striking magnetic behavior is likely to be linked to the unusual spin-orbit-entangled local state of the ${\mathrm{Ir}}^{4+}$ ion and its potential for anisotropic exchange interactions.

Figure 1

The crystal structure of ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ as viewed from the (a) $\left[110\right]$ and (b) $\left[001\right]$ directions [11, 13, 15, 18]. The ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Ir}}^{4+}$ ions occupy oxygen trigonal bipyramids (blue) and distorted oxygen octahedra (orange), respectively. For clarity, Sr ions are not shown in (a). (${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$ is isostructural to ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$.) (c) Schematic level diagrams for ${\mathrm{Ir}}^{4+}$ (after Ref. [10]), ${\mathrm{Ni}}^{2+}$, and ${\mathrm{Co}}^{2+}$ (based on Refs. [10, 19, 20, 21]). ${\mathrm{Ir}}^{4+}{t}_{2g}$ and $e_g$ levels split by the octahedral environment are shown in dark green; dark blue levels show schematically the effects of the trigonal distortion (TD splitting the states by $\mathrm{\Delta }$) and spin-orbit coupling (SO splitting the states by $\lambda$). These similarly sized effects result in spin-orbit entangled ${\mathrm{Ir}}^{4+}$ levels (red, not to scale), derived predominantly from $t_{2g}^5$ configurations, with a relatively small $t_{2g}-e_g$ mixing; electron spins are shown as black arrows: the effective spins are $S=1$ for ${\mathrm{Ni}}^{2+}$ and $S=\frac{3}{2}$ for ${\mathrm{Co}}^{2+}$.

Figure 2

Time dependence of magnetic fields for (a) a capacitor-bank-driven 65 T short-pulse magnet and (b) three examples of the controlled sweep patterns possible with the generator-driven 60 T Long Pulse Magnet. In (a), ${\mu }_0\mathrm{d}H/\mathrm{d}t$ for the short-pulse magnet is shown in blue (right axis). In (b), the three stages in each of the field-sweep patterns are due to three separate coils that are energized in sequence by the generator.

Figure 3

Hysteresis loops and large coercive fields: (a)–(e) Magnetization $M$ as a function of magnetic field ${\mu }_{0}H$ of ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ (SNIO) and ${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$ (SCIO) measured in a series of pulses using a capacitor-bank-driven 65 T pulsed magnet. Sample numbers, field directions, and measurement temperatures $T$ are given in each section of the figure, where S refer to single crystals and P to polycrystals. The vertical jumps in $M$ occur at the coercive field, ${\mu }_0{H}_{\mathrm{c}}$. Data in (b) and (c) are shown for $H\parallel c$ (hysteresis) and $H\perp c$ (no hysteresis). Magnetization units are shown as Bohr magnetons per formula unit, except in the case of (c), where the sample was destroyed in a pulsed-magnet failure before the calibration procedure detailed in Sec. 2 could be carried out. (f) $T$ dependences of the coercive magnetic fields are summarized for ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ samples S2 and S3, and ${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$ sample P4.

Figure 4

Temperature-dependent magnetization: (a) and (b) zero-field cooled (ZFC) and field-cooled (FC) magnetic susceptibility $\chi$ measured in a superconducting magnet as a function of temperature $T$ in an applied field of 0.2 T for (a) ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ single-crystal samples S1 and S2 and polycrystalline sample P1 and (b) ${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$ polycrystalline sample P4. (c) and (d) AC magnetic susceptibility with a ${10}^{-3}$ T AC excitation at 10 Hz and 10 kHz, compared to DC magnetic susceptibility taken at 0.2 T for (c) ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ S1 and (d) ${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$ P4.

Figure 5

Illustration of slow dynamics: The contour plots in (a) and (b) show $\mathrm{d}M/\mathrm{d}H$ versus ${\mu }_{0}H$ and $T$ for ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ polycrystalline sample P2 in a pulsed magnetic field with a sweep rate $\approx 3500$ T/s (a) and in a superconducting magnet (SC) with a magnetic field sweep rate of 0.008 T/s (b). Both (a) and (b) show data recorded on rising field sweeps. Corresponding plots of the hysteresis between falling and rising magnetic field sweeps, defined as hysteresis $=\left[M{(H,T)}_{\mathrm{falling}}-M{(H,T)}_{\mathrm{rising}}\right]$, are shown in (c) (pulsed field) and (d) (superconducting magnet—SC). The contour plots are based on field sweeps at constant temperatures spaced by $1\text{–}2$ K for $T<30$ K and $\approx 5\mathrm{K}$ for $T>30$ K. Note that as the field sweep rate increases, features in $\mathrm{d}M/\mathrm{d}H$ and regions of pronounced hysteresis are pushed to higher $T$.

Figure 6

Magnetization measured in a vibrating sample magnetometer as a function of time $t$ after sweeping from $0\text{–}13$ T at a rate of $0.01 {\mathrm{Ts}}^{-1}$; $t=0$ is the time at which 13 T is reached. Data are shown for sample temperatures of 10, 20, and 30 K. The inset shows an enlargement of data from the main figure, plotted as $\mathrm{\Delta }M=M\left(t\right)-M\left(0\right)$, where $M\left(0\right)$ is the magnetization at $t=0$.

Figure 7

Illustration of sweep-rate dependence of the coercive field for ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$: (a) $M\left(H\right)$ data for polycrystalline sample P3 of ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ measured in the 65 T short-pulse magnet at $T=4$ K. Black dotted lines denote the initial pulse after zero-field cooling while the green solid line indicates data for subsequent pulses. (b) Sweep-rate dependence of coercive magnetic field $\left({\mu }_0{H}_{\mathrm{c}}\right)$. (c) History dependence of coercive magnetic field $\left({\mu }_0{H}_{\mathrm{c}}\right)$ under various sweep rates (plotted as a function of pulse number). For sweep rates larger than 360 T/s, the 65 T short-pulse magnet was used; other data were taken using the generator-driven 60 T Long-Pulse Magnet. Twice during this experiment, the sample was thermally cycled to room temperature and back down to $T=4$ K (denoted by red vertical dashed lines).

Figure 8

Model for the behavior of the low-temperature magnetization $M\left(H\right)$ of ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$. Red arrows represent the magnetic moments of the ${\mathrm{Ni}}^{2+}$ ions $(\approx 1.5{\mu }_{\mathrm{B}})$ and blue arrows those of the ${\mathrm{Ir}}^{4+}$ ions $(\approx 0.5{\mu }_{\mathrm{B}})$. (a) The PDA state at $H=0$. This involves the moments of two ferrimagnetic $c$-axis chains $(1,2)$ being antiparallel to each other. The moments on the third chain (3) are disordered; this is represented by the question marks (?). (b) Increasing $H$ from zero gradually orders the disordered chain (3), leading to an increase in $M$ to a maximum possible value of $\frac{1}{3}{\mu }_{\mathrm{B}}$ per formula unit. (c) At the coercive field $H_{\mathrm{c}}$, the moments on one of the chains (2) flip (i.e., the transition is sharp), increasing $M$ to $\approx {\mu }_{\mathrm{B}}$ per formula unit. (d) At an (as yet inaccessible) even higher $H$, the system becomes ferromagnetic. Though the figure illustrates the situation in ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$, similar physics will apply in the case of ${\mathrm{Sr}}_3{\mathrm{CoIrO}}_6$.