Magnetic properties of double perovskite $Ln_2$CoIrO$_6$ ($Ln$ = Eu, Tb, Ho): hetero-tri-spin $3d$-$5d$-$4f$ systems

TL;DR

This study synthesizes and characterizes Eu, Tb, and Ho-based double perovskites, revealing ferrimagnetic transitions above 100 K, complex magnetic phase behavior, and potential for magnetocaloric applications in hetero-tri-spin 3d-5d-4f systems.

Contribution

It reports the synthesis and magnetic characterization of new iridium-based double perovskites with three magnetic elements, highlighting their magnetic phase transitions and field-induced phenomena.

Findings

Ferrimagnetic transition temperatures above 100 K

Observation of spin-reorientation and spin-flop transitions

Moderate magnetocaloric effect in all compounds

Abstract

The field of double perovskites is now advancing to three magnetic elements on the A, B and B$'$ sites. A series of iridium-based double perovskite compounds, $Ln_2$CoIrO$_6$ ($Ln$ = Eu, Tb, Ho) with three magnetic elements were synthesized as polycrystalline samples. The compounds crystalize in monoclinic structures with the space group $P2_1/n$. Magnetic properties of these hetero-tri-spin $3d$-$5d$-$4f$ systems were studied by magnetic susceptibility and field dependent magnetization in both DC and pulsed magnetic fields. All these compounds show ferrimagnetic transitions at temperatures $T_C$ above 100 K, which are attributable to antiferromagnetic coupling between Co$^{2+}$ and Ir$^{4+}$ spins. For Eu$_2$CoIrO$_6$, the magnetic properties are similar to those of La$_2$CoIrO$_6$. The Eu$^{3+}$ spins show Van Vleck paramagnetism that don't significantly interact with transition-metal cations. By contrast, Tb$_2$CoIrO$_6$ and Ho$_2$CoIrO$_6$ reveal a second transition to antiferromagnetic order below a lower temperature $T_N$. The temperature-induced ferrimagnetic-to-antiferromagnetic phase transition might be explained by a spin-reorientation transition. Moreover, a magnetic-field-induced spin-flop transition with a small hysteresis was observed below $T_N$ in these two compounds. The magnetic moment of all three compounds do not saturate up to 60 T at low temperatures. Moderate magnetocaloric effect was also observed in all three compounds. Our results should motivate further investigation of the spin configuration on single crystals of these iridium-based double perovskites.

Figures

Tables

Table 1. Table 1: Structural parameters, magnetic ordering temperatures, Curie-Weiss temperature and effective moment of double perovskites L ​ n 2 𝐿 subscript 𝑛 2 Ln_{2} B 2+ Ir 4+ O 6 .

$L{n}_2$BIrO6	$a$(Å)	$b$(Å)	$c$(Å)	$\beta$(deg.)	$V$(Å3)	$T_C$(K)	$T_N$(K)	$\theta$(K)	${\mu }_{eff}$(${\mu }_B$/f.u.)
La2CoIrO6 Narayanan et al. (2010)	5.581(9)	5.657(6)	7.907(8)	89.98(1)	249.7(3)	95	n/a	-13.9	4.71
Eu2CoIrO6	5.365(9)	5.741(3)	7.676(0)	90.028(4)	236.4(8)	105	n/a	-5.3	5.50
Tb2CoIrO6	5.319(3)	5.724(7)	7.627(2)	90.047(9)	232.2(6)	117	10	-7.1	14.70
Ho2CoIrO6	5.271(6)	5.697(1)	7.577(4)	90.14(80)	227.5(7)	123	13	-2.6	15.87
La2NiIrO6 Currie et al. (1995); Ferreira et al. (2016)	5.575(3)	5.626(1)	7.898(1)	90.02(7)	247.7(4)	85	n/a	-28	3.28
Nd2NiIrO6 Ferreira et al. (2016)	5.433(0)	5.694(3)	7.763(9)	90.004(0)	240.1(9)	125	5	-32	6.19
Eu2NiIrO6 Ferreira et al. (2016)	5.378(7)	5.715(0)	7.706(1)	90.035(0)	236.8(8)	162	n/a	n/a	n/a
Gd2NiIrO6 Ferreira et al. (2016)	5.326(3)	5.718(9)	7.651(5)	90.026(0)	233.0(7)	170	8	?	11.35
La2MgIrO6 Ferreira et al. (2016); Mugavero III et al. (2010)	5.599(7)	5.606(7)	7.916(4)	90.005(7)	248.5(4)	n/a	10	-10	1.31
Nd2MgIrO6 Ferreira et al. (2016); Mugavero III et al. (2010)	5.478(7)	5.651(7)	7.812(5)	90.021(1)	241.9(1)	9?	5	-19	4.84
Eu2MgIrO6 Mugavero III et al. (2010)	5.391(9)	5.679(7)	7.725(8)	90.059(1)	236.(60)	n/a	10	n/a	n/a
Gd2MgIrO6 Mugavero III et al. (2010)	5.365(4)	5.687(1)	7.701(4)	90.193(3)	234.9(9)	?	n/a	3	10.68

Equations

$$\Delta S_M(T,H)={\int }_0^{H_1}{\left(\frac{\partial M(T,H)}{\partial T}\right)}_H\mathrm{d}H.$$

Full text

PACS numbers

75.50Ee, 75.50.Gg, 75.50.Lk

I INTRODUCTION

The A2BB*′O6 double perovskite family is a focus area of magnetic research due to a wide range of magnetic, magnetocaloric and multiferroic properties that reflect the design flexibility and interplay between charge, spin and lattice in these materials. Vasala and Karppinen (2015). The magnetic phases are controlled by the choice of magnetic or nonmagnetic cations on A, B and B′* sites in these compounds. In general, the A site is occupied by an alkaline or lanthanides ($Ln$) cation and B/B*′* are transition metal elements. For a single magnetic B/B*′-site compound, the superexchange coupling between two nearest cations through intermediate oxygen takes part in the magnetic order. In case of two magnetic B/B′-site cations, the magnetic properties of A2BB′O6 is usually dominated by the magnetic coupling between the local spin moments on B and B′* sites. In these compounds, the ferromagnetic (FM) ordering in the B and B*′* cation sublattices can be explained by the indirect B-O-B*′-O-B exchange interaction Serrate et al. (2007). Moreover, it is possible to have magnetic cations on the A site as well Ferreira et al. (2016); Kim et al. (2015), i.e. in Nd2NiMnO6, where the transition metal cations Ni2+* and Mn4+ order ferromagnetically to each other at 195 K, while the antiferromagnetic exchange between Nd3+ and the transition metals arise at 50 K S$\acute{a}$nchez-Ben$\acute{i}$tez et al. (2011).

Another focus area for double perovskite research is Ir4+ B or B*′* cations. Ir4+ provides strong and unusual spin-orbit-lattice coupling due to the comparable energy scales between spin-orbit coupling (SOC), on-site Coulomb interaction and crystal field energies Kim et al. (2009). For perfect octahedral symmetry, it is know that the 5$d$ levels of Ir should split into a $t_{2g}$ triplet and an $e_{g}$ doublet by the crystal electric field. Then, the strong SOC lifts the $t_{2g}$ orbital degeneracy to an effective $J_{eff}=1/2$ doublet ($e^{\prime}$ level) and an effective $J_{eff}=3/2$ quartet ($u^{\prime\prime}$ level) Kim et al. (2008); Chen et al. (2010). For Ir4+ (5$d^{5}$), the $t_{2g}$ level splits into a fully occupied $u^{\prime\prime}$ level and a half-filled $e^{\prime}$ level, resulting in a total $J_{eff}=1/2$ state. In La2CoIrO6 (monoclinic structure; $P2_{1}/n$), X-ray magnetic circular dichroism (XMCD) experiments confirm the valence states of the magnetic cations are Co2+ and Ir4+ Kolchinskaya et al. (2012); Lee et al. (2015), while distortions from perfect octahedral symmetry of the Ir4+ B*′* site can create a deviation from the $J_{eff}=1/2$ state. The temperature dependence of magnetization reveals magnetic order below $T_{C}$ = 95 K and the hysteresis loops at low temperatures indicate the presence of ferromagnetic (FM)-like components Narayanan et al. (2010); Kolchinskaya et al. (2012); Lee et al. (2015); Song et al. (2017). Further studies have verified a ferrimagnetic (FiM) ground state in which a weak FM moment of canted Co2+ spins is antiferromagnetically coupled to Ir4+ cations with a negative moment Narayanan et al. (2010); Kolchinskaya et al. (2012); Lee et al. (2015). This is explained in terms of the orbital hybridization of the high-spin (HS) Co2+ $t_{2g}$ state and the Ir4+ $J_{eff}=1/2$ state. Recently, an interesting reentrant spin-glass magnetic behavior was observed in this compound Song et al. (2017). Naturally, magnetic A-site substitution modifies the magnetic properties as well as the structure of $Ln_{2}$CoIrO6 double perovskites. Increased complexity of the magnetism is expected with interactions of three magnetic cations.

In this paper, we focus on the $Ln_{2}$CoIrO6 ($Ln$ = Eu, Tb, Ho) family of double perovskites which is a hetero-tri-spin $3d$-$5d$-$4f$ system. Polycrystalline samples were synthesized. The symmetry of those double perovskites is compatible with the $P2_{1}/n$ space group. We performed a systematic investigation of these compounds through DC and pulsed magnetic susceptibility for the first time. All these compounds show a FiM transition at a high temperature $T_{C}$, which are attributable to antiferromagnetic (AFM) coupling between Co2+ and Ir4+ spins. In Eu2CoIrO6, the Van Vleck paramagnetic (PM) Eu3+ cations don’t interact with the transition-metal cations. Meanwhile the magnetic behaviors of Tb2CoIrO6 and Ho2CoIrO6 show a temperature-induced FiM-to-AFM phase transition and a field-induced spin-flop transition below $T_{N}$. A field up to 60 T is not enough to saturate their magnetic moments at low temperatures. Moderate magnetocaloric effect are observed around magnetic transitions for all three compounds.

II EXPERIMENTAL

Polycrystalline samples of a series of lanthanide cobalt iridium oxides Eu2CoIrO6, Tb2CoIrO6 and Ho2CoIrO6 were synthesized using the conventional solid-state-reaction method. Stoichiometric Eu2O3 (99.9 %), Tb4O7 (99.9 %), Ho2O3 (99.9 %), CoO (99.9 %) and Ir (99.9 %) powders were mixed, ground, pelleted and sintered at 1100 *∘*C, 1200 *∘*C and 1270 *∘*C for the first, second and third sintering, respectively. Powder X-ray diffraction (XRD) measurements were collected on a Rikagu X-ray diffraction instrument. The XRD data were analyzed by Rietveld refinement using the software MAUD Lutterotti et al. (1997). Magnetization was carried out between 2 and 300 K using a 14 T Quantum Design Physical Property Measurement System (PPMS) with a vibrating sample magnetometry (VSM) option in applied DC magnetic fields and in a 7 T Magnetic Property Measurement System (MPMS) Superconducting Quantum Interference Device (SQUID). The pulsed field magnetization measurements up to 60 T were performed at NHMFL in Los Alamos, in which the temperature down to 1.36 K was controlled with a 4He system. The pulsed field magnetization data were calibrated against DC measurements.

III RESULTS AND WORKING MODEL

III.1 Structure

Figure 1(a) displays the general structure of double perovskite $Ln_{2}$CoIrO6. The corner-shared CoO6 and IrO6 octahedra alternate along three directions of the crystal, which form two monoclinic sublattices. The $Ln$ cations occupy the voids between the octahedra. The powder XRD patterns of Eu2CoIrO6, Tb2CoIrO6 and Ho2CoIrO6 measured at room temperature are shown in Fig. 1(b-d), which look very similar to that of Eu2NiIrO6 with the monoclinic structure Ferreira et al. (2016). For Eu2CoIrO6, Rietveld refinement shows that this compound is a single-phase system with the space group $P2_{1}/n$, based on the Eu2MgIrO6 structure data Mugavero III et al. (2010). For Tb2CoIrO6, in addition to the Tb2CoIrO6 phase, a minor impurity phase of Tb11O20 (space group $P\bar{1}$ Zhang et al. (1993)) with a volume fraction of 6% was found. Tb11O20 is AFM with a Néel temperature of 5.1 K Baran et al. (2013). For Ho2CoIrO6, less than 8.6% of Ho2O3 (space group $Ia$-3 Koehler et al. (1958)) was present in the sample. Ho2O3 shows a second-order AFM transition with a Néel temperature of 2 K Boutahar et al. (2017). Structural parameters of these samples are listed in Table I. The cation radius decreases in the following order: La${}^{3+}>$Eu${}^{3+}>$Tb${}^{3+}>$Ho3+. The Rietveld fitting results reveal that the monoclinic structure is more distorted as the size of the $Ln$ cation becomes smaller. As can be expected, the structural distortion will result in a change of Co-O-Ir bond angles, which correlate with the magnetic ordering temperature.

III.2 Magnetism

III.2.1 Eu2CoIrO6

Temperature dependent zero-field-cooled (ZFC) and field-cooled (FC) DC magnetic susceptibility $\chi(T)$ measurements of Eu2CoIrO6 performed at 0.2 T are presented in Fig. 2(a). The derivative of the FC susceptibility $d\chi/dT$ reveals a FM-like magnetic transition below the Curie temperature $T_{C}$ = 105 K. Compared to La2CoIrO6, the Eu substitution of La at the A site results in a substantial shift of the $T_{C}$ to a higher temperature. The large contrast between the ZFC and FC data indicates the presence of FM-like components, which is confirmed by the hysteresis in Fig. 2(b). A plateau is clearly observed below $T_{C}$ in the FC curve. A peak exists at $T_{p}$ = 85 K in the ZFC curve. $T_{p}$ shifts to lower temperatures with increasing the external magnetic field, which is not shown here. 1/$\chi$ at high temperatures violates the linear Curie-Weiss law. Instead, the magnetic susceptibility follows a modified Curie-Weiss law with $\chi=\chi_{0}+C/(T-\theta)$ above 160 K, where $\chi_{0}$ is a fitting term and arises mainly from Eu3+, $C$ is the Curie constant and $\theta$ is the Curie-Weiss temperature. This form of susceptibility is consistent with Van Vleck paramagnetism Van Vleck (1932), which is often seen in europium containing compounds Takikawa et al. (2010); Samata et al. (2015); Ferreira et al. (2016). As shown in the inset of Fig. 2(a), the fit gives a Curie-Weiss temperature of $\theta$ = -5.3 K, however we note that in these materials single-ion anisotropies and level splittings can influence or even dominate the Curie-Weiss temperature, in addition to AFM and FM interactions. The effective moment $\mu_{eff}$ = 5.5 $\mu_{B}$/f.u. is calculated with $\chi_{0}$ taken out. As shown in Fig. 2(b), the remanent magnetization of Eu2CoIrO6 at 2 K is found to be 0.5 $\mu_{B}$ per formula unit (f.u.) which is smaller than 0.7 $\mu_{B}$/f.u. of La2CoIrO6 at 5 K Song et al. (2017). The step-like magnetic transition happens at $H_{c}$ = 1.3 T in the initial hysteresis loop, which has been observed in La2CoIrO6 Song et al. (2017).

As its behavior is similar to that of the reference compound La2CoIrO6 Lee et al. (2015); Song et al. (2017), we can hypothesis that the PM Eu3+ doesn’t interact with the other two magnetic cations, and the ground state of the Co2+ and Ir4+ is FiM Kolchinskaya et al. (2012); Lee et al. (2015). The peak in the ZFC curve below $T_{C}$ and the step-like magnetic transition in the $M(H)$ curve are characteristics of AFM-FM evolutions seen in similar materials such as Lu2CoMnO6 Y$\acute{a}\tilde{n}$ez-Vilar et al. (2011), and have also been attributed to spin-glass-like states in La2CoIrO6 Song et al. (2017). The strong linear contribution beyond the hysteresis loop is most likely due to the gradual field alignment of the canted Co2+ and Ir4+ magnetic moments away from the easy axis Narayanan et al. (2010). The effective moment of the HS Co2+ has been reported to be 4.8 $\mu_{B}$ in related double perovskites, which is higher than the spin-only value of 3.87$\mu_{B}$ due to the partial unquenched orbital contribution Blasco et al. (2016). The effective moment of Ir4+ was reported to be 1.3 $\mu_{B}$ in La2MgIrO6 Ferreira et al. (2016). Therefore, the AFM coupling of Co2+ and Ir4+ should result in a saturated spin moment of 3.5 $\mu_{B}$/f.u., neglecting the paramagnetism of Eu3+. However, as shown in Fig. 2(c), $M$ does not saturate even up to 60 T. $M(H)$ varies almost linearly with increasing field and reaches 3.37 $\mu_{B}$/f.u. at 60 T. Since the Co2+ spin is not fully aligned at 60 T, the effective moment of Ir4+ should be less than 1.43 $\mu_{B}$. Nevertheless, Kolchinskaya $et$ $al$ reported an unusually large total magnetic moment 0.38 $\mu_{B}$/f.u. for Ir4+ in La2CoIrO6 by XMCD Kolchinskaya et al. (2012). In this case, the saturation moment of Co2+ and Ir4+ should be 4.42 $\mu_{B}$/f.u., which needs to be confirmed by measurements in higher magnetic fields. Thus, the effective moment of Ir4+ should be in the range of 0.4-1.4 $\mu_{B}$/f.u. in these double perovskites.

III.2.2 Tb2CoIrO6

Fig. 3(a) displays the temperature dependence of susceptibility of Tb2CoIrO6. 1/$\chi$ above 185 K is well fitted by the Curie-Weiss expression, $\chi=C/(T-\theta)$. We report a Curie-Weiss temperature of -7.1 K, however as noted previously this temperature can be strongly influenced by factors besides magnetic exchange interactions. The effective magnetic moment of Tb2CoIrO6 obtained by the fitting is $\mu_{eff}^{exp}=\sqrt{8C}$ = 14.70 $\mu_{B}$/f.u., where $k_{B}$ is the Boltzmann constant. The expected moment of Tb3+ is 9.72 $\mu_{B}$, calculated by $\mu_{Tb}=g_{Tb}\sqrt{J_{Tb}(J_{Tb}+1)}$ where $g_{Tb}$ is the Landé $g$-factor. Based on the value of $\mu_{Ir}$ determined above, the expected effective moment of Tb2CoIrO6 can be calculated to be 14.57-14.63 $\mu_{B}$/f.u. according to $\mu_{eff}=\sqrt{2\mu_{Tb}^{2}+\mu_{Co}^{2}+\mu_{Ir}^{2}}$, which is close to but slightly less than the value obtained experimentally. A sudden jump at $T_{C}$ = 117 K signals the onset of a FM-like ordering. The hysteresis below 100 K in Fig. 3(c) could be explained by the FiM ordering due to the AFM coupling between the canted Co2+ and Ir4+ as was suggested for La2CoIrO6 and for Eu2CoIrO6. The ZFC and FC curves also separate below $T_{C}$ with a peak at 82 K in the ZFC curve, similar to Eu2CoIrO6 and La2CoIrO6. As shown in Fig. 3(c), it is clear that the remanent moment and the coercive field increase with decreasing temperature from 100 to 60 K. Beyond the FiM hysteresis, the magnetization increases nonlinearly with increasing field, indicating a component of paramagnetism of Tb3+.

As the temperature decreases further, a downturn occurs clearly at 56 K in the FC curve. Moreover, an AFM transition is signified by a kink in the ZFC curve around 10 K. Since the spins of magnetic rare earth cations usually order at low temperatures, the magnetic behavior below $T_{N}$ = 10 K might be strongly affected by the alignment of Tb3+ spins. The AFM ordering is confirmed by $M(H)$ curves below 10 K in Fig. 3(c). At 2 K, $M$ increases almost linearly with the magnetic field at the beginning, then undergoes a substantial increase at $H_{m}$ = 2.4 T. Thus, a metamagnetic transition occurs. A hysteresis is observed in the metamagnetic transition, implying a weak first-order transition. It is worthwhile to note that there is a tiny remanent moment of  0.02 $\mu_{B}$/f.u. at 2 K after the magnetic field is turned off, as shown in the inset of Fig. 3(e). This might come from the impurity phase Tb11O20 which shows a remanence in the $M(H)$ curve at 1.9 K Baran et al. (2013). Generally, in an AFM system, the metamagnetic transition corresponds to a spin-flop transition from an AFM state to a spin ferromagnetically polarized state Perry et al. (2001).

Especially interesting is that this compound exhibits a FiM to AFM phase transition with decreasing temperature, which might be caused by a change of the AFM structure type or by the spin-reorientation (SR) transition Horner and Varma (1968). Now let’s focus on the temperature region from 10 to 56 K. Below 56 K, the coercive field of the FiM hysteresis continues to increase with decreasing temperature until it becomes undistinguishable at 10 K, while the remanence starts to decrease with decreasing temperature. The change of the FiM hysteresis indicates that (i) the AFM coupling between Co2+ and Ir4+ doesn’t change, and (ii) The FM component of Co2+ becomes smaller as temperature decreases. Meanwhile, the metamagnetic hysteresis emerges in this temperature region, which is clear at 20 K. Since the $M(H)$ of polycrystalline samples is the average of magnetic moments for different directions, one possible scenario is that the Co spins reoriented and antiferromagnetically ordered along the other direction. This temperature-induced orientational transition can be caused by competing anisotropy of transition metal sublattices. Because of the impurity phase, it’s hard to tell whether the magnetic moments of Co2+ and Ir4+ are compensated below $T_{N}$.

The pulsed field magnetization of Tb2CoIrO6 was carried out at 1.41 K. Since the signal voltage from the coil is proportion to $dM/dt$, the sharp transition at $H_{m}$ results a large voltage which saturated the data acquisition system in a 60 T shot. We solve this problem by combining 10 T data (no saturation problem at 2.4 T) and 60 T (saturation problem near 2.4 T) in Fig. 3(e). Beyond the hysteresis, $M$ increases nonlinearly and does not saturate up to 60 T. The moment reaches 15.33 $\mu_{B}$/f.u. at 60 T.

III.2.3 Ho2CoIrO6

Ho2CoIrO6 shows similar magnetic properties as Tb2CoIrO6. It undergoes a FiM transition at 123 K followed by a divergence between the ZFC and FC curves shown in Fig. 3(b). The inverse of susceptibility presents a linear behavior at high temperature. A Curie-Weiss fit above 185 K gives a Curie-Weiss temperature of $\theta$ = -2.6 K. The obtained $\mu_{eff}^{exp}=15.87\mu_{B}$ from the fit is in reasonably good agreement with the theoretical moment 15.75-15.80 $\mu_{B}$. Broad peaks are observed at 99 K in ZFC curve and 98 K in FC curve which might indicate the SR transition. The kink at 13 K indicates the AFM transition. The increase of susceptibility below 5 K is presumably attributed to the existence of Ho2O6 impurity, which has a strong Curie-Weiss increase at low temperatures. Isothermal magnetization curves are shown in Fig. 3(d). Below $T_{N}$, the magnetization increases linearly in weak fields, as shown in the inset of Fig. 3(d). The field-induced spin-flop transition happens at $H_{m}$ with a small hysteresis. The inset of Fig. 3(f) shows the amplified view of the $M(H)$ curve at 10 K. It is clear that there is no remanence. Thus, the FiM moment vanishes below $T_{N}$. According to our working model, the SR transition happens in a region from 13 to 98 K. Moreover, the magnetic moments of Co2+ and Ir4+ are compensated below $T_{N}$. The main frame of Fig. 3(f) shows further pulsed field magnetization data. The transition at $H_{m}$ was so sharp that even a 10 T shot saturated the data acquisition system. Thus, the pulsed field data are a combined plot of 5 T and 60 T shots. There is no saturation trend up to 60 T at 4.02 K.

III.3 Magnetocaloric effect

The magnetocaloric effect (MCE) is defined as the adiabatic temperature change $\Delta T$ or isothermal magnetic entropy change $\Delta S_{M}$ of a magnetic material due to a varying external magnetic field Zhong et al. (2013). The magnetic entropy change $\Delta S_{M}$ can be measured directly with the calorimetry method or indirectly calculated from magnetization measurements using Maxwell’s thermodynamic relation:

[TABLE]

$-\Delta S_{M}$ usually reaches a maximum around the magnetic transition temperature, such as $T_{C}$. In order to understand the field dependent magnetic behavior of the three compounds and determine their magnetocaloric potential, $M(H)$ curves of these samples were measured at various temperatures. Fig. 4 summarizes the temperature dependence of $-\Delta S_{M}$ of $Ln_{2}$CoIrO6 samples obtained at different magnetic field changes (from 1 T to 8 T). They all show a moderate MCE and a peak around $T_{C}$. For Eu2CoIrO6, $-\Delta S_{M}$ reaches 0.58 J/Kg-K at 8 T. For Tb2CoIrO6 and Ho2CoIrO6, in addition to the peak around $T_{C}$, $-\Delta S_{M}$ becomes negative for small fields below $T_{N}$ which indicates the presence of an AFM component. This behavior is known as the inverse MCE. As the field increased above $H_{m}$, the sign of $-\Delta S_{M}$ changes to positive. The magnitude increases with increasing field and reaches a maximum around $T_{N}$. The peak value for Tb2CoIrO6 and Ho2CoIrO6 at 8 T are 4.91 and 6.32 J/Kg-K, respectively. The reversal of the sign of $-\Delta S_{M}$ at low temperatures is consistent with the spin-flop transition observed in $M(H)$ curves.

IV DISCUSSIONS

Once we settle lanthanide cations on the A site of A2BIrO6, the oxidation states of B and Ir are allowed for combinations of +1/+5, +2/+4 and +3/+3. The combination of +3/+3 is quite rare. To the best of our knowledge, it was only found in La2FeIrO6 Bufaiçal et al. (2014). In La2FeIrO6, the fully occupied $u^{\prime\prime}$ level and fully occupied $e^{\prime}$ level of Ir3+ (5$d^{6}$) lead to a nonmagnetic ground state ($J_{eff}=0$), thus there are only superexchange AFM coupling between Fe3+ cations Bufaiçal et al. (2008). To achieve the combination of +1/+5, one way is to place alkali metal cations on the B site. As is the case of La2LiIrO6, the Ir has been found to be in the oxidation state of 5+ Choy et al. (1995). In case of Ir5+ (5$d^{4}$), a nonmagnetic $J_{eff}=0$ ground state is expected with a fully occupied $u^{\prime\prime}$ level. Therefore, no magnetic transition was found in La2LiIrO6. The combination of +2/+4 is a good playground for studying the magnetic coupling of 3$d$ transition metals to the 5$d$ Ir with strong spin-orbit coupling. In Table I, we listed the structural parameters and magnetic ordering temperatures of our three compounds and the reference compound La2CoIrO6, as well as the other $Ln_{2}$B2+Ir4+O6 materials. It is clear that as the size of lanthanide cation becomes smaller, the lattice constants $a$ and $c$ decrease, enhancing the monoclinic distortion with decreasing the unit-cell volume monotonically. This behavior is consistent with the series of $Ln_{2}$NiIrO6 Ferreira et al. (2016) and $Ln_{2}$CoMnO6 Kim et al. (2015) compounds. The enhanced structural distortion will result in smaller B-O-B′ bond angles which correlate with the magnetic ordering temperature. In $Ln_{2}$CoMnO6, the magnetic transition temperature decreases linearly with the enhancement of monoclinic distortion Kim et al. (2015). However, in $Ln_{2}$NiIrO6 and $Ln_{2}$CoIrO6, $T_{C}$ increases gradually as decreasing the size of rare earth cations, as listed in Table I. Moreover, with magnetic $4f$ rare earth metals, there is an AFM transition at low temperatures in the hetero-tri-spin $3d$-$5d$-$4f$ system, which should be strongly influenced by rare earth magnetic moments. $T_{N}$ also increases with decreasing the size of magnetic rare earth cations. The temperature-induced FiM-to-AFM phase transition could be explained by the spin-reorientation transition scenario. Instead of placing 3$d$ transition metal cations on the B site, the other way to achieve the combination of +2/+4 for B/Ir is the choice of nonmagnetic alkaline earth metal cations on the B site. In La2MgIrO6 Ferreira et al. (2016) and Eu2MgIrO6 Mugavero III et al. (2010), the Ir4+ cations order antiferromagnetically below 10 K. For Nd2MgIrO6 and Gd2MgIrO6, they belong to the hetero-bi-spin $5d$-$4f$ system which exhibits slightly more complex magnetic behavior due to the magnetic coupling between the $Ln^{3+}$ and Ir4+ cations Mugavero III et al. (2010). There are two magnetic transitions in the susceptibility of Nd2MgIrO6 at 5 and 9 K. For Gd2MgIrO6, there is no AFM transition in the susceptibility.

The substitution of the trivalent rare earth cation by the divalent alkaline earth cation on the A site tends to change the Ir valence from 4+ to 5+. Since Ir5+ cations are nominally nonmagnetic, no magnetic transition is found for Ir5+ of the undistorted Sr2YIrO6 ($Fm3m$) Wakeshima et al. (1999); Corredor et al. (2017). By gradually substituting Sr on the A site of La2CoIrO6, the following phase transitions occur at room temperature: $P2_{1}/n\rightarrow P2_{1}/n+I2/m\rightarrow I2/m$ Narayanan et al. (2010), as well as a change of valence state from Co2+/Ir4+ to Co3+/Ir5+ Kolchinskaya et al. (2012). Furthermore, the fully occupied $u^{\prime\prime}$ level of Ir5+ is expected to hamper its magnetic coupling to the 3$d$ transition metal elements on the B site. This is exemplified in Sr2CoIrO6 ($I2/m$), Ir5+ has a paramagnetic moment with almost no orbital contribution, meanwhile Co3+ cations order antiferromagnetically without canting Kolchinskaya et al. (2012).

Finally, by controlling the oxygen deficiency of Sr2CoIrO6-δ, a rhombohedral phase with the composition Sr3CoIrO6 can be formed Mikhailova et al. (2010). It contains parallel one-dimensional chains along the $c$-axis Nguyen and zur Loye (1995).

V CONCLUSIONS

In this work, we reported the synthesis, crystal structures and magnetic behavior of iridium-based double perovskite $Ln_{2}$CoIrO6 ($Ln$ = Eu, Tb, Ho) polycrystalline samples. These compounds crystalize in the monoclinic space group $P2_{1}/n$. All of the compounds exhibited FiM Co2+-Ir4+ interactions at high temperatures. The Eu3+ spins show Van Vleck paramagnetism in Eu2CoIrO6 that don’t show observed interaction with Co2+ or Ir4+. However, with magnetic Tb3+ and Ho3+ cations on the A site, a second AFM transition was observed at low temperatures. A magnetic-field-induced spin-flop transition with a small hysteresis occurred below $T_{N}$ in these two compounds. We used a spin-reorientaion working model to explain the temperature-induced FiM-to-AFM phase transition in this hetero-tri-spin $3d$-$5d$-$4f$ system. A field up to 60 T is not enough to saturate their magnetic moments at low temperatures. Finally, moderate magnetocaloric effect was observed around magnetic transitions for all three compounds. The intriguing magnetic properties of these compounds call for high-quality single crystals. Moreover, to further explore the spin configuration and verify our working model, the spin structure obtained from inelastic neutron scattering experiment will be needed.

VI ACKNOWLEDGEMENTS

This work is supported by the Laboratory-Directed Research and Development program at Los Alamos National Lab under the auspices of the U.S. Department of Energy (DOE). The National High Magnetic Field Lab Pulsed Field facility is supported by the National Science foundation under cooperative Grant Nos. DMR-1157490 and DMR-1644779, the U.S. DOE, and the State of Florida. The work at Rutgers University was supported by the NSF under Grant No. DMR-1629059. The work at Harvey Mudd College was supported by a grant from the Jean Perkins Foundation. We thank John Singleton for the use of his magnetization probe in pulsed field experiments.