We report the observation of room temperature ferromagnetism in high quality, single crystalline dilute Fe-doped $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$. The large equilibrium solubility of Fe ions in the matrix refutes uncertainties about secondary phase magnetism, which has often eclipsed this interesting field of research. While room temperature ferromagnetism is observed at and above 5% Fe concentrations, one finds a highly concave temperature dependence of the susceptibility. Using detailed ab initio calculation, this has been related to intrinsic magnetic inhomogeneities arising from positional disorder. Apart from providing a mechanism for the observed high temperature ferromagnetism, our results point out that intrinsic disorder is a generic and essential component of dilute magnetism.

We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of ${\mathrm{Ba}}_3{\mathrm{ZnIr}}_2{\mathrm{O}}_9$ is a realization of a novel spin-orbital liquid state. Our results reveal that ${\mathrm{Ba}}_3{\mathrm{ZnIr}}_2{\mathrm{O}}_9$ with ${\mathrm{Ir}}^{5+}$ ($5d^4$) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive $J=0$ state but each Ir ion still possesses a weak moment. Ab initio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural ${\mathrm{Ir}}_2{\mathrm{O}}_9$ dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100 mK.

Single crystalline Fe-doped hexagonal BaTiO${}_3$ samples with varying oxygen content are created by specifically intended post-growth annealing treatments, in order to check the influence of defects on the unusual high temperature ferromagnetism observed in this system. The various defects have been shown to play a crucial role in dilute magnetic systems and therefore, it is important to carry out this check for the Fe-doped BaTiO${}_3$ system also, in which unusual ferromagnetism was reported even in its bulk single crystalline form. The x-ray diffraction and dielectric studies carried out here have confirmed that the Fe doping of Ti is intrinsic, while the high resolution transmission electron microscopy (HRTEM) and x-ray photoemission spectroscopy (XPS) studies proved the absence of unwanted magnetic metal clusters in the sample. The transport studies show that the oxygen concentrations could be varied substantially by the thermal treatments. Finally, magnetization measurements on the samples demonstrated that ferromagnetism is stronger in samples with higher oxygen deficiency, which could interestingly be retreated under high oxygen atmosphere and reversibly be taken back to a lower magnetic state. The vacancy-induced ferromagnetism is further confirmed by EPR measurements, which is consistent with earlier studies and, consequently, put the doped BaTiO${}_3$ in the list of true dilute magnetic oxide (DMO) systems.

While it was speculated that $5d^4$ systems would possess nonmagnetic $J=0$ ground state due to strong spin-orbit coupling (SOC), all such systems have invariably shown the presence of magnetic moments so far. A puzzling case is that of ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$, which in spite of having a perfectly cubic structure with largely separated ${\mathrm{Ir}}^{5+}\left(d^4\right)$ ions, has consistently hosted weak magnetic moments. We show from muon spin relaxation $\left(\mu \mathrm{SR}\right)$ measurements that a change in the magnetic environment of the implanted muons in ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$ occurs as the temperature is lowered below 10 K indicating magnetic response has a temperature dependence unlikely for a $J=0$ system. Interestingly, the estimated value of SOC obtained by fitting the resonant inelastic x-ray scattering (RIXS) spectrum of ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$ with an effective atomic many-body Hamiltonian is found to be as high as 0.39 eV, comparable to the reported value of SOC in other magnetic $d^4$ iridates with noncubic distortion. We argue that in addition to strong SOC, the presence of intersite hopping triggers delocalization of holes, resulting in the spontaneous generation of magnetic moments. Our theoretical calculations further indicate that these moments favor the formation of spin-orbital singlets in the case of ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$, which is manifested in $\mu \mathrm{SR}$ experiments measured down to 60 mK.

The magnetic ground states in highly ordered double perovskites LaSr_1−xCa_xNiReO₆ (x = 0.0, 0.5, 1.0) are studied in view of the Goodenough-Kanamori rules of superexchange interactions in this paper. In LaSrNiReO₆, Ni and Re sublattices are found to exhibit curious magnetic states separately, but no long range magnetic ordering is achieved. The magnetic transition at ~255 K is identified with the independent Re sublattice magnetic ordering. Interestingly, the sublattice interactions are tuned by modifying the Ni-O-Re bond angles through Ca doping. Upon Ca doping, the Ni and Re sublattices start to display a ferrimagnetically ordered state at low temperature. The neutron powder diffraction data reveals long range ferrimagnetic ordering of the Ni and Re magnetic sublattices along the crystallographic b-axis. The transition temperature of the ferrimagnetic phase increases monotonically with increasing Ca concentration.

Spin-orbit coupling (SOC) is found to be crucial for understanding the magnetic and electronic properties of $5d$ transition metal oxides. In $5d$ systems, with ${\mathrm{Ir}}^{5+}$ ions, where ideally a nonmagnetic $J=0$ ground state is expected to be stabilized in the presence of strong SOC, often spontaneous moments are generated due to hopping induced superexchange. This effect is more pronounced when the Ir atoms are close by, as in systems with ${\mathrm{Ir}}_2{\mathrm{O}}_9$ dimers in $6H{\mathrm{Ba}}_{3}M{\mathrm{Ir}}_2{\mathrm{O}}_9$ compounds where magnetism is an outcome of complex Ir-O-Ir exchange paths, and is strongly influenced by the presence of local distortions. We find that subtle variations in the local structure of ${\mathrm{Ba}}_{3}M{\mathrm{Ir}}_2{\mathrm{O}}_9$ ($M$ = Mg, Sr, and Ca) lead to markedly different magnetic properties. While SOC plays a pivotal role in explaining the insulating ground states of these systems, it is seen that ${\mathrm{Ba}}_3{\mathrm{MgIr}}_2{\mathrm{O}}_9$, having a $P{6}_3/mmc$ symmetry, does not order down to low temperature despite having antiferromagnetic exchange interactions, while ${\mathrm{Ba}}_3{\mathrm{CaIr}}_2{\mathrm{O}}_9$ shows weak dimer-like features and stabilizes in $C2/c^{\prime }$ magnetic configuration with no net moment, and ${\mathrm{Ba}}_3{\mathrm{SrIr}}_2{\mathrm{O}}_9$ possesses a ground state corresponding to the magnetic space group $C{2}^{\prime }/c^{\prime }$ and exhibits ferromagnet-like features.