The Griffiths phase-like features and the spin-phonon coupling effects observed in Tb₂NiMnO₆ are reported. The double perovskite compound crystallizes in monoclinic P2₁/n space group and exhibits a magnetic phase transition at T_c ∼ 111 K as an abrupt change in magnetization. A negative deviation from ideal Curie--Weiss law exhibited by 1/χ(T) curves and less-than-unity susceptibility exponents from the power-law analysis of inverse susceptibility are reminiscent of Griffiths phase-like features. Arrott plots derived from magnetization isotherms support the inhomogeneous nature of magnetism in this material. The observed effects originate from antiferromagnetic interactions that arise from inherent disorder in the system. Raman scattering experiments display no magnetic-order-induced phonon renormalization below T_c in Tb₂NiMnO₆, which is different from the results observed in other double perovskites and is correlated to the smaller size of the rare earth. The temperature evolution of full-width-at-half-maximum for the stretching mode at 645 cm⁻¹ presents an anomaly that coincides with the magnetic transition temperature and signals a close connection between magnetism and lattice in this material.

We report on the observation of exchange bias (EB) and memory effect in double perovskite ${\text{Sr}}_2{\text{FeCoO}}_6$ . Antiphase boundaries between the ferromagnetic and the antiferromagnetic regions in the disordered glassy phase are assumed as responsible for the observed effect, which reflects in the cooling field dependence and temperature evolution of exchange bias field and in training effect. The spin glass (SG) phase itself is characterized through memory, ageing, and magnetic relaxation experiments. The spin glass transition temperature, $T_g$ , versus $H_{\mathit{dc}}^{2/3}$ follows the Almeida-Thouless line yielding a freezing temperature, $T_f=73\mathrm{K}$ . Time-dependent magnetic relaxation studies reveal the magnetization dynamics of the underlying glassy phase in this double perovskite.

A spin glass state is observed in the double perovskite oxide Sr₂FeCoO₆ prepared through sol-gel technique. Initial structural studies using x rays reveal that the compound crystallizes in tetragonal I4/m structure with lattice parameters, a = 5.4609(2) Å and c = 7.7113(7) Å. The temperature dependent powder x ray diffraction data reveal no structural phase transition in the temperature range 10-300 K. However, the unit cell volume shows an anomaly coinciding with the magnetic transition temperature thereby suggesting a close connection between lattice and magnetism. Neutron diffraction studies and subsequent bond valence sums analysis show that in Sr₂FeCoO₆, the B site is randomly occupied by Fe and Co in the mixed valence states of Fe^3 +/Fe⁴⁺ and Co³⁺/Co⁴⁺. The random occupancy and mixed valence sets the stage for inhomogeneous magnetic exchange interactions and in turn, for the spin glass state in this double perovskite, which is observed as an irreversibility in temperature dependent dc magnetization at T_f ∼ 75 K. Dynamical scaling analysis of χ′(T) yields a critical temperature T_ct = 75.14(8) K and an exponent zν = 6.2(2) typical for spin glasses. The signature of presence of mixed magnetic interactions is obtained from the thermal hysteresis in magnetization of Sr₂FeCoO₆. Combining the neutron and magnetization results of Sr₂FeCoO₆, we deduce that Fe is in low spin state while Co is in both low spin and intermediate spin states.

The critical properties of orthorhombic Pr0.6Sr0.4MnO3 single crystals were investigated by a series of static magnetization measurements along the three different crystallographic axes as well as by specific heat measurements. A careful range-of-fitting-analysis of the magnetization and susceptibility data obtained from the modified Arrott plots shows that Pr0.6Sr0.4MnO3 has a very narrow critical regime. Nevertheless, the system belongs to the three-dimensional (3D) Heisenberg universality class with short-range exchange. The critical exponents obey Widom scaling and are in excellent agreement with the single scaling equation of state M(H,$\epsilon${})=|$\epsilon${}|$\beta${}f\ifmmode\pm\else\textpm\fi{}(H/|$\epsilon${}|($\beta${}+$\gamma${}); with f+ for T>Tc and f$-${} for T<Tc. A detailed analysis of the specific heat that account for all relevant contributions allows us to extract and analyze the contribution related to the magnetic phase transition. The specific heat indicates the presence of a linear electronic term at low temperatures and a prominent contribution from crystal field excitations of Pr. A comparison with data from literature for PrMnO3 shows that a Pr-Mn magnetic exchange is responsible for a sizable shift in the lowest lying excitation.

The magnetism of the double perovskite compounds ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{FeCoO}}_6$ $\left(x=0,1,2\right)$ is contrasted using magnetization, neutron diffraction, and electron paramagnetic resonance with the support from density functional theory calculations. ${\mathrm{La}}_2{\mathrm{FeCoO}}_6$ is identified as a long-range ordered antiferromagnet displaying a near-room temperature transition at $T_N=270$ K, accompanied by a low temperature structural phase transition at $T_S=200$ K. The structural phase transformation at $T_S$ occurs from $R\overline{3}c$ at 300 K to $Pnma$ at 200 K. The density functional theory calculations support an insulating noncompensated antiferromagnetic structure. The long-range ordered magnetism of ${\mathrm{La}}_2{\mathrm{FeCoO}}_6$ transforms to short-range glassy magnetism as La is replaced with Sr in the other two compounds. The magnetism of ${\mathrm{La}}_2{\mathrm{FeCoO}}_6$ is differentiated from the nonequilibrium glassy features of ${\mathrm{Sr}}_2{\mathrm{FeCoO}}_6$ and ${\mathrm{SrLaFeCoO}}_6$ using the cooling-and-heating-in-unequal-fields magnetization protocols. This contrasting magnetism in the ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{FeCoO}}_6$ series is evidenced in electron paramegnetic resonance studies. The electronic density of states estimated using the density functional theory calculations contrast the insulating feature of ${\mathrm{La}}_2{\mathrm{FeCoO}}_6$ from the metallic nature of ${\mathrm{Sr}}_2{\mathrm{FeCoO}}_6$. From the present suite of experimental and computational results on ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{FeCoO}}_6$, it emerges that the electronic degrees of freedom, along with antisite disorder, play an important role in controlling the magnetism observed in double perovskites.