Spinels (AB ₂O₄) with magnetic ions occupying only the octahedral B sites have inherent magnetic frustration which inhibits magnetic long-range order (LRO) but may lead to exotic states. Here we report on the magnetic properties of the tetragonal spinel Zn_0.8Cu_0.2FeMnO₄, the tetragonality resulting from the Jahn–Teller active Mn³⁺ ions. X-ray diffraction and x-ray photoelectron spectroscopy of the sample yielded the composition (

{Zn}_{0.8}^{2 +} {Cu}_{0.2}^{2 +}

) _A [

{Fe}_{0.4}^{2 +} {Fe}_{0.6}^{3 +} M n^{3 +}

] _B O_4‒δ. Analysis of the temperature dependence of magnetization (M), ac magnetic susceptibilities (χ′ and χ′′), dc susceptibility (χ), heat capacity C_p , and neutron diffraction (ND) measurements show complex temperature-dependent short-range order (SRO) but without LRO. The data of χ vs. T fits the Curie–Weiss law: χ = C/(T ‒ θ) from T = 250 K to 400 K with θ ≃ 185 K signifying dominant ferromagnetic (FM) coupling with the FM exchange constant J/k _B = 17 K, and C = 3.29 emu K mol^‒1 Oe^‒1 yielding an effective magnetic moment µ _eff = 5.13 µ _B resulting from the high-spin states of Cu²⁺ (A site) and Fe²⁺ (B site), while the B site trivalent ions Mn³⁺ and Fe³⁺ are in their low-spin states. The extrapolated saturation magnetization obtained from the M vs. H data at T = 2 K is explained using the spin arrangement (Cu²⁺↓) _A [Fe²⁺↑, Fe³⁺↓, Mn³⁺↑] _B leading to FM clusters interact antiferromagnetically at low temperatures. Temperature dependence of d(χT)/dT shows the onset of ferrimagnetism below ∼100 K and peaks near 47 K and 24 K. The relaxation time τ obtained from temperature and frequency dependence of χ″ when fit to the power law and Vogel–Fulcher laws confirm the cluster spin-glass (SG) state. The magnetic field dependence of the SG temperature

T_{SG} (H)

follows the equation:

T_{SG} (H) = T_{SG} (0) [1 - A H^{2 / ϕ}]

with T _SG (0) = 46.6 K, A = 8.6 × 10^‒3 Oe^‒0.593 and

ϕ

= 3.37. The temperature dependence of hysteresis loops yields coercivity H_C ∼ 3.8 kOe at 2 K without exchange-bias, but H_C decreases with increase in T becoming zero above 24 K, the T _SG(H) for H = 800 Oe. Variations of C_p vs. T from 2 K to 200 K in H = 0 and H = 90 kOe do not show any peak characteristic of LRO. However, after correcting for the lattice contribution, a broad weak peak typically of SRO becomes evident centered around 40 K. For T < 9 K, C_p varies as T² ; a typical signature of spin-liquids (SLs). Comparison of the ND measurements at 1.7 K and 79.4 K shows absence of LRO. Time dependence of thermo-remanent magnetization M _TRM(t) studies below 9 K reveal weakening of the inter-cluster interaction with increase in temperature. A summary of these results is that in Zn_0.8Cu_0.2FeMnO₄, ferromagnetic clusters interact antiferromagnetically without LRO but producing a cluster SG state at T _SG(0) = 46.6 K, followed by SL behavior below 9 K.

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