We investigate Cu-doped Ba(Fe 1−x Cu x ) 2 As 2 with transport, magnetic susceptibility, and elastic neutron scattering measurements. In the heavily Cu-doped regime where long-range stripe-type antiferromagnetic order in BaFe 2 As 2 is suppressed, Ba(Fe 1−x Cu x ) 2 As 2 (0.145 x 0.553) samples exhibit spin-glass-like behavior in magnetic susceptibility and insulating-like temperature dependence in electrical transport. Using elastic neutron scattering, we find stripe-type short-range magnetic order in the spin-glass region identified by susceptibility measurements. The persistence of short-range magnetic order over a large doping range in Ba(Fe 1−x Cu x ) 2 As 2 likely arises from local arrangements of Fe and Cu that favor magnetic order, with Cu acting as vacancies relieving magnetic frustration and degeneracy. These results indicate locally broken fourfold rotational symmetry, suggesting that stripe-type magnetism is ubiquitous in iron pnictides. DOI: 10.1103/PhysRevB.96.161106 The parent compounds of iron pnictides such as BaFe 2 As 2 and NaFeAs exhibit stripe-type antiferromagnetic (AF) order below T N that breaks both spin-rotational symmetry and fourfold rotational symmetry of the underlying crystalline lattice [1]. However, a tetragonal-to-orthorhombic structural transition occurs at T s with T N T s , preemptively breaking the fourfold rotational symmetry of the crystal and resulting in an Ising-nematic state in the region. The Ising-nematic state and associated fluctuations have been implicated in the superconducting pairing of iron pnictides [3], although the nature of the nematic state is still under debate [4]. Superconductivity can be induced by substituting Fe with transition metals such as Co and Ni, which also suppresses the magnetic and structural phase transitions [1,5,6]. In the overdoped regime where both the magnetic and structural transitions are suppressed, the system maintains an average fourfold rotational symmetry without long-range magnetic order, although inelastic neutron scattering revealed substantial stripe-type fluctuations even in nonsuperconducting overdoped BaFe 1.7 Ni 0.3 As 2 [7]. For BaFe 2−x T M x As 2 (T M = Co, Ni, Cu), while Co and Ni doping result in superconducting domes with optimal T c ∼ 20 K, optimal T c ∼ 2 K or no superconductivity is observed in AFe 2−x Cu x As 2 (A = Ba,Sr) [8][9][10]. This contrast points to the inadequacy of a simple rigid band picture [11][12][13] and highlights differences between dopants [14,15].Compared to AFe 2−x Cu x As 2 , superconductivity with optimal T c = 11.5 K is observed in NaFe 1−x Cu x As [16,17]. With increasing Cu concentration (x 10%), insulating-like transport and short-range magnetic order develop, evolving towards an insulator with long-range magnetic order and Fe-Cu ordering near x ≈ 50% [18]. The evolution from * Yu.Song@rice.edu † pdai@rice.edu metallic to insulating/semiconducting transport is also observed in Ba(Fe 1−x Cu x ) 2 As 2 (x 0.145), Sr(Fe 1−x Cu x ) 2 As 2 (x 0.06) [10], Fe 1.01−x Cu x Se (x 0.03) [19...