## 1 Introduction  
Transition metal pyro compounds M\({}_{2}\)X\({}_{2}\)O\({}_{7}\) with M-cations (M = Cr, Mn, Fe, Ni, Co, Cu, Zn, Cd, Mg, Hg) and X = P, As, Se, Ge have been widely used in catalysts [1; 2], supercapacitors [3; 4; 5; 6], photoluminescence devices [7], and some other applications [8; 9; 10] due to their excellent chemical stability, facile preparation, magnetic properties, and non-toxicity [11; 12; 13]. The M\({}_{2}\)X\({}_{2}\)O\({}_{7}\) compounds are observed in two types of structure, i.e., dichromatic structure type and thortveitite structure type, depending on the ratio of the M to X ionic radii. Amongst these, copper pyrophosphate (Cu\({}_{2}\)P\({}_{2}\)O\({}_{7}\)) has been well characterized and received much attention as a prospective material for advanced energy storage devices, lightning, photovoltaic devices, sensors, catalysts, etc. [2; 3; 4; 5; 6; 7; 10]. The room-temperature \(\alpha\) phase of Cu\({}_{2}\)P\({}_{2}\)O\({}_{7}\) with space group \(C2/c\) undergoes a solid-solid phase transition to \(\beta\)-phase with space group \(C2/m\) at a slightly elevated temperature of about 339-383 K, as has been established by X-ray diffraction (XRD) [14]. The structure is composed of pyrophosphate (diphosphate) [P\({}_{2}\)O\({}_{7}\)]\({}^{4-}\) ionic groups arranged into layers that are parallel to the (001) lattice plane, and Cu\({}^{2+}\) cations in irregular octahedral coordination by oxygen atoms. Cu\({}^{2+}\) octahedra form a pseudo-hexagonal network between the adjacent [P\({}_{2}\)O\({}_{7}\)]\({}^{4-}\) layers. Each pyrophosphate unit [P\({}_{2}\)O\({}_{7}\)]\({}^{4-}\) consists of two monophosphatetetrahedra [PO4]3- which share one corner via the bridging O(1) atom. In the \(\alpha\) phase, the P\(-\)O(1)\(-\)P bond angle is 157\({}^{\circ}\), whereas it is 180\({}^{\circ}\) in the \(\beta\) phase [15]. [PERSON] and [PERSON] reported that the \(\beta\) phase could be described simply as a disordered \(\alpha\) phase of Cu\({}_{2}\)P\({}_{2}\)O\({}_{7}\), which manifests interesting thermal and dielectric properties [15]. Additionally, the \(\beta\) phase exhibits twice as small \(c\) lattice parameter and a disordered arrangement of the bridging O atoms shared by the two [PO4] tetrahedra in a pyrophosphate group [16]. Since the \(\alpha\) phase is structurally similar to the \(\beta\) phase of Cu\({}_{2}\)P\({}_{2}\)O\({}_{7}\), in the present work we focus on the \(\alpha\) phase which is fully ordered and stable at room temperature. It is well understood that the properties of materials strongly depend on the crystal structure, dimensionality, purity, morphology, and size of their constituent particles [17; 18; 19; 20]. Thus, various methods to synthesize Cu\({}_{2}\)P\({}_{2}\)O\({}_{7}\) with controllable microstructure, shape, and particle size have been considered [5; 6; 13; 17; 21], such as solid-state routes, sol-gel synthesis, chemical bath deposition, co-precipitation, successive ionic layer and adsorption reaction strategy, carbothermal reduction method, and a simple hydrothermal method. Correspondingly, the physical and chemical properties of Cu\({}_{2}\)P\({}_{2}\)O\({}_{7}\) such as structural, morphological, optical, magnetic, and electrochemical properties, thermodynamic stability and phase transitions have been investigated experimentally and theoretically [6; 12; 13; 16; 17; 22; 23]. The magnetic behavior of \(\alpha\)-Cu\({}_{2}\)P\({}_{2}\)O\({}_{7}\) was studied in the early 1970s. Tentative models of the magnetic structure were derived from neutron diffraction and nuclear magnetic resonance data; an antiferromagnetic (AFM) ordering was reported at 27 K [24; 25]. Theoretically, the AFM order in \(\alpha\)-Cu\({}_{2}\)P\({}_{2}\)O\({}_{7}\) was confirmed by [PERSON] et al., in which the magnetism was found to originate from the half-filled Cu \(3d_{x^{2}-y^{2}}\) orbital states [12].