Phototunable Magnetism in Copper Octacyanomolybdate

Table 1

Symmetry properties of the irreducible representations, Γ𝐷(Γ)⊗𝑆⁰⊗𝑇⁰, M𝐷(M)⊗𝑆⁰⊗𝑇⁰, Γ𝐷(Γ)⊗𝑆¹⊗𝑇¹, and M𝐷(𝑀)⊗𝑆¹⊗𝑇¹, available in the Hamiltonian (1) subject to axial isotropy subgroup.

Irreducible representation	Axial isotropy subgroup	Physical character
Γ𝐴𝑔⊗𝑆̆^0⊗𝑇̆^0	𝐂4ℎ𝐋1ST	PM, CDP
Γ𝐵𝑔⊗𝑆̆^0⊗𝑇̆^0	𝐂2ℎ𝐋1ST	Γ-Cu-CDW
Γ𝐴𝑢⊗𝑆̆^0⊗𝑇̆^0	𝐂4𝐋1ST	Γ-Mo-CDW
Γ𝐵𝑢⊗𝑆̆^0⊗𝑇̆^0	𝐒4𝐋1ST	BOW
M𝐴𝑔⊗𝑆̆^0⊗𝑇̆^0	𝐂4ℎ𝐋2ST	M-MoCu-CDW(1)
M𝐵𝑔⊗𝑆̆^0⊗𝑇̆^0	(𝐸+𝐶^+4𝑧𝐚)𝐂2ℎ𝐋2ST	M-MoCu-CDW(2)
M𝐴𝑢⊗𝑆̆^0⊗𝑇̆^0	(𝐸+𝐼𝐚)𝐂4𝐋2ST	M-Mo-CDW(1)
M𝐵𝑢⊗𝑆̆^0⊗𝑇̆^0	(𝐸+𝐶^+4𝑧𝐚)𝐒4𝐋2ST	M-Mo-CDW(2)
Γ𝐴𝑔⊗𝑆̆^1⊗𝑇̆^1	𝐂4ℎ𝐋1A(𝑒𝑧)M(𝑒𝑦)	FM
Γ𝐵𝑔⊗𝑆̆^1⊗𝑇̆^1	(𝐸+𝐶^+4𝑧𝑢2𝑥)𝐂2ℎ𝐋1A(𝑒𝑧)M(𝑒𝑦)	Γ-Cu-AFM
Γ𝐴𝑢⊗𝑆̆^1⊗𝑇̆^1	(𝐸+𝐼𝑢2𝑥)𝐂4𝐋1A(𝑒𝑧)M(𝑒𝑦)	Γ-Mo-AFM
Γ𝐵𝑢⊗𝑆̆^1⊗𝑇̆^1	(𝐸+𝐶^+4𝑧𝑢2𝑥)𝐒4𝐋1A(𝑒𝑧)M(𝑒𝑦)	SBOW
M𝐴𝑔⊗𝑆̆^1⊗𝑇̆^1	(𝐸+𝑢2𝑥𝐚)𝐂4ℎ𝐋2A(𝑒𝑧)M(𝑒𝑦)	M-MoCu-AFM(1)
M𝐵𝑔⊗𝑆̆^1⊗𝑇̆^1	(𝐸+𝑢2𝑥𝐚)(𝐸+𝐶^+4𝑧𝑢2𝑥)𝐂2ℎ𝐋2A(𝑒𝑧)M(𝑒𝑦)	M-MoCu-AFM(2)
M𝐴𝑢⊗𝑆̆^1⊗𝑇̆^1	(𝐸+𝑢2𝑥𝐚)(𝐸+𝐼𝑢2𝑥)𝐂4𝐋2A(𝑒𝑧)M(𝑒𝑦)	M-Mo-AFM(1)
M𝐵𝑢⊗𝑆̆^1⊗𝑇̆^1	(𝐸+𝑢2𝑥𝐚)(𝐸+𝐶^+4𝑧𝑢2𝑥)𝐒4𝐋2A(𝑒𝑧)M(𝑒𝑦)	M-Mo-AFM(2)

Consider 𝐂_4ℎ={𝐸,𝐶_4𝑧,𝐶_2𝑧,𝐶⁻¹_4𝑧,𝐼,𝐼𝐶_4𝑧,𝜎_ℎ,𝐼𝐶⁻¹_4𝑧},  𝐂_2ℎ={𝐸,𝐶_2𝑧,𝐼,𝜎_ℎ},
𝐂₄={𝐸,𝐶_4𝑧,𝐶_2𝑧,𝐶⁻¹_4𝑧},  𝐒₄={𝐸,𝐶_2𝑧,𝐼𝐶_4𝑧,𝐼𝐶⁻¹_4𝑧},
𝐋₁={𝑙_𝑎𝐚+𝑙_𝑏𝐛+𝑙_𝑐𝐜;𝑙_𝑎,𝑙_𝑏,𝑙_𝑐∈𝑍},  𝐋₂={(𝑙₊+𝑙₋)𝐚+(𝑙₊−𝑙₋)𝐛+𝑙_𝑐𝐜;𝑙₊,𝑙₋,𝑙_𝑐∈𝑍},
A(𝑒_𝑧) = {𝑢(𝑒_𝑧,𝜃)∣0≤𝜃≤4𝜋},   M(𝑒_𝜆) = {𝐸,𝑡𝑢_2𝜆},  𝑢_2𝜆=𝑢(𝑒_𝜆,𝜋)∶𝜆=𝑥,𝑦,𝑧.