Transition temperature, magnon frequency ω and exchange interaction J

Ferromagnetic material

Material	Curie Temperature Tc (K)	Exchange interaction J (meV)	Magnon frequency ħω	Magnetization (M) and susceptibility (χ)
	Mean field theory: 2/3*Z[S(S+1)]J		ħωk=2ZJS(1-γk) γk=∑nncos(kδ)/Z Z is the number of nearest neighbor, δ is the nearest neighbor vector. Maximum: (k=π/a) ħωmax=4ZJS For 1 D system, maximum value will be ħωmax=8JS	Bloch theorem ΔM/M0 ∝ T3/2 Mean field theory: χ=Nμ2/[3kB(T-Tc)]
EuO	69.1 (K)		0.5 meV (k=0.2 A) 3.2 meV (k=0.6 A) 4.6 meV (k=0.8 A) 5.5 meV (k=1.0 A)

Materials	Structure	TM (K)	TN (K)	Weak FM	Spin orientation	Exchange interaction J	Magnon frequency ħω	Magnetization (M) and susceptibility (χ)
			The relation between TN and J is missing, I could not find it anywhere.				ħωk=2ZJS√{1-γk2} Taking into account of anisotropy and external field ħωk = 2ZJS√{(1+gμBBA/(2ZSJ))-γk2} ± gμBB At zero external field, we can get finite ħωk even for k=0  because of anisotropy. ħωmin = 2ZJS√{gμBBA/(2ZSJ)(1+gμBBA/(4ZSJ))} If we apply an external field, we can get spin flop when the mode of one branch of the spin wave goes to zero (instability) Bf=√{4ZJSBA/(gμB)} In the case that anisotropy is much smaller than J, in other words: gμBBA>>2ZSJ, we get ħωmax=2ZJS,   k=π/(2a) Then, ħωmin = √{gμBBA*(2ZSJ)	Mean field theory: χ=C/(T+TN)
MnF2			67.4 K				k‖z ħωmax=54.8 cm-1 k‖x ħωmax=50.4 cm-1 because of anisotropy ħωmin=8.715 cm-1 e.g. μBBA = 0.737 cm-1 then we can calculate (using the first order): ħωmin=√{gμBBA*ħωmax}=8.99 cm-1
BiFeO3	Rhombohedra (distorted perovskite)		640 K	supposably weakly ferromagnetic below TN			ħωmax=445 (assuming kBTN=ħωmax) ħωmin= 18.2 cm-1 We can estimate the anisotropy energy: μBBA = (ħωmin)2/(għωmax) = 0.372 cm-1, corresponding to BA=0.8 T, which does not look right. In any case, there is no real data on ħωmax., if we can succesfully get the spin flop, then we probably can get ħωmax.
Fe2O3 Hematite	Rhombohedra (corundum)	260 K	950 K	weakly ferromagnetic between TN and TM	‖[111]c below TM ⊥[111]c between TM and TN
Cr2O3	Rhombohedra (corundum)		312 K			94 K	ħωmax=600 K
RbMnF3	cubic perovskite		82 K			J1=3.4 K	ħωmax=100 K (Windsor CG and Stevenson RWH, Proc.Phys. Soc. 87, 501) ħωmin ~ 0
KMnF3	cubic perovskite		88K