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2009 METALS, SUPERCONDUCTORS...Intrinsic diamagnetic length scales of Condon domain phase in BeMagnetic quantum oscillations which are the result of Landauquantization of the quasiparticle spectrum are a powerfultool in investigation of Fermi surfaces of wide spectrumof substances, including traditional normal metals, lowdimensionalsystems and superconductors. The increasein the amplitude of the dHvA oscillations at low temperatureunder quantizing magnetic field gives rise to the magneticinstability with formation of nonuniform diamagneticphase (Condon domains). The low curvature of the quasi-2D ’cigar’-like part of Fermi surface of beryllium results inrelatively high amplitude of dHvA oscillations and makesit favorable to observe the diamagnetic instability in beryllium.We show that the properties of correlated electrons innormal metals at the conditions of diamagnetic instabilitywhen the differential magnetic susceptibility a =µ 0 max{∂ ˜M/∂B} ≥ 1 ( ˜M is oscillating part of the magnetizationand B is magnetic induction of the sample) can bedescribed by the effective energy functionalthe size and the shape of the sample, and short-range electroninteraction on the scale of r c which gives rise to positiveenergy of interface boundaries.Thus, for a plate-like sample of thickness L, the minimizationof total free energy of periodic domain structureG PDS = G d−d + G σ , containing two terms, e. g. dipoledipoleenergy G d−d = (7/π 3 )ζ(3)y 2 0D, where ζ(3) is zetafunction,and surface energy of separation of two domainsG σ = (2L/D)σ (σ is the surface energy of a single domainwall), allows to calculate the steady-state period of the domainstructureD = 25/2 π(r c L) 1/2[7ζ(3)] 1/2 (sec 2 y2 02 − a)1/4 . (14)We calculate the expected values of domain wall width andperiod of the domain structure by use of measured valuesof the jump of magnetic induction at the domain wall δB(figure 101).G = − 1 2 K sin2 Θ + 1 2 A(∂ ζΘ) 2 . (12)In Eq. (12) we use a variable Θ = πy/2y 0 where y = 4πkMis a reduced magnetization, k = 2πF/(B a ) 2 = 2π/∆H, F =(F h +F w )/2 is average fundamental frequency of the dHvAoscillations (F h = 970.9 T and F w = 942.2 T are two fundamentalfrequencies corresponding to two extremal crosssectionsof ’cigar’-like Fermi surface of Be), ∆H is dHvAperiod. The uniform magnetization y 0 = y 0 (a) is given inexplicit form by equation y 0 = asin y 0 . Parameters K andA in Eq. (12) are defined asK = 4asin 2 y 02 (1 − acos2 y 02 ), A = a(2r cy 0 /π) 2 . (13)The first term in RHS of Eq. (12) is analogous to the easyaxiscrystallographic anisotropy (K > 0), while the gradientterm (ζ is coordinate) accounts for the short-range correlationson the scale of the cyclotron radius r c and correspondsto the exchange interaction in the physics of spinmagnetism. It follows from Eq. (12) that there is a closeanalogy between easy-axis anisotropy ferromagnetic sampleand the system which shows the diamagnetic instability.Thus, the problem of the diamagnetic length scales can besolved by the standard methods of the physics of magneticmaterials.We assume the existence of periodic domain structure withalternative magnetization ±y 0 in neighboring domains. Periodof the domain structure D is defined by competitionbetween long-range dipole-dipole interaction dependent onFigure 101: (a) Temperature dependence of the domain wallwidth δ = δ(T ) and (b) period of the Condon domain structureD = D(T ) at fixed value of B a = 2.642 T and Dingle temperaturesT D = 1.9 K in beryllium plate-like sample with the width L = 1.8mm. Circles (triangles) represent the diamagnetic length-scalescalculated from the data [G. Solt and V. S. Egorov, Physica B 318,231 (2002)] when heating (cooling).W. JossN. Logoboy (The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel and The Instituteof Superconductivity, Department of Physics, Bar-Ilan University, Ramat-Gan, Israel)73