Direct Observation of Condon Domains in Silver by Hall Probes

Abstract

Using a set of micro Hall probes for the detection of the local induction, the inhomogeneous Condon domain structure has been directly observed at the surface of a pure silver single crystal under strong Landau quantization in magnetic fields up to 10 T. The inhomogeneous induction occurs in the theoretically predicted part of the Condon domain phase diagram. Information about size, shape, and orientation of the domains is obtained by analyzing Hall probes placed along and across the long sample axis and by tilting the sample. On a beryllium surface the induction inhomogeneity is almost absent although the expected induction splitting here is at least 10 times higher than in silver.

Diamagnetic length scales of the Condon domain phase in Lifschitz–Kosevich–Shoenberg approximation

“…A set of micro Hall probes was used for detection of local induction at the surface of the pure silver single crystal 2.4×1.6×1.0 mm 3 (T D = 0.2 K) in the magnetic field up to 10 T and temperature interval T =1.3−3 K. The detection of the inhomogeneous induction was attributed to the presence of the CD structure with the period evaluated as being certainly larger than the distance of ≈ 150 µm between the edge probes (under limit for period). This result is in contradiction with the proposed in [5] expression D ≈ (Lδ) 1/2 (β = 1) that gives much lower value for D ≈ 30 µm. Under the conditions of experiment, a = 4.35 Eq.…”

“…Unfortunately, we cannot discuss Condon's estimations [22] which are represented in [1] without prove. As we see below, Condon's result is in contradiction with experiment [5]. In order to calculate a quantity such as the surface energy of the DW Eq.…”

“…The important information about the size of the domains, the domain wall (DW) width and surface energy of the interface boundaries is still lacking. The attempt of direct measurement of the period of the domain structure in plate-like sample of silver by the Hall probe technique [5] revealed the value of ∼150 µm instead of expected one ∼30 µm at the conditions of experiment (applied magnetic field µ 0 H = 10 T, temperature T = 1.3 K and plate thickness L ≈1 mm). Calculation of the contribution of the short-range interaction (on the scale of cyclotron radius r c ) into the free energy density was carried out by Privorotskii [16].…”

“…The horizontal asymptote for δ is 2rc (not shown). Circle (square) corresponds to the values of characteristic lengths calculated at the conditions of experiment [2] ( [5]). The nearest vicinity of the critical point (α (rc/L) 2/3 ) where periodic domain structure transforms into the modulated structure is excluded from the consideration.…”

“…Further development of the experimental technique including the standard ac method with different modulation levels, frequencies and magnetic field ramp rates allowed us to reconstruct the magnetization reversal in beryllium [8]. The detection of giant nonlinear response at the crossing critical point, a →1, where a = µ 0 max{∂M/∂B} is a differential magnetic susceptibility, offered a way to construct the diamagnetic phase diagrams [5], [13]- [15].…”