Diamagnetic domains in beryllium observed by muon-spin-rotation spectroscopy

Abstract

Dia- and paramagnetic (Condon) domains were observed in single crystal beryllium for applied fields $\mathit{H}||[0001]$ of 1--3 T, at temperatures $T=0.1--3$ K, by muon-spin-rotation $(\ensuremath{\mu}\mathrm{SR})$ spectroscopy at PSI. On varying H, the domains with magnetization parallel and opposite to $\mathit{H}$ reappear in each de Haas--van Alphen period $\ensuremath{\Delta}H,$ detected by the doublet splitting in the precession frequency spectrum. As H varies within the ``domain section'' $\ensuremath{\delta}H$ of a dHvA cycle, the domain inductions ${B}_{1}{,B}_{2}$ stay constant, while the volume fractions of the para- and diamagnetic regions vary linearly. The beat in the susceptibility amplitude $a(B)=4\ensuremath{\pi}{(dM/dB)}_{\mathrm{max}},$ with a period of $\ensuremath{\approx}33\ensuremath{\cdot}\ensuremath{\Delta}H,$ allowed us to determine ${B}_{i}$ and $\ensuremath{\delta}H$ for different regimes. As a increases by a factor of $\ensuremath{\approx}3,$ the sections $\ensuremath{\delta}H$ grow, $|{B}_{2}\ensuremath{-}{B}_{1}\stackrel{\ensuremath{\rightarrow}}{|}\ensuremath{\Delta}H,$ and the uniform state between two domain sections shows an increasingly strong diamagnetism, $\ensuremath{-}4\ensuremath{\pi}\ensuremath{\chi}\ensuremath{\gg}1.$ The domains persist up to $T\ensuremath{\approx}3$ K and at fields down to $H\ensuremath{\approx}1$ T. On varying H, a slight ``field overheating'' was observed. The domain area in the phase diagram is much larger than expected, while other predictions of the theory proved to be qualitatively correct.