Observation of Diamagnetic Domains in Beryllium by Muon Spin Rotation Spectroscopy

Abstract

Spectroscopic evidence is given for the recurrent "domain phase" with oppositely magnetized regions in diamagnetic beryllium. A periodic splitting of the precession frequency of implanted muons in a Be single crystal was observed as the strength of the applied field H k ͗0001͘ varied near H 0 2.74 T. On sweeping H downwards, the doublet emerges and persists within more than one third of each de Haasvan Alphen cycle, the positions of the lines fixed, with the lower frequency (diamagnetic) component gaining and the higher (paramagnetic) one losing intensity. The line splitting gives DB ഠ 29 G for the induction difference in domains at T 0.8 K.

Order Parameter for a Diamagnetic Phase Transition

“…While attention of experimentalists has been directed primarily at Condon domains [3,7,8] the presence of temperature critical phenomena which should accompany diamagnetic phase transitions remain uncertain, except for [11]. Recently the instability of an electron gas has been emphasized to occur as a phase transition accompanied by the strong (critical) temperature dependence of the spontaneous magnetization, specific heat, and susceptibility temperature jumps [12].…”

“…To our knowledge, there have been discovered only two metals in which magnetic order is of orbital origin: silver and beryllium [7,8]. Condon domains were directly measured in silver by using the nuclear magnetic resonance [7] and in beryllium by the muon spin rotation resonance [8].…”

“…Condon domains were directly measured in silver by using the nuclear magnetic resonance [7] and in beryllium by the muon spin rotation resonance [8]. The properties of these domains have been extensively studied theoretically [5,6,9,10].While attention of experimentalists has been directed primarily at Condon domains [3,7,8] the presence of temperature critical phenomena which should accompany diamagnetic phase transitions remain uncertain, except for [11]. Recently the instability of an electron gas has been emphasized to occur as a phase transition accompanied by the strong (critical) temperature dependence of the spontaneous magnetization, specific heat, and susceptibility temperature jumps [12].…”

Size-dependent effects on the magnetization dynamics of Condon domains

“…3 and discovered in silver by means of nuclear magnetic resonance 4 and in beryllium and white tin by means of muon spin-rotation spectroscopy. [5][6][7][8][9] Domain formation at diamagnetic phase transitions was theoretically studied in Refs. 2, 3, 10-20.…”

Quantizing field-induced magnetic phase in a three-dimensional electron gas

“…4 In the case of magnetic ordering in an electron gas under high-quantizing magnetic field the elementary magnets arising are the orbital magnetic moments of conduction electrons, i.e., the spontaneous long-range order periodically occurs for nonlocalized magnetic moments of conduction electrons. Condon domains have been recently observed in beryllium by SR. 7 The properties of these domains have been extensively studied in theoretical work. [8][9][10] The phase transition to the domain phase is a particular case of the instability of an electron gas named diamagnetic phase transition.…”