At finite temperatures, fluctuations invariably introduce disorder and are responsible for ultimately destroying ordered phases. Here we present an un

Thermally induced magnetic order from glassiness in elemental neodymium

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2022-07-05 19:00:10

At finite temperatures, fluctuations invariably introduce disorder and are responsible for ultimately destroying ordered phases. Here we present an unusual magnetic transition in elemental neodymium where, with increasing temperature, long-range multiply periodic ‘multi-Q’ magnetic order emerges from a self-induced spin glass. Using temperature-dependent spin-polarized scanning tunnelling microscopy, we characterize the local order of a previously reported spin glass phase, and quantify the emergence of long-range multi-Q order with increasing temperature. We develop two analysis tools that allow us to determine the glass transition temperature from measurements of the spatially dependent magnetization. We compare these observations with atomistic spin dynamics simulations, which reproduce the qualitative observation of a phase transition from a low-temperature spin glass phase to an intermediate ordered multi-Q phase. These simulations trace the origin of the unexpected high-temperature order in weakened frustration driven by temperature-dependent sublattice correlations. These findings constitute an example of order from disorder, and provide a platform to study the rich magnetization dynamics of a self-induced spin glass.

Ordered phases tend towards disorder with increasing temperature, resulting from entropy. There are a few exceptions to such intuition, as exemplified by the ferroelectric Rochelle salt. In this material there are two relevant Curie temperatures (TC), and for both T < TC1 and T > TC2, the material exhibits a disordered paraelectric phase, but oddly an ordered ferroelectric phase stabilizes for TC1 < T < TC2 (ref. 1). For magnetic systems, the presence of re-entrant spin glasses in alloys shows similar order from disorder behaviour, but the source of this phenomena is still being heavily debated owing to the coexistence of both glassy behaviour and long-range order2. Moreover, a study on Y2Ni7 was initially interpreted to show thermally induced spontaneous magnetization3, but was later found to be flawed by sample impurities4. Theoretically, there are mechanisms that predict the appearance of ferromagnetic order at increasing temperature5. For example, in itinerant electron systems, ferromagnetic order may arise if a peak in the density of states shifts such that the Stoner criterion is satisfied at finite temperature, but not at T = 0. Another heavily discussed mechanism to create magnetic order from an increase in temperature is known as order from disorder, and is related to a macroscopic degeneracy of the ground state that is broken by finite-temperature contributions of spin excitations to the free energy6,7. For example, the observation of a spiral phase seen in PrPtAl was connected to the concept of order from disorder8. These proposed mechanisms provide counterexamples to basic thermodynamic intuition, where increasing temperature, and thus increasing entropy, should produce more disorder.

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