Research Article

Self-induced spin glass state in elemental and crystalline neodymium

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Science  29 May 2020:
Vol. 368, Issue 6494, eaay6757
DOI: 10.1126/science.aay6757

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A structurally ordered spin glass

Spin glasses that form in disordered materials such as magnetic alloys have locally varying magnetic patterns, and their spin relaxation occurs over time scales spanning many orders of magnitude. Kamber et al. used spin-polarized scanning tunneling microscopy to image the magnetism on the (0001) surface of thick, single-crystal films of neodymium as a function of temperature and magnetic field. Despite the lack of structural disorder, they found a spectral distribution of degenerate magnetic wave vectors, or Q states, that exhibited spatiotemporal variation. In this spin-Q glass, pockets of nearly degenerate spin spiral states formed with varying periodicity. Ab initio electronic structure coupled to atomistic spin dynamics calculations suggests that the double hexagonal closed packed crystal structure in neodymium drove strongly frustrated magnetism that created these pockets.

Science, this issue p. eaay6757

Structured Abstract


Spin glasses are one of the more intriguing, but least understood, magnetic states of matter. In stark contrast to ordered magnets, spin glasses form a state characterized by seemingly random and uncorrelated magnetic patterns lacking long-range order. The distinguishing feature of spin glasses is aging: The magnetic state depends on its history, which is driven by multiple time scales. Despite decades of theoretical developments, there is still no clear understanding about when spin glass behavior arises. It is commonly believed that disorder is a key ingredient, in addition to competing magnetic interactions, as exhibited by the textbook example of dilute magnetic alloys.


Despite more than 50 years of investigation, there is still no consensus on the magnetic ground state of the element neodymium (Nd). Below the Néel temperature, previous experiments reported the onset of static spin spirals with different periodicities, or so-called “multi-Q states,” as well as evidence of additional phase transitions. Although these observations illustrate the complexity in this material, it is not well understood how the multiplicity of these Q states depends on temperature and the exchange landscape of the material and which real-space magnetic interactions cause the multi-Q states.


We show that single-crystalline elemental Nd exhibits unconventional spin glass behavior well described by the recently proposed concept of self-induced spin glassiness. Traditional spin glasses, such as the hallmark metallic alloy Cu-Mn, are based on competing interactions and disorder. By contrast, self-induced spin glasses can be created solely by competing interactions without strong disorder, for example, in systems with long-range magnetic interactions. We studied Nd by growing ultraclean, epitaxial thick islands and films, both of which were representative of bulk Nd. Using spin-polarized scanning tunneling microscopy, magnetic images of the surface revealed strong, local, noncolinear magnetic order at the atomic scale with a multiplicity of Q states and no long-range order (left). We quantified the role of defects on the glassiness, showing that cleaner samples led to more pronounced glassy behavior exemplified by the increased mixing of distinct Q states. The spatially dependent Q states were defined by a spectral distribution of degenerate magnetic wave vectors (right), which varied spatially and with time. Harnessing ab initio and atomic spin dynamics calculations, we quantified the magnetic interactions, which illustrated strongly competing, distance-dependent interactions intricately linked to the crystal structure of Nd. Moreover, the resultant energy landscape illustrates many favorable Q states, showing that glassiness in Nd results from the conditions required for self-induced spin glasses. When probing the response to applied magnetic fields and temperature, we observed the existence of multiple time scales reminiscent of aging in traditional spin glass materials. The calculated autocorrelation function, a mean-field picture of the aging dynamics, also showed aging behavior reminiscent of traditional spin glasses (bottom). Experiments also showed that the aging dynamics were strongly dependent on the underlying value of Q, leading to behavior reminiscent of the concept of dynamic heterogeneity observed in structural glasses. In this way, the energy landscape can be described by a rugged, multiwell potential composed of degenerate Q states. Unlike traditional spin glasses, competing interactions in Nd are driven by its electronic and the structural properties, which lead to self-induced glassiness.


Our findings not only suggest that glassy behavior can be found in elements with crystalline order, but also unravel the decades-long debate about the magnetic behavior of Nd. The coexistence of short-range order exhibited by degenerate Q states and aging dynamics manifested by multiple time scales provides the first experimental confirmation of self-induced glassiness. The existence of strong local Q order and the Q-dependent dynamics may imply that multiple but select time scales exist, resulting from a rugged, multiwell landscape, when compared with traditional spin glasses. This provides a new platform with which to explore dynamic heterogeneity in a spin glass material. It remains to be understood what is particularly special about the crystal structure and electronic properties in Nd, and this will necessitate a deeper theoretical understanding of the role of electron correlation effects, as well as the interplay between spin and orbital degrees of freedom. The example here expands our views on magnetic states of matter, inviting further research into aging behavior in magnetic systems.

Spin-Q glass.

(Left) Real-space magnetization image with spin-polarized scanning tunneling microscopy at T = 1.3 K of thick films of Nd(0001). The surface shows multi-Q states but no long-range order. (Right) Sketch of spin-Q glass in both real and reciprocal spaces, with color illustrating the distribution of Q states in real space derived from flat pockets in Q-space. (Bottom) Calculated autocorrelation function for Nd with increasing waiting time (tw) illustrating aging behavior.


Spin glasses are a highly complex magnetic state of matter intricately linked to spin frustration and structural disorder. They exhibit no long-range order and exude aging phenomena, distinguishing them from quantum spin liquids. We report a previously unknown type of spin glass state, the spin-Q glass, observable in bulk-like crystalline metallic neodymium thick films. Using spin-polarized scanning tunneling microscopy combined with ab initio calculations and atomistic spin-dynamics simulations, we visualized the variations in atomic-scale noncolinear order and its response to magnetic field and temperature. We quantified the aging phenomena relating the glassiness to crystalline symmetry and the energy landscape. This result not only resolves the long-standing debate of the magnetism of neodymium, but also suggests that glassiness may arise in other magnetic solids lacking extrinsic disorder.

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