Spin Fluctuation Theory of Itinerant Electron Magnetism

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    Spin Fluctuations in Itinerant Electron Magnetism

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    Payment details. In addition to the experimental evidence for the itinerant moment antiferromagnetic order in TiAu, density functional theory DFT calculations confirm the spin density wave SDW small moment ordering. It comes as no surprise then, that no reports of physical properties of TiAu exist. Here we report the magnetic and electronic properties of phase-pure orthorhombic TiAu, and that it is an itinerant electron antiferromagnet. By analogy with local moment AFMs, the TiAu zero-field-cooled and field-cooled data are indistinguishable.

    Puzzling at first, the origin of this behaviour was reconciled in the case of IFMs, when spin fluctuation effects were considered by Moriya 3 , 4. The self-consistent renormalization theory unified the local and itinerant pictures of ferromagnetism, and postulated a new origin for the Curie—Weiss-like susceptibility in the latter, as the interactions of the spatially extended modes of spin fluctuations 10 , Therefore, this suggests that Pmma TiAu is the first IAFM metal with no magnetic constituents, with the magnetic ground state strongly affected by spin fluctuations.

    The arrows identify the crystallographic directions, marked by a , b and c axes. By contrast with most known weak itinerant ferro- or antiferro- magnets, the TiAu electrical resistivity Fig. Although often the gap opening associated with the SDW ordering results in a resistivity increase, a similar drop was observed in BaFe 2 As 2 single crystals In the absence of local moment ordering, the decrease in the resistivity at T N results from the balance of the loss of scattering due to Fermi surface nesting see below and the gap opening due to the SDW AFM state. At the same temperature in TiAu, a small peak becomes visible in the specific heat data C p Fig.

    Distinguishing between local and itinerant moment magnetism is inherently difficult, especially in the nearly unexplored realm of IAFMs. It is therefore surprising that in TiAu, the evidence points toward its itinerant magnetic moment character. Another argument is the small magnetic entropy S m grey area, Fig. Even though the S m calculated after assuming a polynomial non-magnetic C p around the transition dashed line, Fig.

    The entropy S m solid blue line, right axis is calculated by subtracting a polynomial non-magnetic component dashed blue line from the measured specific heat data blue circles. It has been shown by Sandeman et al. The argument requires that the paramagnetic Fermi level lie in between the two peaks of the DOS, and this is indeed revealed by the band structure calculations for TiAu, as is shown below. It results that, as the Fermi sea is polarized by the applied magnetic field H , the majority and minority spin Fermi levels feel the effect of the two DOS peaks at different values of induced magnetization.

    The DOS peak that is closest to the Fermi level will lead to a sharp increase decrease in the population of the majority minority spin band, resulting in a metamagnetic transition. Muon spin relaxation data shown in Fig. The time spectra in ZF are fitted with the relaxation function G t , expected for a Lorentzian distribution of local fields 16 :. Uncertainties are statistical in origin and represent one standard deviation.

    Detailed reasoning for the choice of this fitting function is given in the Supplementary Note 2. The temperature dependence of the relaxation rate a and the magnetic volume fraction f are shown in Fig. An important feature found in both ZF and LF time spectra is the absence of dynamic relaxation, expected for critical slowing down of spin fluctuations around T N.

    See ref. Together with the ZF relaxation function equation 1 which solely involves static effects, the present data indicate complete absence of dynamic critical behaviour. Although occurring in a limited temperature region, the aforementioned phase separation indicates that the transition is likely first-order, without dynamic critical behaviour.

    Such tendencies were also seen in the itinerant ferromagnet Sr,Ca RuO 3 close to the disappearance of static magnetic order around a Ca concentration of 0.

    Developments of the theory of spin fluctuations and spin fluctuation-induced superconductivity

    The first-order transition may be a generic feature of weak magnetic order in itinerant—electron systems Although this indicates a very small ordered moment in TiAu, it is not possible to estimate the moment size since the hyperfine coupling constant could depend strongly on the assumption of the location of muon sites.

    However, the same line shape was also observed in Sr 1. The magnitude of the ordered moment is estimated to be 0. The neutron data eliminate the possibility that the observed magnetism is due to dilute magnetic impurities. These arguments suggest that the magnetism of the present system is an intrinsic feature of TiAu. Even though the experimental evidence demonstrates long-range antiferromagnetic, small moment ordering in orthorhombic TiAu, a comparison between the experimental data with theoretical results from band structure calculations are of interest.

    These were performed using a full-potential DFT 21 while taking spin—orbit coupling into account see the Methods section for more details. However the uncertainty in determining the exact wavevector from DFT does not affect the conclusions from the overwhelming experimental evidence for the itinerant AFM order in TiAu.

    This DFT overestimate compared to the experimental moment estimate of 0. In the case of TiAu this may be remedied by future dynamical mean-field theory calculations, beyond the scope of this mainly experimental report of IAFM TiAu. It is instructive to analyse the origin of magnetism in TiAu using the input from the band structure calculations. In this case, the Q dependence of the interaction strength I Q is unimportant. Indeed, the calculated Fermi surface of the non-magnetic TiAu Fig. The colour scale indicates degree of electron polarization, ranging from spin-up red to spin-down purple.

    The Fermi surface is coloured for ease of viewing. The arrows identify the wavevectors in the reciprocal space, marked by k a , k b and k c. This goes to show that, while magnetism in TiAu is close to the itinerant limit, its mechanism is more complicated than in Cr In the latter, the small magnetization decrease at T N had been attributed to the small spin susceptibility and not the larger orbital component being affected by the gap associated with the SDW transition.

    Conversely, the larger magnetization change in TiAu might indicate a sizable effect on the orbital magnetization, as the SDW transition is now associated with more two dimensional nesting than that in Cr. Experimental evidence for the itinerant character of the magnetic state in TiAu includes small magnetic moment in the ordered state compared to the paramagnetic moment, as well as small magnetic entropy at T N.

    It is readily apparent that strong spin fluctuations are at play in this magnetic system. The exact role of the spin fluctuations, their strength, as well as the details of the magnetic structure in the ordered state, remain to be fully elucidated with further experiments. Additionally, doping experiments are underway, indicating that the magnetic order in doped TiAu is suppressed to 0 in a quantum critical regime with strong spin fluctuations. More detailed calculations using dynamical mean-field theory, left to a future in-depth theoretical study on the IAFM.

    Ultimately, the search for IAFMs appears to be a promising avenue for furthering our understanding of the complex magnetism, and providing the unifying picture for local and itinerant moment magnetism. Polycrystalline samples of TiAu were prepared by arcmelting, with mass losses no more than 0. X-ray photoemission spectroscopy was performed on the polished surface of the TiAu sample, using an XPS Phi Quantera spectrometer with a monochromatic Al X-ray source and Ar ion sputtering gun, used to cleanse the surface of contaminants. The alignment was checked by comparing the binding energy of the C1 s peak to the published one More details can be found in the Supplementary Note 1.

    Heat treatment annealing at several different temperatures resulted in no measurable changes in either the structural or physical properties. The d. Specific heat using an adiabatic relaxation method, and four-probe d. The cut TiAu samples of thickness around 0. For the neutron diffraction measurements the sample was sealed with helium exchange gas and mounted in a closed cycle refrigerator with a base temperature of 2. Supplementary Fig. The solid curve is a fit to Gaussian instrumental peaks solid curve.

    To characterize the sample and search for possible structural changes associated with the magnetic phase transition the BT-1 high resolution powder diffractometer was used. Band structure calculations were performed using the full-potential linearized augmented plane-wave method implemented in the WIEN2K package The PBE-GGA was used as the exchange potential, the default generalized gradient approximation for the exchange-correlation potential in WIEN2K 31 and spin—orbit coupling was included in a second-variational fashion The lattice parameters and atomic positions were determined from both neutron and X-ray diffraction and are reported in the Supplementary Table 1.

    In order to make the Fermi surface plot shown in Fig. How to cite this article: Svanidze, E. An itinerant antiferromagnetic metal without magnetic constituents. Heisenberg, W. Zur theorie des ferromagnetismus. Physik 49 , — Stoner, E. Collective electron ferromagnetism. A , — Moriya, T. Effect of spin fluctuations on itinerant electron ferromagnetism. Effect of spin fluctuations on itinerant electron ferromagnetism II.

    Itinerant electron magnetism. Matthias, B. Ferromagnetism in solid solutions of Scandium and Indium. Ferromagnetism of a Zirconium-Zinc compound. Donkersloot, H. Martensic transformations in gold-titanium, palladium-titanium and platinum-titanium alloys near the equiatomic composition. Less-Common Met. Schubert, K.

    Bibliographic Information

    Einige strukturdaten metallischer phasen VII. Naturwissenschaften 49 , 57 Hasegawa, H. Effect of spin fluctuations on itinerant electron antiferromagnetism. Wang, X. Anisotropy in the electrical resistivity and susceptibility of superconducting BaFe2As2 single crystals. Fisher, M. Relation between the specific heat and susceptibility of an antiferromagnet. Resistive anomalies at magnetic critical points.

    Sandeman, K.