Novel Itinerant Antiferromagnet TiAu

Itinerant and local moment magnetism have substantively different origins, and require distinct theoretical treatment. A unified theory of magnetism has long been sought after, and remains elusive, mainly due to the limited number of known itinerant magnetic systems. In the case of the two such examples discovered several decades ago, the itinerant ferromagnets ZrZn_2 and Sc_3In, the understanding of their magnetic ground states draws on the existence of 3d electrons subject to strong spin fluctuations. Similarly, in Cr, an elemental itinerant antiferromagnet (IAFM) with a spin density wave (SDW) ground state, its 3d character has been deemed crucial to it being magnetic. Here we report the discovery of the first IAFM compound with no magnetic constituents, TiAu. Antiferromagnetic order occurs below a Neel temperature T_N ~ 36 K, about an order of magnitude smaller than in Cr, rendering the spin fluctuations in TiAu more important at low temperatures. This new IAFM challenges the currently limited understanding of weak itinerant antiferromagnetism, while providing long sought-after insights into the effects of spin fluctuations in itinerant electron systems.

. 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 10 . 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. 2b), such that T N in this AFM metal can be determined, as shown by Fisher 11,12 , from peaks in C p (most visible in C p /T), d(M T )/dT and dρ/dT (Fig. 2c). Distinguishing between local and itinerant moment magnetism is inherently difficult, especially in the nearly unexplored realm of IAFMs. It is therefore striking that in TiAu, abundant evidence points towards its itinerant magnetic moment character. The fact that the peak in C p is not as strong as the Fisher prediction 11 is one such argument favoring the itinerant moment scenario in TiAu. Another argument is the small magnetic entropy S m (grey area, Fig. 2c) associated with the transition (solid blue line, Fig. 2c). Even though the S m calculated after assuming a polynomial non-magnetic C p around the transition (dashed line, Fig. 2c) is an underestimate, it amounts to only 0.2 Despite the remarkably large paramagnetic moment µ P M 0.8 µ B , derived from the Curie-Weiss-like fit of the inverse susceptibility (Fig. 1a, right axis), the field-dependent magnetization M (H) does not saturate up to 7 T, and the maximum measured magnetization is only 0.01 µ B (Fig. 3). A closer look at the low temperature M (H) reveals a weak metamagnetic transition starting around µ 0 H = 3.6 T for T = 2 K (circles, Fig. 3). This is most apparent in the derivative dM/dH (open symbols) rather than in the as-measured isotherms (full symbols), with the latter nearly indistinguishable well below (T = 2 K) and above (T = 60 K) the magnetic ordering temperature. It has been shown by Sandeman et. al. 13 that, within the Stoner theory, the presence of a sharp double peak structure in the electronic DOS sufficiently close to the Fermi level results in a metamagnetic transition.
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 calculation for TiAu, shown in the inset of Fig. 5a 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 (µSR) data shown in Fig. 4 unambiguously confirm the static magnetic order developing in the full volume fraction, with the transition temperature corresponding to the anomaly in the magnetic susceptibility, resistivity and specific heat shown in Fig. 2c. For temperatures above 35 K, the total asymmetry undergoes a negligibly small relaxation, signaling lack of static magnetic order (Fig. 4a). In the time spectra observed in zero field (ZF), a fast decaying front end begins to develop around 35 K, and becomes more pronounced for lower temperatures. This early time decay results from the build up of static internal field, since a small longitudinal field (LF), µ 0 H = 0.01 T, eliminates this relaxation via the decoupling effect (Fig. 4b). The time spectra in ZF are fitted with the relaxation function, expected for a Lorentzian distribution of local fields 9 : where f represents the volume fraction with static magnetic order. As shown in the Supplementary Material, a slightly better fit can be obtained by a phenomenological function composed of the sum of two exponential terms; but current analysis is more applicable since it can be directly compared with µSR results in other systems, as shown in Table SM1 in Supplementary Material. The temperature dependence of the relaxation rate a and the magnetic volume fraction f are shown in Fig. 4c. A reasonably sharp transition occurs below T N = 36 K to a state with 100% ordered volume, preceeded on cooling by a small temperature region around T N characterized by the finite volume fraction f , which suggests co-existence of ordered and paramagnetic volumes in real space via phase separation. axis. Together with the present µSR data, that show a magnetic phase fraction of 100%, these results eliminate the possibility that the observed magnetism is due to dilute magnetic impurities or a minority phase. These arguments demonstrate that the magnetism of the present system is due to a generic feature of TiAu.
Of particular interest is the comparison between the experimental evidence for the antiferromagnetic order in TiAu with the theoretical results from band structure calcula-tions. A number of possible magnetic configurations were considered: ferromagnetic (FM), AFM SDW with modulation vectors Q1 = (0, 2π/3b, 0) (AFM1) and Q2 = (0, π/b, 0) (AFM2). Their energies relative to the non-magnetic state were estimated to be E FM = −25 meV/Ti, E AFM1 = −42 meV/Ti and E AFM2 = −30 meV/Ti, respectively. These energy values suggest that AFM1 would be the ground state configuration, while the neutron diffraction data show a wavevector Q exp = (0, π/b, 0) (Fig. 4d) In the case of TiAu this may be remedied by future DMFT calculations.
The Fermi surface of the non-magnetic TiAu (Fig. 5c)  No saturation is achieved for magnetic fields up to 7 T. A metamagnetic transition is observed around 4 T in the T = 2 K isotherm, but not in the one above the magnetic order.  Au, confirming the purity of the 1:1 P mma phase, consistent with neutron (below) and xray (not shown) diffraction data. XPS is also employed in determining the valence of elements in many compounds [2][3][4][5] . Fig. SM6b

II. STRUCTURAL ANALYSIS
Neutron diffraction data were collected on the BT-1 powder diffractometer and BT-7 thermal triple-axis spectrometer at the NIST Center for Neutron Research. While BT-1 data were used for the crystallographic analysis, a magnetic peak corresponding to the (0, 1/2, 0) was observed in the BT-7 data (see main text). The BT-1 diffraction pattern recorded at T = 5 K (black) is shown in Fig. SM7 with all peaks identified as the orthorhombic P mma TiAu phase (vertical marks). The inset shows the pattern measured on BT-7 (squares) at T = 2.6 K along with Gaussian peak fits (line). The results of structural refinements of the data below (T = 5 K) and above (T = 60 K) T N as well as those obtained from room temperature x-ray diffraction are summarized in Table SM

III. MUON SPIN RELAXATION
The initial fit of the muon spin relaxation data included two simple exponential relaxing components, yielding the black curve shown in Fig. SM8. The asymmetry function had the following form: However, considering the polycrystalline nature of our sample, the isotropy of overall local magnetic field dictates 1/3 of all muons to have spin parallel to the local field, hence showing no relaxation arising from the random static magnetic field in the sample. In a system with randomly oriented, dense, and static magnetic moments, a Gaussian Kubo- while in dilute spin systems a corresponding Lorentzian relaxation function is due to the Lorentzian internal field distribution 9 : A Lorentzian KT (t) = A 1 3 For the polycrystalline TiAu sample a Lorentzian function is more appropriate and yields a better fit, shown in Fig. SM8 (blue line).

IV. BAND STRUCTURE CALCULATIONS
Band structure calculations were performed using full-potential linearized augmented plane wave (FP-LAPW) method implemented in the WIEN2K package 14 . PBE-GGA was used as the exchange potential, as the default suggestion by WIEN2K 15 . A 10·10·10 k-point grid was used, and shift away from high symmetry directions was allowed. The convergence