Revealing the Correlation of OER with Magnetism: A New Descriptor of Curie/Neel Temperature for Magnetic Electrocatalysts

Abstract Developing accurate descriptors for oxygen evolution reaction (OER) is of great significance yet challenging, which roots in and also boosts the understanding of its intrinsic mechanisms. Despite various descriptors are reported, it still has limitations in the facile prediction, given that complicated analytical techniques as well as time‐consuming modeling and calculations are indispensable. In the present work, strong correlation of magnetic property with OER performance is revealed by in‐depth investigations on the crystal and electronic structures. A facile descriptor of Curie/Neel temperature (T C/N) is developed for La2− xSrxCo2O6− δ perovskite oxides, based on the inference that both magnetism and OER are rooted in the electron exchange interaction. Specifically, both the T C/N and OER activity are proportional to the degree of p‐d orbital hybridization, which increases with enlarged bond angle of Co─O─Co and/or increased oxidation of Co. This finding reveals that T C/N from magnetic characterizations is an effective descriptor in designing novel OER electrocatalysts, and interdisciplinary researches are advantageous for revealing the controversial mechanisms of OER process.


Supporting Information
Revealing the correlation of OER with magnetism: A new descriptor of Curie/Neel temperature for magnetic electrocatalysts Xiaoning Li, Ying Bai*, and Zhenxiang Cheng* Figure S1. Fitting of Co L-edge XANES spectra for all the samples with different Co 2+ /Co 3+ /Co 4+ ratios.

Magnetic properties and useful parameters for OER
Figure S3a-f are the temperature dependent magnetization (M-T) curves measured in the zero-field cooling (ZFC) and field cooling (FC) modes. The main difference between the two modes lies in whether a magnetic field is applied during the cooling process, wherein a magnetic field of 500 Oe is applied during cooling before data is collected in the warming process for the latter mode. The ZFC and FC curves of all samples are coinciding with each other before diverging at certain low temperatures. This originates in the fact that when longrange (ferro/ferri/antiferro-) magnetic orderings exist, the magnetic moments will be aligned along the applied magnetic field, which will be frozen when cooled down below the diverging point. In this respect, larger magnetization is recorded in the FC curve below the diverging point. However, this kind of discrepancy is vanished given the thermal fluctuation is high enough to disorder any magnetic moments. The Curie/Neel temperature (T C/N ) is a temperature point when all long-range ordered magnetic moments are thermally disordered, above which materials will be paramagnetic [1,2] . Hence, the first lowest point in the differentiation of dM/dT based on FC curves can be regarded as T C/N , as marked in Figure S3 with arrows.
There are two transition temperatures in the M-T curve of LSCO07 sample, which may be  The plots of reciprocal magnetic susceptibility against temperature (1/-T) obtained from FC curves are displayed in Figure S4a. Curie-Weiss law can be applied to fit the linear paramagnetic region above the T C/N of FC curves with the Equation S1 [3] .  (S1) The Curie constant C equals to the reciprocal of the slope of resultant fitting lines, while the intersection on the T-axis is regarded as paramagnetic Curie-Weiss temperature or Weiss temperature (T  ) [4] . Different from the Curie/Neel temperature (T C/N ), the Weiss temperature (T  ) is essentially the arithmetic average of the interspin coupling constants (exchange integrals) of the Hamiltonian [5] . When ferromagnetic exchange coupling overwhelms antiferromagnetic one, T  will be positive. On the contrary, a negative T  is obtained instead.
For the paramagnetic materials without a T C , T  should be near zero when fitting the whole region with Curie-Weiss law in theory. Furthermore, the effective magnetic moment (U eff ) and possible spin configuration can be roughly estimated based on the Curie constant C from Curie-Weiss fitting of paramagnetic region, according to the Equation S2, 3 [3] √ (2) where k and N are the Boltzmann constant and the number of magnetic ions in the unit cell respectively, g is the Lande factor, J is the total quantum number and μ B is the Bohr magneton.
The Lande factor g is 2.0023 for a free electron, and for the condense matters it can be estimated by electron spin resonance (ESR) measurements. With g known, the spin quantum number S can be calculated, as it is equaled to J when the total quantum number L=0 in the 3d transition metal oxides. Then, the specific spin configuration and e g electron number can be estimated with the consideration that the number of unpaired electron is 2S [3] . Here, the e g electron number is not the main subject in present work, so we just plot the resultant T  , U eff and T C/N obtained from magnetic measurements ( Figure S4b). Remarkably, T C/N is increasing at first and decreasing afterwards with increasing of Sr content, achieving the maximum in the LSCO10. However, when it comes to T  and U eff , a negative T  is observed at LSCO15 and LSCO17 together with a jump of U eff . The distinctiveness of T  and U eff from T C/N is reckonable, as T C/N is proportional to the orbital hybridization while T  is indicative for antiferro-/ferro-magnetic ground states and U eff is indicative for unpaired electron numbers.