Erratum: Twofold and fourfold symmetric anisotropic magnetoresistance effect in a model with crystal field (J. Phys. Soc. Jpn. (2015) 84 (094710) DOI: 10.7566/JPSJ.84.094710)

We found errors in the higher-order (HO) terms with ð=Þ² in ^ð ₀ ² _; ^Þ of Eq. (44), ^ð ₂ ² _; ^Þ of Eq. (46), ^ð ₄ ² _; ^Þ of Eq. (47), C₄ of Eq. (62), and c⁰₄ of Eq. (63) in the original paper.¹⁾ The HO terms did not have a crucial role in the paper. In particular, the HO term in C₄ (i.e., c⁰₄) was finally ignored because of its small value. Therefore, this correction does not affect the main results of the paper. (Equation Presented) For C₄ of Eq. (62) consisting of ^ð ₄ ² _; ^Þ , “þc⁰₄” in the right-hand side of Eq. (62) must be deleted. In addition, c⁰₄ of Eq. (63) should be deleted. On the basis of the correction of C₄, we make the following corrections: (I) Sentences on lines 9–14 in Sect. 3.1(ii) starting from “Also, c⁰₄ of Eq. (63) …” should be deleted. (II) Another paragraph in Sect. 3.1 starting from “With regard to C₄,…” must be deleted. Note here that Eq. (71) is regarded as Eq. (62) excluding c⁰₄. (III) The dot-dashed curves in Fig. 6 should be deleted. (IV) A paragraph in Sect. 3.1 starting from “We next determine …” must be replaced by “We next determine the effective value of the undefined parameter = by comparing C₄ obtained by PT with that obtained by the EDM. Note that the value of = is necessary for calculations of C₂ and C₄ by the EDM [see Eqs. (58) and (59)], although = is not included in C₂ and C₄ obtained by the PT [see Eqs. (61) and (62)]. We here put r_"1 = r_"ð1 þ Þ; ð4Þ r_"2 = r_"; ð5Þ where η represents the difference between r_"1=r_" and r_"2=r_". Figure 4 shows the jj= dependence of C₄ of Eqs. (62) and (59) for the systems with H = 1 eV, Δ = 0:1 eV, λ = 0:01 eV,^37Þ _"= ¼ 1, r ¼ 0, r ¼ 0:01,^43Þ r_"=r ¼ 1, and η ¼ 0, 1, and 2. Here, r ¼ 0 and r ¼ 0:01 are set on the basis of those for Fe₄N.^19Þ The range of jj= is roughly assumed to be 1=2 ≤ |λ|/δγ ≤ 3/2 considering the aforementioned parameters and δγ/Δ ≪ 1. We find that C₄ obtained by the EDM is nearly constant and is close to that obtained by the PT [i.e., Eq. (71)] at each η. Therefore, jj= is considered to be valid for 1/2 ≤ |λ|/δγ ≤ 3/2. We choose |λ|/δγ = 1/2 in this study.”