Correction: Tas et al. Magnetic Properties of All-d Metallic Heusler Compounds: A First-Principles Study. Magnetism 2024, 4, 400–411

There were some errors in the original publication [1]. Some texts need to be updated in Abstract and main text.

In Abstract, the sentence “while the Ru-based compounds consistently deviate from the predicted Slater–Pauling values” should be deleted.

In Abstract, the sentence “and to Ru-based compounds for heavier Z atoms” should be updated to “and deviate from the Slater–Pauling rule for heavier Z atoms. Ru-based compounds have two less valence electrons per unit cell compared to the corresponding Co- and Rh-based compounds and their total spin magnetic moments follow also a Slater–Pauling rule”.

In Section 3.1, paragraph 3, “4d and 5d bands” should be updated to “4d valence bands”.

In Section 3.2, paragraph 1, “When a 4d element” should be updated to “When a 3d element”.

In Section 3.2, paragraph 2, “as the 5d states” should be updated to “as the 4d states”.

In Section 3.2, paragraph 3, the word “only” should be deleted.

In Section 3.2, paragraph 4, the sentence “However, when Ru substitutes for Co, the total spin magnetic moment for isovalent compounds is constantly lower than the value predicted by the Slater–Pauling rule, as shown in the upper panel of Figure 4.” should be updated to “When Ru substitutes for Co (Ru has one valence electron less than Co and Rh), the total spin magnetic moment also closely matches the values predicted by the Slater–Pauling rule, as shown in the upper panel of Figure 4.”.

In Section 3.2, paragraph 4, the sentence “it mirrors the behavior of Ru compounds, with the exception of Rh₂MnCr.” should be updated to “it deviates from the Slater–Pauling rule.”.

In Section 3, Table 4 should be updated to the following version:

Table 4. These data are similar to Table 3 for all compounds under study assuming only the L2₁ lattice structure.

L21	mCo,Rh,Ru (μB)	mMn (μB)	mZ (μB)	mf.u. (μB)	Zt
Ru2MnSc	−0.20	3.10	−0.09	2.61	26
Ru2MnY	−0.15	3.60	−0.02	3.28
Ru2MnLu	−0.19	3.41	−0.01	3.03
Ru2MnTi	−0.01	3.33	−0.01	3.28	27
Ru2MnZr	0.01	3.63	−0.04	3.62
Ru2MnHf	−0.00	3.55	−0.06	3.49
Co2MnSc	0.82	3.12	−0.44	4.31	28
Co2MnY	0.85	3.46	−0.35	4.82
Co2MnLu	0.76	3.27	−0.30	4.49
Rh2MnSc	0.28	3.96	−0.22	4.31
Rh2MnY	0.25	4.17	−0.13	4.53
Rh2MnLu	0.39	4.07	−0.12	4.42
Ru2MnV	0.07	3.44	0.44	4.01
Ru2MnNb	0.18	3.70	0.01	4.07
Ru2MnTa	0.19	3.71	−0.02	4.06
Co2MnTi	1.05	3.23	−0.45	4.87	29
Co2MnZr	0.98	3.47	−0.37	5.07
Co2MnHf	0.98	3.43	−0.35	5.03
Rh2MnTi	0.33	4.07	0.05	4.78
Rh2MnZr	0.28	4.20	−0.03	4.72
Rh2MnHf	0.28	4.17	−0.03	4.71
Ru2MnCr	−0.08	3.32	1.89	5.05
Ru2MnMo	0.35	3.75	0.03	4.49
Ru2MnW	0.39	3.85	0.01	4.63
Co2MnV	1.15	3.07	0.25	5.62	30
Co2MnNb	1.22	3.50	−0.13	5.80
Co2MnTa	1.19	3.44	−0.13	5.70
Rh2MnV	0.33	3.90	0.14	4.70
Rh2MnNb	0.19	4.05	−0.05	4.39
Rh2MnTa	0.17	4.04	−0.04	4.35
Co2MnCr	1.23	2.95	1.32	6.73	31
Co2MnMo	1.40	3.38	0.20	6.37
Co2MnW	1.39	3.41	0.11	6.29
Rh2MnCr	0.26	3.79	2.85	7.17
Rh2MnMo	0.09	3.92	−0.50	3.59
Rh2MnW	0.10	3.90	−0.27	3.83

Table 4. These data are similar to Table 3 for all compounds under study assuming only the L2₁ lattice structure.

L21	mCo,Rh,Ru (μB)	mMn (μB)	mZ (μB)	mf.u. (μB)	Zt
Ru2MnSc	−0.20	3.10	−0.09	2.61	26
Ru2MnY	−0.15	3.60	−0.02	3.28
Ru2MnLu	−0.19	3.41	−0.01	3.03
Ru2MnTi	−0.01	3.33	−0.01	3.28	27
Ru2MnZr	0.01	3.63	−0.04	3.62
Ru2MnHf	−0.00	3.55	−0.06	3.49
Co2MnSc	0.82	3.12	−0.44	4.31	28
Co2MnY	0.85	3.46	−0.35	4.82
Co2MnLu	0.76	3.27	−0.30	4.49
Rh2MnSc	0.28	3.96	−0.22	4.31
Rh2MnY	0.25	4.17	−0.13	4.53
Rh2MnLu	0.39	4.07	−0.12	4.42
Ru2MnV	0.07	3.44	0.44	4.01
Ru2MnNb	0.18	3.70	0.01	4.07
Ru2MnTa	0.19	3.71	−0.02	4.06
Co2MnTi	1.05	3.23	−0.45	4.87	29
Co2MnZr	0.98	3.47	−0.37	5.07
Co2MnHf	0.98	3.43	−0.35	5.03
Rh2MnTi	0.33	4.07	0.05	4.78
Rh2MnZr	0.28	4.20	−0.03	4.72
Rh2MnHf	0.28	4.17	−0.03	4.71
Ru2MnCr	−0.08	3.32	1.89	5.05
Ru2MnMo	0.35	3.75	0.03	4.49
Ru2MnW	0.39	3.85	0.01	4.63
Co2MnV	1.15	3.07	0.25	5.62	30
Co2MnNb	1.22	3.50	−0.13	5.80
Co2MnTa	1.19	3.44	−0.13	5.70
Rh2MnV	0.33	3.90	0.14	4.70
Rh2MnNb	0.19	4.05	−0.05	4.39
Rh2MnTa	0.17	4.04	−0.04	4.35
Co2MnCr	1.23	2.95	1.32	6.73	31
Co2MnMo	1.40	3.38	0.20	6.37
Co2MnW	1.39	3.41	0.11	6.29
Rh2MnCr	0.26	3.79	2.85	7.17
Rh2MnMo	0.09	3.92	−0.50	3.59
Rh2MnW	0.10	3.90	−0.27	3.83

In Section 3, Figure 4 should be updated to the following version:

The caption does not change.

In Section 4, paragraph 1, the sentence “In the Ru-based compounds, the 5d valence states result in total spin magnetic moments that are about 2 μ_B lower than those of the corresponding Co-based compounds.” should be updated to “In the Ru-based compounds, the total spin magnetic moments are about 2 μ_B lower than those of the corresponding Co-based compounds in accordance with the smaller number of valence electrons of the Ru atoms.”.

In Section 4, paragraph 1, the sentence “for lighter Z elements and to Ru-based compounds for heavier Z elements.” should be updated to “compounds only for the lighter Z elements.”.

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.