Table 1.

Calculated theoretical quantum numbers of RE³⁺ ions in RECrO₃ single crystals based on the Hund’s rule: number of 4f (4d for Y³⁺ ion) electrons, spin S, orbital L, total angular momentum J, Landé factors g_J, and the ground-state term ${}^{2S+1}L_J$

RECrO3 single crystals grown by the FZ method
RE3+ =	Y3+	Eu3+	Gd3+	Tb3+	Dy3+
4dn ion	0
4fn ions		6	7	8	9
S	0	3	7/2	3	5/2
L	0	3	0	3	5
J	0	0	7/2	6	15/2
$g_J$	–	–	2	1.5	1.33
${}^{2S+1}L_J$	${}^{1}S_0$	${}^{7}F_0$	${}^{8}S_{7/2}$	${}^{7}F_6$	${}^{6}H_{15/2}$
${\mu }_{\text{eff}-\text{meas}}\left({\mu }_{\text{B}}\right)$	3.95	6.44	8.40	10.51	11.35
${\mu }_{\text{eff}-\text{theo}}^{\text{RE}}\left({\mu }_{\text{B}}\right)$	0	0	7.937	9.721	10.646
${\mu }_{\text{eff}-\text{theo}}^{\text{total}}\left({\mu }_{\text{B}}\right)$	3.873	3.873	8.832	10.464	11.328
$M_{\text{meas}}\left({\mu }_{\text{B}}\right)$	∼0.147	0.245 (1)	6.43	6.248 (1)	4.834 (1)
$M_{\text{sat}-\text{theo}}^{\text{RE}}\left({\mu }_{\text{B}}\right)$	0	0	7	9	10
$M_{\text{sat}-\text{theo}}^{\text{total}}\left({\mu }_{\text{B}}\right)$	3	3	7.616	9.487	10.440
TN (K)	141.5 (1)	181.6 (1)	169.3 (1)	157.9 (1)	148.5 (1)
θCW (K)	−433.2 (6)	−450.4 (15)	−20.33 (4)	−53.3 (1)	−56.5 (1)

RE3+ =	Ho3+	Er3+	Tm3+	Yb3+	Lu3+
4fn ion	10	11	12	13	14
S	2	3/2	1	1/2	0
L	6	6	5	3	0
J	8	15/2	6	7/2	0
$g_J$	1.25	1.2	1.167	1.143	–
${}^{2S+1}L_J$	${}^{5}I_8$	${}^{4}I_{15/2}$	${}^{3}H_6$	${}^{2}F_{7/2}$	${}^{1}S_0$
${\mu }_{\text{eff}-\text{meas}}\left({\mu }_{\text{B}}\right)$	11.03	10.20	8.35	5.63	4.98
${\mu }_{\text{eff}-\text{theo}}^{\text{RE}}\left({\mu }_{\text{B}}\right)$	10.607	9.581	7.561	4.536	0
${\mu }_{\text{eff}-\text{theo}}^{\text{total}}\left({\mu }_{\text{B}}\right)$	11.292	10.334	8.495	5.964	3.873
$M_{\text{meas}}\left({\mu }_{\text{B}}\right)$	3.999 (1)	6.385 (1)	2.868 (1)	0.883 (1)	1.197 (1)
$M_{\text{sat}-\text{theo}}^{\text{RE}}\left({\mu }_{\text{B}}\right)$	10	9	7	4	0
$M_{\text{sat}-\text{theo}}^{\text{total}}\left({\mu }_{\text{B}}\right)$	10.440	9.487	7.616	5	3
TN (K)	143.2 (1)	135.4 (1)	125.9 (1)	117.9 (1)	122.3 (1)
θCW (K)	19.6 (1)	−30.0 (1)	−90.6 (4)	−17.4 (1)	−110.4 (2)

We listed values of the measured (meas) (μ_eff-meas) and theoretical (theo) effective PM moments $\left({\mu }_{\text{eff}-\text{theo}}^{\text{Cr}}=g_J{\mu }_{\text{B}}\sqrt{S\left(S+1\right)}=3.873{\mu }_{\text{B}}\left({\text{Cr}}^{3+}:3d^3,J=S=\frac{3}{2},g_J=2\right),{\mu }_{\text{eff}-\text{theo}}^{\text{RE}}=g_J{\mu }_B\sqrt{J\left(J+1\right)},\text{and}{\mu }_{\text{eff}-\text{theo}}^{\text{total}}=\sqrt{{\left({\mu }_{\text{eff}-\text{theo}}^{\text{RE}}\right)}^2+{\left({\mu }_{\text{eff}-\text{theo}}^{\text{Cr}}\right)}^2}\right)$, the measured moment (M_meas per formula at 1.8 K and 14 T), and the theoretical saturation moments $\left(M_{\text{sat}-\text{theo}}^{\text{Cr}}=g_J{\mu }_{\text{B}}S=3{\mu }_B,M_{\text{sat}-\text{theo}}^{\text{RE}}=g_J{\mu }_{\text{B}}J,\text{and}{M}_{\text{sat}-\text{theo}}^{\text{total}}=\sqrt{{\left(M_{\text{sat}-\text{theo}}^{\text{RE}}\right)}^2+{\left(M_{\text{sat}-\text{theo}}^{\text{Cr}}\right)}^2}\right)$. The values of T_N, μ_eff-meas, and CW temperature (θ_CW) were extracted from the M-T measurements by the CW-law fitting. The values of M_meas were extracted from the M-B data. The numbers in parenthesis are the estimated standard deviations of the (next) last significant digit. Some parameters of YCrO₃ (Zhu et al., 2020a) and GdCrO₃ (Zhu et al., 2020c) were referred to in our previous studies.