THE EUROPEAN SCHOOL ON MAGNETISM Concept tests Leon Abelmann leon.manucodiata.org
Peer instruction for active learning https://youtu.be/Z9orbxoRofI
A THE EUROPEAN SCHOOL ON MAGNETISM The H field Spontaneous magnetisation Direct exchange Leon Abelmann � 3
To increase the field far away from a permanent magnet I can increase: A (purple) : magnetisation at constant volume B (blue) : volume at constant moment C (green) : moment at constant magnetisation D (orange) : magnetisation at constant moment Multiple answers possible � 4
R B B H H H H H H H H I I A B C D (purple) (blue) (green) (orange) � 5
A Probability of finding the electron in the nucleus A (purple) : 0 0 B (blue) : 0 Minimum C (green) : Maximum 0 D (orange) : Maximum Minimum � 6
E Uniformly magnetised bar magnet B = μ 0 ( H + M ) M B H M B H M B H A B C (purple) (blue) (green) � 7
B orbital moment B - A (red) (pointing at you) + B (blue) (pointing from you) 0 C (green) H-atom � 8
D x M M Hole in a permanent magnet with magnetisation M : H in x is parallel to M A (purple) B (blue) : H in x is anti-parallel to M C (green) : H = 0 � 9
C - - - + + + + H + H H 2 A (purple) : m H + ≥ m H B (blue) : m H + ≥ m H 2 C (green) : m H ≥ m H 2 � 10
F Hunds rule: Mn: [Ar] 3d 5 4s 2 Fe: [Ar] 3d 6 4s 2 Co: [Ar] 3d 7 4s 2 Ionized Fe: A (purple) Fe 2+ : [Ar] 3d 4 4s 2 B (blue) Fe 2+ : [Ar] 3d 5 4s 1 C (green) Fe 2+ : [Ar] 3d 6 4s 0 D (orange) None of the above � 11
G [He] 2s 2 2p 4 [Ar] 3d 5 4s 2 O Mn O Mn O 2p: [He] 2s 2 2p 6 [Ar] 3d 5 O 2- Mn 2+ O 2- Mn 2+ O 2- 1 2 2p: 1 2 A (red) 3d: 3d: B (blue) 3d: C (green) � 12
THE EUROPEAN SCHOOL ON MAGNETISM Anti-ferro and ferri-magnetism Anisotropy - phenomenological Anisotropy - pair model Leon Abelmann � 13
H B in x: x B=0 A B C cubic A (purple) : down B (blue) : up C (green) : zero D (orange) : None of the above � 14
I p a B A (purple) : E p > E a B (blue) : E p < E a C (green) : E p = E a � 15
J Mn: [Ar] 3d 5 4s 2 is not a ferromagnet because: A (purple) : Mn has a half filled d-shell B (blue) : Mn oxidises too fast C (green) : Mn is an anti-ferromagnet D (orange) : Another reason � 16
K 1 0 0 0 T T T A (purple) : Para-, Ferro-, Anti-ferro B (blue) : Anti-ferro-, Para-, Ferromagnetic C (green) : Para-, Anti-ferro, Anti-ferro D (orange) : Ferro-, Anti-ferro, Para � 17
L 100%Fe 100%Co Fe-Cr Co-Cr 100%Ni 100%Cr Image from Rajat Roy E ff ect Cr on Fe di ff erent from Co and Ni because: A (purple) : Cr chemically reacts with Ni, Co B (blue) : Cr couples anti-ferromagnetically C (green) : All of the above D (orange) : None of the above � 18
Γ M 𝛥 =- dE/d 𝜄 θ 0 45 90 135 180 The easy axis is at 𝜄 = A (purple) : 0 B (blue) : 45 C (green) : 90 D (orange) : 135 � 19
N θ θ b b a a E=K u1 cos 2 ( 𝜄 ) + K 2 cos 2 (2 𝜄 ) First b/a=1, if I increase b/a, then A (purple) : K u1 increases B (blue) : K u1 decreases C (green) : K u1 = 0 � 20
O K 1 K tot K tot K tot K tot =0 K 2 A B C D K 1, K 2 uni-axial A (purple) B (blue) C (green) D (orange) � 21
P M Uni-axial: A E=K u1 cos 2 ( 𝜄 ) K u1 B C Cubic: E=K 1 ( 𝛽 12 𝛽 22 + 𝛽 12 𝛽 32 + 𝛽 22 𝛽 32 ) 0 1 T/T c If T-dependence K u1 is as indicated, than K1 A (purple) : K 1 less T-dependent B (blue) : K 1 same as K u1 C (green) : K 1 more T-dependent � 22
Q θ θ b b a a E=K u1 cos 2 ( 𝜄 ) + K 2 cos 2 (2 𝜄 ) If I increase b/a, then A (purple) : K 2 increases but K 2 <0 B (blue) : K 2 increases (K 2 >0 is ok) C (green) : K 2 decreases but K 2 >0 D (orange) : K 2 decreases (K 2 <0 is ok) � 23
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