Time reversal symmetry and

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Presentation transcript:

Time reversal symmetry and PHY 745 Group Theory 11-11:50 AM MWF Olin 102 Plan for Lecture 29: Time reversal symmetry and Magnetic groups Chap. 16 in DDJ Effects of magnetic configurations on point groups and space groups Examples of magnetic point groups Note: These slides contain materials from an electronic version of the Dresselhaus textbook. 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Topic for presentation 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Vibrational mode analysis Presentation ideas Digest the content of a literature paper which involves aspects of group theory and present the theory and results. Find a particular molecule or crystal and analyze its group theoretic aspects Band structure analysis; find at least 3 special k-points or directions, analyzing their groups and compatibility relationships Point group analysis, finding selection rules for various transitions between representations Vibrational mode analysis 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Group theory describing magnetic configurations 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

When is magnetic ordering important? What does time reversal symmetry have to do with magnetic configurations? Time reversal symmetry does not effect charge density Time reversal symmetry does effect internal spin so that the effects of the T operator on the group operations must be taken into account 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Example #1: 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

(non-magnetic crystal) Example #2: (non-magnetic crystal) 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Example #2: (space group) 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Example of possibility #3: C2h(C2) C2h(Ci) C2h(C1h) 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Example of #3 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

D4h(D2h) -- continued H TAk 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Some character table analysis for magnetic groups 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28

Example: MnF2 and NiF2 3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28

3/31/2017 PHY 745 Spring 2017 -- Lecture 28