forked from GuiguBabel/The-Oxford-Solid-State-Basics
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy path20 Collective Magnetism.srt
More file actions
3430 lines (2858 loc) · 98.1 KB
/
20 Collective Magnetism.srt
File metadata and controls
3430 lines (2858 loc) · 98.1 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1
00:00:00,000 --> 00:00:05,549
这是一个让我们重新开始的方法。欢迎回来,现在是该课程的第20讲
that's a let's get started again welcome
back this is now the 20th lecture of the
2
00:00:05,549 --> 00:00:09,120
我们上次离开时的凝聚态过程我们在谈论磁性
condensed matter course when we last
left off we were talking about magnetism
3
00:00:09,120 --> 00:00:13,200
我们一次要考虑一个原子的磁性,在本讲座中,我们
and we're thinking about magnetism one
atom at a time and in this lecture we're
4
00:00:13,200 --> 00:00:17,520
要进行某种升级,并开始考虑其他方面的集体磁性
gonna sort of upgrade and start thinking
about collective magnetism in other
5
00:00:17,520 --> 00:00:24,119
当我们有很多原子时,使用磁
words magnetism when we have lots of
atoms collective magnetism using the
6
00:00:24,119 --> 00:00:29,490
当您将很多东西放在一起时,更多的是不同的主题
theme that more is different when you
put lots of things together you can get
7
00:00:29,490 --> 00:00:32,759
新的和不同的物理学现在我们确实开始了一些集体
new and different physics now we did
start a little bit of a collective
8
00:00:32,759 --> 00:00:36,570
上次我们谈论匈奴规则时的吸引力
magnetism last time when we were talking
about huns rules there was the when you
9
00:00:36,570 --> 00:00:40,320
谈到匈奴人的规则,一个分子在hoon的作用下具有推动力,
talked about huns rules a molecule there
was the driving force by hoon's role to
10
00:00:40,320 --> 00:00:44,700
尝试使分子中原子之间的自旋对齐,但也有共价键
try to align spins between atoms in a
molecule but there's also the covalent
11
00:00:44,700 --> 00:00:47,940
试图阻止自对准旋转的键合物理,因此您可以
bonding physics which tried to
anti-aligned spin so you could make a
12
00:00:47,940 --> 00:00:51,449
单重或共价键,而这两个事物相互竞争,
singlet or covalent bond and those two
things compete with each other and
13
00:00:51,449 --> 00:00:54,660
正确获取详细信息以找出旋转将对齐还是反旋转
getting the details right to figure out
whether the spins will align or anti
14
00:00:54,660 --> 00:00:59,340
对齐是一个复杂的过程,我们将要知道
aligned is sort of a complicated process
and we're going to you know brush that
15
00:00:59,340 --> 00:01:04,110
完全在地毯下,然后尝试退后一步,看看
entirely under the rug and try to take a
step back and look at a model that's
16
00:01:04,110 --> 00:01:07,439
会给我们带来很多我们感兴趣的物理学
going to sort of give us much of the
physics that were interested in without
17
00:01:07,439 --> 00:01:12,000
在细节上陷入困境,所以我们有一些近似
getting too bogged down in the details
so we have a couple of approximation in
18
00:01:12,000 --> 00:01:19,229
我们的模型,所以我们的玩具模型将没有电子跳跃,因此我们不必
our model so our toy model will have one
no electron hopping so we don't have to
19
00:01:19,229 --> 00:01:24,330
担心任何种类的乐队物理学,我们都不必担心绘制紧密的绑定
worry about any sort of band physics we
don't have to worry draw a tight binding
20
00:01:24,330 --> 00:01:27,060
模型,我们将不得不担心保利顺磁性所有这些
model we'd have to worry about pauli
paramagnetism all of that has been
21
00:01:27,060 --> 00:01:33,240
扔掉,所以没有电子跳动,我们可以假设在每个原子上都有
thrown out so with no electron hopping
we can assume that on each atom there is
22
00:01:33,240 --> 00:01:43,049
每个原子离子原子I上的每个原子上的自旋si
a spin spin si on each atom on each atom
ion atom I and I put spin in quotes
23
00:01:43,049 --> 00:01:48,180
因为这个旋转我真正的意思是一个磁矩
because this spin what I really mean is
a magnetic moment that magnetic moment
24
00:01:48,180 --> 00:01:51,990
可能是由于实际的电子自旋,可能是由于许多电子自旋
maybe from an actual electron spin it
may be from many electron spins it may
25
00:01:51,990 --> 00:01:57,000
是轨道角动量,可能是轨道和自旋的某种组合,但
be orbital angular momentum it may be
some combination of orbital and spin but
26
00:01:57,000 --> 00:02:00,899
角动量,但通常在您制作此类玩具时
an angular momentum but generally when
you sort of make these sort of toy
27
00:02:00,899 --> 00:02:05,369
不管它实际上来自什么,您都称其为自旋模型,然后我们将
models you just call it spin no matter
what it's actually from and then we'll
28
00:02:05,369 --> 00:02:10,830
写下哈密顿量,所以这是一个哈密顿量,三个H等于
write down the Hamiltonian so here's a
Hamiltonian three H equals and then it
29
00:02:10,830 --> 00:02:13,890
有两块,第一块应该寻找
has two pieces the first piece should
look for
30
00:02:13,890 --> 00:02:22,860
G mu bb点SI只是自旋与外部磁场的耦合
G mu b b dot SI that's just the coupling
of the spin to the external magnetic
31
00:02:22,860 --> 00:02:26,489
领域,这是赋予我们力量磁性的术语,然后我们将添加
field this is the term that gave us
power magnetism then we're going to add
32
00:02:26,489 --> 00:02:32,670
为此,我要再加上一个负号和一个1/2的小数
to it another term sum over oops i'm
going to put a minus sign and a 1/2 out
33
00:02:32,670 --> 00:02:46,500
在i和j / adams的前面加上j的逗号j IJ si点s J,所以这里的术语是
front some i and j / adams i comma j of
j IJ s i dot s J so this term here is an
34
00:02:46,500 --> 00:02:53,910
交互项,因此j IJ是原子ID i与j之间的交互
interaction term so j IJ is the
interaction between atom ID i and j
35
00:02:53,910 --> 00:03:10,950
在原子i和j之间,我们将J IJ设为j ji,这也是
between atoms i and j and we will set J
IJ equal to j ji and this is also
36
00:03:10,950 --> 00:03:18,600
有时也称为等值,在此交换中,交换常数为
sometimes called also equals and on this
exchange the exchange constant this is
37
00:03:18,600 --> 00:03:22,190
大部分时间如何在凝聚态物理中使用单词交换
how the word exchange is used in
condensed matter physics most the time
38
00:03:22,190 --> 00:03:29,040
并且在其中放置了1/2的事实以防止计数过度,我们希望J 1 2为
and the fact of 1/2 is put in there to
prevent over-counting we want J 1 2 to
39
00:03:29,040 --> 00:03:33,780
是原子1和2之间的相互作用,但总和为s 1
be the interaction between atom 1 & 2
but in that sum there will be a term s 1
40
00:03:33,780 --> 00:03:38,310
s 2在另一个术语s 2 s 1中,我们不想过多地计算它们,所以我们只是
s 2 in another term which is s 2 s 1 we
don't want to over count them so we just
41
00:03:38,310 --> 00:03:46,500
将1/2放在前面,这样这个模型模型3哈密顿量3 3被称为
put a 1/2 out front ok so this model
model 3 the Hamiltonian 3 3 is known as
42
00:03:46,500 --> 00:03:51,440
哈密顿3的3含义在之后被称为海森堡模型
the 3 meaning of the Hamiltonian 3 is
known as the Heisenberg model after
43
00:03:51,440 --> 00:03:58,560
每个人最喜欢的不确定物理学家海森堡模型都经常研究
everyone's favorite uncertain physicist
Heisenberg model very frequently studied
44
00:03:58,560 --> 00:04:04,019
凝聚态物理中的模型,并且很好地表示了许多磁体
model in condensed matter physics and a
very good representation of many magnets
45
00:04:04,019 --> 00:04:15,510
现在我们将j IJ设置为j
now we're going to simplify this even
further simplify by setting j IJ equal
46
00:04:15,510 --> 00:04:23,070
如果i和j是j个邻居的邻居,则将其设置为j,我们将其设置为
to j if i and j are neighbors by j
neighbors and we're going to set it
47
00:04:23,070 --> 00:04:27,370
等于0,否则换句话说,我们将保持
equal to 0 otherwise
in other words we're just gonna keep
48
00:04:27,370 --> 00:04:33,490
跟踪彼此之间最接近的自旋之间的相互作用
track of interaction between spins that
happen to be nearest neighbors with each
49
00:04:33,490 --> 00:04:37,510
另外,它是一个很好的近似值,它旋转到接近
other it's a fairly good approximation
that spins on atoms that are close to
50
00:04:37,510 --> 00:04:40,420
彼此见面,如果彼此相距较远,则看不见
each other see each other and if they're
farther from each other they don't see
51
00:04:40,420 --> 00:04:43,960
彼此,然后我们也将简化,这是一种简化
each other and then we're also going to
simplify so this is simplification one
52
00:04:43,960 --> 00:04:48,100
简化二是四现在我们将外部磁场设置为
and simplification two is four now we're
gonna set the external magnetic field to
53
00:04:48,100 --> 00:04:55,570
零,我们可能稍后再放回去,所以我们的哈密顿量现在采用H的形式
zero and we may put it back in later
so our Hamiltonian now takes the form H
54
00:04:55,570 --> 00:05:03,610
是IJ的负1/2和,我会这样写,所以这个符号表示I和J
is minus 1/2 sum over I J and I'll write
like this so this notation means I and J
55
00:05:03,610 --> 00:05:16,270
或邻居括号符号,所以是标准的J si S,所以我们只求和
or neighbors bracket notation so a
standard J si s J so we're only summing
56
00:05:16,270 --> 00:05:20,530
当我和J成为邻居时,常量只是一个常量J,在这里知道
over I and J being neighbors and the
constant is just a constant J here know
57
00:05:20,530 --> 00:05:23,770
您可以从这种情况中获得一些可能性
there's a couple possibilities of what
you can get out of this sort of
58
00:05:23,770 --> 00:05:32,410
哈密顿量,所以可能性一,让我们写下情况一,情况一是J
Hamiltonian so possibility one so let's
write down case one case one is that J
59
00:05:32,410 --> 00:05:37,960
大于0在这种情况下为了使哈密顿量成为能量
is greater than 0 in which case in order
to make the energy of that Hamiltonian
60
00:05:37,960 --> 00:05:42,310
相邻站点的两个自旋应尽可能小,以尝试与
as small as possible the two spins on
adjacent sites will try to align with
61
00:05:42,310 --> 00:05:48,460
彼此旋转,所以当旋转对齐时,您得到的是
each other so spins align and when the
spins align what you get is
62
00:05:48,460 --> 00:05:57,520
铁磁性铁磁性磁化强度不等于0
ferromagnetism ferromagnetism a
magnetization which is not equal to 0
63
00:05:57,520 --> 00:06:03,670
现在,在这个哈密顿量中,旋转的方向无关紧要
now it doesn't matter in this
Hamiltonian which direction the spins
64
00:06:03,670 --> 00:06:07,360
只要自旋彼此对齐,所有对齐
all align in as long as the spins are
all aligned with each other so they can
65
00:06:07,360 --> 00:06:09,520
他们都指向上,他们都可以朝下,他们都可以指向
all be pointing up they can all be
pointing down they can all be pointing
66
00:06:09,520 --> 00:06:12,640
现在到左边,我将把右边的东西放到相同的位置
to the left now I'll be putting the
right same you'll end up with the same
67
00:06:12,640 --> 00:06:14,890
能量重要的是所有旋转
energy
what's important is all the spins
68
00:06:14,890 --> 00:06:19,750
彼此对齐确定,所以这是更容易研究的案例
aligned with each other ok so this is
the easy case to study the more
69
00:06:19,750 --> 00:06:29,200
要研究的复杂案例是案例二,现在J小于零,而J小于
complicated case to study is case two is
J less than zero now with J less than
70
00:06:29,200 --> 00:06:35,790
邻居希望事前对齐为零
zero the neighbors want to ante align
71
00:06:36,930 --> 00:06:42,550
为了使哈密顿量尽可能小或使能量尽可能小
in order to make the Hamiltonian as
small as possible or the energy as small
72
00:06:42,550 --> 00:06:47,620
因此,如果我们有一个让我们在这里看到的东西,那么我们所拥有的就是
as possible so then what we have is if
we have a let's see right down here so
73
00:06:47,620 --> 00:06:53,699
如果我们有一个像这样的方格,每个格上都有一个自旋
if we have like a square lattice like
this each with a spin on it if the first
74
00:06:53,699 --> 00:06:57,580
旋转指向上方,然后第二个旋转将要指向
spin is pointing up
then the second spin will want to point
75
00:06:57,580 --> 00:07:01,000
降低以使能量尽可能小,然后第三次
down in order to make the energy as
small as possible and then the third
76
00:07:01,000 --> 00:07:04,210
旋转将指向这一点将向下指向这一点将这一点将
spin will point up this one will point
down this one point up this one will
77
00:07:04,210 --> 00:07:09,370
指向下方等等,我们将交替旋转
point down and so forth and so on and
we'll get these alternating spin
78
00:07:09,370 --> 00:07:19,300
结构,这就是所谓的反铁磁体,有时也称为
structures this is what's known as an
antiferromagnet or sometimes known as a
79
00:07:19,300 --> 00:07:26,949
露易·纳塔尔(Louie natal)出生后就意识到了这些
nail state and he PL nail state after
Louie natal who realized that these
80
00:07:26,949 --> 00:07:33,039
事物实际上存在于自然界中,那么有趣的是
things actually exist in nature and then
what's interesting about these is that
81
00:07:33,039 --> 00:07:41,289
它们具有磁阶,但没有净磁化强度,
they have magnetic order magnetic order
but they have no net magnetization and
82
00:07:41,289 --> 00:07:46,000
等于零,为什么它们没有很好的净磁化强度,因为
equals zero why they have no net
magnetization well because you have the
83
00:07:46,000 --> 00:07:49,060
向上旋转的次数至少与向下旋转的次数相同
same number of up pointing spins as you
have down pointing spins well at least
84
00:07:49,060 --> 00:07:52,419
如果我把它们画得更对齐,那看起来就像是一个平等
if I if I drew them more aligned it
would look like there was an equal
85
00:07:52,419 --> 00:07:56,949
向上旋转的旋转次数向下旋转的旋转我的绘图不太好
number of up spin pointing spins is down
pointing spins my drawing isn't so good
86
00:07:56,949 --> 00:08:03,729
路易斯现在知道这种情况怎么可能发生
so how is it that Louie now knew that
this sort of situation could occur well
87
00:08:03,729 --> 00:08:07,330
在其中一项家庭作业中减去您要完成的作业
on one of the homework assignments less
homework assignment you're meant to
88
00:08:07,330 --> 00:08:11,740
计算像这样的状态的磁化率,实际上
calculate the magnetic susceptibility of
a state like this and there's actually
89
00:08:11,740 --> 00:08:14,320
您可以寻找的一些特征和磁化率
some signature and the magnetic
susceptibility that you can look for
90
00:08:14,320 --> 00:08:18,009
这就是Niall在看的东西,是什么让他
which was a which was the thing that
Niall is looking at and what made him
91
00:08:18,009 --> 00:08:21,990
意识到这些反铁磁状态实际上存在
realize that these anti ferromagnetic
states actually exist
92
00:08:21,990 --> 00:08:28,509
但在现代时代,实际上有一种非常直接的方式来观察这种
but in the modern era there's actually a
very direct way to see this sort of
93
00:08:28,509 --> 00:08:33,339
物理是要对其进行中子散射,所以让我确保你
physics which is to do neutron
scattering on it so let me make sure you
94
00:08:33,339 --> 00:08:40,050
可以写下中子散射所能看到的
can write that down you can see with
neutron scattering
95
00:08:40,979 --> 00:08:49,720
或中子衍射,我想我们应该称其为基本晶格
or neutron diffraction I guess we should
call it so the elementary lattice
96
00:08:49,720 --> 00:08:56,160
常数可能是a,但中子实际上看到了晶格常数
constant here might be a but the
neutrons actually see a lattice constant
97
00:08:56,160 --> 00:09:00,940
这么大,这就是现在的晶胞,因为如果中子是
which is this big this is the unit cell
now because the neutrons if a neutron is
98
00:09:00,940 --> 00:09:05,560
随着自旋向上而来,它将自旋视为与原子不同的原子
coming in with spin up it sees an up
spin as being a different atom from a
99
00:09:05,560 --> 00:09:08,620
向下旋转和中子看到向上旋转的原因与
Down spin and the reason that neutrons
see an up spin is being different from a
100
00:09:08,620 --> 00:09:12,639
向下旋转是中子自身旋转并且相互作用不同
Down spin is the neutrons themselves
have spin and they interact differently
101
00:09:12,639 --> 00:09:16,600
你知道如果进入的中子是自旋原子,它将相互作用
with you know if the neutron coming in
is a spin up atom it will interact
102
00:09:16,600 --> 00:09:20,079
与此原子不同,因此与该原子不同,因为它们的自旋为NT
differently with this atom then with
this atom because their spins are NT
103
00:09:20,079 --> 00:09:24,459
对齐,因此它会看到一个很大的质数,因此当您执行
aligned so it sees a unit cell which is
this big a prime so when you do your
104
00:09:24,459 --> 00:09:29,259
中子衍射实验,您会发现它具有不同大小的晶胞
neutron diffraction experiment you will
see it a different size of the unit cell
105
00:09:29,259 --> 00:09:35,110
当反铁磁性发生时,您会得到一个更大的晶胞,我应该
when antiferromagnetism occurs you get a
bigger unit cell I should actually
106
00:09:35,110 --> 00:09:38,680
在这里再评论一件事,这有点微妙,但有一项作业
comment one more thing here which is a
little subtle but there's a homework
107
00:09:38,680 --> 00:09:43,600
还要在这张照片上画作业,否则我应该有
assignment on it as well then in this
picture I've drawn or I should have
108
00:09:43,600 --> 00:09:47,410
如果我是一个更好的艺术家,就画画。
drawn if I was a better artist up spins
down spins up spin down spin up spin
109
00:09:47,410 --> 00:09:50,170
向下旋转,这是一种非常经典的思维方式,我正在思考这些
down spin and that's a very classical
way of thinking I'm thinking of these
110
00:09:50,170 --> 00:09:53,769
自旋实际上是您的向量,您可以指向任何方向
spins is actually being your vectors
that you can point in any direction in
111
00:09:53,769 --> 00:09:58,449
如果您在旋转方面有很大的旋转,那么您知道五个半
space if you have large spins in the
sense of spin you know five halves or
112
00:09:58,449 --> 00:10:03,190
自旋s等于2或s等于9个一半或s等于3或4或类似的值
spin s equals 2 or s equals 9 halves or
s equals 3 or 4 or something like that
113
00:10:03,190 --> 00:10:07,720
然后把这些图片放在这些自旋的脑海中,只是矢量
then having this picture in your head of
these spins is just being vectors that
114
00:10:07,720 --> 00:10:11,949
可以指向太空中的任何方向是一张相当不错的古典图画
can point any direction in space is a
fairly good classical picture which is
115
00:10:11,949 --> 00:10:15,970
相当准确,但是如果您正在谈论旋转1/2则不是很好
fairly accurate but if you're talking
about spin 1/2 then it's not so good
116
00:10:15,970 --> 00:10:19,180
不再需要真正考虑量子力学了
anymore you really have to think in
terms of quantum mechanics and you can't
117
00:10:19,180 --> 00:10:24,189
画出这些向上旋转的图片向上旋转向下旋转旋转1/2 T
draw these pictures of up spin down spin
up spin down spin and spin 1/2 an T for
118
00:10:24,189 --> 00:10:27,939
我们的磁铁是非常复杂的野兽,想起来是不对的
our magnet is a very complicated beast
and it's not really right to think of it
119
00:10:27,939 --> 00:10:31,060
这样,这更像是一种经典的直觉,适用于大型
this way this is sort of more of a
classical intuition that works for large
120
00:10:31,060 --> 00:10:35,740
大旋转但是小旋转不太好,大概可以用
large spins but not so well for small
spins and that will be presumably worked
121
00:10:35,740 --> 00:10:42,610
可以在家庭作业中完成,所以对此案再发表一则评论
out in a homework assignment all right
so one more comment about this this case
122
00:10:42,610 --> 00:10:47,709
反铁磁性的原因是您可以拥有反铁磁性
of antiferromagnetism
is that you can have antiferromagnets
123
00:10:47,709 --> 00:10:53,680
反铁磁耦合磁在三角形晶格上,然后
anti ferromagnetic coupling
mag on a triangular lattice and then
124
00:10:53,680 --> 00:11:01,420
您会得到一些非常奇怪的三角形格子,让我们想象一下
you'll get something really strange
triangular lattice so let's imagine we
125
00:11:01,420 --> 00:11:06,009
这里有一个三角形,三角形中有三个原子,如果第一个发生
have a triangle here three atoms in
triangle and if the first one happens to
126
00:11:06,009 --> 00:11:10,569
有旋转的第二个想要在这里旋转指向
have is spin up the second one up here
wants to have spin pointing in the
127
00:11:10,569 --> 00:11:15,040
与这个方向相反,所以他指向旋转,然后这个想要
opposite direction from this one so he
points spin down and then this one wants
128
00:11:15,040 --> 00:11:17,769
对每个邻居都有相反的指向旋转,但是他在
to have an opposite pointing spin to
each of his neighbors but he's in
129
00:11:17,769 --> 00:11:22,329
麻烦他可以指出,然后使这个家伙相反的方向,但
trouble he can point up and then make
the opposite direction of this guy but
130
00:11:22,329 --> 00:11:25,269
与这个人相同的方向,否则他可以指向下方,相反
the same direction as this guy or he can
point down in which case he's opposite
131
00:11:25,269 --> 00:11:28,600
这个人对这个人的方向相同,所以这个人有麻烦,他不能
this guy the same direction at this guy
so this guy's in trouble and he can't
132
00:11:28,600 --> 00:11:35,310
高兴地指出任一方向,所以这就是你所说的沮丧
point happily either direction so this
is what you call frustrated frustrated
133
00:11:35,310 --> 00:11:46,500
反铁磁体这几天一切都会引起挫败,所以再多
antiferromagnet everything causes
frustration these days okay so one more
134
00:11:46,500 --> 00:11:51,250
这种反铁磁性或类似的物理原理
case in of this anti anti ferromagnetism
or similar physics to anti
135
00:11:51,250 --> 00:11:58,000
我想提及的铁磁性是您有基础或
ferromagnetism that i want to mention is
the possibility that you have a basis or
136
00:11:58,000 --> 00:12:04,810
让我们以两个原子为基础,我们两个或两个以上或更多,我是
let's let's consider a two atom basis
our two two or more or more and i'm
137
00:12:04,810 --> 00:12:12,130
是晶格的基础,所以对于晶体,让我们考虑一个大原子
basis for our lattice so for a crystal
so let's consider for example a big atom
138
00:12:12,130 --> 00:12:18,519
一个小原子一个大原子一个小原子大原子你会把它们变得越来越小
a small atom a big atom small atom big
atom you get them small and big out of
139
00:12:18,519 --> 00:12:27,189
像这样的小四大,所以这是两个原子的基础,现在想象我们有
small four big like this so here's a two
atom basis okay now imagine that we have
140
00:12:27,189 --> 00:12:33,430
反铁磁耦合,其中相邻原子要具有点
anti ferromagnetic coupling where the
neighboring atoms want to have point
141
00:12:33,430 --> 00:12:37,990
它们的旋转方向相反,所以大原子指向上方,小原子指向上方
their spins in opposite directions so
the big atom say points up and the small
142
00:12:37,990 --> 00:12:42,819
原子点大降低点,点向上点小,员工降低大点
atom points down big out on points up
small an employee's down big atom points
143
00:12:42,819 --> 00:12:51,779
好的,我们可以继续前进这里,并获得想法,好的
up okay we can keep going here and get
the idea and okay up down
144
00:12:52,980 --> 00:13:01,980
如果大原子上的自旋不等于小原子上的自旋,那么
if the spin on the big atom is not equal
to the spin on the small atom then what
145
00:13:01,980 --> 00:13:06,930
我们将拥有的磁化强度将不等于零,因为您将拥有
we'll have is will have magnetization
not equal to zero because you'll have
146
00:13:06,930 --> 00:13:11,100
磁化强度指向上方,那么您的磁化强度指向下方是
more magnetization pointing up then you
have magnetization pointing down is that
147
00:13:11,100 --> 00:13:14,220
很清楚这是怎么工作的,即使你有反铁磁性
is that clear how that works so even
though you have anti ferromagnetic
148
00:13:14,220 --> 00:13:18,660
耦合,每个相邻的自旋都想指向相反的方向,您会得到一个
coupling and each neighboring spin wants
to point in opposite direction you get a
149
00:13:18,660 --> 00:13:23,340
剩余的净磁化强度,因为某些自旋大于另一个
net magnetization left over because some
of the spins are bigger than the other
150
00:13:23,340 --> 00:13:33,120
自旋,这就是所谓的仙子磁力仙子磁力,它可能
spins and this is what is known as fairy
magnetism fairy magnetism and it may
151
00:13:33,120 --> 00:13:37,110
看起来有点奇怪或不寻常,但实际上很常见
seem like it's it's kind of strange or
unusual but it's actually quite common
152
00:13:37,110 --> 00:13:43,830
事实上,世界上最常见的磁铁是自然界中的铁3氧化物4
in fact the world's most common magnet
occurring in nature it's iron 3 oxide 4
153
00:13:43,830 --> 00:13:48,060
您可以在其中找到的磁铁矿或磁铁矿
otherwise known as magnetite or
lodestone that you can you'll find in
154
00:13:48,060 --> 00:13:51,060
地球有时会被拉出地球并被它磁化
the earth sometimes and it's magnetized
when you pull it out of the earth and it
155
00:13:51,060 --> 00:13:56,310
会直接粘在冰箱上,实际上是由磁铁组成的
will stick to your refrigerator directly
is actually a fairy magnet it's made up
156
00:13:56,310 --> 00:14:00,870
一种原子类型上大于一个原子类型上更大的矩
of more than one type of atom larger
larger moments on one type of atom
157
00:14:00,870 --> 00:14:05,730
彼此之间的力矩较小,彼此反对齐,则存在
smaller moments on the other and they
anti align with each other then there's
158
00:14:05,730 --> 00:14:09,960
社区中关于您是否应该称呼磁铁的争论
an argument in the community as to
whether you should call a fairy magnet a
159
00:14:09,960 --> 00:14:13,980
铁磁体的子集,这是您知道人们会争论的地方
subset of a Ferro magnet and this is
where you know people will argue with
160
00:14:13,980 --> 00:14:18,180
彼此直到脸色发青并且没有实际的好答案
each other till they're blue in the face
and there's no actual good answer to
161
00:14:18,180 --> 00:14:22,890
这是因为人们都同时使用它,所以有人说仙女磁铁是
this because people use it both ways so
some people say that a fairy magnet is a
162
00:14:22,890 --> 00:14:27,450
铁磁磁体的子集,因为它的磁化强度非零,因此会坚持
subset of a Ferro magnet because it has
nonzero magnetization it will stick to
163
00:14:27,450 --> 00:14:32,460
您的冰箱,您知道这是我们认为是磁铁的特性
your refrigerator you know it's as the
property that we think of as a magnet on
164
00:14:32,460 --> 00:14:36,090
另一方面,有些人认为应该保留“铁磁”一词
the other hand some people think that
the word Ferro magnet should be reserved
165
00:14:36,090 --> 00:14:39,570
对于所有旋转都指向相同方向的情况,我们应该调用
for the case where all the spins point
in the same direction and we should call
166
00:14:39,570 --> 00:14:42,900
这是一个神仙的磁铁,有别于所有自旋的情况
this a fairy magnet to distinguish it
from the case where all the spins are
167
00:14:42,900 --> 00:14:45,870
指向同一方向,所以无论如何,您应该意识到
pointing in the same direction so anyway
you should just be aware that that's