20 Collective Magnetism.srt

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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

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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

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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

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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

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当我们有很多原子时，使用磁
words magnetism when we have lots of
atoms collective magnetism using the

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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有两块，第一块应该寻找
has two pieces the first piece should
look for

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 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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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 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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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铁磁性铁磁性磁化强度不等于0 
ferromagnetism ferromagnetism a
magnetization which is not equal to 0

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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

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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

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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

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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

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能量重要的是所有旋转
energy
what's important is all the spins

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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

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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

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邻居希望事前对齐为零
zero the neighbors want to ante align

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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意识到这些反铁磁状态实际上存在
realize that these anti ferromagnetic
states actually exist

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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

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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

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可以写下中子散射所能看到的
can write that down you can see with
neutron scattering

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

168
00:14:45,870 --> 00:14:50,460
社区中几乎没有命名冲突，所以如果
that there's that little conflict of
nomenclature in the community okay so if

169
00:14:50,460 --> 00:14:56,580
我们很好，我们仍然做得不错，所以让我们继续
we're so good we're doing well still all
right so let's move on to actually maybe

170
00:14:56,580 --> 00:14:59,850
你知道我会再写一遍写下海森堡哈密顿量H 
you know I'll write it again well write
down the Heisenberg Hamiltonian H

171
00:14:59,850 --> 00:15:06,010
海森堡再减去邻居IJ的1/2和
Heisenberg again minus 1/2 sum over
neighbors IJ

172
00:15:06,010 --> 00:15:13,660
 J si SJ，正如我提到的，让我们主要关注J 
J si SJ and as I mentioned and let's
we're gonna sort of focus mostly on J

173
00:15:13,660 --> 00:15:19,660
大于零，换句话说就是铁磁情况
greater than zero in other words the
ferromagnetic case and as I mentioned

174
00:15:19,660 --> 00:15:24,490
只要这个旋转点，哈密顿量就不会在意
this Hamiltonian doesn't care which
direction the spins point as long as

175
00:15:24,490 --> 00:15:27,699
不幸的是，他们现在都指向同一方向
they're all pointing in the same
direction now unfortunately most

176
00:15:27,699 --> 00:15:31,660
材料并不像大多数材料实际上更喜欢旋转
materials aren't like that most
materials actually prefer the spins to

177
00:15:31,660 --> 00:15:36,310
指向某个特定方向，所以这是为了表示我们
point in some particular direction and
so this is in order to represent that we

178
00:15:36,310 --> 00:15:39,760
需要在汉密尔顿语中添加另一个术语，它们实际上是首先
need to add another term to the
Hamiltonian they're actually first let's

179
00:15:39,760 --> 00:15:42,550
这是我在上一堂课中提到的，但我会再次提及
this is something I mentioned in the
last lecture but I'll mention it again

180
00:15:42,550 --> 00:15:46,540
一件事，很明显，方向不是全部
one thing that would make it obvious
that the directions aren't all

181
00:15:46,540 --> 00:15:51,370
等效的是，如果您想象有一个非常长的单位晶格， 
equivalent is if you imagine having a
very long tetr-a g''l unit cell whether

182
00:15:51,370 --> 00:15:55,149
你知道晶体在一个方向上很长很薄，那么你可能
you know the crystal is very long and
thin in one direction then you might

183
00:15:55,149 --> 00:16:00,790
想象一下，也许旋转想沿着特别长的细线指向
imagine that maybe the spins want to
point along particular the long thin

184
00:16:00,790 --> 00:16:07,750
轴可能使您可能想要向上或想要向下但不
axes maybe so you might have s wanting
to be up or s wanting to be down but not

185
00:16:07,750 --> 00:16:13,209
两者之间的任何方向，所以这是您可能会期望的一种情况
any direction in between so this is sort
of a case where you might expect this

186
00:16:13,209 --> 00:16:17,980
存在某种各向异性，因此为了表示我们写下一个
sort of anisotropy to exist so in order
to represent that we write down an

187
00:16:17,980 --> 00:16:24,699
哈密​​尔顿DH的附加术语，我看到了Trippy或我看到了Trippy 
additional term of the Hamiltonian D H
and I saw trippy or a time I saw trippy

188
00:16:24,699 --> 00:16:31,170
不会叫它D我不确定哪个可能在所有原子上采用总和形式
wouldn't call it D I'm not sure which
might take the form sum over all atoms

189
00:16:31,170 --> 00:16:37,899
在前面放一个减去Kappa的物体，就像在Z方向上保持不变的si 
put a minus a Kappa out front that's
like some constant si in the Z Direction

190
00:16:37,899 --> 00:16:43,570
平方，这为什么会偏向于具有特定的自旋
squared so why is this going to prefer
having the spin in some particular

191
00:16:43,570 --> 00:16:49,269
方向很好，它想最大化SZ的大小，因此，如果SC指向
direction well it wants to maximize the
magnitude of SZ so if SC is pointing in

192
00:16:49,269 --> 00:16:53,589
哈密​​顿量沿向上或向下的方向
the in the direct up direction or the
direct down direction this Hamiltonian

193
00:16:53,589 --> 00:16:57,459
尽可能地小，与
is as small as possible it's as negative
as you possibly can as compared to

194
00:16:57,459 --> 00:17:01,990
在SZ上光束中的s点等于零平面
having s point in the beam on the SZ
equals zero plane and where this gets

195
00:17:01,990 --> 00:17:07,449
负数较少，因此这种各向异性项是我们要使用的
less negative so this kind of term this
anisotropy term is one we're going to

196
00:17:07,449 --> 00:17:17,410
考虑很多，所以也许我什至会写下来，就像不停下来
consider a lot so maybe I'll even write
down like to have s up or s down not

197
00:17:17,410 --> 00:17:23,800
现在侧向指向立方晶体时，您可能会想到dh 
as pointing sideways now for a cubic
crystal you might expect something d-h

198
00:17:23,800 --> 00:17:28,600
立方的，稍微复杂一点，可以使自旋指向
cubic which is a little more complicated
that would allow the spin to point along

199
00:17:28,600 --> 00:17:34,510
任何晶体和轴，但不在晶体AXYZ之间
any of the crystal and axes but not in
between the crystal AXYZ an appropriate

200
00:17:34,510 --> 00:17:41,650
哈密​​顿量可能是这样的si X到第四加si Y 
Hamiltonian for that might be something
like this si X to the fourth plus si Y

201
00:17:41,650 --> 00:17:48,580
到第四个加si Z到第四个，我写这个给
to the fourth plus si Z to the fourth
and the reason I wrote this to the

202
00:17:48,580 --> 00:17:52,300
第四次幂是因为如果我将它们写为平方次幂，那么你只是
fourth power is it because if I wrote
them to the squared power then you just

203
00:17:52,300 --> 00:17:56,440
得到sx平方加y平方加Z平方，即s平方，即
get s x squared plus y squared plus Z
squared which is just s squared and that

204
00:17:56,440 --> 00:17:59,770
不在乎旋转指向哪个方向，因为它只是幅度
doesn't care which direction the spin is
pointing because it's just the magnitude

205
00:17:59,770 --> 00:18:03,400
旋转，但是如果您将其写为第四至第四，这就是为什么
of the spin but if you write it as
fourth s x to the fourth that's why this

206
00:18:03,400 --> 00:18:06,820
所需的力量，那么这更倾向于让它一直指向
force that's needed for it then this
prefers to have this been pointing along

207
00:18:06,820 --> 00:18:10,570
晶轴之一，但不在晶轴之间，因此我们可能
one of the crystalline axes but not in
between the crystalline axes so we might

208
00:18:10,570 --> 00:18:14,080
也考虑一下这一点，但主要是我们要专注于这一点
consider this one a little bit as well
but mainly we're gonna focus on this one

209
00:18:14,080 --> 00:18:20,830
只需再给一个评论再发表一次，您就会知道我们在这里写的是
just one comment comment again for small
you know the what we've written here is

210
00:18:20,830 --> 00:18:25,480
当我们将旋转视为经典时，这是基于我们对旋转的直觉
sort of based on our intuition for spins
when we're thinking them as classical

211
00:18:25,480 --> 00:18:29,650
向量我们认为它们是小旋转的经典向量
vector we're thinking of them as
classical vectors for small spins small

212
00:18:29,650 --> 00:18:40,360
这些可能很琐碎，这些术语可能很琐碎，我的意思是
spins these can be trivial these these
terms can be trivial what do I mean by

213
00:18:40,360 --> 00:18:46,570
好吧，假设我尝试将其写下来旋转1/2 
that well suppose I try to write this
down for a spin 1/2

214
00:18:46,570 --> 00:18:53,290
记住这个自旋1/2 Polly算子Sigma Z如果是Pauli自旋矩阵
remember this spin 1/2 Polly operator
Sigma Z this the Pauli spin matrix if

215
00:18:53,290 --> 00:18:59,110
您将其平方为自旋1/2，它是自旋矩阵Sigma Z的1/2 
you square it for spin 1/2
it's been 1/2 the spin matrix Sigma Z

216
00:18:59,110 --> 00:19:03,160
平方只是1这是一个非常无趣的运算符
squared is just 1 it's a very
uninteresting operator it's just gives

217
00:19:03,160 --> 00:19:06,310
您是一个常数，因此，如果您尝试写下这样的术语以旋转1/2 
you a constant so if you try to write
down a term like this for a spin 1/2

218
00:19:06,310 --> 00:19:10,780
旋转它不会执行任何操作，也不会指定此bin想要的方向
spin it would do nothing it wouldn't
specify which direction this bin wants

219
00:19:10,780 --> 00:19:15,370
要指出的是，如果您进行旋转-或旋转3则将是
to point in however if you did it for a
spin - or spin 3 it would it would be an

220
00:19:15,370 --> 00:19:19,810
不与1平方的类似自旋矩阵变得不平凡，因此
analogous spin matrix which it does not
square to 1 it becomes non trivial so

221
00:19:19,810 --> 00:19:22,960
只是要警告您不能写下来，我看到了两个B 
that's just something to be warned about
you can't write down and I saw two B

222
00:19:22,960 --> 00:19:28,960
足够小旋转的条件好吧，所以我们需要考虑一下
terms for small enough spins ok alright
so we need to think about this

223
00:19:28,960 --> 00:19:33,549
各向异性，这将使自旋指向某些方向
anisotropy which will prefer
the spins to point in some directions

224
00:19:33,549 --> 00:19:37,179
在其他方向上，我们需要考虑两种可能性
over other directions and we need to
think about two possibilities one

225
00:19:37,179 --> 00:19:42,309
可能是各向异性强，另一个可能是
possibility is that the anisotropy is
strong and the other possibility is that

226
00:19:42,309 --> 00:19:47,950
各向异性很弱，所以也许我会在这里写下弱点
the anisotropy is weak so maybe I'll
write down the weak case over here we

227
00:19:47,950 --> 00:19:55,210
我可以寻求重复吗，我的意思是这个卡伯这个系数出现了
can I sought repeat by which I mean that
this Kappa this coefficient that occurs

228
00:19:55,210 --> 00:20:00,909
各向异性项中的远小于j发生的交换常数
in the anisotropy term is much less than
the j the exchange constant that occurs

229
00:20:00,909 --> 00:20:09,039
在海森堡任期中，在这种情况下，必须要做的就是首先
in the heisenberg term now in this case
what one has to do is one has to first

230
00:20:09,039 --> 00:20:15,369
或最重要的是首先旋转与邻居旋转对齐
or most importantly first you spins
aligned with neighbors it spins aligned

231
00:20:15,369 --> 00:20:21,100
和邻居在一起，当我首先说的时候，这是最重要的
with neighbors and when I say that first
I mean it's most important to align with

232
00:20:21,100 --> 00:20:25,389
您的邻居，因为J是系统中的大能量尺度
your neighbors because J is the big
energy scale in the system once you've

233
00:20:25,389 --> 00:20:34,359
与邻居对齐，然后沿着具有各向异性的直线对齐
aligned with your neighbors second you
align along a line with anisotropy with

234
00:20:34,359 --> 00:20:45,009
各向异性轴，所以首先您与邻居对齐，然后每个人都决定
anisotropy axis so first you align with
your neighbors and then everyone decides

235
00:20:45,009 --> 00:20:48,519
如果现在它们都与反社会的p轴对齐的话，他们的状况会更好
that they're better off if they all
align with the antisocial p axis now if

236
00:20:48,519 --> 00:20:54,580
您将其与强各向异性的情况进行比较，我寻求
you compare that to the case over here
strong anisotropy strong and I sought

237
00:20:54,580 --> 00:21:02,379
您的P表示这个Kappa这个各向异性常数Kappa大得多
your P meaning this kappa this
anisotropy constant Kappa is much bigger

238
00:21:02,379 --> 00:21:10,809
比J大，那么首先要沿着各向异性轴对齐
than J then first you want to align
along anisotropy axis aligned along

239
00:21:10,809 --> 00:21:19,960
各向异性，例如，如果我们使用的话，所有自旋都将指向上方或下方
anisotropy for example all spins will
point either up or down if we're using

240
00:21:19,960 --> 00:21:23,980
上下颠簸，然后每个人都必须指向上方或下方
that up and down on a satrapy then
everyone has to point either up or down

241
00:21:23,980 --> 00:21:27,639
那是你首先要做的，因为那是第二个
that's what you do first because that's
the big energy scale in the second in

242
00:21:27,639 --> 00:21:35,639
系统，但是第二步，您与邻居对齐与邻居对齐
the system but then second you align
with neighbors aligned with neighbors

243
00:21:36,160 --> 00:21:40,660
现在看来这是一个微不足道的区别，因为在
now this may seem like it's a trivial
distinction because at the end of the

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00:21:40,660 --> 00:21:44,500
当天的地面状态是相同的地面状态是每个人都保持一致
day the ground state is the same the
ground state is that everyone's aligned

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00:21:44,500 --> 00:21:47,560
和他们的邻居，每个人都团结一致，现在是诚实的占领轴
with their neighbors and everyone's
aligned along now be honest occupy axis

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00:21:47,560 --> 00:21:50,710
所以我为什么要为此做很多事情，这使两者有所不同
so why did I make a big deal about this
well it makes a difference the two

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00:21:50,710 --> 00:21:54,520
如果您考虑一下低能量激发，则极限会有所不同
limits make are different if you think
about what the low energy excitations

248
00:21:54,520 --> 00:22:05,020
在这种情况下，低能量激发就是
are so in this case the low energy
excitations energy excitations our small

249
00:22:05,020 --> 00:22:10,120
一堆旋转的角旋转，每个人或多或少地停留
angular rotations of a whole bunch of
spins that everyone stays more or less

250
00:22:10,120 --> 00:22:13,960
与他们的邻居对齐，但他们只旋转了一点
aligned with their neighbors but they
rotate just a little bit from the

251
00:22:13,960 --> 00:22:22,300
各向异性轴，所以这是一个小旋转小旋转
anisotropy axis so this is a small
rotations small rotations staying

252
00:22:22,300 --> 00:22:37,150
与邻居对齐排列，而这里的低能量激发是
aligned aligned with neighbors whereas
over here the low energy excitations are

253
00:22:37,150 --> 00:22:48,190
完全不同的低能量激发在这里
completely different low energy
excitations here the thing that's

254
00:22:48,190 --> 00:22:51,850
重要的是您必须与各向异性轴保持一致，因此
important is that you have to stay
aligned with the anisotropy axis so the

255
00:22:51,850 --> 00:22:58,420
低能量激发是使一些自旋翻转，但保持对齐
low energy excitation is to flip some
spin flips a spin but keep it aligned

256
00:22:58,420 --> 00:23:10,390
与各向异性轴，但保持对齐，但保持在各向异性轴上
with the anisotropy axis but stay
aligned but stay on anisotropy axis okay

257
00:23:10,390 --> 00:23:14,050
清楚这两者之间有什么区别吗，所以这是
is it clear what the difference is
between these two okay so this is an

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00:23:14,050 --> 00:23:17,410
这里有趣的案例，人们对此很有意思
interesting case here and it's
sufficiently interesting that people

259
00:23:17,410 --> 00:23:25,300
经过大量研究，他们为此模型写下了一个有效的模型
study in a lot and they write down an
effective model for this one model which

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00:23:25,300 --> 00:23:32,380
具有以下属性，我们写一些正负i等于或等于s 
has the following properties we write
some sigma i which is plus or minus s

261
00:23:32,380 --> 00:23:40,690
自旋的大小，然后si是z帽中的σ 
the magnitude of the spin and then s i
is as a vector is sigma i in the z hat

262
00:23:40,690 --> 00:23:45,310
方向，所以基本上我们只让旋转具有完整的幅度
direction so basically we're only
letting the spin have complete magnitude

263
00:23:45,310 --> 00:23:49,140
指向正上方或指向正下方的全幅
pointing exactly up or a full magnitude
pointing exactly down

264
00:23:49,140 --> 00:23:56,000
然后我们可以写出非常类似于海森堡形式的哈密顿量
and then we can write out a Hamiltonian
very similar to the Heisenberg form

265
00:23:56,120 --> 00:24:03,450
海森堡形式H等于还可以，所以I和J上将有负1/2的和
Heisenberg form H equals okay so
there'll be minus 1/2 sum over I and J

266
00:24:03,450 --> 00:24:10,410
邻居J Sigma I Sigma J，然后加上好耦合到外部
neighbors J Sigma I Sigma J and then
plus well couple it to the external

267
00:24:10,410 --> 00:24:20,730
场G mu BB Sigma I这个哈密顿量被称为缓和模型缓和
field G mu B B Sigma I this Hamiltonian
is known as the easing model easing

268
00:24:20,730 --> 00:24:26,910
的模型，因为它是由伦茨（Lunz）发明的。 
model because it was invented by Lenz
not easing easing was the graduate

269
00:24:26,910 --> 00:24:33,090
借给这个项目的学生在1925年将其作为一个项目，他为此解决了
student who lends gave this to as a
project in 1925 and he solved this for

270
00:24:33,090 --> 00:24:38,400
他的博士学位研究项目，现在我要在一维的情况下
his PhD project and what in one
dimensional case now I'm gonna make a

271
00:24:38,400 --> 00:24:43,170
这个缓动模型很重要，因为这个缓动模型非常简单
big deal about this easing model because
this easing model it's extremely simple

272
00:24:43,170 --> 00:24:47,700
但是它也非常复杂，很简单，因为在每个站点上只有
and yet it's also extremely complex it's
simple because on each site there's only

273
00:24:47,700 --> 00:24:50,820
一个自由度，你要么不指向上方，要么指向下方
one degree of freedom and you don't
either it points up or it points down

274
00:24:50,820 --> 00:24:54,360
没有其他可能性，所以这是非常简单的自由度
there's no other possibilities so it's
very simple degrees of freedom and yet

275
00:24:54,360 --> 00:24:58,590
它只耦合到它的邻居，但是这个模型的物理原理是
and it couples only to its neighbor and
yet the physics of this model are

276
00:24:58,590 --> 00:25:02,490
非常复杂，说这个世界可能并不夸张
extremely complex and it's probably not
an exaggeration to say the world has

277
00:25:02,490 --> 00:25:06,960
从这个模型中学到了更多关于统计力学的知识
learned more about statistical mechanics
from this one model than from anything

278
00:25:06,960 --> 00:25:12,990
否则我们可能会进行研究，以便在1925年通过一维轻松解决此模型
else we possibly studied so easing solve
this model in 1925 in one-dimension

279
00:25:12,990 --> 00:25:17,550
在二次世界大战期间，萨加尔非常有名地设法解决了这一难题， 
during world war ii on sagar very
famously managed to solve it without

280
00:25:17,550 --> 00:25:22,410
二维磁场没有人同时解决过二维模型
magnetic field in two dimensions no one
has solved the model either in two

281
00:25:22,410 --> 00:25:25,920
具有磁场的尺寸或三维尺寸或更高尺寸
dimensions with a magnetic field or in
three dimensions or any higher dimension

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00:25:25,920 --> 00:25:30,000
从那时起，已经有很多研究了成千上万的论文
since then so it's been a lot of study
thousands and thousands of papers have

283
00:25:30,000 --> 00:25:33,600
从那时起就已经写过关于该模型的文章，我应该在最后一提
been written about this model since then
and I should mention just in the last

284
00:25:33,600 --> 00:25:37,950
几年来，人们对解决这种模式进行了真正英勇的攻击
few years there's been a really valiant
assault against solving this model in

285
00:25:37,950 --> 00:25:42,030
三个维度，也许几年之内可能会有解决方案
three dimensions and maybe within a few
years there will be a solution maybe not

286
00:25:42,030 --> 00:25:47,190
我们可以保持乐观，但是这个模型如此有趣的原因是
we can be optimistic but the reason that
this is this model is so interesting is

287
00:25:47,190 --> 00:25:51,390
因为它展示了很多有趣的物理学，尤其是关于
because it shows an awful lot of
interesting physics particularly about

288
00:25:51,390 --> 00:25:55,170
即使在此模型中也只有一个自由度
phase transitions even in this this
model it only has one degree of freedom

289
00:25:55,170 --> 00:26:02,370
在每个站点上的每个网站上都可以，所以我们将回到实际的
on each on each site okay so we'll come
back to the easing model actually in the

290
00:26:02,370 --> 00:26:05,410
下节课，然后我们会问
next
lecture and then we will ask the

291
00:26:05,410 --> 00:26:11,350
问题，我们要把它放在这里，不，我们把它放在这里，好
question we're going to put it here no
let's put it over here here okay

292
00:26:11,350 --> 00:26:15,880
对于我们写下的任何模型，如果有
for any model that we write down so
we're starting here if we have a

293
00:26:15,880 --> 00:26:25,900
哈密​​顿量是海森堡形式的H加各向异性形式，如果
Hamiltonian which is H of the Heisenberg
form plus the anisotropy form and if the

294
00:26:25,900 --> 00:26:29,040
各向异性很强，我们可以用缓动代替组合
anisotropy is strong we can just replace
the combination with the easing

295
00:26:29,040 --> 00:26:39,880
哈密​​顿量的确使整个系统对准系统将直线对准T 
Hamiltonian does does the whole system
align the system align a line at T

296
00:26:39,880 --> 00:26:46,360
等于零，在模型中答案是
equals zero and in the model the answer
is yes

297
00:26:46,360 --> 00:27:01,660
在模型中是，但在实际磁体中不是，在实际磁体中不是，不是所有的自旋
in model yes but in real magnets no so
in real magnets not all the spins in the

298
00:27:01,660 --> 00:27:06,040
系统实际上确实相互对齐，并且要了解为什么这样做，我们必须
system actually do align with each other
and to understand why this is we have to

299
00:27:06,040 --> 00:27:10,090
意识到我们实际上在我们的哈密顿量中遗漏了一些重要的东西
realize that we actually left something
important out of our Hamiltonian so

300
00:27:10,090 --> 00:27:14,980
让我们做一个Gedanken实验让我们假设你有一个很大的
let's do a little bit of a Gedanken
experiment let's imagine you have a big

301
00:27:14,980 --> 00:27:18,760
一些磁性材料的另一块大一些磁性材料的
chunk of some magnetic material another
big chunk of some magnetic material the

302
00:27:18,760 --> 00:27:22,750
这一个有一个磁化这里这个一个有一个磁化然后
this one has a magnetization here this
one has a magnetization here then you

303
00:27:22,750 --> 00:27:26,650
将这两块材料很好地整合在一起
bring these two chunks of materials
together well what happens well you've

304
00:27:26,650 --> 00:27:30,010
可能是当您还是个孩子的时候，当您带他们去做的时候
probably done this when you were a kid
at some point and when you bring them

305
00:27:30,010 --> 00:27:34,240
在一起，您意识到他们想要像这样坐着
together you realize that they want to
sit like this they want to sit

306
00:27:34,240 --> 00:27:37,930
从头到尾，因为它们具有偶极相互作用，所以磁铁想
head-to-tail because they have a dipolar
interaction and so the magnets want to

307
00:27:37,930 --> 00:27:41,650
并肩而终，他们真的不想在一起
come together head to tail and they
really don't want to come together head

308
00:27:41,650 --> 00:27:46,480
朝着这样的方向前进，这告诉我们，我们省略了一些重要的内容
to head like this so this is telling us
that we we left out some important piece

309
00:27:46,480 --> 00:27:54,940
物理和我们遗漏的东西我们遗漏了磁能磁能
of physics and what we left out we left
out magnetic energy magnetic energy

310
00:27:54,940 --> 00:28:02,880
这是思考它或偶极-偶极相互作用的一种方式
that's one way of thinking about it or
dipole-dipole interaction

311
00:28:08,110 --> 00:28:14,240
在上一讲中，我提到如果您正在考虑两个旋转
in the last lecture I mentioned that if
you are thinking about two spins in a

312
00:28:14,240 --> 00:28:18,980
给定原子并询问他们是否要对准偶极-偶极子
given atom and asking whether they want
to align or not the dipole-dipole

313
00:28:18,980 --> 00:28:23,900
两个自旋和原子之间的相互作用很小，因此您可以忽略它
interaction between two spins and atom
is insanely small so you could ignore it

314
00:28:23,900 --> 00:28:28,130
是的，但是如果您有很大一部分材料，那么您将拥有巨大的数量
that's true but if you have a big chunk
of a material you have an insanely large

315
00:28:28,130 --> 00:28:34,070
每个那里的电子数量极少的偶极矩
number of electrons there each with an
insanely small amount of dipole moment

316
00:28:34,070 --> 00:28:37,040
而你把它们放在一起实际上变成了一个相当大的偶极矩
and you put them all together actually
becomes a reasonably big dipole moment

317
00:28:37,040 --> 00:28:41,720
而您确实需要担心这种偶极子的能量
and you do have to worry about this
dipole dipole energy another way of

318
00:28:41,720 --> 00:28:48,860
想一想完全相同的物理学，如果您认为
thinking about it exactly the same
physics is to well okay if you think

319
00:28:48,860 --> 00:28:53,480
关于这两张图片中的磁力线这里的磁力线
about the magnetic field lines in these
two pictures here magnetic field lines

320
00:28:53,480 --> 00:28:57,650
在这张照片中看起来像这样，而在这张照片中，磁性
look kind of like this in this picture
whereas in this picture the magnetic

321
00:28:57,650 --> 00:29:01,520
磁力线看起来像这样，您还记得磁能
field lines kind of look like this and
you remember that the magnetic energy

322
00:29:01,520 --> 00:29:08,450
总磁能为B的积分D 3 R平方超过2微米， 
total magnetic energy is integral D 3 R
of B squared over 2 mu naught and

323
00:29:08,450 --> 00:29:12,740
如果您长时间对准偶极子，则总的d平方要小得多
there's the total d squared is a lot
smaller if you long align your dipoles

324
00:29:12,740 --> 00:29:17,930
从头到尾，所以您通过放置偶极子来减少磁能
head to tail so you're reducing magnetic
energy by putting your dipoles

325
00:29:17,930 --> 00:29:22,730
以这种方式从头到尾，因此在实际身体中实际发生的情况
head-to-tail in this way so what
actually happens in a real physical

326
00:29:22,730 --> 00:29:30,100
系统，所以我们现在可以写出h等于H Heisenberg Heisenberg加h各向异性
system so we can now write h equals H
Heisenberg Heisenberg plus h anisotropy

327
00:29:30,100 --> 00:29:36,860
各向异性加上我们将添加H偶极相互作用或磁性
anisotropy plus we're gonna add H
dipolar interaction or magnetic magnetic

328
00:29:36,860 --> 00:29:44,360
相互作用的磁能，那么实际发生的是你得到的是你的
interaction magnetic energy then what
actually happens is you get here's your

329
00:29:44,360 --> 00:29:50,240
大型系统有时系统会分解为所谓的域
big system the system will break up into
what are known as domains sometimes

330
00:29:50,240 --> 00:29:59,330
所谓的老虎钳域老虎钳域
called vise domains vise domains where
some point up some point down some point

331
00:29:59,330 --> 00:30:03,920
这样，他们会分解成许多小领域现在发生了什么
up like this they'll break up into many
little domains now what's going on here

332
00:30:03,920 --> 00:30:10,190
在本材料的这一点上，您将在旁边旋转
at some point in this in this material
you will have up spins right next to

333
00:30:10,190 --> 00:30:14,630
向下旋转，这使哈密顿语中的海森堡术语非常不愉快
down spins and that makes the Heisenberg
term in the Hamiltonian very unhappy

334
00:30:14,630 --> 00:30:16,909
因为海森堡超过了汉密尔顿
because that Heisenberg out term of the
Hamilton

335
00:30:16,909 --> 00:30:23,539
一旦上升旋转成为下一个上升旋转，那么这会产生一些能源成本
once the up spins to be next up spins so
there's some energy cost along that that

336
00:30:23,539 --> 00:30:27,349
沿着那个过渡，这就是所谓的域墙，也许我什至会
transition along that what's what's
known as a domain wall maybe I'll even

337
00:30:27,349 --> 00:30:30,919
写下这是一个过渡，称为
write that down
this is a the transition is called a

338
00:30:30,919 --> 00:30:40,489
两者之间的畴壁，所以有一些海森堡能量来自旋
domain wall between the two so there's
some Heisenberg energy to have up spins

339
00:30:40,489 --> 00:30:45,049
靠近畴壁上的向下旋转，但您牺牲了海森堡能量
next to down spins on the domain wall
but you sacrifice that Heisenberg energy

340
00:30:45,049 --> 00:30:50,090
为了节省磁能或偶极能， 
on the domain wall in order to save
magnetic energy or dipolar energy for

341
00:30:50,090 --> 00:30:57,470
如果您有不同类型的各向异性，整个系统就可以了
the whole system as a whole okay if if
you had a different type of anisotropy

342
00:30:57,470 --> 00:31:03,049
我寻找你的作品，例如立方各向异性域壁
and I sought your piece for example
cubic anisotropy the domain wall

343
00:31:03,049 --> 00:31:10,899
结构可能看起来有所不同，您可能会有类似如下的内容
structure might look different you might
have something that looks like like this

344
00:31:11,229 --> 00:31:15,320
在此指向正确的位置，它像这样向下产生
where this points up this points right
it spawns left down down like that and

345
00:31:15,320 --> 00:31:19,970
这是将每种偶极子从头到尾与下一个偶极子放在一起
this was putting each dipole sort of
head to tail with the next dipole that

346
00:31:19,970 --> 00:31:28,070
现在可以更好地提高能量在这种情况下发生的是
improves the energy even better now what
happens in this case is that overall the

347
00:31:28,070 --> 00:31:32,989
这些磁铁之一的总磁化强度现在又为零，因为您
total magnetization of one of these
magnets is now zero again because you

348
00:31:32,989 --> 00:31:36,649
上域与下域一样多，却没有
have just as many up domains as you have
down domains and you get no

349
00:31:36,649 --> 00:31:40,549
完全磁化，然后您可能会知道挠头说好
magnetization at all and then you might
you know scratch your head and say well

350
00:31:40,549 --> 00:31:43,879
等一下，我知道磁铁存在，你知道，那我们要怎么做
wait a second I know magnets exist and
you know so how is it we're gonna get

351
00:31:43,879 --> 00:31:47,690
马格努斯是我们磁铁中的罪恶，所以现在我们必须开始思考
Magnus a ssin out of our magnets and so
now we have to start thinking a little

352
00:31:47,690 --> 00:31:50,989
仔细一点，我们可以做的第一件事实际上我想我有一张幻灯片
bit carefully the first thing we can do
in actually I guess I have a slide

353
00:31:50,989 --> 00:31:54,919
比再次绘制图片更好，您可以做的第一件事就是
better than drawing the pictures again
the first thing you can do is you can

354
00:31:54,919 --> 00:32:01,399
想象一下，如果您在系统外部添加磁场，那么
imagine if you add a magnetic field
externally to the system the size of the

355
00:32:01,399 --> 00:32:05,450
领域，我们会做出反应，布雷特，你知道如果你的磁场
domains will we react will Breit and you
know if the magnetic field that you

356
00:32:05,450 --> 00:32:10,879
应用指向上，您将获得更多的向上域名，而不是向下的域名，您将获得
apply is pointing up you'll get more up
domains than down domains and you'll get

357
00:32:10,879 --> 00:32:15,889
再次净磁化，但是如果您去除磁场， 
a net magnetization again but still if
you take away the magnetic field the

358
00:32:15,889 --> 00:32:20,239
领域回到这里的旧平衡状态，您将一无所有
domains move back to their old
equilibrium over here and you'll have no

359
00:32:20,239 --> 00:32:24,259
磁化，所以我们认为这应该是费罗
magnetization so this thing that we
thought was supposed to be a Ferro

360
00:32:24,259 --> 00:32:28,580
磁铁实际上是对位磁铁，它可以是非常好的功率磁铁， 
magnet is in fact a para magnet it can
be a very good power magnet which gives

361
00:32:28,580 --> 00:32:30,990
您会为非常小的磁铁带来很高的磁化强度
you a very high magnetization for a very
small magnet

362
00:32:30,990 --> 00:32:36,210
磁场，但不幸的是，它仍然是功率磁铁，所以我们将如何获得
field but it's still unfortunately a
power magnet so how are we going to get

363
00:32:36,210 --> 00:32:41,970
即使在没有施加磁场的情况下，它也具有磁性
this thing to be magnetic even in the
absence of an applied magnetic field so

364
00:32:41,970 --> 00:32:46,530
制作真正磁铁的整个技巧就是60冰箱那种东西
the whole trick to making a real magnet
the kind of thing that 60 refrigerator

365
00:32:46,530 --> 00:32:51,570
是找到一种方法来防止域从此配置退回
is to find a way to prevent the domains
from going back from this configuration

366
00:32:51,570 --> 00:32:56,429
以此配置为例，您引用在高磁场中训练磁体的方式， 
to this configuration so you quote train
a magnet in a high magnetic field so it

367
00:32:56,429 --> 00:32:59,370
进入这些配置之一，其中更多的旋转
gets to one of these configurations
where there's more up spins the

368
00:32:59,370 --> 00:33:03,179
公告是这张图片中的上升时刻和下降时刻，但随后您
announcements are up moments and down
moments in this picture but then you

369
00:33:03,179 --> 00:33:08,240
找到一种方法来防止域移回，这就是所谓的
find a way to prevent the domains from
moving back this is what's called

370
00:33:08,240 --> 00:33:20,970
钉住畴壁钉住畴壁以及您的方式
pinning pinning of domain walls pinning
domain walls and the way it's you

371
00:33:20,970 --> 00:33:28,290
通常会按此顺序固定域墙，以及是否正在尝试
typically pin a domain wall is with this
order and whether one is trying to

372
00:33:28,290 --> 00:33:32,070
设计一个磁铁，让您知道我们在电动机中的用途，无论您是否尝试
design a magnet for you know for our use
in electrical motors whether you trying

373
00:33:32,070 --> 00:33:34,620
做一个磁铁，可以粘在冰箱上
to make a magnet that will stick to your
refrigerator where they're trying to

374
00:33:34,620 --> 00:33:39,150
制作磁盘驱动器的磁铁制作优质磁铁的整个技术是
make a magnet for a magnetic disk drive
the whole art to making good magnets is

375
00:33:39,150 --> 00:33:43,980
弄清楚如何使无序现象阻止磁畴移动
to figure out how to make the disorder
prevent the magnetic domains from moving

376
00:33:43,980 --> 00:33:46,920
回到原始配置，磁化强度回到
back to their original configuration
where the magnetization goes back to

377
00:33:46,920 --> 00:33:51,540
零好吧，为什么这种疾病会帮助您呢，所以这里是
zero okay so why is it the disorders
gonna help you alright so here's here's

378
00:33:51,540 --> 00:33:56,100
应该在这里显示的图片，所以我提到这很轻松
the picture that's supposed to show us
here so this is an easing did I mention

379
00:33:56,100 --> 00:34:00,030
关于放宽还是结冰的整个过程我不是说我做到了吗
the whole business about easing versus
icing I didn't say that did I did I did

380
00:34:00,030 --> 00:34:04,620
我说那好吧，让我告诉你，德国人很放松，显然是这样
I say that okay so let me tell you so
easing was German and apparently the way

381
00:34:04,620 --> 00:34:09,899
我认为这在德国正在减少，但随后他
it's pronounced is is is easing in
Germany I believe but then after he

382
00:34:09,899 --> 00:34:13,889
完成他的论文，他去了美国，人们叫他
finished his dissertation he went to the
United States and people called him

383
00:34:13,889 --> 00:34:17,250
为他的余生锦上添花，所以美国每个人都呼吁
icing for the rest of his life
and so everyone the United States calls

384
00:34:17,250 --> 00:34:20,790
在欧洲，每个人都将其称为Isaac模型
it the Isaac model everyone in Europe
calls it the easing model I'll probably

385
00:34:20,790 --> 00:34:24,899
永远不会弄直，但我认为称它为宽松是正确的
never get it straight but I think it is
correct to call it to call it easing

386
00:34:24,899 --> 00:34:30,000
无论如何，所以这是一个缓和的磁铁，所有旋转都指向上或下
anyway so this is an easing magnet all
the spins are pointing either up or down

387
00:34:30,000 --> 00:34:35,369
相互作用的高点，自旋之间的相互作用不愉快
and the highs in the interaction the
interaction between spins is unhappy

388
00:34:35,369 --> 00:34:40,530
沿着域壁，我在此处绘制了所有不愉快的红色旋转
along the domain wall and I've drawn all
the unhappy spins in red here where the

389
00:34:40,530 --> 00:34:45,210
向上旋转遇到向下旋转好吗，如果您从上到下进行计数
up spins meet the down spins okay and if
you count them from top to bottom

390
00:34:45,210 --> 00:34:52,230
这些红色债券中有12个存在不愉快的联系
there are 12 of these red bonds where
there's an unhappy connection now in

391
00:34:52,230 --> 00:34:56,730
这张图片有一个绿色的小原子，应该是缺陷
this picture there's a little green atom
there which is supposed to be a defect

392
00:34:56,730 --> 00:35:01,890
如果您碰巧在域上移动，则根本不会旋转
someplace where there's no spin at all
if you happen to move over the domain

393
00:35:01,890 --> 00:35:06,570
墙到这里不同的位置，这样他们就可以通过缺陷
wall to a different position over here
so they goes through the defect there's

394
00:35:06,570 --> 00:35:12,270
现在只有10个红色债券而不是12个，因此如果
only 10 red bonds now not 12
so the energy actually drops if the

395
00:35:12,270 --> 00:35:17,460
畴壁经历缺陷，畴壁穿过的能量较低
domain wall goes through the defect it's
a lower energy for domain walls to go

396
00:35:17,460 --> 00:35:22,710
通过缺陷，以便他们想要坚持缺陷，这就是您固定域的方式
through defects so they want to stick on
the defect and that's how you pin domain

397
00:35:22,710 --> 00:35:28,320
通过一次在系统中放置缺陷来使墙壁具有某种混乱
wall with a with some disorder by
putting defects in the system the once

398
00:35:28,320 --> 00:35:32,040
畴壁在这种配置下，您会带走磁性
the the domain walls are in this
configuration you take away the magnetic

399
00:35:32,040 --> 00:35:35,160
场，但他们不能后退，因为他们不得不放弃一些
field but then they can't move back
because they would have to give up some

400
00:35:35,160 --> 00:35:39,330
能量回到原来的位置，因为它们被卡在
energy to move back to their original
position because they're stuck on the

401
00:35:39,330 --> 00:35:43,560
缺陷好吧，这是一般的物理原理。 
defects okay that's the general the
general physics of how it is you make a

402
00:35:43,560 --> 00:35:49,830
到目前为止M都不为零的真实磁体，所以很好，所以自
real magnet which has M not equal to
zero so far so good okay so since the

403
00:35:49,830 --> 00:35:54,390
您知道基本物理学确实全部包裹在
you know the fundamental physics is
really all wrapped up in the physics of

404
00:35:54,390 --> 00:35:58,740
域名墙以及域名墙的移动方式值得思考
the domain wall and how the domain wall
moves it's worth thinking about the

405
00:35:58,740 --> 00:36:02,460
磁畴壁更仔细一点，结果发现大多数磁铁
domain wall a little bit more carefully
and it turns out that most magnets in

406
00:36:02,460 --> 00:36:06,930
自然不是各向异性强的发烧型，但有
nature are not of the eezing type where
the anisotropy is strong but there are

407
00:36:06,930 --> 00:36:12,720
这种类型的各向异性很弱，所以我们必须考虑一下
this type where the anisotropy is quite
weak so we have to sort of think about

408
00:36:12,720 --> 00:36:18,420
领域壁垒发生的情况不是在宽松限制内，而是在周末我
what happens in for domain walls in not
in the easing limit but in the weekend I

409
00:36:18,420 --> 00:36:22,410
看到这里是极限，毫无疑问，域名墙看起来是什么
saw to be limit over here there's no
question of what a domain wall looks

410
00:36:22,410 --> 00:36:26,520
就像放宽限制一样，您只是知道旋转，然后它们相遇
like for the easing limit you just have
you know up spins and then they meet

411
00:36:26,520 --> 00:36:30,660
向下旋转，中间没有有趣的事情发生，但是在这里
down spins and nothing interesting
happens in between but over here where

412
00:36:30,660 --> 00:36:34,830
我们有，如果您在这里旋转，而我有，我可以寻求重复
we have we can I sought repeat if you
have up spins over here and you have

413
00:36:34,830 --> 00:36:40,349
向下旋转的方式请记住，为此要做的最重要的事情
down spins way over here remember that
the most important thing to do for this

414
00:36:40,349 --> 00:36:44,280
一周的各向异性极限是使每个人尽可能保持一致
week anisotropy limit is to keep
everyone as aligned as possible with

415
00:36:44,280 --> 00:36:48,060
他们的邻居，所以你从上旋转到下旋转的方法就是
their neighbor so the way you get from
up spin to down spin is to just slightly

416
00:36:48,060 --> 00:36:54,210
将旋转旋转一次，使其与邻居相邻一点，最终使其旋转
rotate each spin just a little bit from
his neighbor and eventually make it from

417
00:36:54,210 --> 00:36:57,890
向上指向下方并缓慢旋转
pointing up to pointing down with a slow
rotation okay

418
00:36:57,890 --> 00:37:03,920
这就是所谓的，说超过n次旋转好吧，我没有
and this is what's known as let's say
this goes over n spins okay I didn't

419
00:37:03,920 --> 00:37:07,450
画得很好，但是你就明白了，这就是所谓的砌墙
draw that very well but you get the idea
and this is what's known as a block wall

420
00:37:07,450 --> 00:37:16,730
在Felix阻塞后，阻塞墙或在AL墙中钉墙猫墙
block wall or or in the AL wall nail
wall meow wall after Felix block the

421
00:37:16,730 --> 00:37:20,870
同样是布洛赫（Bloch）定理的人，而路易安娜（loujain al）是意识到我们应该
same Bloch's theorem guy and loujain al
the guy who realized that we should have

422
00:37:20,870 --> 00:37:25,250
反铁磁体，所以让我们尝试计算能量和
antiferromagnets so let's try to
calculate the energy and the width of

423
00:37:25,250 --> 00:37:30,710
这个方块好吧，方块墙和
this block okay there is a slight
difference between a block wall and in

424
00:37:30,710 --> 00:37:36,010
 AL墙取决于旋转的旋转是否在
the AL wall it depends on whether the
rotation of the spin is in the plane of

425
00:37:36,010 --> 00:37:41,690
这些原子或者它垂直于原子平面，就知道
of these atoms or it's transverse to the
plane of the atoms it's you know it's

426
00:37:41,690 --> 00:37:44,600
这是一个细节，您可能不必担心，但是有一点点
it's a detail that you probably don't
have to worry about but there's a slight

427
00:37:44,600 --> 00:37:48,200
无论如何，两者之间的差异我想我在这里画的实际上是
difference between the two at any rate I
think what I've drawn here is actually a

428
00:37:48,200 --> 00:37:56,480
堵墙，让我们尝试计算该能量，因此这一能量
block wall so let's try to calculate the
energy of this so the energy in this one

429
00:37:56,480 --> 00:38:04,010
尺寸图片将是II猜测值减去J si点s I加1的总和
dimensional picture it's going to be sum
over I I guess minus J si dot s I plus 1

430
00:38:04,010 --> 00:38:10,220
在这里您可能会认为您可能会认为我遗漏了1/2的因数
and here you might have think you might
think that I've left out a factor of 1/2

431
00:38:10,220 --> 00:38:15,310
但是我没有，因为自从我在这里，我只是在一个维度上进行总结
but but I haven't because here since I'm
I'm summing over I only in one dimension

432
00:38:15,310 --> 00:38:23,090
 s1 s2现在只在一个学期出现，所以我得到1/2的因数，如果
s1 s2 only occurs in one term now okay
so I got the factor of 1/2 right and if

433
00:38:23,090 --> 00:38:30,470
我对齐所有对齐的自旋，然后得到II的总和，猜想我等于1到N 
I align all the spins aligned I then get
a sum over I I guess I equals 1 to N of

434
00:38:30,470 --> 00:38:35,150
每一个负J平方彼此对齐，并且
minus J s squared
every one is aligned with each other and

435
00:38:35,150 --> 00:38:43,850
如果我每次都扭曲-对齐，那么我将其称为
if I twist it each twist
- aligned I'm then gonna let's call that

436
00:38:43,850 --> 00:38:49,340
 Δe等于Δe扭转自旋所付出的能量
Delta e equals Delta e the amount of
energy you pay to twist the spin from

437
00:38:49,340 --> 00:38:56,450
从上到下将在I上求和等于J平方的N乘以1 
top to to bottom that will be sum over I
equals 1 to N of J s squared times 1

438
00:38:56,450 --> 00:39:02,210
减去theta的余弦值，所以每次您旋转一点自旋时
minus cosine of theta I so for each time
you twist the spin a little bit you have

439
00:39:02,210 --> 00:39:10,839
今天就向我支付这种余弦能量是可以的，所以如果那是theta我
to pay this sort of cosine energy today
to I is is okay so if one that's theta I

440
00:39:10,839 --> 00:39:15,249
旋转从一步到另一步的旋转，因此我们假设
the rotation of the spin from one step
to the next so let's assume that the

441
00:39:15,249 --> 00:39:21,909
 theta很小，如果我们需要从一路走到最左边
theta is small and if we need to get
from from all the way to the left all

442
00:39:21,909 --> 00:39:25,989
在n次旋转中向右转的方式让我们只声明所有Thetas为n之上的PI 
the way to right in n spins let's just
declare all the Thetas to be PI over n

443
00:39:25,989 --> 00:39:31,179
所以我们必须旋转pi旋转n步，所以说theta是PI超过N 
so we have to make a pi rotation and n
steps so we'll say theta is PI over N so

444
00:39:31,179 --> 00:39:37,859
余弦theta余弦theta大约是N的1减去1/2 PI 
cosine theta cosine theta is then
approximately 1 minus 1/2 PI over N

445
00:39:37,859 --> 00:39:45,219
如果我将其插入此处，则平方，我将得到总共n次旋转
squared if I plug that into here I'll
get a total of n spins I'm summing over

446
00:39:45,219 --> 00:39:54,519
我有J的平方，N的平方有1/2 PI，然后乘以
I have J s squared and 1/2 PI over N
squared I multiply that out I then get

447
00:39:54,519 --> 00:40:02,979
 PI在N上平方2 J平方，毫不奇怪，这告诉我
PI squared over 2 J s squared over N and
unsurprisingly this tells me that the

448
00:40:02,979 --> 00:40:08,829
如果我旋转此能量，则能量会降低，每次旋转所需的旋转会更平滑
energy is lower if I rotate this the the
spins more smoothly that each spin wants

449
00:40:08,829 --> 00:40:12,939
与他的邻居尽可能保持一致，所以如果我们只是
to be as aligned as possible with his
neighbor and so if we were only

450
00:40:12,939 --> 00:40:16,630
考虑到哈密顿量的这一部分，如果旋转它们会旋转
considering this part of the Hamiltonian
the spins would if they rotated they

451
00:40:16,630 --> 00:40:20,140
会无限地缓慢旋转，那样他们会很开心，但是他们
would rotate infinitely slowly and they
would be most happy that way but they

452
00:40:20,140 --> 00:40:24,429
有，但这必须与各向异性能量竞争，我看到了Trippy 
had but this has to compete with the
anisotropy energy and I saw trippy

453
00:40:24,429 --> 00:40:31,299
能量和各向同性，希望自旋直接指向上方
energy and an isotropy which wants the
spins to be either pointing directly up

454
00:40:31,299 --> 00:40:36,009
或直接下降，所以我们必须估计您要消耗多少能量
or directly down and so we have to
estimate how much energy you're going to

455
00:40:36,009 --> 00:40:41,799
支付在这堵墙中既不向上也不向下的n个旋转，这是
pay to have n spins in this wall which
are neither up nor down and okay this is

456
00:40:41,799 --> 00:40:46,599
一个非常粗略的近似值，但我们只能说，每次自旋不是
a rather crude approximation but we'll
just say that each spin that's not

457
00:40:46,599 --> 00:40:51,609
向上和向下指点，您要支付能量K s平方好，我的意思是这个数字是
pointing up and down you pay an energy K
s squared ok I mean this this number is

458
00:40:51,609 --> 00:40:55,209
可能偏离2倍或PI或类似的数值，但至少会
probably off by a factor of 2 or PI or
something like that but at least it will

459
00:40:55,209 --> 00:41:00,609
给我们正确的数量级，以便块壁e的总能量
give us the order of magnitude correctly
so the total energy of the block wall-e

460
00:41:00,609 --> 00:41:06,909
总的是海森堡能量PI的平方与2 J平方的平方之和
total is the sum of the Heisenberg
energy PI squared over 2 J s squared

461
00:41:06,909 --> 00:41:13,809
超过n加各向异性能量和Kappa平方，则我们必须
over n plus the anisotropy energy and
Kappa s squared and then we have to

462
00:41:13,809 --> 00:41:22,180
最小化等于0的总DN集，这使我们
minimize this de total DN set that equal
to 0 and that gives us

463
00:41:22,180 --> 00:41:28,970
区分我们只是得到n等于pi的平方根平方2 J 
differentiate that we just get n equals
square root of pi squared over 2 J over

464
00:41:28,970 --> 00:41:33,920
 Kappa，所以这告诉我们的是，如果各向异性
Kappa and so not surprisingly what this
is telling us is that if the anisotropy

465
00:41:33,920 --> 00:41:40,100
极小，而Heisenberg耦合极强
is extremely small then and the and the
Heisenberg coupling is extremely strong

466
00:41:40,100 --> 00:41:43,940
那么旋转会非常缓慢地旋转，而如果您处于另一个极限
then the spins rotate extremely slowly
whereas if you're in the other limit

467
00:41:43,940 --> 00:41:48,800
各向异性大而海森堡耦合小则
where the anisotropy is large and the
Heisenberg coupling is small then the

468
00:41:48,800 --> 00:41:54,410
自旋旋转的次数非常小n甚至可能直接从上到下旋转
spins rotate in a very small number n
maybe even directly from up to down in

469
00:41:54,410 --> 00:42:01,550
现在，一步一步地制作出真正的磁铁，通常情况下，您可以拥有一个
one in one step now in real magnets it's
very often the case often you can have a

470
00:42:01,550 --> 00:42:09,080
 n大于或等于100个原子的情况，因此您可以拥有
case where n is greater than or about
equal to 100 atoms so you can have these

471
00:42:09,080 --> 00:42:14,390
这些砌块墙或这些畴壁或钉子墙实际上相当
these block walls or these domain walls
or nail walls be actually quite quite

472
00:42:14,390 --> 00:42:18,640
现在，如果您开始考虑，这实际上非常重要
wide now this is actually quite
important if you start thinking about

473
00:42:18,640 --> 00:42:27,700
多晶材料多晶脆片晶体晶体晶体
polycrystalline material polycrystalline
crisps crystal crystalline crystalline

474
00:42:28,450 --> 00:42:36,350
磁铁，所以现在我们谈论的是许多与
magnets so now we're talking about lots
of little crystal lights separated from

475
00:42:36,350 --> 00:42:43,040
磁性材料彼此相互作用，如果晶体的大小轻一些
each other of magnetic material and if
the size of the crystal light a number

476
00:42:43,040 --> 00:42:47,510
穿过的原子数小于该魔数，即畴壁的大小
of atoms going across is less than this
magic number the size of the domain wall

477
00:42:47,510 --> 00:42:52,880
然后整个原子必须指向整个晶体光
then the whole atom the whole crystal
light has to point have its

478
00:42:52,880 --> 00:42:56,480
指向一个方向的磁化只能指向一个方向
magnetization pointing in just one
direction has to point in only one

479
00:42:56,480 --> 00:43:00,140
方向，您知道每个晶体我都可以指向不同的方向，但是每个
direction you know each crystal I can
point in a different direction but each

480
00:43:00,140 --> 00:43:03,320
晶体光只能指向一个方向，其原因是
crystal light has to be pointed only in
one direction and the reason for this is

481
00:43:03,320 --> 00:43:07,280
因为您在一个水晶灯中没有足够的空间来旋转
because you don't have enough space
within one crystal light to rotate the

482
00:43:07,280 --> 00:43:12,050
从一个方向旋转到另一个方向，它太僵硬了，你不知道
spin from one direction to another it's
too stiff you can't you know the the

483
00:43:12,050 --> 00:43:15,950
邻居之间的耦合太强，无法旋转
coupling between neighbors is too strong
in order to get the spins to rotate

484
00:43:15,950 --> 00:43:20,300
在一个水晶光中，您可能会认为这一百个原子相当
within one crystal light and you might
think that this hundred atoms is rather

485
00:43:20,300 --> 00:43:23,960
之所以小，是因为每个原子只有一个埃或两个埃，或者
small you know because each atom is only
an angstrom or two angstroms or

486
00:43:23,960 --> 00:43:27,380
但如果您在这个方向上有100个原子，在另一个方向上有100个原子
something but if you have 100 atoms in
this direction 100 atoms in another

487
00:43:27,380 --> 00:43:31,490
朝着另一个方向的100个原子突然间，你有一百万个原子
direction 100 atoms in another direction
all of a sudden you have a million atoms

488
00:43:31,490 --> 00:43:34,160
你说的是这些水晶灯实际上可以有很多
you're talking about so these crystal
lights can actually have an awful lot of

489
00:43:34,160 --> 00:43:36,410
它们中的原子，您仍然可以将它们视为
atoms in them and you can still think of
them as

490
00:43:36,410 --> 00:43:41,600
微观的单个磁铁指向一个方向还可以
microscopic individual magnets pointing
in just one direction okay so so so far

491
00:43:41,600 --> 00:43:44,450
太好了，我会忍受开玩笑的冲动
so good
I will resist the urge to make jokes

492
00:43:44,450 --> 00:43:51,800
关于一个方向好吧，让我们想象一下，我们采取其中一个
about one direction alright okay so
let's imagine that we take one of these

493
00:43:51,800 --> 00:43:58,220
水晶灯，我们将在此处应用陶瓷水晶灯，并假设
crystal lights and we are going to apply
ceramic crystal light here and suppose

494
00:43:58,220 --> 00:44:02,600
它在此ray z帽子中有一个防锯齿的P轴，然后它想要指向
it has an anti saw through P axis in
this ray z hat then it wants to point

495
00:44:02,600 --> 00:44:07,040
它是上下磁铁，为了争辩，我们将磁铁
it's magnet up or down and let's for the
sake of argument we'll put the magnetic

496
00:44:07,040 --> 00:44:12,920
在那个方向上的磁场以及能量，然后磁矩可以
field in that direction as well the
energy and then the magnetic moment can

497
00:44:12,920 --> 00:44:17,210
指向任何方向，我们喜欢晶体光的能量
be pointing in any direction we like the
energy of that crystal light is some

498
00:44:17,210 --> 00:44:22,070
 Enoch将会是负m点B，然后是各向异性能量
Enoch there's going to be minus m dot B
and then there's the anisotropy energy

499
00:44:22,070 --> 00:44:30,680
减去Kappa MZ的平方，希望磁化强度指向
minus Kappa MZ squared this that wants
the the magnetization to point either

500
00:44:30,680 --> 00:44:38,240
直接向上或直接向下，所以如果我们确定可以的话，如果
directly up or directly down so if we
decide that okay so if the angle between

501
00:44:38,240 --> 00:44:49,130
 M和B是Theta，那么我们可以将此能量重写为V naught减去MB余弦
M and B is Theta then we can rewrite
this energy as V naught minus M B cosine

502
00:44:49,130 --> 00:44:56,080
 theta减去Kappa M平方余弦平方theta，实际上我们甚至可以
theta minus Kappa M squared cosine
squared theta and in fact we might even

503
00:44:56,080 --> 00:45:03,830
令x等于余弦theta，那么我们得到的是一个零的负M的二次轴
let x equals cosine theta and then what
we have is a quadratic ax naught minus M

504
00:45:03,830 --> 00:45:13,160
 BX减去K M平方x平方，我们可以画出这个东西啊，我
B X minus Kappa M squared x squared and
we can plot this thing ah oops I'm

505
00:45:13,160 --> 00:45:16,850
房间快要用完了吗，我们可以将其绘制为theta的函数
running out of room aren't I okay we can
plot this thing as a function of theta

506
00:45:16,850 --> 00:45:21,470
或作为X的函数，所以这就是能量，让我们从B开始
or as a function of X so this is the
energy and let's start in the case of B

507
00:45:21,470 --> 00:45:25,010
等于零，所以您拥有晶体光和零磁场，并且您的
equals zero so you have your crystal
light and zero magnetic field and your

508
00:45:25,010 --> 00:45:31,370
此处的能量x等于减一减一，此处的能量x等于加
energy over here is x equals minus one
minus one and over here is x equals plus

509
00:45:31,370 --> 00:45:38,180
我们这里拥有的是x等于减1是theta等于pi x等于
one what we have here is so x equals
minus one is theta equals pi x equals

510
00:45:38,180 --> 00:45:43,130
加一是theta等于零，所以这就是磁化强度
plus one is theta equals zero so this
over here is the magnetization pointing

511
00:45:43,130 --> 00:45:50,180
向下和上方，我们的晶体光的磁化指向上方
down and over here we have the crystal
light with the magnetization pointing up

512
00:45:50,180 --> 00:45:56,090
能量是二次方像这样所以有两个稳定的
and the energy is quadratic looks kind
of like this so there's two stable

513
00:45:56,090 --> 00:46:00,080
点这里的稳定点是使磁化强度指向下方
points the stable point here is to have
the magnetization pointing down in the

514
00:46:00,080 --> 00:46:03,200
这里的稳定点是使磁化指向上方，这非常重要
stable point here is to have the
magnetization pointing up and it's much

515
00:46:03,200 --> 00:46:06,380
让磁化指向任何其他方向不太高兴，这是
less happy to have the magnetization
pointing in any other direction this is

516
00:46:06,380 --> 00:46:12,320
不足为奇，因为它是各向异性轴想要夜晚
not surprising because it's the
anisotropy axis wants the the night

517
00:46:12,320 --> 00:46:18,070
磁化点向上或向下都好现在让我们添加一个非零磁场
ization point either up or down okay
now let's add a non zero magnetic field

518
00:46:18,070 --> 00:46:25,150
好吧，现在让我们让V等于零或小于零但不等于零
okay so now we'll let V naught equal to
zero or be small but not equal to zero

519
00:46:25,150 --> 00:46:30,610
等于零，所以现在又是收获，我们有一个抛物线，它仍然是二次方
equals zero so now it's Reap lot again
we have a parabola it's still quadratic

520
00:46:30,610 --> 00:46:37,340
但是抛物线现在因为能量中的线性项而移动了
but the parabola is now shifted because
of the linear term in that in the energy

521
00:46:37,340 --> 00:46:42,530
这样抛物线的峰值将不再位于中心
so that the peak of the parabola will
not be in the center anymore will be

522
00:46:42,530 --> 00:46:47,660
偏心，所以我们将得到一个像这样的抛物线，在这里我们再次
off-center so we'll get a parabola looks
like this and again over here what we

523
00:46:47,660 --> 00:46:52,040
即使磁场指向上方，磁化强度仍指向下方
have is magnetization pointing down even
though the magnetic field is pointing up

524
00:46:52,040 --> 00:46:56,750
在这里，我们的磁化指向上方，磁铁和
and here we have the magnetization
pointing up and the magnet and the

525
00:46:56,750 --> 00:47:01,520
磁场指向上方，因此此点具有磁化指向
magnetic field pointing up so this point
here having the magnetization pointing

526
00:47:01,520 --> 00:47:07,360
在相同的磁场方向上，这绝对是稳定的最小值
in the same direction of magnetic field
this is definitely the stable minimum

527
00:47:08,470 --> 00:47:17,660
而这里的这一点是亚稳态的，以便从
whereas this point over here is
metastable in order to get from the

528
00:47:17,660 --> 00:47:21,380
磁化的亚稳态情况指向与
metastable case of the magnetization
pointing in the opposite direction as a

529
00:47:21,380 --> 00:47:25,310
磁场以确保能够下降到此处
magnetic field in order to secure to get
down to here where it would rather be it

530
00:47:25,310 --> 00:47:31,370
必须克服激活障碍，这意味着您必须承担所有
has to get over this activation barrier
and this means you have to take all of

531
00:47:31,370 --> 00:47:35,110
您的原子中可能含有一百万个这些原子，并以某种方式将它们全部翻转
your atoms with maybe a million of these
atoms and somehow flip them all over

532
00:47:35,110 --> 00:47:40,640
同时进行热或量子隧穿，这是一个过程
simultaneously either thermally or by a
quantum tunneling and that's a process

533
00:47:40,640 --> 00:47:44,470
这是如此的困难，以至于在低温下它可能永远不会发生，所以
that's so difficult that at low
temperature it may never happen so the

534
00:47:44,470 --> 00:47:51,020
这些你可以拥有这些磁铁的小晶体在
these you can have these little crystals
of magnets have their magnetic in the

535
00:47:51,020 --> 00:47:56,660
现在方向错误，让我们再加一点磁场
wrong direction now let's turn up the
magnetic field a little bit more so now

536
00:47:56,660 --> 00:48:05,670
我们又有一个大的磁场B又有一个抛物线
we have a large magnetic field large B
again we have a parabola but the met but

537
00:48:05,670 --> 00:48:09,870
抛物线的最大值一直移到左侧
the maximum of the parabola has been
shifted all the way off to the left this

538
00:48:09,870 --> 00:48:14,250
 X是负1，这是x等于加1，抛物线的最大值超过了
X is minus 1 this is x equals plus 1 and
the maximum of the parabola is way over

539
00:48:14,250 --> 00:48:22,380
在这里离开情节，所以这一点在这里，磁化指向
here off the plot and so this point here
with the magnetization pointing in the

540
00:48:22,380 --> 00:48:27,420
磁场的相反方向限制现在变得不稳定，而
opposite direction limit of the magnetic
field is now unstable and whereas this

541
00:48:27,420 --> 00:48:32,250
此处的唯一点是磁化强度指向相同的唯一稳定点
point over here is the only stable point
with the magnetization pointing the same

542
00:48:32,250 --> 00:48:36,960
磁场方向也可以，所以如果磁场足够大
direction as a magnetic field ok so if
the magnetic field is turned up enough

543
00:48:36,960 --> 00:48:41,880
然后您可以将所有Magna zatia翻转过来，指向
then you can flip over all of the Magna
zatia's to point in the direction of the

544
00:48:41,880 --> 00:48:48,330
磁场很清楚是如何运作的，所以这是你的照片
magnetic field is that clear how that
works ok so this is a picture you've

545
00:48:48,330 --> 00:48:52,920
之前看到的是所谓的硬铁磁体的图片，也许我
seen before it's a picture of a
so-called hard Ferro magnet maybe I

546
00:48:52,920 --> 00:49:02,130
甚至应该写下这个词，因为它经常用硬铁磁性
should even write that word down because
it's used often hard Ferro magnet hard

547
00:49:02,130 --> 00:49:08,520
铁磁体是当您实际上B中的M不等于0时， 
Ferro magnet is when you actually have M
not equal to 0 in B equals 0 and the way

548
00:49:08,520 --> 00:49:12,240
你会得到坚硬的铁磁体，我们知道了如何使你变得坚硬
you get hard ferromagnets you know we
explained that how you could get hard

549
00:49:12,240 --> 00:49:16,290
通过固定畴壁来获得铁磁体，但您也可以考虑
ferromagnets by pinning the domain walls
but you can also think about getting

550
00:49:16,290 --> 00:49:20,940
含有很多微晶的硬铁​​磁体，您需要
hard ferromagnets from having lots of
little crystallites and they you need to

551
00:49:20,940 --> 00:49:25,230
为了推动微晶翻转，你必须给它们一些
in order to push the crystallites to
flip over you have to give them some

552
00:49:25,230 --> 00:49:28,500
矫顽场，你必须给他们有限的磁场
coercive field you have to give them a
finite magnetic field in the wrong

553
00:49:28,500 --> 00:49:32,520
方向和相反的方向，以使它们全部翻转
direction and in the opposite direction
to get them to all flip over if you just

554
00:49:32,520 --> 00:49:35,730
在不翻转的方向上给它一个小的磁场
give it a small magnetic field in the
other direction they don't flip over and

555
00:49:35,730 --> 00:49:39,570
如果您考虑一下，这就是这些磁铁的磁滞回线的原因
this is what gives these magnets
hysteresis loops now if you think about

556
00:49:39,570 --> 00:49:43,950
一秒钟，您意识到将图片固定在
it for a second you realize that this
picture of pinning domain walls in a

557
00:49:43,950 --> 00:49:47,580
水晶磁铁，此图片显示在哪里该图片在哪里
crystalline magnet this picture oops
where to go this picture here where the

558
00:49:47,580 --> 00:49:51,150
畴壁卡在其位置，因为它具有能量激活
domain wall is stuck on its position
because it has an energy activation

559
00:49:51,150 --> 00:49:57,360
离开该位置的障碍，在此位置原子使它降低
barrier to get off of that that position
here where the atom gives it a lower

560
00:49:57,360 --> 00:50:01,980
能量，如果畴壁达到那个点，则与
energy if the domain wall goes to that
that point it's extremely similar to

561
00:50:01,980 --> 00:50:04,980
我们在这里拥有的所有这些小水晶灯唯一的区别
what we have here with all these little
crystal lights the only difference here

562
00:50:04,980 --> 00:50:09,300
就是您可以认为，在水晶灯的作用下，畴壁总是
is that you can think with the crystal
lights the domain walls are always

563
00:50:09,300 --> 00:50:12,600
在微晶之间，如果您想以某种方式思考
between the crystallites if you want to
think of it that way that some crystal

564
00:50:12,600 --> 00:50:14,380
灯会指向某些方向
lights will point in one direction in
some

565
00:50:14,380 --> 00:50:17,950
将指向另一个方向并移动域墙，您必须翻转
will point in the other direction and to
move the domain wall you have to flip

566
00:50:17,950 --> 00:50:22,210
多于一个的微晶，所以它的物理原理极其相似
over one more crystallite so it's
extremely similar physics the moral of

567
00:50:22,210 --> 00:50:26,710
故事是，为了得到真正的磁铁，硬铁磁铁会以某种方式
the story is that in order to get a real
magnet a hard Ferro magnet somehow or

568
00:50:26,710 --> 00:50:30,070
其他您是否必须使系统混乱
other you have to have disorder in your
system whether it's making the system

569
00:50:30,070 --> 00:50:34,810
进入小小的水晶灯或放置障碍物，它会固定
into small little crystal lights or
putting disorder and it's going to pin

570
00:50:34,810 --> 00:50:39,880
域名墙的位置还可以，今天就完成了
the position of the domain walls okay
that's all for today I will see you is

571
00:50:39,880 --> 00:50:44,060
是星期四星期四，是的，星期四好，周末愉快
it Thursday Thursday yeah Thursday okay
have a good weekend

572
00:50:44,060 --> 00:50:47,790
 [掌声] 
[Applause]