居里点（），又作居里温度（Curie temperature，Tc）或磁性转变点。是指磁性材料中自发磁化强度降到零时的温度，是铁磁性或亚铁磁性物质转变成顺磁性物质的临界点。低于居里点温度时该物质成为铁磁体，此时和材料有关的磁场很难改变。当温度高于居里点时，该物质成为顺磁体，磁体的磁场很容易随周围磁场的改变而改变。这时的磁敏感度约为10−6。居里点由物质的化学成分和晶体结构决定。居里温度是以皮埃尔·居里命名的，他表明在临界温度以上磁性材料会失去磁性。
居里點的溫度可以用平均場理論估計。
磁矩
磁矩是原子内的永久偶极矩，包含电子的角动量和自旋，他们之间的关系是 \mu_l = \frac{el}{2m_e}, me 是电子质量, μl 是磁矩, l是角动量; 这个比例被称作 gyromagnetic ratio（旋磁比）.
原子中的电子从它们自己的角动量和它们围绕原子核的轨道动量贡献磁矩。与来自电子的磁矩相比，来自原子核的磁矩是微不足道的。热作用在更高能量的电子上结果就是扰乱了秩序，并破坏了偶极子之间的对齐。
铁磁性、顺磁性、亚铁磁性和反铁磁性材料有不同的固有磁矩结构。在材料特定的居里温度()下，这些属性会发生变化。从反铁磁性到顺磁性（或反之亦然）的过渡发生在奈尔温度(), 这与居里温度类似。
File:Diagram of Ferromagnetic Magnetic Moments.png|铁磁性: 铁磁性材料中的磁矩。在没有施加磁场的情况下，磁矩是有序的且具有相同的大小。
File:Diagram of Paramagnetic Magnetic Moments.png|顺磁性: 顺磁性材料中的磁矩。在没有施加磁场的情况下，这些磁矩是无序的，并且在施加的磁场的情况下有序。
File:Diagram of Ferrimagnetic Magnetic Moments.png|亚铁磁性: 亚铁磁性材料中的磁矩。由于由两种不同的离子组成，磁矩相反地对齐并且具有不同的大小。 这是在没有施加磁场的情况下。
File:Diagram of Antiferromagnetic Magnetic Moments.png|反铁磁性: 反铁磁性材料中的磁矩。这些磁矩是相反的，并且具有相同的大小。 这是在没有施加磁场的情况下。
在居里温度下改变特性的具有磁矩的材料
铁磁性，顺磁性，亚铁磁性和反铁磁性结构由固有磁矩组成。 如果结构中的所有电子都配对，则由于它们的相反自旋和角动量，这些力矩会抵消。 因此，即使施加磁场，这些材料也具有不同的性质，并且没有居里温度。
顺磁性
当一些材料的温度高于居里点时，材料会表现出顺磁性，这样的材料叫顺磁性材料。当没有受到外部磁场的影响时，顺磁性材料不会表现磁性；反之则会表现磁性。没有受到外部磁场影响时，材料内部的磁矩是无序排列的。也就是说，材料内部的粒子不整齐且没有顺磁力线方向排列。当受到磁场影响时，这些磁矩会顺磁场线整齐排列，并且产生感应磁场。
对于顺磁性，这种对外加磁场的响应是正的，称为磁化率。磁化率仅适用于居里温度以上的无序状态。
顺磁性的来源（具有居里温度的材料）包括：
- 所有含未配对电子的原子；
- 内电子层未被填满的原子；
- 自由基；
- 金属。
超過居禮溫度後，原子被激發， 旋轉的方向變成隨機的原子变为有序，材料具有铁磁性。在这个过程中，玻尔兹曼因子贡献很大，因为它倾向于使相互作用的粒子在同一方向上排列。这会导致铁磁体具有较强的磁场和较高的居里温度，约 1000K（730℃）
在居里温度以下，原子有序排列，从而导致自发磁性，材料具有铁磁性。在居里温度以上，该材料是顺磁性的，因为当该材料经历相变时，原子会失去其有序的磁矩。
当没有外加磁场时，材料具有自发磁化，这是有序磁矩的结果；也就是说，对于亚铁磁性材料，一种离子的磁矩对准一个方向，有一个大小，另一种离子的磁矩对准相反方向，有一个不同的大小。因为磁矩在相反的方向有着不同的大小，所以仍然有自发磁化，存在磁场。它以路易·奈尔（Louis Néel，1904-2000 年）的名字命名，他因在该领域的工作而获得了 1970 年的诺贝尔物理学奖。
材料有方向相反的相等磁矩，导致在奈尔温度以下磁矩为零和净磁性为零。反铁磁性材料在有或没有外加磁场的情况下有很弱的磁性。
与铁磁性材料相似，磁性相互作用通过交换相互作用结合在一起；否则，热无序将克服磁矩的弱相互作用。奈尔温度时无序出现。
居里 - 韦斯定律
居里-韦斯定律是居里定律的修正版本，是基于平均场论近似的简单模型，在材料温度远高于其对应居里温度（即）时较为适用，但却因原子间的局部波动作用无法在居里点附近对磁化率进行描述。而的情况下，在居里定律和居里-韦斯定律均不成立。
Curie's law for a paramagnetic material:
:\chi = \frac{M}{H} =\frac{M \mu_0}{B} =\frac{C}{T}
:C = \frac{\mu_0 \mu_\mathrm{B}^2}{3 k_\mathrm{B}}N_A g^2 J(J+1)
The Curie–Weiss law is then derived from Curie's law to be:
:\chi = \frac{C}{T-T_\mathrm{C}}
where:
:T_\mathrm{C} = \frac{C \lambda }{\mu_0}
是Weiss分子场常数。
For full derivation see 居里-韦斯定律.
物理
从上方接近居里温度
As the Curie–Weiss law is an approximation, a more accurate model is needed when the temperature, , approaches the material's Curie temperature, .
Magnetic susceptibility occurs above the Curie temperature.
An accurate model of critical behaviour for magnetic susceptibility with critical exponent :
:\chi \sim \frac{1}{(T - T_\mathrm{C})^\gamma}
The critical exponent differs between materials and for the mean-field model is taken as = 1.
As temperature is inversely proportional to magnetic susceptibility, when approaches the denominator tends to zero and the magnetic susceptibility approaches infinity allowing magnetism to occur. This is a spontaneous magnetism which is a property of ferromagnetic and ferrimagnetic materials.
从下方接近居里温度
Magnetism depends on temperature and spontaneous magnetism occurs below the Curie temperature. An accurate model of critical behaviour for spontaneous magnetism with critical exponent :
:M \sim (T - T_\mathrm{C})^\beta
The critical exponent differs between materials and for the mean-field model as taken as = where .That is, the magnetic moments are completely aligned and at their strongest magnitude of magnetism due to no thermal disturbance.
In paramagnetic materials temperature is sufficient to overcome the ordered alignments. As the temperature approaches 0 K, the 熵 decreases to zero, that is, the disorder decreases and becomes ordered. This occurs without the presence of an applied magnetic field and obeys the 热力学第三定律.
硫酸钆 continues to satisfy Curie's law at 1 K. Between 0 and 1 K the law fails to hold and a sudden change in the intrinsic structure occurs at the Curie temperature.
Ising相变模型
The Ising model is mathematically based and can analyse the critical points of phase transitions in ferromagnetic order due to spins of electrons having magnitudes of ±. The spins interact with their neighbouring dipole electrons in the structure and here the Ising model can predict their behaviour with each other.
This model is important for solving and understanding the concepts of phase transitions and hence solving the Curie temperature. As a result, many different dependencies that affect the Curie temperature can be analysed.
For example, the surface and bulk properties depend on the alignment and magnitude of spins and the Ising model can determine the effects of magnetism in this system.
Weiss磁畴和表面和体积居里温度
Materials structures consist of intrinsic magnetic moments which are separated into domains called Weiss domains.This can result in ferromagnetic materials having no spontaneous magnetism as domains could potentially balance each other out.
This allows for the surface Curie temperature to be ferromagnetic above the bulk Curie temperature when the main state is disordered, i.e. Ordered and disordered states occur simultaneously.
The angular momentum of an electron is either + or − due to it having a spin of , which gives a specific size of magnetic moment to the electron; the Bohr magneton.Electrons orbiting around the nucleus in a current loop create a magnetic field which depends on the Bohr Magneton and magnetic quantum number.
For terbium which is a rare-earth metal and has a high orbital angular momentum the magnetic moment is strong enough to affect the order above its bulk temperatures. It is said to have a high anisotropy on the surface, that is it is highly directed in one orientation. It remains ferromagnetic on its surface above its Curie temperature while its bulk becomes ferrimagnetic and then at higher temperatures its surface remains ferrimagnetic above its bulk Néel Temperature before becoming completely disordered and paramagnetic with increasing temperature. The anisotropy in the bulk is different from its surface anisotropy just above these phase changes as the magnetic moments will be ordered differently or ordered in paramagnetic materials.as the crystal lattice will not be as compact.
The alignment of magnetic moments in the composite material affects the Curie temperature. If the materials moments are parallel with each other the Curie temperature will increase and if perpendicular the Curie temperature will decreaseDoping a material can also affect its Curie temperature.
The extreme of this is superparamagnetism which only occurs in small ferromagnetic particles and is where fluctuations are very influential causing magnetic moments to change direction randomly and thus create disorder.
The Curie temperature of nanoparticles are also affected by the crystal lattice structure, body-centred cubic (bcc), face-centred cubic (fcc) and a hexagonal structure (hcp) all have different Curie temperatures due to magnetic moments reacting to their neighbouring electron spins. fcc and hcp have tighter structures and as a results have higher Curie temperatures than bcc as the magnetic moments have stronger effects when closer together.
Pressure also affects the density of states (DOS).This is a function that determines the wave of a single electron or paired electrons inside the material. Having control over the probability of where the electron will be allows the Curie temperature to be altered. For example, the delocalised electrons can be moved onto the same plane by applied strains within the crystal lattice.
Ferroelectric and dielectric
Materials are only ferroelectric below their corresponding transition temperature .Ferroelectric materials are all pyroelectric and therefore have a spontaneous electric polarisation as the structures are unsymmetrical.
Ferroelectric materials' polarization is subject to hysteresis (Figure 4); that is they are dependent on their past state as well as their current state. As an electric field is applied the dipoles are forced to align and polarisation is created, when the electric field is removed polarisation remains. The hysteresis loop depends on temperature and as a result as the temperature is increased and reaches the two curves become one curve as shown in the dielectric polarisation (Figure 5).
相对介电常数
A modified version of the Curie–Weiss law applies to the dielectric constant, also known as the relative permittivity:
:\epsilon = \epsilon_0 + \frac{C}{T-T_\mathrm{0}}.
应用
A heat-induced ferromagnetic-paramagnetic transition is used in magneto-optical storage media, for erasing and writing of new data. Famous examples include the Sony Minidisc format, as well as the now-obsolete CD-MO format. Curie point electro-magnets have been proposed and tested for actuation mechanisms in passive safety systems of fast breeder reactors, where control rods are dropped into the reactor core if the actuation mechanism heats up beyond the material's curie point.Other uses include temperature control in soldering irons,and stabilizing the magnetic field of tachometer generators against temperature variation.
参见
- 铁电性
- 居里定律
参考资料
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