3
$\begingroup$

I know what anti-ferromagnetism is. But in a paper I came across "short-range antiferromagnetic order". Can someone please explain to me what it is or suggest me the book/(or any material).

$\endgroup$
  • $\begingroup$ Can you link to the paper so we can see the context? $\endgroup$ – taciteloquence Apr 12 at 7:28
0
$\begingroup$

As far as I have seen, the term "short-range antiferromagnetic order" is not necessarily very well defined. It would most likely refer to the staggered spin correlations $C_s = (-1)^r \vec S_i \cdot \vec S_{i+r}$ decaying with an exponential. $C_s \propto e^{-r/\xi}$. It's definitely not long range order (where $C_s(r\to \infty) \neq 0$ nor is it quasi-long-range order $C_s \propto r^{-b}$.

Short-range order on Wikipedia

My qualifications: I'm a computational physicist studying quantum (antiferro)magnetism.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

Magnetic ordering is usually measured using a spin-spin correlation function, like $S_{i,j} = \langle S_z(r_i) s_z(r_j) \rangle$. If the system has antiferromagnetic order, the Fourier transform of this correlator will have a peak of $k = \pi$ for a a one-dimensional system, or at $(\pi, \pi )$ in two dimensions etc. If the system is perfectly ordered, this peak will be a $\delta$-function. If the ordering reduces with the separation $| r_i - r_j |$, however, the peak will be broadened. If the correlator decays as a power-law of the separation - one of the best-known examples is the Kosterlitz-Thouless transition - the ordering is often called "quasi-long range order". However, if the decay is exponential, there is only antiferromagnetic order over separations comparable to the length-scale of the exponential, and this is called "short-range ordering".

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ So if we have a one dimensional spin chain of consecutive spin-up (say it is represented by 1 ) and spin-down (say it is represented by 0 ) and if the system is perfectly ordered then the spin chain will look like 1010101010101010101010 and this pattern will continue up to infinity. right...? And if the system has short-order ordering , then we will have 010101010 only upto a certain finite distance. $\endgroup$ – physu Apr 12 at 18:41
  • $\begingroup$ Can you suggest me a book? $\endgroup$ – physu Apr 12 at 18:44
  • $\begingroup$ Thanks for pointing out the typo in my answer. Yes, ...10101010... is an example of a perfectly ordered AF state. For a book, what type of system do you have in mind? $\endgroup$ – Clara Diaz Sanchez Apr 12 at 18:46
  • $\begingroup$ About the book... I just wanted to study what you mentioned in your answer in detail. $\endgroup$ – physu Apr 12 at 18:50
  • $\begingroup$ Almost any condensed matter textbook will discuss correlation functions. You can take a look at en.wikipedia.org/wiki/… to see the difference between ferromagnetic and antiferromagnetic correlation functions, and then look at the page's "Further reding". $\endgroup$ – Clara Diaz Sanchez Apr 12 at 18:57

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.