Friday, February 23, 2018

Spin ice in a nutshell

What is spin ice? What its definitive and experimental signatures?

A good place to start is the lucid discussion by Roderich Moessner and Art Ramirez in a 2006 article on Geometrical Frustration. They emphasise two organising principles: local constraints on neigbouring spins and the emergence of new entities such as gauge fields.

First, let's discuss the "ice" bit since this involves some beautiful chemistry, physics, statistical mechanics, and history. In the solid phase of water at atmospheric pressure (ice Ih) the water molecules form a hexagonal lattice, with the oxygen atoms located a the vertices of the lattice. The molecules interact with one another via hydrogen bonds.

Now the key point is that there are many different ways of orienting the water molecules (arranging the protons). The only constraint is that one has to have two protons covalently bonded to the oxygen and two protons on next-nearest neighbour water molecules hydrogen bonded to the oxygen. This is known as the ice rule. Suppose we assign an Ising spin variable (+1,-1)=(in, out)  = (covalent, Hbond) to each "bond" on the lattice. Then the ice rule is that on each tetrahedron the sum of the four "spins" must be zero.

How much degeneracy is there?
There are 2^4= 16 possible spin states on a tetrahedron. But, only six (a fraction of 3/8) satisfy the ice rule. To see this, put +1 on site one, then one must put +1 on one of the other three sites, and -1 on the other two. This gives 6 = 2 x 3 options.
If one neglects the interaction between vertices, the thermodynamic entropy per tetrahedron (water molecule) is

S = k ln (3/2)

Historical asides.
This "residual" entropy in ice was observed experimentally by William Giauque in the chemistry department at Berkeley in the 1930s.
Linus Pauling explained this in 1935, even arguing it as evidence for a specific crystal structure of ice.
Pauling's picture led to the ice-type models that are very important  (from a mathematical and conceptual point of view) in classical statistical mechanics as they are exactly soluble in two dimensions.
In 1956 Phil Anderson (who else!) noted that Pauling's problem was equivalent to that of Ising spins on a pyrochlore lattice.
It was not until four decades later than an experimental realisation was observed in a magnetic material. The experimental data is shown below.

But there is much more to spin ice. The local constraints lead naturally to an emergent gauge field (a pseudo-magnetic field), analogues of "magnetic monopoles", and unusual spin correlations (algebraic correlations without criticality). I now discuss the latter as they can be viewed as a "smoking gun" of spin ice.

The "magnetic field" B satisfies the constraint Div B =0. As a result the spin correlations have a dipolar form, i.e. they have a distance and directional dependence similar to the magnetic field associated with a magnetic dipole. This means the spin correlations fall off algebraically. This is in contrast to conventional magnets where spin correlations decay exponentially, except at a critical point. Furthermore, if one plots or measures the static spin structure factor S(q) one finds "pinch points" occur in high symmetry planes. The figure below shows an experimental measurement for Holonium Titanate, taken from here.

Wednesday, February 21, 2018

What makes a good theory or modelling paper?

There is an excellent editorial in the journal Langmuir
Writing Theory and Modeling Papers for Langmuir: The Good, the Bad, and the Ugly
Han Zuilhof, Shu-Hong Yu, David S. Sholl

The article is written in the context of a specific journal, that has a focus on surface and colloid chemistry, and predominantly experimental papers and readers.
The article is structured around the five questions below, that should actually be asked about any theory or computational paper.

Who is the intended audience?
Specifically, will the paper have an influence on the experimental community?

Are approximations and limitations clearly described? 

What physical insight is gained? 

Where does theory touch reality? 
Specifically, how does the work relate to experiment? Does it suggest new experiments to test the theory?

How can calculations be made reproducible? 

This is helpful advice and good for anyone to reflect on. On the other hand, this is so basic that the need for such an editorial reflects how bad science, and particularly computational modelling, has gotten. It is just too easy to download some software, run it for some complex chemical system that is fashionable, produce some pretty graphs, and write a paper....

Monday, February 19, 2018

The value of vacations (again).

This is almost the same post I wrote a year ago. 
This is the first week of classes for the beginning of the academic year in Australia.

In preparation for a busy semester, I took last week off work and visited my son in Canberra (where I grew up) and spent some time hiking in one of my favourite places, Kosciusko National Park. This reminded me of the importance of vacations and down time, of the therapeutic value of the nature drug, and of turning off your email occasionally.

One thing I am very thankful for is that my mental health is so much better than it was a year ago, arguably because of being pro-active.

Below is a picture of our campsite near Mount Tate. My son pointed out that it is possible that night we were the highest people in Australia since we did not see anyone else for 24 hours and you are not allowed to camp near some of the higher peaks, such as Mt. Kosciusko.

Sunday, February 11, 2018

Rethinking On-Line courses

About five years ago Massive On-Line Courses (MOOCs) were all the rage among politicians and university managers. Like most hyped up fashions, they have lost their gloss as reality has set in. There are no simple panaceas, particularly technological ones, for the complexities of tertiary education. I have previously expressed skepticism and concern about MOOCs, but recently I have rethought some of my views.

Last year I was visiting some friends in a small Majority World college and I noticed that one of the administrators had a copy of the book Poor Economics on his desk. I told him how much I liked it and he said that he had really enjoyed and benefited from taking the associated on-line course at MIT. Then he said, "But the online course I really like is the Oxford one, From Poverty to Prosperity, by Paul Collier.'' Wow!

To me, this represents the best of on-line courses; when they provide access to educational opportunities that were inconceivable a decade ago.

I have also been helping another friend with an on-line Masters course. A positive here is that it is not a substitute for regular classes for traditional students in physical classrooms but a course for students who are in life situations (family, jobs, location, ...) that do not afford them the luxury of full-time study in a traditional setting. I think a big positive is having an excellent on-line tutor who actively engages with the students.

Overall, I think the key issue here is that On-line courses are not a desirable substitute for traditional courses, but rather can complement them. Similarly, I think within traditional contexts (i.e. students on physical campuses) "blended courses" (i.e. ones with a mixture of face-to-face and on-line interaction) can be superior to traditional ones. For example, I have found that an on-line quiz about pre-lecture reading seems to increase the quality of the experience for students who then come to the lecture.

However, I want to emphasize a basic claim: the ideal educational environment and strategy for most students (particularly young undergraduates) is one where you have a group of students and a teacher in a physical classroom interacting with each other. People are relational and learning best happens in the context of relationships.

I welcome comments.

Postscript (Feb. 13).
I forgot to link to this excellent NYT article.
Online Courses Are Harming the Students Who Need the Most Help Economic View, by Susan Dynarski

Saturday, February 3, 2018

Seth Olsen (1975-2018): theoretical chemist

I was very sad to learn last week of the tragic death of Seth Olsen in an accident. He was a former collaborator and colleague at UQ.

Seth was an outstanding and energetic scientist who easily crossed discipline boundaries, especially between chemistry, physics, and molecular biology.

Much of what I know about computational quantum chemistry, fluorescent proteins, conical intersections, and diabatic states, I learnt from Seth. He played a significant role in this blog. A search revealed that his name is mentioned in more than 70 posts. Many posts were stimulated by his work, his questions, or his suggestions. He often wrote comments, covering a wide range of topics. I found his interest helpful and stimulating.

Seth grew up in the USA. He was a physics major at the College of William and Mary. In 2004 he completed a Ph.D in in Biophysics and Computational Biology at The University of Illinois at Urbana-Champaign. His thesis was entitled, ` Electronic Excited States of Green Fluorescent Protein Chromophore Models,'' and his advisor was Todd Martínez, now at Stanford.

I first met Seth in 2005 when he was a postdoc with Sean Smith at the Centre for Computational Molecular Science at University of Queensland. During that time he met Louise Kettle, a Ph.D student in chemistry, who he later married.

I was very happy when in 2008 I was able to persuade Seth to join my group as a Research Fellow. He helped my group expand from condensed matter into chemical physics.  In 2010 I was pleased when Seth was awarded a 5-year Australian Research Fellowship. We continued to collaborate, although in many ways I was the junior author.

A significant contribution of Seth was to use high-level quantum chemistry calculations to show that the low-lying excited electronic states of the chromophore molecule in the green fluorescent protein has a natural description in terms of the resonant colour theory of organic dyes developed in the middle of the twentieth century by Brooker, Platt, and Moffitt. In different words, he used quantum chemistry to justify and parametrise a simple effective Hamiltonian for a complex system. Furthermore, he provided a rigorous quantum chemical justification for the colour theory description of a very wide class of organic dyes based on the methine motif. These results provide chemical and physical insight, an understanding of trends, elucidate design principles, and make modeling in condensed environments such as proteins, solvents, and glasses much more feasible.

I had great respect for Seth's integrity, both personal and scientific. He carefully checked calculations and arguments, would not rush to publish, and would not indulge in hype. Much of my skepticism and caution about computational materials science I gained from Seth's critiques.

Seth had his priorities right, putting family first.
My kids thought Seth was pretty cool, particularly when he came to a group social at our house with a backpack that contained a home brew beer set up!

My sincere condolences to Louise and their three young children.

Don't know what else to say. This is the saddest blog post I have had to write.

Friday, January 26, 2018

A spicy scientific scandal

I am often on the lookout for interesting molecules and solids which involve short hydrogen bonds, particularly biomolecules where this bond may play a key role in functionality. Such bonds are of interest from a physics point of view because then the quantum motion of the proton matters.
Consequently, the following paper (published in October 2016) caught my attention.

Proton Probability Distribution in the O···H···O Low-Barrier Hydrogen Bond: A Combined Solid-State NMR and Quantum Chemical Computational Study of Dibenzoylmethane and Curcumin Xianqi Kong, Andreas Brinkmann Victor Terskikh, Roderick E. Wasylishen, Guy M. Bernard∥, Zhuang Duan∥, Qichao Wu∥, and Gang Wu

The authors state their motivation.
Curcumin was selected in our study, in part because it is being touted as a wonder drug and is of intense interest to the pharmaceutical and medical community.31−33
This sounds quite exciting. Could low barrier hydrogen bonds be important in curing cancer?
Curcumin is a major ingredient of tumeric, the yellow spice, which features heavily in Asian cooking.
This got me Googling and it turns out the claims of a "wonder drug" are dubious.

Experimental studies of curcumin turn out to be particularly problematic, as explained in a blog post
Curcumin will waste your time by Derek Lowe. It is worth reading because it highlights the need for replication studies and publication of null results.

But it gets worse. References 31 and 32 have the same last author, Bharat Aggarwal, who it turns out has been the major proponent of the "wonder drug". In 2015 he "retired" from the University of Texas, following allegations of scientific fraud. By August 2106, eighteen published papers by him had been withdrawn.

To illustrate the problem of metrics, in 2016 Aggarwal had an h-index of 160, and in 2015, Thomson Reuters (ISI Web of Science) listed him among the World's Most Influential Scientific Minds.

I should stress that none of this invalidates the results of the hydrogen bonding paper that got me on this trail.

Tuesday, January 23, 2018

Emergent stories

Steve Blundell has written a very nice article
Emergence, causation and storytelling: condensed matter physics and the limitations of the human mind

The article is lucid, creative, and stimulating.
He explores some issues that are of particular interest to philosophers such as the differences between "weak" and "strong" emergence, which are sometimes called "epistemological" and "ontological" emergence, respectively.

Part of his argument is based on the fact that human minds are finite and constrained by the physical world and that "information is physical". Unlike the philosophers, he argues that emergence always has both an ontological and an epistemological character.

To illustrate his arguments Steve uses several beautiful examples.

"To work, stories have to be succinct, told well, have a point and express some truth."
This is to accommodate the physical limitations of the human mind.

Number theory.
Integers are defined by the rules of a very simple algebra. Yet, rich phenomena emerge such as how the asymptotic distribution of prime numbers [given by the zeros of the Riemann zeta function] can be described by random matrix theory.

Conway's game of life.
He considers the "Scattering"  and the creation and destruction of "objects" such as spaceships, "Canada geese" (shown below), and "pulsars".

How emergence comes into play is described by the figure below.

This reminds me a bit of particle physics experiments. New entities emerge from the underlying rules encoded in the Standard Model.

Spin ice.
Emergent gauge field and magnetic monopoles.
This is also discussed as an example of emergence in a 2016 article by Rehn and Moessner.