What is multiferroicity?

(A post summarizing recent US science-related events will be coming later.  For now, here is my promised post about multiferroics, inspired in part by a recent visit to Rice by Yoshi Tokura.)

Electrons carry spins and therefore magnetic moments (that is, they can act in some ways like little bar magnets), and as I was teaching undergrads this past week, under certain conditions some of the electrons in a material can spontaneously develop long-range magnetic order.  That is, rather than being, on average, randomly oriented, instead below some critical temperature the spins take on a pattern that repeats throughout the material.  In the ordered state, if you know the arrangement of spins in one (magnetic) unit cell of the material, that pattern is repeated over many (perhaps all, if the system is a single domain) the unit cells.  In picking out this pattern, the overall symmetry of the material is lowered compared to the non-ordered state.  (There can be local moment magnets, when the electrons with the magnetic moments are localized to particular atoms; there can also be itinerant magnets, when the mobile electrons in a metal take on a net spin polarization.)  The most famous kind of magnetic order is ferromagnetism, when the magnetic moments spontaneously align along a particular direction, often leading to magnetic fields projected out of the material.    Magnetic materials can be metals, semiconductors, or insulators.

In insulators, an additional kind of order is possible, based on electric polarization, $\mathbf{P}$.  There is subtlety about defining polarization, but for the purposes of this discussion, the question is whether the atoms within each unit cell bond appropriately and are displaced below some critical temperature to create a net electric dipole moment, leading to ferroelectricity.  (Antiferroelectricity is also possible.) Again, the ordered state has lower symmetry than the non-ordered state.  Ferroelectric materials have some interesting applications.  

BiFeO3, a multiferroic antiferromagnet,
image from here.

Multiferroics are materials that have simultaneous magnetic order and electric polarization order.  A good recent review is here.  For applications, obviously it would be convenient if both the magnetic and polarization ordering happened well above room temperature.  There can be deep connections between the magnetic order and the electric polarization - see this paper, and this commentary.   Because of these connections, the low energy excitations of multiferroics can be really complicated, like electromagnons.  Similarly, there can be combined "spin textures" and polarization textures in such materials - see here and here.   Multiferroics raise the possibility of using applied voltages (and hence electric fields) to flip $\mathbf{P}$, and thus toggle around $\mathbf{M}$.  This has been proposed as a key enabling capability for information processing devices, as in this approach.  These materials are extremely rich, and it feels like their full potential has not yet been realized.  

Science updates - brief items

Here are a couple of neat papers that I came across in the last week.  (Planning to write something about multiferroics as well, once I have a bit of time.)

• The idea of directly extracting useful energy from the rotation of the earth sounds like something out of an H. G. Wells novel.  At a rough estimate (and it's impressive to me that AI tools are now able to provide a convincing step-by-step calculation of this; I tried w/ gemini.google.com) the rotational kinetic energy of the earth is about $2.6 \times 10^{29}$ J.  The tricky bit is, how do you get at it?  You might imagine constructing some kind of big space-based pick-up coil and getting some inductive voltage generation as the earth rotates its magnetic field past the coil.  Intuitively, though, it seems like while sitting on the (rotating) earth, you should in some sense be comoving with respect to the local magnetic field, so it shouldn't be possible to do anything clever that way.  It turns out, though, that Lorentz forces still apply when moving a wire through the axially symmetric parts of the earth's field.  This has some conceptual contact with Faraday's dc electric generator.   With the right choice of geometry and materials, it is possible to use such an approach to extract some (tiny at the moment) power.  For the theory proposal, see here.  For an experimental demonstration, using thermoelectric effects as a way to measure this (and confirm that the orientation of the cylindrical shell has the expected effect), see here.  I need to read this more closely to decide if I really understand the nuances of how it works.
• On a completely different note, this paper came out on Friday.  (Full disclosure:  The PI is my former postdoc and the second author was one of my students.)  It's an impressive technical achievement.  We are used to the fact that usually macroscopic objects don't show signatures of quantum interference.  Inelastic interactions of the object with its environment effectively suppress quantum interference effects on some time scale (and therefore some distance scale).  Small molecules are expected to still show electronic quantum effects at room temperature, since they are tiny and their electronic levels are widely spaced, and here is a review of what this could do in electronic measurements.  Quantum interference effects should also be possible in molecular vibrations at room temperature, and they could manifest themselves through the vibrational thermal conduction through single molecules, as considered theoretically here.  This experimental paper does a bridge measurement to compare the thermal transport between a single-molecule-containing junction between a tip and a surface, and an empty (farther spaced) twin tip-surface geometry.  They argue that they see differences between two kinds of molecules that originate from such quantum interference effects.

As for more global issues about the US research climate, there will be more announcements soon about reductions in force and the forthcoming presidential budget request.  (Here is an online petition regarding the plan to shutter the NIST atomic spectroscopy group.)  Please pay attention to these issues, and if you're a US citizen, I urge you to contact your legislators and make your voice heard.  

March Meeting 2025, Day 4 and wrap-up

 I saw a couple of interesting talks this morning before heading out:

• Alessandro Chiesa of Parma spoke about using spin-containing molecules potentially as qubits, and about chiral-induced spin selectivity (CISS) in electron transfer.  Regarding the former, here is a review.  Spin-containing molecules can have interesting properties as single qubits, or, for spins higher than 1/2, qudits, with unpaired electrons often confined to a transition metal or rare earth ion somewhat protected from the rest of the universe by the rest of the molecule.  The result can be very long coherence times for their spins.  Doing multi-qubit operations is very challenging with such building blocks, however.  There are some theory proposals and attempts to couple molecular qubits to superconducting resonators, but it's tough!   Regarding chiral induced spin selectivity, he discused recent work trying to use molecules where a donor region is linked to an acceptor region via a chiral bridge, and trying to manipulate spin centers this way.  A question in all the CISS work is, how can the effects be large when spin-orbit coupling is generally very weak in light, organic molecules?  He has a recent treatment of this, arguing that if one models the bridge as a chain of sites with large $U/t$, where $U$ is the on-site repulsion energy and $t$ is the hopping contribution, then exchange processes between sites can effectively amplify the otherwise weak spin-orbit effects.  I need to read and think more about this.
• Richard Schlitz of Konstanz gave a nice talk about some pretty recent research using a scanning tunneling microscope tip (with magnetic iron atoms on the end) to drive electron paramagnetic resonance in a single pentacene molecule (sitting on MgO on Ag, where it tends to grab an electron from the silver and host a spin).  The experimental approach was initially explained here.  The actual polarized tunneling current can drive the resonance, and exactly how depends on the bias conditions.  At high bias, when there is strong resonant tunneling, the current exerts a damping-like torque, while at low bias, when tunneling is far off resonance, the current exerts a field-like torque.  Neat stuff.
• Leah Weiss from Chicago gave a clear presentation about not-yet-published results (based on earlier work), doing optically detected EPR of Er-containing molecules.  These condense into mm-sized molecular crystals, with the molecular environment being nice and clean, leading to very little inhomogeneous broadening of the lines.  There are spin-selective transitions that can be driven using near telecom-wavelength (1.55 $\mu m$) light.  When the (anisotropic) $g$-factors of the different levels are different, there are some very promising ways to do orientation-selective and spin-selective spectroscopy.  Looking forward to seeing the paper on this.

And that's it for me for the meeting.  A couple of thoughts:

• I'm not sold on the combined March/April meeting.  Six years ago when I was a DCMP member-at-large, the discussion was all about how the March Meeting was too big, making it hard to find and get good deals on host sites, and maybe the meeting should split.  Now they've made it even bigger.  Doesn't this make planning more difficult and hosting more expensive since there are fewer options?  (I'm not an economist, but....)  A benefit for the April meeting attendees is that grad students and postdocs get access to the career/networking events held at the MM.  If you're going to do the combination, then it seems like you should have the courage of your convictions and really mingle the two, rather than keeping the March talks in the convention center and the April talks in site hotels.
• I understand that van der Waals/twisted materials are great laboratories for physics, and that topological states in these are exciting.  Still, by my count there were 7 invited sessions broadly about this topic, and 35 invited talks on this over four days seems a bit extreme.  
• By my count, there were eight dilution refrigerator vendors at the exhibition (Maybell, Bluefors, Ice, Oxford, Danaher/Leiden, Formfactor, Zero-Point Cryo, and Quantum Design if you count their PPMS insert).  Wow.  

I'm sure there will be other cool results presented today and tomorrow that I am missing - feel free to mention them in the comments.

March Meeting 2025, Day 3

Another busy day at the APS Global Physics Summit.  Here are a few highlights:

• Shahal Ilani of the Weizmann gave an absolutely fantastic talk about his group's latest results from their quantum twisting microscope.  In a scanning tunneling microscope, because tunneling happens at an atomic-scale location between the tip and the sample, the momentum in the transverse direction is not conserved - that is, the tunneling averages over a huge range of $\mathbf{k}$ vectors for the tunneling electron.  In the quantum twisting microscope, electrons tunnel from a flat (graphite) patch something like $d \sim$ 100 nm across, coherently, through a couple of layers of some insulator (like WSe2) and into a van der Waals sample.  In this case, $\mathbf{k}$ in the plane is comparatively conserved, and by rotating the sample relative to the tip, it is possible to build up a picture of the sample's electronic energy vs. $\mathbf{k}$ dispersion, rather like in angle-resolved photoemission.  This has allowed, e.g., mapping of phonons via inelastic tunneling.  His group has applied this to magic angle twisted bilayer graphene, a system that has a peculiar combination of properties, where in some ways the electrons act like very local objects, and in other ways they act like delocalized objects.  The answer seems to be that this system at the magic angle is a bit of an analog of a heavy fermion system, where there are sort of local moments (living in very flat bands) interacting and hybridizing with "conduction" electrons (bands crossing the Fermi level at the Brillouin zone center).  The experimental data (movies of the bands as a function of energy and $\mathbf{k}$ in the plane as the filling is tuned via gate) are gorgeous and look very much like theoretical models.
• I saw a talk by Roger Melko about applying large language models to try to get efficient knowledge of many-body quantum states, or at least the possible outputs of evolution of a quantum system like a quantum computer based on Rydberg atoms.  It started fairly pedagogically, but I confess that I got lost in the AI/ML jargon about halfway through.
• Francis M. Ross, recipient of this year's Keithley Award, gave a great talk about using transmission electron microscopy to watch the growth of materials in real time.  She had some fantastic videos - here is a review article about some of the techniques used.  She also showed some very new work using a focused electron beam to make arrays of point defects in 2D materials that looks very promising.
• Steve Kivelson, recipient of this year's Buckley Prize, presented a very nice talk about his personal views on the theory of high temperature superconductivity in the cuprates.  One basic point:  these materials are balancing between multiple different kinds of emergent order (spin density waves, charge density waves, electronic nematics, perhaps pair density waves).   This magnifies the effects of quenched disorder, which can locally tip the balance one way or another.  Recent investigations of the famous 2D square lattice Hubbard model show this as well.  He argues that the ground state of the Hubbard model for a broad range $1/2 < U/t < 8$, where $U$ is the on-site repulsion and $t$ is the hopping term, the ground state is in fact a charge density wave, not a superconductor.  However, if there is some amount of disorder in the form of $\delta t/t \sim 0.1-0.2$, the result is a robust, unavoidable superconducting state.  He further argues that increasing the superconducting transition temperature requires striking a balance between the underdoped case (strong pairing, weak superfluid phase stiffness) and the overdoped case (weak pairing, strong superfluid stiffness), and that one way to achieve this would be in a bilayer with broken mirror symmetry (say different charge reservoir layers above and below, and/or a big displacement field perpendicular to the plane).  (Apologies for how technical that sounded - hard to reduce that one to something super accessible without writing much more.)

A bit more tomorrow before I depart back to Houston.

March Meeting 2025, Day 2

I spent a portion of today catching up with old friends and colleagues, so fewer highlights, but here are a couple:

• Like a few hundred other people, I went to the invited talk by Chetan Nayak, leader of Microsoft's quantum computing effort. It was sufficiently crowded that the session chair warned everyone about fire code regulations and that people should not sit on the floor blocking the aisles.  To set the landscape:  Microsoft's approach to quantum computing is to develop topological qubits based on interesting physics that is predicted to happen (see here and here) if one induces superconductivity (via the proximity effect) in a semiconductor nanowire with spin-orbit coupling.  When the right combination of gate voltage and external magnetic field is applied, the nanowire should cross into a topologically nontrivial state with majorana fermions localized to each end of the nanowire, leading to "zero energy states" seen as peaks in the conductance $dI/dV$ centered at zero bias ($V=0$).  A major challenge is that disorder in these devices can lead to other sources of zero-bias peaks (Andreev bound states).  A 2023 paper outlines a protocol that is supposed to give good statistical feedback on whether a given device is in the topologically interesting or trivial regime.  I don't want to rehash the history of all of this.  In a paper published last month, a single proximitized, gate-defined InAs quantum wire is connected to a long quantum dot to form an interferometer, and the capacitance of that dot is sensed via RF techniques as a function of the magnetic flux threading the interferometer, showing oscillations with period $h/2e$, interpreted as charge parity oscillations of the proximitized nanowire.  In new data, not yet reported in a paper, Nayak presented measurements on a system comprising two such wires and associated other structures.  The argument is that each wire can be individually tuned simultaneously into the topologically nontrivial regime via the protocol above.  Then interferometer measurements can be performed in one wire (the Z channel) and in a configuration involving two ends of different wires (the X channel), and they interpret their data as early evidence that they have achieved the desired majorana modes and their parity measurements.  I look forward to when a paper is out on this, as it is hard to make informed statements about this based just on what I saw quickly on slides from a distance.  
• In a completely different session, Garnet Chan gave a very nice talk about applying advanced quantum chemistry and embedding techniques to look at some serious correlated materials physics.  Embedding methods are somewhat reminiscent of mean field theories:  Instead of trying to solve the Schrödinger equation for a whole solid, for example, you can treat the solid as a self-consistent theory of a unit cell or set of unit cells embedded in a more coarse-grained bath (made up of other unit cells appropriately averaged).  See here, for example. He presented recent results on computing the Kondo effect of magnetic impurities in metals, understanding the trends of antiferromagnetic properties of the parent cuprates, and trying to describe superconductivity in the doped cuprates.  Neat stuff.
• In the same session, my collaborator Silke Buehler-Paschen gave a nice discussion of ways to use heavy fermion materials to examine strange metals, looking beyond just resistivity measurements.  Particularly interesting is the idea of trying to figure out quantum Fisher information, which in principle can tell you how entangled your many-body system is (that is, estimating how many other degrees of freedom are entangled with one particular degree of freedom).  See here for an intro to the idea, and here for an implementation in a strange metal, Ce3Pd20Si6.  

More tomorrow....

(On a separate note, holy cow, the trade show this year is enormous - seems like it's 50% bigger than last year.  I never would have dreamed when I was a grad student that you could go to this and have your pick of maybe 10 different dilution refrigerator vendors.  One minor mystery:  Who did World Scientific tick off?  Their table is located on the completely opposite side of the very large hall from every other publisher.)

March Meeting 2025, Day 1

The APS Global Physics Summit is an intimate affair, with a mere 14,000 attendees, all apparently vying for lunch capacity for about 2,000 people.   The first day of the meeting was the usual controlled chaos of people trying to learn the layout of the convention center while looking for talks and hanging out having conversations.  On the plus side, the APS wifi seems to function well, and the projectors and slide upload system are finally technologically mature (though the pointers/clickers seem to have some issues).  Some brief highlights of sessions I attended:

• I spent the first block of time at this invited session about progress in understanding quantum spin liquids and quantum spin ice.  Spin ices are generally based on the pyrochlore structure, where atoms hosting local magnetic moments sit at the vertices of corner-sharing tetrahedra, as I had discussed here.  The idea is that the crystal environment and interactions between spins are such that the moments are favored to satisfy the ice rules, where in each tetrahedron two moments point inward toward the center and two point outward.  Classically there are a huge number of spin arrangements that all have about the same ground state energy.  In a quantum spin ice, the idea is that quantum fluctuations are large, so that the true ground state would be some enormous superposition of all possible ice-rule-satistfying configurations.  One consequence of this is that there are low energy excitations that look like an emergent form of electromagnetism, including a gapless phonon-like mode.  Bruce Gaulin spoke about one strong candidate quantum spin ice, Ce2Zr2O7, in a very pedagogical talk that covered all this.  A relevant recent review is this one.   There were two other talks in the session also about pyrochlores, an experimentally focused one by Sylvain Petit discussing Tb2Ti2O7 (see here), and a theory talk by Yong-Baek Kim focused again on the cerium zirconate.    Also in the session was an interesting talk by Jeff Rau about K2IrCl6, a material with a completely different structure that (above its ordering temperature of 3 K) acts like a "nodal line spin liquid".
• In part because I had students speaking there, I also attended a contributed session about nanomaterials (wires, tubes, dots, particles, liquids).  There were some neat talks.  The one that I found most surprising was from the Cha group at Cornell, where they were using a method developed by the Schroer group at Yale (see here and here) to fabricate nanowires of two difficult to grow, topologically interesting metals, CoIn3 and RhIn3.  The idea is to create a template with an array of tubular holes, and squeeze that template against a bulk crystal of the desired material at around 350C, so that the crystal is extruded into the holes to form wires.  Then the template can be etched away and the wires recovered for study.  I'm amazed that this works.
• In the afternoon, I went back and forth between the very crowded session on fractional quantum anomalous Hall physics in stacked van der Waals materials, and a contributed session about strange metals.  Interesting stuff for sure.

I'm still trying to figure out what to see tomorrow, but there will be another update in the evening.

March Meeting 2025, Day 0

Technically, this year the conference is known as the APS Global Physics Summit rather than the March Meeting, but I'm keeping my blog post titles consistent with previous years.   Over 14,000 physicists have descended upon Anaheim, and there are parallel events in more than a dozen countries around the world as well.

Late this afternoon I attended an APS town hall session about "Protecting Science".  There were brief remarks by APS President John Doyle, APS CEO Jonathan Bagger, and APS External Affairs Officer Francis "Slake" Slakey, followed by an audience Q&A.  It was a solid event attended by about 300 people in person and more online, as the society tries to thread its way through some very challenging times for science and scholarship in the US.  Main take-aways from the intro remarks:

• The mission and values of the APS have not changed. 
• Paraphrasing:  We must explain to the public and officials the wonder of science and the economic impact of what we do.  Discovery and application reinforce each other, and this dynamic is what drives progress.  We need the public to hear this.  We need Congress to hear this.  We need the executive branch and its advisors to hear this.   APS needs to promote physics, and physicists need to tell the truth, even when uncomfortable.  The truth is our currency with the public.  It is our superpower.  APS is not a blue or red state organization; it's an organization that champions physics.
• Slake thanked and asked the audience to stand and thank the many federal science agency employees who are feeling dispirited and unsupported.  "You are part of this community and no federal disruption is going to change that."
• Slake also mentioned that the critical short-term issue is the upcoming budget.  The White House will announce its version in April, and the APS is pursuing a 50-state coordinated approach to have people speak to their congressional delegations in their states and districts, to explain what the harm and true costs are if the science agency budgets are slashed.  They are targeting certain key states in particular (Alaska, Kansas, Indiana, Pennsylvania, Maine, South Dakota were mentioned).
• APS is continuing its support for bridge and mentorship programs, as well as the STEP-UP program; see here.  These programs are open to all.  

Tomorrow, some highlights of the scientific program.  Apologies for unavoidably missing a lot of cool stuff - I go to my students' sessions and try to see other topics that interest me, but because the meeting is so large, with so many parallel talks, I know that I inevitably can't see all the exciting science.

The 2025 Wolf Prize in Physics

One nice bit of condensed matter/nanoscale physics news:  This year's Wolf Prize in Physics has gone to three outstanding scientists, Jim Eisenstein, Moty Heiblum, and Jainendra Jain, each of whom have done very impactful work involving 2D electron gases - systems of electrons confined to move only in two dimensions by the electronic structure and alignment of energy bands at interfaces between semiconductors.  Of particular relevance to these folks are the particularly clean 2D electron gases at the interfaces between GaAs and AlGaAs, or in GaAs quantum wells embedded in AlGaAs.

A thread that connects all three of these scientists is the fractional quantum Hall effect in these 2D systems.  Electrons confined to move in 2D, in the presence of a magnetic field perpendicular to the plane of motion, form a remarkable system.  The quantum wavefunction of an electron in this situation changes as the magnetic induction $B$ is increased.  The energy levels of such an electron are given by $(n+1/2)\hbar \omega_{c}$, where $\omega_c \equiv eB/m*$ is the cyclotron frequency.  These energy levels are called Landau Levels.  The ratio between the 2D density of electrons and the density of magnetic flux in fundamental units ($B/(h/e)$) is called the "filling factor", $\nu$, and when this is an integer, the Hall conductance is quantized in fundamental units - see here.  

Figure 4 from this article by Jain, with $R_{xx}(B)$ data from here.  Notice how the data around $B=0$ looks a lot like the data around $\nu = 1/2$, which looks a lot like the data around $\nu=1/4$. 

A remarkable thing happens when $\nu = 1/2$ - see the figure above.  There is no quantum Hall effect there; in fact, if you look at the longitudinal resistance $R_{xx}$ as a function of $B$ near $\nu = 1/2$, it looks remarkably like $R_{xx}(B)$ near $B = 0$.  At this half-integer filling factor, the 2D electrons plus the magnetic flux "bundle together", leading to a state with new low-energy excitations called composite fermions that act like they are in zero magnetic field.  In many ways the FQHE looks like the integer quantum Hall effect for these composite fermions, though the situation is more complicated than that.  Jainendra Jain did foundational work on the theory of composite fermions, among many other things.

Jim Eisenstein has done a lot of great experimental work involving composite fermions and even-denominator FQH states.  My postdoctoral mentor, Bob Willett, and he are first two authors on the paper where an unusual quantum Hall state was discovered at $\nu = 5/2$, a state still under active investigation for potential topological quantum computing applications.   One particularly surprising result from Eisenstein's group was the discovery that some "high" Landau level even-denominator fillings ($\nu = 9/2, 11/2$) showed enormously anisotropic resistances, with big differences between $R_{xx}$ and $R_{yy}$, an example of the onset of a "stripe" phase of alternating fillings.  

Another very exciting result from Eisenstein's group used 2D electron gases in close proximity parallel layers and in high magnetic fields, as well as 2D electron gases near 2D hole gases.  Both can allow the formation of excitons, bound states of electrons and holes, but with the electrons and holes in neighboring layers so that they could not annihilate each other.  Moreover, a Bose-Einstein condensation of those excitons is possible leading to remarkable superflow of excitons and resonant tunneling between the layers.  This review article is a great discussion of all of this.

Moty Heiblum's group at the Weizmann Institute has been one of the world-leading groups investigating "mesoscopic" physics of confined electrons in the past 30+ years.  They have performed some truly elegant experiments using 2D electron gases as their platform.  A favorite of mine (mentioned in my textbook) is this one, in which they make a loop-shaped interferometer for electrons which shows oscillations in the conductance as they thread magnetic flux through the loop; they then use a nearby quantum point contact as a charge sensor near one arm of the interferometer, a which-path detector that tunably suppresses the quantum interference. 

His group also did foundational work on the use of shot noise as a tool to examine the nature and transport of charge carriers in condensed matter systems (an idea that I found inspiring).  Their results showing that the quasiparticles in the fractional quantum Hall regime can have fractional charges are remarkable.  More recently, they have shown how subtle these measurements really can be, in 2D electron systems that can support neutral excitations as well as charged ones.

All in all, this is a great recognition of outstanding scientists for a large volume of important, influential work.

(On a separate note:  I will be attending 3+ days of the APS meeting next week.  I'll try to do my usual brief highlight posts, time permitting.  If people have suggestions of cool content, please let me know.)