Quantum spin liquids on geometrically frustrated kagome lattices

Gomilšek, Matjaž (author), Zorko, Andrej (mentor)

In this Thesis we study the paradigmatic quantum kagome antiferromagnet (QKA) herbertsmithite and the recently synthesized Zn-brochantite by a variety of experimental techniques. We find that herbertsmithite possesses two types of defects at low temperatures, d_I and d_II, not just one type as previously believed. We prove that the dominant d_I defects are strongly coupled to the kagome quantum spin liquid (QSL) state of herbertsmithite, while they are usually considered quasi-free, and find that they have a substantially higher antiferromagnetic Weiss temperature (5.2 K) than previously believed. The newly discovered enigmatic d_II defects, on the other hand, are almost uncoupled from the kagome spins with a near-zero Weiss temperature. We attribute d_I defects to extra Cu2+ on the interlayer Zn2+ site, and d_II defects to spinons pinned to local distortions of the kagome planes. Unexpectedly, we find that both types of defects independently prove a subtle global structural distortion breaking global threefold symmetry in herbertsmithite thus disproving the idea of its perfect kagome lattice. In a comprehensive study of a new QKA, Zn-brochantite, ZnCu3(OH)6SO4, we prove that it is a gapless QSL with a spinon Fermi surface, i.e. a spinon metal. We find that this QSL state is present in two temperature regions with a crossover in between where the free-spinon density of states (DOS) is changing, a unique form of QKA behaviour. We also observe a high-temperature quantum-critical region in Zn-brochantite. Importantly, we discover a quantum spin liquid version of the Kondo effect, the first observation of this effect in any 2D QSL, despite it being theoretically predicted over a decade ago. We establish an effective model of Kondo spinon pinning, where the crossover in the free-spinon DOS of the spinon metal QSL arises from an effective depletion of spinons from the QSL as they start to Kondo screen the defects below their Kondo temperature of T_K = 1.25(5) K. We also find a field-induced spinon pairing instability of the gapless spinon metal QSL resulting in a gapped QSL that might be called a "spinon superconductor". In support of our experimental work we derive closed-form solutions for polarization curves of a muon dipolarly coupled to an arbitrary quantum spin, as well as their half-classical infinite-spin limit. We also develop a new method, in four increasingly refined variants, for extracting weak intrinsic signals from multi-temperature inelastic neutron scattering (INS) data even when a substantial background contribution is present. It enables us to apply INS to Zn-brochantite despite its signal being too weak to be observable using standard methods. We expect very wide applicability of the new method as it can dramatically shorten measurements times of weak signals, e.g. from QSL's, and enable previously infeasible inelastic scattering experiments.

• Language: English
• Keywords: kagome, quantum spin liquid, defects, threefold symmetry breaking, spinon Fermi surface, gapless, spinon metal, quantum criticality, crossover, density of states, Kondo effect, field-induced instability, spinon pairing, gapped, mu-OH(D), INS
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2018
• PID: 20.500.12556/RUL-100614
• COBISS.SI-ID: 3192420
• Publication date in RUL: 01.04.2018

Secondary language

• Language: Slovenian
• Title: Kvantne spinske tekočine na geometrijsko frustriranih mrežah kagome

Abstract

V tem Doktoratu proučujemo paradigmatičen kvantni kagome antiferromagnet (QKA) herbertsmithite in nedavno sintetiziran Zn-brochantite z množico eksperimentalnih tehnik. V primeru herbertsmithita ugotovimo, da ima dve vrsti defektov pri nizkih temperaturah, tipa d_I in tipa d_II, ne zgolj eno vrsto, kot je bilo mišljeno doslej. Dokažemo, da so dominantni defekti tipa d_I močno sklopljeni s stanjem kagome kvantne spinske tekočine (QSL) v herbertsmithitu, čeprav so ponavadi obravnavani kot kvazi-prosti, in ugotovimo, da imajo znatno višjo antiferomagnetno Weissovo temperaturo (5.2 K) kot je bilo mišljeno doslej. Na novo odkriti enigmatični defekti tipa d_II so, po drugi strani, skoraj nesklopljeni s kagome spini ter imajo skoraj ničelno Weissovo temperaturo. Defekte tipa d_I pripišemo dodatnemu Cu2+ na medravninskem Zn2+ mestu, defekte tipa d_II pa spinonom pripetim na lokalne distorzije kagome ravnin. Nepričakovano ugotovimo, da obeh vrsti defektov neodvisno dokažeta prisotnost blage globalne strukturne distorzije v herbertsmithitu, ki zlomi njegovo trištevno simetrijo, ter ovrže hipotezo o njegovi popolni kagome mreži. V obsežni študiji novega QKA, Zn-brochantita, ZnCu3(OH)6SO4, pokažemo, da je ta QSL brez energijske reže s spinonsko Fermijevo površino, torej spinonska kovina. Ugotovimo, da je to QSL stanje prisotno v dveh temperaturnih območjih z razširjenim prehodom (ang. crossover) med obema preko katerega se gostota stanj (DOS) prostih spinonov zvezno spreminja, obnašanje ki je unikatno med QKA. Opazimo tudi visokotemperaturno kvantno-kritično območje v Zn-brochantitu. Pomembno je naše odkritje kvantno-spinsko-tekočinske različice Kondovega pojava, prvo odkritje tega pojava v katerikoli 2D QSL, kljub njegovi teoretični napovedi že pred dobrim desetletjem. Vzpostavimo efektiven model Kondovega pripetja spinonov, kjer razširjen prehod v DOS prostih spinonov iz QSL spinonske kovine izhaja iz efektivnega izčrpanja spinonov iz QSL, ko ti začnejo Kondovo senčiti defekte pod njihovo Kondovo temperaturo T_K = 1.25(5) K. Najdemo tudi nestabilnost QSL spinonske kovine brez energijske reže na tvorbo vezanih parov spinonov v polju, ki rezultira v QSL z energijsko režo, ki bi ji lahko rekli "spinonski superprevodnik". V podporo našemu eksperimentalnemu delu izpeljemo analitične rešitve za polarizacijske krivulje miona, dipolno sklopljenega s poljubnim kvantnim spinom, ter njihovo polklasično limito neskončnega spina. Razvijemo tudi novo metodo, v štirih čedalje bolj izpopolnjenih različicah, za ekstrakcijo šibkega intrinzičnega signala iz večtemperaturnih meritev neelastičnega nevtronskega sipanja (INS) tudi ob velikem prispevku ozadja. Ta nam omogoči uporabo INS na Zn-brochantitu kljub temu, da je signal prešibak, da bi bil opazen s standardnimi metodami. Pričakujemo široko uporabnost nove metode, saj lahko bistveno skrajša čas merjenja šibkih signalov, na primer QSL, ter omogoči prej neizvedljive eksperimente neelastičnega sipanja.

• Keywords: kagome, kvantna spinska tekočina, defekt, zlom trištevne simetrije, spinonska Fermijeva površina, spinonska kovina, kvantna kritičnost, razširjen prehod, gostota stanj, Kondov pojav, nestabilnost v polju, pari spinonov, energijska reža, mu-OH(D), INS